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# Mandelbrot set

 This page uses content from Wikipedia. The original article was at Mandelbrot_set. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Mandelbrot set
You are encouraged to solve this task according to the task description, using any language you may know.

Generate and draw the Mandelbrot set.

Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .

## 11l

Translation of: Python
F mandelbrot(a)   R (0.<50).reduce(0i, (z, _) -> z * z + @a) F step(start, step, iterations)   R (0 .< iterations).map(i -> @start + (i * @step)) V rows = (step(1, -0.05, 41).map(y -> (step(-2.0, 0.0315, 80).map(x -> (I abs(mandelbrot(x + 1i * @y)) < 2 {‘*’} E ‘ ’)))))print(rows.map(row -> row.join(‘’)).join("\n"))

## ACL2

(defun abs-sq (z)   (+ (expt (realpart z) 2)      (expt (imagpart z) 2))) (defun round-decimal (x places)   (/ (floor (* x (expt 10 places)) 1)      (expt 10 places))) (defun round-complex (z places)   (complex (round-decimal (realpart z) places)            (round-decimal (imagpart z) places))) (defun mandel-point-r (z c limit)   (declare (xargs :measure (nfix limit)))   (cond ((zp limit) 0)         ((> (abs-sq z) 4) limit)         (t (mandel-point-r (+ (round-complex (* z z) 15) c)                            c                            (1- limit))))) (defun mandel-point (z iters)   (- 5 (floor (mandel-point-r z z iters) (/ iters 5)))) (defun draw-mandel-row (im re cols width iters)   (declare (xargs :measure (nfix cols)))   (if (zp cols)       nil       (prog2$(cw (coerce (list (case (mandel-point (complex re im) iters) (5 #\#) (4 #\*) (3 #\.) (2 #\.) (otherwise #\Space))) 'string)) (draw-mandel-row im (+ re (/ (/ width 3))) (1- cols) width iters)))) (defun draw-mandel (im rows width height iters) (if (zp rows) nil (progn$ (draw-mandel-row im -2 width width iters)               (cw "~%")               (draw-mandel (- im (/ (/ height 2)))                            (1- rows)                            width                            height                            iters)))) (defun draw-mandelbrot (width iters)   (let ((height (floor (* 1000 width) 3333)))        (draw-mandel 1 height width height iters)))
Output:
> (draw-mandelbrot 60 100)
#
..
.####
.     # .##.
##*###############.
#.##################
.######################.
######.  #######################
##########.######################
##############################################
##########.######################
######.  #######################
.######################.
#.##################
##*###############.
.     # .##.
.####
..                     

Library: Lumen

with Lumen.Binary;package body Mandelbrot is   function Create_Image (Width, Height : Natural) return Lumen.Image.Descriptor is      use type Lumen.Binary.Byte;      Result : Lumen.Image.Descriptor;      X0, Y0 : Float;      X, Y, Xtemp : Float;      Iteration   : Float;      Max_Iteration : constant Float := 1000.0;      Color : Lumen.Binary.Byte;   begin      Result.Width := Width;      Result.Height := Height;      Result.Complete := True;      Result.Values := new Lumen.Image.Pixel_Matrix (1 .. Width, 1 .. Height);      for Screen_X in 1 .. Width loop         for Screen_Y in 1 .. Height loop            X0 := -2.5 + (3.5 / Float (Width) * Float (Screen_X));            Y0 := -1.0 + (2.0 / Float (Height) * Float (Screen_Y));            X := 0.0;            Y := 0.0;            Iteration := 0.0;            while X * X + Y * Y <= 4.0 and then Iteration < Max_Iteration loop               Xtemp := X * X - Y * Y + X0;               Y := 2.0 * X * Y + Y0;               X := Xtemp;               Iteration := Iteration + 1.0;            end loop;            if Iteration = Max_Iteration then               Color := 255;            else               Color := 0;            end if;            Result.Values (Screen_X, Screen_Y) := (R => Color, G => Color, B => Color, A => 0);         end loop;      end loop;      return Result;   end Create_Image; end Mandelbrot;

with Lumen.Image; package Mandelbrot is    function Create_Image (Width, Height : Natural) return Lumen.Image.Descriptor; end Mandelbrot;

with System.Address_To_Access_Conversions;with Lumen.Window;with Lumen.Image;with Lumen.Events;with GL;with Mandelbrot; procedure Test_Mandelbrot is    Program_End : exception;    Win : Lumen.Window.Handle;   Image : Lumen.Image.Descriptor;   Tx_Name : aliased GL.GLuint;   Wide, High : Natural := 400;    -- Create a texture and bind a 2D image to it   procedure Create_Texture is      use GL;       package GLB is new System.Address_To_Access_Conversions (GLubyte);       IP : GLpointer;   begin  -- Create_Texture      -- Allocate a texture name      glGenTextures (1, Tx_Name'Unchecked_Access);       -- Bind texture operations to the newly-created texture name      glBindTexture (GL_TEXTURE_2D, Tx_Name);       -- Select modulate to mix texture with color for shading      glTexEnvi (GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_MODULATE);       -- Wrap textures at both edges      glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);      glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);       -- How the texture behaves when minified and magnified      glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);      glTexParameteri (GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);       -- Create a pointer to the image.  This sort of horror show is going to      -- be disappearing once Lumen includes its own OpenGL bindings.      IP := GLB.To_Pointer (Image.Values.all'Address).all'Unchecked_Access;       -- Build our texture from the image we loaded earlier      glTexImage2D (GL_TEXTURE_2D, 0, GL_RGBA, GLsizei (Image.Width), GLsizei (Image.Height), 0,                    GL_RGBA, GL_UNSIGNED_BYTE, IP);   end Create_Texture;    -- Set or reset the window view parameters   procedure Set_View (W, H : in Natural) is      use GL;   begin  -- Set_View      GL.glEnable (GL.GL_TEXTURE_2D);      glClearColor (0.8, 0.8, 0.8, 1.0);       glMatrixMode (GL_PROJECTION);      glLoadIdentity;      glViewport (0, 0, GLsizei (W), GLsizei (H));      glOrtho (0.0, GLdouble (W), GLdouble (H), 0.0, -1.0, 1.0);       glMatrixMode (GL_MODELVIEW);      glLoadIdentity;   end Set_View;    -- Draw our scene   procedure Draw is      use GL;   begin  -- Draw      -- clear the screen      glClear (GL_COLOR_BUFFER_BIT or GL_DEPTH_BUFFER_BIT);      GL.glBindTexture (GL.GL_TEXTURE_2D, Tx_Name);       -- fill with a single textured quad      glBegin (GL_QUADS);      begin         glTexCoord2f (1.0, 0.0);         glVertex2i (GLint (Wide), 0);          glTexCoord2f (0.0, 0.0);         glVertex2i (0, 0);          glTexCoord2f (0.0, 1.0);         glVertex2i (0, GLint (High));          glTexCoord2f (1.0, 1.0);         glVertex2i (GLint (Wide), GLint (High));      end;      glEnd;       -- flush rendering pipeline      glFlush;       -- Now show it      Lumen.Window.Swap (Win);   end Draw;    -- Simple event handler routine for keypresses and close-window events   procedure Quit_Handler (Event : in Lumen.Events.Event_Data) is   begin  -- Quit_Handler      raise Program_End;   end Quit_Handler;    -- Simple event handler routine for Exposed events   procedure Expose_Handler (Event : in Lumen.Events.Event_Data) is      pragma Unreferenced (Event);   begin  -- Expose_Handler      Draw;   end Expose_Handler;    -- Simple event handler routine for Resized events   procedure Resize_Handler (Event : in Lumen.Events.Event_Data) is   begin  -- Resize_Handler      Wide := Event.Resize_Data.Width;      High := Event.Resize_Data.Height;      Set_View (Wide, High);--        Image := Mandelbrot.Create_Image (Width => Wide, Height => High);--        Create_Texture;      Draw;   end Resize_Handler; begin   -- Create Lumen window, accepting most defaults; turn double buffering off   -- for simplicity   Lumen.Window.Create (Win           => Win,                        Name          => "Mandelbrot fractal",                        Width         => Wide,                        Height        => High,                        Events        => (Lumen.Window.Want_Exposure  => True,                                          Lumen.Window.Want_Key_Press => True,                                          others                      => False));    -- Set up the viewport and scene parameters   Set_View (Wide, High);    -- Now create the texture and set up to use it   Image := Mandelbrot.Create_Image (Width => Wide, Height => High);   Create_Texture;    -- Enter the event loop   declare      use Lumen.Events;   begin      Select_Events (Win   => Win,                     Calls => (Key_Press    => Quit_Handler'Unrestricted_Access,                               Exposed      => Expose_Handler'Unrestricted_Access,                               Resized      => Resize_Handler'Unrestricted_Access,                               Close_Window => Quit_Handler'Unrestricted_Access,                               others       => No_Callback));   end;exception   when Program_End =>      null;end Test_Mandelbrot;
Output:

## ALGOL 68

Plot part of the Mandelbrot set as a pseudo-gif image.

 INT pix = 300, max iter = 256, REAL zoom = 0.33 / pix;[-pix : pix, -pix : pix] INT plane;COMPL ctr = 0.05 I 0.75 # center of set #; # Compute the length of an orbit. #PROC iterate = (COMPL z0) INT:  BEGIN COMPL z := 0, INT iter := 1;        WHILE (iter +:= 1) < max iter # not converged # AND ABS z < 2 # not diverged #        DO z := z * z + z0        OD;        iter  END; # Compute set and find maximum orbit length. #     INT max col := 0;FOR x FROM -pix TO pixDO FOR y FROM -pix TO pix   DO COMPL z0 = ctr + (x * zoom) I (y * zoom);      IF (plane [x, y] := iterate (z0)) < max iter      THEN (plane [x, y] > max col | max col := plane [x, y])      FI   ODOD; # Make a plot. #FILE plot;INT num pix = 2 * pix + 1;make device (plot, "gif", whole (num pix, 0) + "x" + whole (num pix, 0));open (plot, "mandelbrot.gif", stand draw channel);FOR x FROM -pix TO pixDO FOR y FROM -pix TO pix   DO INT col = (plane [x, y] > max col | max col | plane [x, y]);      REAL c = sqrt (1- col / max col); # sqrt to enhance contrast #      draw colour (plot, c, c, c);      draw point (plot, (x + pix) / (num pix - 1), (y + pix) / (num pix  - 1))   ODOD;close (plot)

## ALGOL W

Generates an ASCII Mandelbrot Set. Translated from the sample program in the Compiler/AST Interpreter task.

begin    % This is an integer ascii Mandelbrot generator, translated from the   %    % Compiler/AST Interpreter Task's ASCII Mandelbrot Set example program %    integer leftEdge, rightEdge, topEdge, bottomEdge, xStep, yStep, maxIter;    leftEdge   := -420;    rightEdge  :=  300;    topEdge    :=  300;    bottomEdge := -300;    xStep      :=    7;    yStep      :=   15;     maxIter    :=  200;     for y0 := topEdge step - yStep until bottomEdge do begin        for x0 := leftEdge step xStep until rightEdge do begin            integer x, y, i;            string(1) theChar;            y := 0;            x := 0;            theChar := " ";            i := 0;            while i < maxIter do begin                integer x_x, y_y;                x_x := (x * x) div 200;                y_y := (y * y) div 200;                if x_x + y_y > 800 then begin                    theChar := code( decode( "0" ) + i );                    if i > 9 then theChar := "@";                    i := maxIter                end;                y := x * y div 100 + y0;                x := x_x - y_y + x0;                i := i + 1            end while_i_lt_maxIter ;            writeon( theChar );        end for_x0 ;        write();    end for_y0end.
Output:
1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333222222222222222222222222222222222222222
1111111111111222222222233333333333333333333333344444456655544443333332222222222222222222222222222222222
[email protected]@6665444444333333222222222222222222222222222222
[email protected]@@@7654444443333333222222222222222222222222222
[email protected]@@@98755544444433333332222222222222222222222222
[email protected]@@    @@@76555544444333333322222222222222222222222
[email protected]@      @987666555544433333333222222222222222222222
[email protected]@@@@[email protected]@@@@@    @@@@@@[email protected]
[email protected]   @@@               @@@@@@ 8544333333333222222222222222222
[email protected]@@                        @86554433333333322222222222222222
[email protected]@ @                         @@87655443333333332222222222222222
[email protected]@[email protected]@@                            @@@@65444333333332222222222222222
[email protected]@@@@@@@@@@@[email protected]@@                              @@765444333333333222222222222222
[email protected]@@         @@@@                                @855444333333333222222222222222
11124444444455[email protected]@@             @                                 @655444433333333322222222222222
[email protected]@                                                @86655444433333333322222222222222
111                                                                 @@876555444433333333322222222222222
[email protected]@                                                @86655444433333333322222222222222
[email protected]@@             @                                 @655444433333333322222222222222
[email protected]@@         @@@@                                @855444333333333222222222222222
[email protected]@@@@@@@@@@@[email protected]@@                              @@765444333333333222222222222222
[email protected]@[email protected]@@                            @@@@65444333333332222222222222222
[email protected]@ @                         @@87655443333333332222222222222222
[email protected]@@                        @86554433333333322222222222222222
[email protected]   @@@               @@@@@@ 8544333333333222222222222222222
[email protected]@@@@[email protected]@@@@@    @@@@@@[email protected]
[email protected]@      @987666555544433333333222222222222222222222
[email protected]@@    @@@76555544444333333322222222222222222222222
[email protected]@@@98755544444433333332222222222222222222222222
[email protected]@@@7654444443333333222222222222222222222222222
[email protected]@6665444444333333222222222222222222222222222222
1111111111111222222222233333333333333333333333344444456655544443333332222222222222222222222222222222222
1111111111111112222222222222333333333333333333333333333333333333222222222222222222222222222222222222222
1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222
1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222
1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211
1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111


## Applesoft BASIC

This version takes into account the Apple II's funky 280×192 6-color display, which has an effective resolution of only 140×192 in color.

 10  HGR220  XC = -0.5           : REM CENTER COORD X30  YC = 0              : REM   "      "   Y40  S = 2               : REM SCALE45  IT = 20             : REM ITERATIONS50  XR = S * (280 / 192): REM TOTAL RANGE OF X60  YR = S              : REM   "     "   "  Y70  X0 = XC - (XR/2)    : REM MIN VALUE OF X80  X1 = XC + (XR/2)    : REM MAX   "   "  X90  Y0 = YC - (YR/2)    : REM MIN   "   "  Y100 Y1 = YC + (YR/2)    : REM MAX   "   "  Y110 XM = XR / 279       : REM SCALING FACTOR FOR X120 YM = YR / 191       : REM    "      "     "  Y130 FOR YI = 0 TO 3     : REM INTERLEAVE140   FOR YS = 0+YI TO 188+YI STEP 4 : REM Y SCREEN COORDINATE145   HCOLOR=3 : HPLOT 0,YS TO 279,YS150     FOR XS = 0 TO 278 STEP 2     : REM X SCREEN COORDINATE170       X = XS * XM + X0  : REM TRANSL SCREEN TO TRUE X180       Y = YS * YM + Y0  : REM TRANSL SCREEN TO TRUE Y190       ZX = 0200       ZY = 0210       XX = 0220       YY = 0230       FOR I = 0 TO IT240         ZY = 2 * ZX * ZY + Y250         ZX = XX - YY + X260         XX = ZX * ZX270         YY = ZY * ZY280         C = IT-I290         IF XX+YY >= 4 GOTO 301300       NEXT I301       IF C >= 8 THEN C = C - 8 : GOTO 301310       HCOLOR = C : HPLOT XS, YS TO XS+1, YS320     NEXT XS330   NEXT YS340 NEXT YI

By making the following modifications, the same code will render the Mandelbrot set in monochrome at full 280×192 resolution.

 150 FOR XS = 0 TO 279301 C = (C - INT(C/2)*2)*3310 HCOLOR = C: HPLOT XS, YS

## Arturo

Translation of: Nim
inMandelbrot?: function [c][    z: to :complex [0 0]    do.times: 50 [        z: c + z*z        if 4 < abs z -> return false    ]    return true] mandelbrot: function [settings][    y: 0    while [y < settings\height][        Y: settings\yStart + y * settings\yStep        x: 0        while [x < settings\width][            X: settings\xStart + x * settings\xStep            if? inMandelbrot? to :complex @[X Y] -> prints "*"            else -> prints " "            x: x + 1        ]        print ""        y: y + 1    ]] mandelbrot #[ yStart: 1.0 yStep: neg 0.05               xStart: neg 2.0 xStep: 0.0315              height: 40 width: 80 ]
Output:
                                                           **
******
********
******
******** **   *
***   *****************
************************  ***
****************************
******************************
*******************************
************************************
*         **********************************
** ***** *     **********************************
***********   ************************************
************** ************************************
***************************************************
******************************************************
************************************************************************
******************************************************
***************************************************
************** ************************************
***********   ************************************
** ***** *     **********************************
*         **********************************
************************************
*******************************
******************************
****************************
************************  ***
***   *****************
******** **   *
******
********
******
**

## AutoHotkey

Max_Iteration := 256Width := Height := 400 File := "MandelBrot." Width ".bmp"Progress, b2 w400 fs9, Creating Colours ...Gosub, CreateColoursGosub, CreateBitmapProgress, OffGui, -CaptionGui, Margin, 0, 0Gui, Add, Picture,, %File%Gui, Show,, MandelBrotReturn GuiClose:GuiEscape:ExitApp   ;---------------------------------------------------------------------------CreateBitmap: ; create and save a 32bit bitmap file;---------------------------------------------------------------------------    ; define header details    HeaderBMP  := 14    HeaderDIB  := 40    DataOffset := HeaderBMP + HeaderDIB    ImageSize  := Width * Height * 4 ; 32bit    FileSize   := DataOffset + ImageSize    Resolution := 3780 ; from mspaint     ; create bitmap header    VarSetCapacity(IMAGE, FileSize, 0)    NumPut(Asc("B")   , IMAGE, 0x00, "Char")    NumPut(Asc("M")   , IMAGE, 0x01, "Char")    NumPut(FileSize   , IMAGE, 0x02, "UInt")    NumPut(DataOffset , IMAGE, 0x0A, "UInt")    NumPut(HeaderDIB  , IMAGE, 0x0E, "UInt")    NumPut(Width      , IMAGE, 0x12, "UInt")    NumPut(Height     , IMAGE, 0x16, "UInt")    NumPut(1          , IMAGE, 0x1A, "Short") ; Planes    NumPut(32         , IMAGE, 0x1C, "Short") ; Bits per Pixel    NumPut(ImageSize  , IMAGE, 0x22, "UInt")    NumPut(Resolution , IMAGE, 0x26, "UInt")    NumPut(Resolution , IMAGE, 0x2A, "UInt")     ; fill in Data    Gosub, CreatePixels     ; save Bitmap to file    FileDelete, %File%    Handle := DllCall("CreateFile", "Str", File, "UInt", 0x40000000            , "UInt", 0, "UInt", 0, "UInt", 2, "UInt", 0, "UInt", 0)    DllCall("WriteFile", "UInt", Handle, "UInt", &IMAGE, "UInt"            , FileSize, "UInt *", Bytes, "UInt", 0)    DllCall("CloseHandle", "UInt", Handle) Return   ;---------------------------------------------------------------------------CreatePixels: ; create pixels for [-2 < x < 1] [-1.5 < y < 1.5];---------------------------------------------------------------------------    Loop, % Height // 2 + 1 {        yi := A_Index - 1        y0 := -1.5 + yi / Height * 3 ; range -1.5 .. +1.5        Progress, % 200*yi // Height, % "Current line: " 2*yi " / " Height        Loop, %Width% {            xi := A_Index - 1            x0 := -2 + xi / Width * 3 ; range -2 .. +1            Gosub, Mandelbrot            p1 := DataOffset + 4 * (Width * yi + xi)            NumPut(Colour, IMAGE, p1, "UInt")            p2 := DataOffset + 4 * (Width * (Height-yi) + xi)            NumPut(Colour, IMAGE, p2, "UInt")        }    }Return   ;---------------------------------------------------------------------------Mandelbrot: ; calculate a colour for each pixel;---------------------------------------------------------------------------    x := y := Iteration := 0    While, (x*x + y*y <= 4) And (Iteration < Max_Iteration) {        xtemp := x*x - y*y + x0        y := 2*x*y + y0        x := xtemp        Iteration++    }    Colour := Iteration = Max_Iteration ? 0 : Colour_%Iteration% Return   ;---------------------------------------------------------------------------CreateColours: ; borrowed from PureBasic example;---------------------------------------------------------------------------    Loop, 64 {        i4 := (i3 := (i2 := (i1 := A_Index - 1) + 64) + 64) + 64        Colour_%i1% := RGB(4*i1 + 128, 4*i1, 0)        Colour_%i2% := RGB(64, 255, 4*i1)        Colour_%i3% := RGB(64, 255 - 4*i1, 255)        Colour_%i4% := RGB(64, 0, 255 - 4*i1)    }Return   ;---------------------------------------------------------------------------RGB(r, g, b) { ; return 24bit color value;---------------------------------------------------------------------------    Return, (r&0xFF)<<16 | g<<8 | b}

## AWK

BEGIN {  XSize=59; YSize=21;  MinIm=-1.0; MaxIm=1.0;MinRe=-2.0; MaxRe=1.0;  StepX=(MaxRe-MinRe)/XSize; StepY=(MaxIm-MinIm)/YSize;  for(y=0;y<YSize;y++)  {    Im=MinIm+StepY*y;    for(x=0;x<XSize;x++)        {      Re=MinRe+StepX*x; Zr=Re; Zi=Im;      for(n=0;n<30;n++)          {        a=Zr*Zr; b=Zi*Zi;        if(a+b>4.0) break;        Zi=2*Zr*Zi+Im; Zr=a-b+Re;      }      printf "%c",62-n;    }    print "";  }  exit;}
Output:
>>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<==========
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<=======
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<======
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<====
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<===
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<==
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<=
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<
><;;;;;;::::9875&      .3                       *9;;;<<<<<<
>;;;;;;::997564'        '                       8:;;;<<<<<<
>::988897735/                                 &89:;;;<<<<<<
>::988897735/                                 &89:;;;<<<<<<
>;;;;;;::997564'        '                       8:;;;<<<<<<
><;;;;;;::::9875&      .3                       *9;;;<<<<<<
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<=
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<==
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<===
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<====
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<=======


## B

This implements a 16bit fixed point arithmetic Mandelbrot set calculation.

Works with: The Amsterdam Compiler Kit - B version V6.1pre1
main() {  auto cx,cy,x,y,x2,y2;  auto iter;   auto xmin,xmax,ymin,ymax,maxiter,dx,dy;   xmin = -8601;  xmax =  2867;  ymin = -4915;  ymax =  4915;   maxiter = 32;   dx = (xmax-xmin)/79;  dy = (ymax-ymin)/24;   cy=ymin;  while( cy<=ymax ) {    cx=xmin;    while( cx<=xmax ) {      x = 0;      y = 0;      x2 = 0;      y2 = 0;      iter=0;      while( iter<maxiter ) {        if( x2+y2>16384 ) break;        y = ((x*y)>>11)+cy;        x = x2-y2+cx;        x2 = (x*x)>>12;        y2 = (y*y)>>12;        iter++;      }      putchar(' '+iter);      cx =+ dx;    }    putchar(13);    putchar(10);    cy =+ dy;  }   return(0);}
Output:
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
!!!!!!!!!!!!!"""""""""#######################$$%'+)%%%$$$$#####""""""""""" !!!!!!!!!!!"""""""#######################$$$$%%%&&(+,)++&%$$######""""""
!!!!!!!!!"""""#######################$$%%%%&')*5:/+('&%%$$#######"""
!!!!!!!!""""#####################$$%%%&&&''),@@@@@@@,'&%%%%%$$$$######## !!!!!!!"""####################$$$$%%%&'())((())*,@@@@@@/+))('&&&&)'%$$######
!!!!!!""###################$%%%%%%&&&'[email protected]@=/<@@@@@@@@@@@@@@@/[email protected]%%$#####
!!!!!"################$$%%%%%%%%%%&&&&'),[email protected]@@@@@@@@@@@@@@@@@@@@@@@@1(&&%$$####
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!!!!#$%%%%%%'''[email protected]@@@@@@@@8/[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3(%%# !!!#$$%&&&&''()/[email protected]@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?'&%%$$$$# !!!(**+/+<523/80/[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+)'&&%%$$$$# !!!#$$$%&&&&''()[email protected]@@@@@@@@@@@@@[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%#
!!!!#$%%%%%&'''/,[email protected]@@@@@@@@;/[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0'%%# !!!!####%%%%%&'(*-:2.,/?-5+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+(&%$$## !!!!"##########$$$$%%&(-(''''(''''''((*,[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@4+).&%$$### !!!!!"################$$%%%%%%%%%%&&&&')<,[email protected]@@@@@@@@@@@@@@@@@@@@@@@@/('&%%#### !!!!!!""##################$$%%%%%%&&&'*[email protected]@@[email protected]@@@@@@@@@@@@@@@1,,@//9)%%$#####
!!!!!!!"""####################%%%&(())((()**[email protected]@@@@@/+)))'&&&')'%$$###### !!!!!!!!""""#####################$$%%%&&&''(,@@@@@@@+'&&%%%%%$$######## !!!!!!!!!"""""#######################$$%%%%&')*[email protected]+('&%%%$#######""" !!!!!!!!!!!"""""""######################$%%%&&(+-).*&%$$######"""""" !!!!!!!!!!!!!"""""""""#######################$$%%'3(%%%$######"""""""""" !!!!!!!!!!!!!!!""""""""""""#####################################""""""""""""""""  ## BASIC Works with: QBasic This is almost exactly the same as the pseudocode from the Wikipedia entry's "For programmers" section (which it's closely based on, of course). The image generated is very blocky ("low-res") due to the selected video mode, but it's fairly accurate. SCREEN 13WINDOW (-2, 1.5)-(2, -1.5)FOR x0 = -2 TO 2 STEP .01 FOR y0 = -1.5 TO 1.5 STEP .01 x = 0 y = 0 iteration = 0 maxIteration = 223 WHILE (x * x + y * y <= (2 * 2) AND iteration < maxIteration) xtemp = x * x - y * y + x0 y = 2 * x * y + y0 x = xtemp iteration = iteration + 1 WEND IF iteration <> maxIteration THEN c = iteration ELSE c = 0 END IF PSET (x0, y0), c + 32 NEXTNEXT ### AmigaBASIC Translation of: QBasic SCREEN 1,320,200,5,1WINDOW 2,"Mandelbrot",,0,1 maxIteration = 100xmin = -2xmax = 1ymin = -1.5ymax = 1.5xs = 300ys = 180st = .01 ' use e.g. st = .05 for a coarser but faster picture ' and perhaps also lower maxIteration = 10 or soxp = xs / (xmax - xmin) * styp = ys / (ymax - ymin) * st FOR x0 = xmin TO xmax STEP st FOR y0 = ymin TO ymax STEP st x = 0 y = 0 iteration = 0 WHILE (x * x + y * y <= (2 * 2) AND iteration < maxIteration) xtemp = x * x - y * y + x0 y = 2 * x * y + y0 x = xtemp iteration = iteration + 1 WEND IF iteration <> maxIteration THEN c = iteration ELSE c = 0 END IF COLOR c MOD 32 AREA ((x0 - xmin) * xp / st, (y0 - ymin) * yp / st) AREA STEP (xp, 0) AREA STEP (0, yp) AREA STEP (-xp, 0) AREA STEP (0, -yp) AREAFILL NEXTNEXT ' endless loop, use Run -> Stop from the menu to stop programWHILE (1)WEND ### BASIC256 fastgraphics graphsize 384,384refreshkt = 319 : m = 4.0xmin = -2.1 : xmax = 0.6 : ymin = -1.35 : ymax = 1.35dx = (xmax - xmin) / graphwidth : dy = (ymax - ymin) / graphheight for x = 0 to graphwidth jx = xmin + x * dx for y = 0 to graphheight jy = ymin + y * dy k = 0 : wx = 0.0 : wy = 0.0 do tx = wx * wx - wy * wy + jx ty = 2.0 * wx * wy + jy wx = tx wy = ty r = wx * wx + wy * wy k = k + 1 until r > m or k > kt if k > kt then color black else if k < 16 then color k * 8, k * 8, 128 + k * 4 if k >= 16 and k < 64 then color 128 + k - 16, 128 + k - 16, 192 + k - 16 if k >= 64 then color kt - k, 128 + (kt - k) / 2, kt - k end if plot x, y next y refreshnext ximgsave "Mandelbrot_BASIC-256.png", "PNG"  Image generated by the script: ### BBC BASIC  sizex% = 300 : sizey% = 300 maxiter% = 128 VDU 23,22,sizex%;sizey%;8,8,16,128 ORIGIN 0,sizey% GCOL 1 FOR X% = 0 TO 2*sizex%-2 STEP 2 xi = X%/200 - 2 FOR Y% = 0 TO sizey%-2 STEP 2 yi = Y% / 200 x = 0 y = 0 FOR I% = 1 TO maxiter% IF x*x+y*y > 4 EXIT FOR xt = xi + x*x-y*y y = yi + 2*x*y x = xt NEXT IF I%>maxiter% I%=0 COLOUR 1,I%*15,I%*8,0 PLOT X%,Y% : PLOT X%,-Y% NEXT NEXT X% ### ARM BBC BASIC The ARM development second processor for the BBC series of microcomputers came with ARM BBC Basic V. In version 1.0 this included a built-in MANDEL function that uses D% (depth) to update C% (colour) at given coordinates x and y. Presumably this was for benchmarking/demo purposes; it was removed from later versions. This can be run in BeebEm. Select BBC model as Master 128 with ARM Second Processor. Load disc armdisc3.adl and switch to ADFS. At the prompt load ARM Basic by running the AB command.  10MODE5:VDU520D%=100 : REM adjust for speed/precision30FORX%=0 TO 1279 STEP840FORY%=0 TO 1023 STEP450MANDEL (Y%-512)/256, (X%-640)/25651REM (not sure why X and Y need to be swapped to correct orientation)60GCOL0,C%70PLOT69,X%,Y%80NEXT90NEXT ### GW-BASIC 10 SCALE# = 1/60 : ZEROX = 16020 ZEROY = 100 : MAXIT = 3230 SCREEN 140 FOR X = 0 TO 2*ZEROX - 150 CR# = (X-ZEROX)*SCALE#60 FOR Y = 0 TO ZEROY70 CI# = (ZEROY-Y)*SCALE#80 ZR# = 090 ZI# = 0100 FOR I = 1 TO MAXIT110 BR# = CR# + ZR#*ZR# - ZI#*ZI#120 ZI# = CI# + 2*ZR#*ZI#130 ZR# = BR#140 IF ZR#*ZR# + ZI#*ZI# > 4 THEN GOTO 170150 NEXT I160 GOTO 190170 PSET (X, Y), 1 + (I MOD 3)180 PSET (X, 2*ZEROY-Y), 1+(I MOD 3)190 NEXT Y200 NEXT X ### Liberty BASIC Any words of description go outside of lang tags. nomainwin WindowWidth =440WindowHeight =460 open "Mandelbrot Set" for graphics_nsb_nf as #w #w "trapclose [quit]"#w "down" for x0 = -2 to 1 step .0033 for y0 = -1.5 to 1.5 step .0075 x = 0 y = 0 iteration = 0 maxIteration = 255 while ( ( x *x +y *y) <=4) and ( iteration <maxIteration) xtemp =x *x -y *y +x0 y =2 *x *y +y0 x = xtemp iteration = iteration + 1 wend if iteration <>maxIteration then c =iteration else c =0 end if call pSet x0, y0, c scan nextnext #w "flush" wait sub pSet x, y, c xScreen = 10 +( x +2) /3 *400 yScreen = 10 +( y +1.5) /3 *400 if c =0 then col$ ="red"    else        if c mod 2 =1 then col$="lightgray" else col$ ="white"    end if    #w "color "; col$#w "set "; xScreen; " "; yScreenend sub [quit]close #wend  ### Locomotive Basic Translation of: QBasic This program is meant for use in CPCBasic specifically, where it draws a 16-color 640x400 image in less than a minute. (Real CPC hardware would take far longer than that and has lower resolution.) 1 MODE 3 ' Note the CPCBasic-only screen mode!2 FOR xp = 0 TO 6393 FOR yp = 0 TO 3994 x = 0 : y = 05 x0 = xp / 213 - 2 : y0 = yp / 200 - 16 iteration = 07 maxIteration = 1008 WHILE (x * x + y * y <= (2 * 2) AND iteration < maxIteration)9 xtemp = x * x - y * y + x010 y = 2 * x * y + y011 x = xtemp12 iteration = iteration + 113 WEND14 IF iteration <> maxIteration THEN c = iteration ELSE c = 015 PLOT xp, yp, c MOD 1616 NEXT17 NEXT ### OS/8 BASIC Works under BASIC on a PDP-8 running OS/8. Various emulators exist including simh's PDP-8 emulator and the PDP-8/E Simulator for Classic Macintosh and OS X. 10 X1=59\Y1=2120 I1=-1.0\I2=1.0\R1=-2.0\R2=1.030 S1=(R2-R1)/X1\S2=(I2-I1)/Y140 FOR Y=0 TO Y150 I3=I1+S2*Y60 FOR X=0 TO X170 R3=R1+S1*X\Z1=R3\Z2=I380 FOR N=0 TO 3090 A=Z1*Z1\B=Z2*Z2100 IF A+B>4.0 GOTO 130110 Z2=2*Z1*Z2+I3\Z1=A-B+R3120 NEXT N130 PRINT CHR$(62-N);140 NEXT X150 PRINT160 NEXT Y170 END
Output:
>>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<===========
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<========
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<=======
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<=====
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<====
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<===
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<==
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<=
><;;;;;;::::9875&      .3                       *9;;;<<<<<<=
>;;;;;;::997564'        '                       8:;;;<<<<<<=
>::988897735/                                 &89:;;;<<<<<<=
>::988897735/                                 &89:;;;<<<<<<=
>;;;;;;::997564'        '                       8:;;;<<<<<<=
><;;;;;;::::9875&      .3                       *9;;;<<<<<<=
><<<<;;;;;:::972456-567763                      +9;;<<<<<<<=
>=<<<<<<<<;;;:599999999886                    %78:;;<<<<<<==
>>=<<<<<<<<<<<;;;::::::999752                 *79:;<<<<<<===
>>==<<<<<<<<<<<<<;;;;::::996. &2           45335:;<<<<<<====
>>>==<<<<<<<<<<<<<<<;;;;;;:98888764     5789999:;;<<<<<=====
>>>>===<<<<<<<<<<<<<<<;;;;;;;::9974    (.9::::;;<<<<<=======
>>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<========
>>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<===========

### Quite BASIC

 1000 REM Mandelbrot Set Project1010 REM Quite BASIC Math Project1015 REM 'http://www.quitebasic.com/prj/math/mandelbrot/1020 REM ------------------------ 1030 CLS1040 PRINT "This program plots a graphical representation of the famous Mandelbrot set.  It takes a while to finish so have patience and don't have too high expectations;  the graphics resolution is not very high on our canvas."2000 REM Initialize the color palette2010 GOSUB 30002020 REM L is the maximum iterations to try2030 LET L = 1002040 FOR I = 0 TO 1002050 FOR J = 0 TO 1002060 REM Map from pixel coordinates (I,J) to math (U,V)2060 LET U = I / 50 - 1.52070 LET V = J / 50 - 12080 LET X = U2090 LET Y = V2100 LET N = 02110 REM Inner iteration loop starts here 2120 LET R = X * X2130 LET Q = Y * Y2140 IF R + Q > 4 OR N >= L THEN GOTO 21902150 LET Y = 2 * X * Y + V2160 LET X = R - Q + U2170 LET N = N + 12180 GOTO 21202190 REM Compute the color to plot2200 IF N < 10 THEN LET C = "black" ELSE LET C = P[ROUND(8 * (N-10) / (L-10))]2210 PLOT I, J, C 2220 NEXT J2230 NEXT I2240 END3000 REM Subroutine -- Set up Palette3010 ARRAY P3020 LET P[0] = "black"3030 LET P[1] = "magenta"3040 LET P[2] = "blue"3050 LET P[3] = "green"3060 LET P[4] = "cyan"3070 LET P[5] = "red"3080 LET P[6] = "orange"3090 LET P[7] = "yellow"3090 LET P[8] = "white"3100 RETURN

### Run BASIC

'Mandelbrot V4 for RunBasic'Based on LibertyBasic solution'copy the code and go to runbasic.com'http://rosettacode.org/wiki/Mandelbrot_set#Liberty_BASIC'May 2015 (updated 29 Apr 2018)''Note - we only get so much processing time on the server, so the'graph is computed in three or four pieces'WindowWidth  = 320  'RunBasic max size 800 x 600WindowHeight = 320'print zone -2 to 1 (X)'print zone -1.5 to 1.5 (Y)  a = -1.5  'graph -1.5 to -0.75, first "loop" b = -0.75  'adjust for max processor time (y0 for loop below) 'open "Mandelbrot Set" for graphics_nsb_nf as #w  not used in RunBasic graphic #w, WindowWidth, WindowHeight'#w "trapclose [quit]"       not used in RunBasic'#w "down"                   not used in RunBasic cls '#w flush() #w cls("black")render #w '#w flush()input "OK, hit enter to continue"; guesscls [man_calc]'3/screen size 3/800 = 0.00375  ** 3/790 = 0.0037974'3/screen size (y) 3/600 = .005 ** 3/590 = 0.0050847'3/215 = .0139 .0068 = 3/440cc = 3/299'    for x0 = -2 to 1 step cc        for y0 = a to b step  cc         x = 0        y = 0         iteration    =   0        maxIteration = 255          while ( ( x *x +y *y) <=4) and ( iteration <maxIteration)            xtemp      =x *x -y *y +x0            y          =2 *x *y +y0            x          = xtemp            iteration  = iteration + 1        wend         if iteration <>maxIteration then            c =iteration        else            c =0        end if         call pSet x0, y0, c        'scan why scan? (wait for user input) with RunBasic ?    nextnext '#w flush()  'what is flush? RunBasic uses the render command.render #w input "OK, hit enter to continue"; guessclsa = a + 0.75b = b + 0.75if b > 1.6 then goto[quit] else goto[man_calc] sub pSet x, y, c    xScreen = 5+(x +2)   /3 * 300 'need positive screen number    yScreen = 5+(y +1.5) /3 * 300 'and 5x5 boarder    if c =0 then        col$="red" else if c mod 2 =1 then col$ ="lightgray" else col$="white" end if #w "color "; col$    #w "set "; xScreen; " "; yScreenend sub [quit]'clsprintprint "This is a Mandelbrot Graph output from www.runbasic.com" render #wprint "All done, good bye."end

### Sinclair ZX81 BASIC

Translation of: QBasic

Requires at least 2k of RAM.

Glacially slow, but does eventually produce a tolerable low-resolution image (screenshot here). You can adjust the constants in lines 30 and 40 to zoom in on a particular area, if you like.

 10 FOR I=0 TO 63 20 FOR J=43 TO 0 STEP -1 30 LET X=(I-52)/31 40 LET Y=(J-22)/31 50 LET XA=0 60 LET YA=0 70 LET ITER=0 80 LET XTEMP=XA*XA-YA*YA+X 90 LET YA=2*XA*YA+Y100 LET XA=XTEMP110 LET ITER=ITER+1120 IF XA*XA+YA*YA<=4 AND ITER<200 THEN GOTO 80130 IF ITER=200 THEN PLOT I, J140 NEXT J150 NEXT I

### Microsoft Small Basic

 GraphicsWindow.Show()size = 500half = 250GraphicsWindow.Width = size * 1.5GraphicsWindow.Height = sizeGraphicsWindow.Title = "Mandelbrot"For px = 1 To size * 1.5  x_0 = px/half - 2  For py = 1 To size    y_0 = py/half - 1    x = x_0    y = y_0    i = 0    While(c <= 2 AND i<100)      x_1 = Math.Power(x, 2) - Math.Power(y, 2) + x_0      y_1 = 2 * x * y + y_0      c = Math.Power(Math.Power(x_1, 2) + Math.Power(y_1, 2), 0.5)      x = x_1      y = y_1      i = i + 1    EndWhile    If i < 99 Then      GraphicsWindow.SetPixel(px, py, GraphicsWindow.GetColorFromRGB((255/25)*i, (255/25)*i, (255/5)*i))    Else       GraphicsWindow.SetPixel(px, py, "black")    EndIf    c=0 EndForEndFor

### TI-Basic Color

 ClrDraw~2->Xmin:1->Xmax:~1->Ymin:1->YmaxAxesOffFnOff For(A,~2,1,.034	For(B,~1,1,.036		A+B[i]->C		DelVar Z9->N		While abs(Z)<=2 and N<24			Z^^2+C->Z			N+1->N		End		Pt-On(real(C),imag(C),N	EndEnd

### Visual BASIC for Applications on Excel

Works with: Excel 2013

Based on the BBC BASIC version. Create a spreadsheet with -2 to 2 in row 1 and -2 to 2 in the A column (in steps of your choosing). In the cell B2, call the function with =mandel(B$1,$A2) and copy the cell to all others in the range. Conditionally format the cells to make the colours pleasing (eg based on values, 3-color scale, min value 2 [colour red], midpoint number 10 [green] and highest value black. Then format the cells with the custom type "";"";"" to remove the numbers.

 Function mandel(xi As Double, yi As Double) maxiter = 256x = 0y = 0 For i = 1 To maxiter    If ((x * x) + (y * y)) > 4 Then Exit For    xt = xi + ((x * x) - (y * y))    y = yi + (2 * x * y)    x = xt    Next mandel = iEnd Function

File:Vbamandel.png Edit: I don't seem to be able to upload the screenshot, so I've shared it here: https://goo.gl/photos/LkezpuQziJPAtdnd9

### Microsoft Super Extended Color BASIC (Tandy Color Computer 3)

 1 REM MANDELBROT SET - TANDY COCO 32 POKE 65497,110 HSCREEN 220 HCLS30 X1=319:Y1=19140 I1=-1.0:I2=1.0:R1=-2:R2=1.050 S1=(R2-R1)/X1:S2=(I2-I1)/Y160 FOR Y=0 TO Y170 I3=I1+S2*Y80 FOR X=0 TO X190 R3=R1+S1*X:Z1=R3:Z2=I3100 FOR N=0 TO 30110 A=Z1*Z1:B=Z2*Z2120 IF A+B>4.0 GOTO 150130 Z2=2*Z1*Z2+I3:Z1=A-B+R3140 NEXT N150 HSET(X,Y,N-16*INT(N/16))160 NEXT X170 NEXT Y180 GOTO 180

 10  CLS20  SCREEN $8030 FOR X=1 TO 199: 40 FOR Y=1 TO 99:50 LET I=060 LET CX=(X-100)/5070 LET CY=(Y-100)/5080 LET VX=090 LET VY=0100 REM START OF THE CALCULATION LOOP110 LET I=I+1120 LET X2 = VX*VX130 LET Y2 = VY*VY140 LET VY = CY + (VX+VX)*VY150 LET VX = CX + X2-Y2160 IF I<32 AND (X2+Y2)<4 THEN GOTO 100170 LET YR = 199-Y180 PSET X,Y,I190 PSET X,YR,I200 :NEXT:NEXT  ## Befunge Using 14-bit fixed point arithmetic for simplicity and portability. It should work in most interpreters, but the exact output is implementation dependent, and some will be unbearably slow. X scale is (-2.0, 0.5); Y scale is (-1, 1); Max iterations 94 with the ASCII character set as the "palette". 0>:00p58*#@_0>:01p78vv$$<@^+1g00,+55_v# !\+*9<>4v@v30p20"?~^"< ^+1g10,+*8<@>p0\>\::*::882**02g*0v >^*:*" d":+*:-*"[Z"+g3 < |<v-*"[Z"+g30*g20**288\--\<#>2**5#>8*:*/00g"P"*58*:*v^v*288 p20/**288:+*"[Z"+-<:>*%03 p58*:*/01g"3"* v>::^ \_^#!:-1\+-*2*:*85<^  Output: }}}}}}}}}|||||||{{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzyyyyxwusjuthwyzzzzzzz{{{{{{{ }}}}}}}}|||||||{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzyyyyxwwvtqptvwxyyzzzzzzz{{{{{ }}}}}}}||||||{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzzyyyyxwvuqaZlnvwxyyyzzzzzzz{{{{ }}}}}}|||||{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzzyyyyxxvqXp^g Ynslvxyyyyyzzzzz{{{ }}}}}}||||{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzzyyyxxxxwvtp 6puwxyyyyyyzzzz{{ }}}}}||||{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzyyyxxxxxwwvvqc &8uvwxxxyyyyyzzz{ }}}}|||{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzyyyywwvtvvvvuutsp Hrtuuvwxxxxwqxyzz }}}}||{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzyyyyyxwvqemrttj m id+ PRUiPp_rvvvvudwxyz }}}||{{{{{{{{{{{{{{{{{{{{{zzzzzzyyyyyyyxxxwurf ZnW 4nrslnobgwyy }}}||{{{{{{{{{{{{{{{{{{{zzzzyyyyyyyyyyxxxwvusg N Uquxyy }}||{{{{{{{{{{{{{{{{{zzzzyyyyyyyyyyyxxxxwvrrrkC grwxxy }}|{{{{{{{{{{{{{{{zzzzyxxxxxyyyyyxxxxxwwukM!f ptvwxy }}|{{{{{{{{{{zzzzzzyyxwsuwwwwwwwwwwwwwvvurn[ ptuox }|{{{{{{{zzzzzzzzyyyxxvptuuvvumsuvvvvvvu hjx }|{{{{zzzzzzzzzyyyyyxxwusogoqsqg]pptuuttlc ntwx }{{{zzzzzzzzzyyyyyyxxwwuto - O jpssrO nsvx }{{zzzzzzzzzyyyyyyxwwwvrrT4 TonR Ufwy }{zzzzzzzzyyyyyxxwttuutqe Dj uxy }zzzzzzzzyxxxxxwwvuppnpn  twxy }yyyxxwvwwwxwvvvrtppc Y auwxxy dqtvwxyy }yyyxxwvwwwxwvvvrtppc Y auwxxy }zzzzzzzzyxxxxxwwvuppnpn  twxy }{zzzzzzzzyyyyyxxwttuutqe Dj uxy }{{zzzzzzzzzyyyyyyxwwwvrrT4 TonR Ufwy }{{{zzzzzzzzzyyyyyyxxwwuto - O jpssrO nsvx }|{{{{zzzzzzzzzyyyyyxxwusogoqsqg]pptuuttlc ntwx }|{{{{{{{zzzzzzzzyyyxxvptuuvvumsuvvvvvvu hjx }}|{{{{{{{{{{zzzzzzyyxwsuwwwwwwwwwwwwwvvurn[ ptuox }}|{{{{{{{{{{{{{{{zzzzyxxxxxyyyyyxxxxxwwukM!f ptvwxy }}||{{{{{{{{{{{{{{{{{zzzzyyyyyyyyyyyxxxxwvrrrkC grwxxy }}}||{{{{{{{{{{{{{{{{{{{zzzzyyyyyyyyyyxxxwvusg N Uquxyy }}}||{{{{{{{{{{{{{{{{{{{{{zzzzzzyyyyyyyxxxwurf ZnW 4nrslnobgwyy }}}}||{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzyyyyyxwvqemrttj m id+ PRUiPp_rvvvvudwxyz }}}}|||{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzyyyywwvtvvvvuutsp Hrtuuvwxxxxwqxyzz }}}}}||||{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzyyyxxxxxwwvvqc &8uvwxxxyyyyyzzz{ }}}}}}||||{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzzyyyxxxxwvtp 6puwxyyyyyyzzzz{{ }}}}}}|||||{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzzyyyyxxvqXp^g Ynslvxyyyyyzzzzz{{{ }}}}}}}||||||{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzzyyyyxwvuqaZlnvwxyyyzzzzzzz{{{{ }}}}}}}}|||||||{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzzyyyyxwwvtqptvwxyyzzzzzzz{{{{{ }}}}}}}}}|||||||{{{{{{{{{{{{{{{{{{{{{{{{{{zzzzzzzzzyyyyxwusjuthwyzzzzzzz{{{{{{{ ## Bourne Again SHell Works with: BASH version 4 ((xmin=-8601)) # int(-2.1*4096)((xmax=2867)) # int( 0.7*4096) ((ymin=-4915)) # int(-1.2*4096)((ymax=4915)) # int( 1.2*4096) ((maxiter=30)) ((dx=(xmax-xmin)/72))((dy=(ymax-ymin)/24)) C='0123456789'((lC={#C})) for((cy=ymax;cy>=ymin;cy-=dy)) ; do for((cx=xmin;cx<=xmax;cx+=dx)) ; do ((x=0,y=0,x2=0,y2=0)) for((iter=0;iter<maxiter && x2+y2<=16384;iter++)) ; do ((y=((x*y)>>11)+cy,x=x2-y2+cx,x2=(x*x)>>12,y2=(y*y)>>12)) done ((c=iter%lC)) echo -n {C:c:1} done echodone Output: 1111111111111222222222222333333333333333333333333333333333222222222222222 1111111111112222222233333333333333333333344444456015554444333332222222222 1111111111222222333333333333333333333444444445556704912544444433333222222 1111111112222333333333333333333333444444444555678970508655544444333333222 1111111222233333333333333333333444444444556667807000002076555544443333333 1111112223333333333333333333444444455577898889016000003099766662644333333 1111122333333333333333334444455555566793000800000000000000931045875443333 1111123333333333333344455555555566668014000000000000000000000009865544333 1111233333333344445568277777777777880600000000000000000000000009099544433 1111333344444445555678041513450199023000000000000000000000000000807544433 1112344444445555556771179000000000410000000000000000000000000000036544443 1114444444566667782404400000000000000000000000000000000000000000775544443 1119912160975272040000000000000000000000000000000000000000000219765544443 1114444444566667792405800000000000000000000000000000000000000000075544443 1113344444445555556773270000000000500000000000000000000000000000676544443 1111333344444445555678045623255199020000000000000000000000000000707544433 1111233333333444445568177777877777881500000000000000000000000009190544433 1111123333333333333344455555555566668126000000000000000000000009865544333 1111122333333333333333334444455555566793000100000000000000941355975443333 1111112223333333333333333334444444455588908889016000003099876670654433333 1111111222233333333333333333334444444445556667800000002976555554443333333 1111111112222333333333333333333333444444444555679060608655544444333333222 1111111111222222333333333333333333333444444445556702049544444433333222222 1111111111112222222233333333333333333333344444456205554444333333222222222 1111111111111222222222222333333333333333333333333333333333222222222222222  ## Brace This is a simple Mandelbrot plotter. A longer version based on this smooths colors, and avoids calculating the time-consuming black pixels: http://sam.ai.ki/brace/examples/mandelbrot.d/1 #!/usr/bin/env bxuse b Main(): num outside = 16, ox = -0.5, oy = 0, r = 1.5 long i, max_i = 100, rb_i = 30 space() uint32_t *px = pixel() num d = 2*r/h, x0 = ox-d*w_2, y0 = oy+d*h_2 for(y, 0, h): cmplx c = x0 + (y0-d*y)*I repeat(w): cmplx w = 0 for i=0; i < max_i && cabs(w) < outside; ++i w = w*w + c *px++ = i < max_i ? rainbow(i*359 / rb_i % 360) : black c += d An example plot from the longer version: ## Brainf***  A mandelbrot set fractal viewer in brainf*ck written by Erik Bosman+++++++++++++[->++>>>+++++>++>+<<<<<<]>>>>>++++++>--->>>>>>>>>>+++++++++++++++[[>>>>>>>>>]+[<<<<<<<<<]>>>>>>>>>-]+[>>>>>>>>[-]>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>[-]+<<<<<<<+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>>>+>>>>>>>>>>>>>>>>>>>>>>>>>>>+<<<<<<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+[>>>>>>[>>>>>>>[-]>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>[-]+<<<<<<++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>>+<<<<<<+++++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>>+<<<<<<<<<<<<<<<<[<<<<<<<<<]>>>[[-]>>>>>>[>>>>>>>[-<<<<<<+>>>>>>]<<<<<<[->>>>>>+<<+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<+<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<<<]>>>>>>>>>+++++++++++++++[[>>>>>>>>>]+>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>[-<<<<+>>>>]<<<<[->>>>+<<<<<[->>[-<<+>>]<<[->>+>>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[>[-]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+<<<<<<<<<]>>>>>>>>>[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<<<[->>>[-<<<+>>>]<<<[->>>+>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<<]>>[->>>>>>>>>+<<<<<<<<<]<<+>>>>>>>>]<<<<<<<<<[>[-]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+<<<<<<<<<]>>>>>>>>>[>>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>>>>>>]<<<<<<<<<-<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+>>>>>>>>>>>>>>>>>>>>>+<<<[<<<<<<<<<]>>>>>>>>>[>>>[-<<<->>>]+<<<[->>>->[-<<<<+>>>>]<<<<[->>>>+<<<<<<<<<<<<<[<<<<<<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>[-<<<<->>>>]+<<<<[->>>>-<[-<<<+>>>]<<<[->>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]<<<<<<<[->+>>>-<<<<]>>>>>>>>>++++++++++++++++++++++++++>>[-<<<<+>>>>]<<<<[->>>>+<<[-]<<]>>[<<<<<<<+<[-<+>>>>+<<[-]]>[-<<[->+>>>-<<<<]>>>]>>>>>>>>>>>>>[>>[-]>[-]>[-]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-]>>>>>>[>>>>>[-<<<<+>>>>]<<<<[->>>>+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>[-<<<<<<<<<+>>>>>>>>>]>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>>>>>>]+>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<<<[->>[-<<+>>]<<[->>+>+<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[>[-]<->>>[-<<<+>[<->-<<<<<<<+>>>>>>>]<[->+<]>>>]<<[->>+<<]<+<<<<<<<<<]>>>>>>>>>[>>>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<<<[->>[-<<+>>]<<[->>+>>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[>[-]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+<<<<<<<<<]>>>>>>>>>[>>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>]>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>>>>>>]<<<<<<<<<-<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[>>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<<<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>>[-]>>>]<<<<<<<<<[<<<<<<<<<]>>>>+>[-<-<<<<+>>>>>]>[-<<<<<<[->>>>>+<++<<<<]>>>>>[-<<<<<+>>>>>]<->+>]<[->+<]<<<<<[->>>>>+<<<<<]>>>>>>[-]<<<<<<+>>>>[-<<<<->>>>]+<<<<[->>>>->>>>>[>>[-<<->>]+<<[->>->[-<<<+>>>]<<<[->>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>+<]]+>>>[-<<<->>>]+<<<[->>>-<[-<<+>>]<<[->>+<<<<<<<<<<<[<<<<<<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>[-<<<<+>>>>]<<<<[->>>>+>>>>>[>+>>[-<<->>]<<[->>+<<]>>>>>>>>]<<<<<<<<+<[>[->>>>>+<<<<[->>>>-<<<<<<<<<<<<<<+>>>>>>>>>>>[->>>+<<<]<]>[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>>]<<]>[->>>>+<<<[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>>+<<<]<<<<<<<<<<<<]>>>>[-]<<<<]>>>[-<<<+>>>]<<<[->>>+>>>>>>[>+>[-<->]<[->+<]>>>>>>>>]<<<<<<<<+<[>[->>>>>+<<<[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>[->>>>+<<<<]>]<[->>>>-<<<<<<<<<<<<<<+>>>>>>>>>>]<]>>[->>>+<<<<[->>>>-<<<<<<<<<<<<<<+>>>>>>>>>>]>]<[->>>>+<<<<]<<<<<<<<<<<]>>>>>>+<<<<<<]]>>>>[-<<<<+>>>>]<<<<[->>>>+>>>>>[>>>>>>>>>]<<<<<<<<<[>[->>>>>+<<<<[->>>>-<<<<<<<<<<<<<<+>>>>>>>>>>>[->>>+<<<]<]>[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>>]<<]>[->>>>+<<<[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>>+<<<]<<<<<<<<<<<<]]>[-]>>[-]>[-]>>>>>[>>[-]>[-]>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>[-<<<<+>>>>]<<<<[->>>>+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>>>>>>]+>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>[-<<<<+>>>>]<<<<[->>>>+<<<<<[->>[-<<+>>]<<[->>+>+<<<]+>>>>>>>>>]<<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<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>[-]<<<+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>-<<<<<[<<<<<<<<<]]>>>]<<<<.>>>>>>>>>>[>>>>>>[-]>>>]<<<<<<<<<[<<<<<<<<<]>++++++++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>+>>>>>>>>>+<<<<<<<<<<<<<<<[<<<<<<<<<]>>>>>>>>[-<<<<<<<<+>>>>>>>>]<<<<<<<<[->>>>>>>>+[-]>[>>>>>>>>>]<<<<<<<<<[>>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<<<<<<<[<<<<<<<<<]>>>>>>>>[-]+>>]<<<<<<<<<<]]>>>>>>>>[-<<<<<<<<+>>>>>>>>]<<<<<<<<[->>>>>>>>+>[>+>>>>>[-<<<<<->>>>>]<<<<<[->>>>>+<<<<<]>>>>>>>>]<+<<<<<<<<[>>>>>>[->>+<<]<<<<<<<<<<<<<<<]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>[-]<->>>>>>>>[-<<<<<<<<+>[<->-<<+>>]<[->+<]>>>>>>>>]<<<<<<<[->>>>>>>+<<<<<<<]<+<<<<<<<<<]>>>>>>>>-<<<<<[-]+<<<]+>>>>>>>>[-<<<<<<<<->>>>>>>>]+<<<<<<<<[->>>>>>>>->[>>>>>>[->>+<<]>>>]<<<<<<<<<[>[-]<->>>>>>>>[-<<<<<<<<+>[<->-<<+>>]<[->+<]>>>>>>>>]<<<<<<<[->>>>>>>+<<<<<<<]<+<<<<<<<<<]>+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>+>>>>>>>>>>>>>>>>>>>>>>>>>>>+<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>>[-<<<<<<->>>>>>]+<<<<<<[->>>>>>->>[-<<<<<<<<+>>>>>>>>]<<<<<<<<[->>>>>>>>+<<<<<<<<<<<<<<<<<[<<<<<<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>>>>>[-<<<<<<<<->>>>>>>>]+<<<<<<<<[->>>>>>>>-<<[-<<<<<<+>>>>>>]<<<<<<[->>>>>>+<<<<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>[-]<<<+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>->>>>>>>>>>>>>>>>>>>>>>>>>>>-<<<<<<[<<<<<<<<<]]>>>]  Output: AAAAAAAAAAAAAAAABBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDEGFFEEEEDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB AAAAAAAAAAAAAAABBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDEEEFGIIGFFEEEDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBB AAAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEEEFFFI KHGGGHGEDDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBB AAAAAAAAAAAABBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEEFFGHIMTKLZOGFEEDDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBB AAAAAAAAAAABBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEEEFGGHHIKPPKIHGFFEEEDDDDDDDDDCCCCCCCCCCBBBBBBBBBBBBBBBBBB AAAAAAAAAABBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEEFFGHIJKS X KHHGFEEEEEDDDDDDDDDCCCCCCCCCCBBBBBBBBBBBBBBBB AAAAAAAAABBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEEFFGQPUVOTY ZQL[MHFEEEEEEEDDDDDDDCCCCCCCCCCCBBBBBBBBBBBBBB AAAAAAAABBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEFFFFFGGHJLZ UKHGFFEEEEEEEEDDDDDCCCCCCCCCCCCBBBBBBBBBBBB AAAAAAABBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEFFFFFFGGGGHIKP KHHGGFFFFEEEEEEDDDDDCCCCCCCCCCCBBBBBBBBBBB AAAAAAABBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEEEEFGGHIIHHHHHIIIJKMR VMKJIHHHGFFFFFFGSGEDDDDCCCCCCCCCCCCBBBBBBBBB AAAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDEEEEEEFFGHK MKJIJO N R X YUSR PLV LHHHGGHIOJGFEDDDCCCCCCCCCCCCBBBBBBBB AAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDEEEEEEEEEFFFFGH O TN S NKJKR LLQMNHEEDDDCCCCCCCCCCCCBBBBBBB AAAAABBCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDEEEEEEEEEEEEFFFFFGHHIN Q UMWGEEEDDDCCCCCCCCCCCCBBBBBB AAAABBCCCCCCCCCCCCCCCCCCCCCCCCCDDDDEEEEEEEEEEEEEEEFFFFFFGHIJKLOT [JGFFEEEDDCCCCCCCCCCCCCBBBBB AAAABCCCCCCCCCCCCCCCCCCCCCCDDDDEEEEEEEEEEEEEEEEFFFFFFGGHYV RQU QMJHGGFEEEDDDCCCCCCCCCCCCCBBBB AAABCCCCCCCCCCCCCCCCCDDDDDDDEEFJIHFFFFFFFFFFFFFFGGGGGGHIJN JHHGFEEDDDDCCCCCCCCCCCCCBBB AAABCCCCCCCCCCCDDDDDDDDDDEEEEFFHLKHHGGGGHHMJHGGGGGGHHHIKRR UQ L HFEDDDDCCCCCCCCCCCCCCBB AABCCCCCCCCDDDDDDDDDDDEEEEEEFFFHKQMRKNJIJLVS JJKIIIIIIJLR YNHFEDDDDDCCCCCCCCCCCCCBB AABCCCCCDDDDDDDDDDDDEEEEEEEFFGGHIJKOU O O PR LLJJJKL OIHFFEDDDDDCCCCCCCCCCCCCCB AACCCDDDDDDDDDDDDDEEEEEEEEEFGGGHIJMR RMLMN NTFEEDDDDDDCCCCCCCCCCCCCB AACCDDDDDDDDDDDDEEEEEEEEEFGGGHHKONSZ QPR NJGFEEDDDDDDCCCCCCCCCCCCCC ABCDDDDDDDDDDDEEEEEFFFFFGIPJIIJKMQ VX HFFEEDDDDDDCCCCCCCCCCCCCC ACDDDDDDDDDDEFFFFFFFGGGGHIKZOOPPS HGFEEEDDDDDDCCCCCCCCCCCCCC ADEEEEFFFGHIGGGGGGHHHHIJJLNY TJHGFFEEEDDDDDDDCCCCCCCCCCCCC A PLJHGGFFEEEDDDDDDDCCCCCCCCCCCCC ADEEEEFFFGHIGGGGGGHHHHIJJLNY TJHGFFEEEDDDDDDDCCCCCCCCCCCCC ACDDDDDDDDDDEFFFFFFFGGGGHIKZOOPPS HGFEEEDDDDDDCCCCCCCCCCCCCC ABCDDDDDDDDDDDEEEEEFFFFFGIPJIIJKMQ VX HFFEEDDDDDDCCCCCCCCCCCCCC AACCDDDDDDDDDDDDEEEEEEEEEFGGGHHKONSZ QPR NJGFEEDDDDDDCCCCCCCCCCCCCC AACCCDDDDDDDDDDDDDEEEEEEEEEFGGGHIJMR RMLMN NTFEEDDDDDDCCCCCCCCCCCCCB AABCCCCCDDDDDDDDDDDDEEEEEEEFFGGHIJKOU O O PR LLJJJKL OIHFFEDDDDDCCCCCCCCCCCCCCB AABCCCCCCCCDDDDDDDDDDDEEEEEEFFFHKQMRKNJIJLVS JJKIIIIIIJLR YNHFEDDDDDCCCCCCCCCCCCCBB AAABCCCCCCCCCCCDDDDDDDDDDEEEEFFHLKHHGGGGHHMJHGGGGGGHHHIKRR UQ L HFEDDDDCCCCCCCCCCCCCCBB AAABCCCCCCCCCCCCCCCCCDDDDDDDEEFJIHFFFFFFFFFFFFFFGGGGGGHIJN JHHGFEEDDDDCCCCCCCCCCCCCBBB AAAABCCCCCCCCCCCCCCCCCCCCCCDDDDEEEEEEEEEEEEEEEEFFFFFFGGHYV RQU QMJHGGFEEEDDDCCCCCCCCCCCCCBBBB AAAABBCCCCCCCCCCCCCCCCCCCCCCCCCDDDDEEEEEEEEEEEEEEEFFFFFFGHIJKLOT [JGFFEEEDDCCCCCCCCCCCCCBBBBB AAAAABBCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDEEEEEEEEEEEEFFFFFGHHIN Q UMWGEEEDDDCCCCCCCCCCCCBBBBBB AAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDEEEEEEEEEFFFFGH O TN S NKJKR LLQMNHEEDDDCCCCCCCCCCCCBBBBBBB AAAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDEEEEEEFFGHK MKJIJO N R X YUSR PLV LHHHGGHIOJGFEDDDCCCCCCCCCCCCBBBBBBBB AAAAAAABBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEEEEFGGHIIHHHHHIIIJKMR VMKJIHHHGFFFFFFGSGEDDDDCCCCCCCCCCCCBBBBBBBBB AAAAAAABBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEFFFFFFGGGGHIKP KHHGGFFFFEEEEEEDDDDDCCCCCCCCCCCBBBBBBBBBBB AAAAAAAABBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEFFFFFGGHJLZ UKHGFFEEEEEEEEDDDDDCCCCCCCCCCCCBBBBBBBBBBBB AAAAAAAAABBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEEFFGQPUVOTY ZQL[MHFEEEEEEEDDDDDDDCCCCCCCCCCCBBBBBBBBBBBBBB AAAAAAAAAABBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDDEEEEEEFFGHIJKS X KHHGFEEEEEDDDDDDDDDCCCCCCCCCCBBBBBBBBBBBBBBBB AAAAAAAAAAABBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEEEFGGHHIKPPKIHGFFEEEDDDDDDDDDCCCCCCCCCCBBBBBBBBBBBBBBBBBB AAAAAAAAAAAABBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDDDEEEEEFFGHIMTKLZOGFEEDDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBB AAAAAAAAAAAAABBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEEEFFFI KHGGGHGEDDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBB AAAAAAAAAAAAAAABBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDEEEFGIIGFFEEEDDDDDDDDCCCCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBB ## C ### PPM non interactive Here is one file program. It directly creates ppm file.  /* c program: -------------------------------- 1. draws Mandelbrot set for Fc(z)=z*z +c using Mandelbrot algorithm ( boolean escape time ) ------------------------------- 2. technique of creating ppm file is based on the code of Claudio Rocchini http://en.wikipedia.org/wiki/Image:Color_complex_plot.jpg create 24 bit color graphic file , portable pixmap file = PPM see http://en.wikipedia.org/wiki/Portable_pixmap to see the file use external application ( graphic viewer) */ #include <stdio.h> #include <math.h> int main() { /* screen ( integer) coordinate */ int iX,iY; const int iXmax = 800; const int iYmax = 800; /* world ( double) coordinate = parameter plane*/ double Cx,Cy; const double CxMin=-2.5; const double CxMax=1.5; const double CyMin=-2.0; const double CyMax=2.0; /* */ double PixelWidth=(CxMax-CxMin)/iXmax; double PixelHeight=(CyMax-CyMin)/iYmax; /* color component ( R or G or B) is coded from 0 to 255 */ /* it is 24 bit color RGB file */ const int MaxColorComponentValue=255; FILE * fp; char *filename="new1.ppm"; char *comment="# ";/* comment should start with # */ static unsigned char color[3]; /* Z=Zx+Zy*i ; Z0 = 0 */ double Zx, Zy; double Zx2, Zy2; /* Zx2=Zx*Zx; Zy2=Zy*Zy */ /* */ int Iteration; const int IterationMax=200; /* bail-out value , radius of circle ; */ const double EscapeRadius=2; double ER2=EscapeRadius*EscapeRadius; /*create new file,give it a name and open it in binary mode */ fp= fopen(filename,"wb"); /* b - binary mode */ /*write ASCII header to the file*/ fprintf(fp,"P6\n %s\n %d\n %d\n %d\n",comment,iXmax,iYmax,MaxColorComponentValue); /* compute and write image data bytes to the file*/ for(iY=0;iY<iYmax;iY++) { Cy=CyMin + iY*PixelHeight; if (fabs(Cy)< PixelHeight/2) Cy=0.0; /* Main antenna */ for(iX=0;iX<iXmax;iX++) { Cx=CxMin + iX*PixelWidth; /* initial value of orbit = critical point Z= 0 */ Zx=0.0; Zy=0.0; Zx2=Zx*Zx; Zy2=Zy*Zy; /* */ for (Iteration=0;Iteration<IterationMax && ((Zx2+Zy2)<ER2);Iteration++) { Zy=2*Zx*Zy + Cy; Zx=Zx2-Zy2 +Cx; Zx2=Zx*Zx; Zy2=Zy*Zy; }; /* compute pixel color (24 bit = 3 bytes) */ if (Iteration==IterationMax) { /* interior of Mandelbrot set = black */ color[0]=0; color[1]=0; color[2]=0; } else { /* exterior of Mandelbrot set = white */ color[0]=255; /* Red*/ color[1]=255; /* Green */ color[2]=255;/* Blue */ }; /*write color to the file*/ fwrite(color,1,3,fp); } } fclose(fp); return 0; } ### PPM Interactive Infinitely zoomable OpenGL program. Adjustable colors, max iteration, black and white, screen dump, etc. Compile with gcc mandelbrot.c -lglut -lGLU -lGL -lm • OpenBSD users, install freeglut package, and compile with make mandelbrot CPPFLAGS='-I/usr/local/include pkg-config glu --cflags' LDLIBS='-L/usr/local/lib -lglut pkg-config glu --libs -lm' Library: GLUT #include <stdio.h>#include <stdlib.h>#include <math.h>#include <GL/glut.h>#include <GL/gl.h>#include <GL/glu.h> void set_texture(); typedef struct {unsigned char r, g, b;} rgb_t;rgb_t **tex = 0;int gwin;GLuint texture;int width, height;int tex_w, tex_h;double scale = 1./256;double cx = -.6, cy = 0;int color_rotate = 0;int saturation = 1;int invert = 0;int max_iter = 256; void render(){ double x = (double)width /tex_w, y = (double)height/tex_h; glClear(GL_COLOR_BUFFER_BIT); glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_REPLACE); glBindTexture(GL_TEXTURE_2D, texture); glBegin(GL_QUADS); glTexCoord2f(0, 0); glVertex2i(0, 0); glTexCoord2f(x, 0); glVertex2i(width, 0); glTexCoord2f(x, y); glVertex2i(width, height); glTexCoord2f(0, y); glVertex2i(0, height); glEnd(); glFlush(); glFinish();} int dump = 1;void screen_dump(){ char fn[100]; int i; sprintf(fn, "screen%03d.ppm", dump++); FILE *fp = fopen(fn, "w"); fprintf(fp, "P6\n%d %d\n255\n", width, height); for (i = height - 1; i >= 0; i--) fwrite(tex[i], 1, width * 3, fp); fclose(fp); printf("%s written\n", fn);} void keypress(unsigned char key, int x, int y){ switch(key) { case 'q': glFinish(); glutDestroyWindow(gwin); return; case 27: scale = 1./256; cx = -.6; cy = 0; break; case 'r': color_rotate = (color_rotate + 1) % 6; break; case '>': case '.': max_iter += 128; if (max_iter > 1 << 15) max_iter = 1 << 15; printf("max iter: %d\n", max_iter); break; case '<': case ',': max_iter -= 128; if (max_iter < 128) max_iter = 128; printf("max iter: %d\n", max_iter); break; case 'c': saturation = 1 - saturation; break; case 's': screen_dump(); return; case 'z': max_iter = 4096; break; case 'x': max_iter = 128; break; case ' ': invert = !invert; } set_texture();} void hsv_to_rgb(int hue, int min, int max, rgb_t *p){ if (min == max) max = min + 1; if (invert) hue = max - (hue - min); if (!saturation) { p->r = p->g = p->b = 255 * (max - hue) / (max - min); return; } double h = fmod(color_rotate + 1e-4 + 4.0 * (hue - min) / (max - min), 6);# define VAL 255 double c = VAL * saturation; double X = c * (1 - fabs(fmod(h, 2) - 1)); p->r = p->g = p->b = 0; switch((int)h) { case 0: p->r = c; p->g = X; return; case 1: p->r = X; p->g = c; return; case 2: p->g = c; p->b = X; return; case 3: p->g = X; p->b = c; return; case 4: p->r = X; p->b = c; return; default:p->r = c; p->b = X; }} void calc_mandel(){ int i, j, iter, min, max; rgb_t *px; double x, y, zx, zy, zx2, zy2; min = max_iter; max = 0; for (i = 0; i < height; i++) { px = tex[i]; y = (i - height/2) * scale + cy; for (j = 0; j < width; j++, px++) { x = (j - width/2) * scale + cx; iter = 0; zx = hypot(x - .25, y); if (x < zx - 2 * zx * zx + .25) iter = max_iter; if ((x + 1)*(x + 1) + y * y < 1/16) iter = max_iter; zx = zy = zx2 = zy2 = 0; for (; iter < max_iter && zx2 + zy2 < 4; iter++) { zy = 2 * zx * zy + y; zx = zx2 - zy2 + x; zx2 = zx * zx; zy2 = zy * zy; } if (iter < min) min = iter; if (iter > max) max = iter; *(unsigned short *)px = iter; } } for (i = 0; i < height; i++) for (j = 0, px = tex[i]; j < width; j++, px++) hsv_to_rgb(*(unsigned short*)px, min, max, px);} void alloc_tex(){ int i, ow = tex_w, oh = tex_h; for (tex_w = 1; tex_w < width; tex_w <<= 1); for (tex_h = 1; tex_h < height; tex_h <<= 1); if (tex_h != oh || tex_w != ow) tex = realloc(tex, tex_h * tex_w * 3 + tex_h * sizeof(rgb_t*)); for (tex[0] = (rgb_t *)(tex + tex_h), i = 1; i < tex_h; i++) tex[i] = tex[i - 1] + tex_w;} void set_texture(){ alloc_tex(); calc_mandel(); glEnable(GL_TEXTURE_2D); glBindTexture(GL_TEXTURE_2D, texture); glTexImage2D(GL_TEXTURE_2D, 0, 3, tex_w, tex_h, 0, GL_RGB, GL_UNSIGNED_BYTE, tex[0]); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST); render();} void mouseclick(int button, int state, int x, int y){ if (state != GLUT_UP) return; cx += (x - width / 2) * scale; cy -= (y - height/ 2) * scale; switch(button) { case GLUT_LEFT_BUTTON: /* zoom in */ if (scale > fabs(x) * 1e-16 && scale > fabs(y) * 1e-16) scale /= 2; break; case GLUT_RIGHT_BUTTON: /* zoom out */ scale *= 2; break; /* any other button recenters */ } set_texture();} void resize(int w, int h){ printf("resize %d %d\n", w, h); width = w; height = h; glViewport(0, 0, w, h); glOrtho(0, w, 0, h, -1, 1); set_texture();} void init_gfx(int *c, char **v){ glutInit(c, v); glutInitDisplayMode(GLUT_RGB); glutInitWindowSize(640, 480); gwin = glutCreateWindow("Mandelbrot"); glutDisplayFunc(render); glutKeyboardFunc(keypress); glutMouseFunc(mouseclick); glutReshapeFunc(resize); glGenTextures(1, &texture); set_texture();} int main(int c, char **v){ init_gfx(&c, v); printf("keys:\n\tr: color rotation\n\tc: monochrome\n\ts: screen dump\n\t" "<, >: decrease/increase max iteration\n\tq: quit\n\tmouse buttons to zoom\n"); glutMainLoop(); return 0;} ### ASCII Not mine, found it on Ken Perlin's homepage, this deserves a place here to illustrate how awesome C can be:  main(k){float i,j,r,x,y=-16;while(puts(""),y++<15)for(x=0;x++<84;putchar(" .:-;!/>)|&IH%*#"[k&15]))for(i=k=r=0;j=r*r-i*i-2+x/25,i=2*r*i+y/10,j*j+i*i<11&&k++<111;r=j);}  There may be warnings on compiling but disregard them, the output will be produced nevertheless. Such programs are called obfuscated and C excels when it comes to writing such cryptic programs. Google IOCCC for more. .............::::::::::::::::::::::::::::::::::::::::::::::::....................... .........::::::::::::::::::::::::::::::::::::::::::::::::::::::::................... .....::::::::::::::::::::::::::::::::::-----------:::::::::::::::::::............... ...:::::::::::::::::::::::::::::------------------------:::::::::::::::............. :::::::::::::::::::::::::::-------------;;;!:H!!;;;--------:::::::::::::::.......... ::::::::::::::::::::::::-------------;;;;!!/>&*|I !;;;--------::::::::::::::........ ::::::::::::::::::::-------------;;;;;;!!/>)|.*#|>/!!;;;;-------::::::::::::::...... ::::::::::::::::-------------;;;;;;!!!!//>|: !:|//!!!;;;;-----::::::::::::::..... ::::::::::::------------;;;;;;;!!/>)I>>)||I# H&))>////*!;;-----:::::::::::::.... ::::::::----------;;;;;;;;;;!!!//)H: #| IH&*I#/;;-----:::::::::::::... :::::---------;;;;!!!!!!!!!!!//>|.H: #I>/!;;-----:::::::::::::.. :----------;;;;!/||>//>>>>//>>)|% %|&/!;;----::::::::::::::. --------;;;;;!!//)& .;I*-H#&||&/ *)/!;;-----:::::::::::::: -----;;;;;!!!//>)IH:- ## #&!!;;-----:::::::::::::: ;;;;!!!!!///>)H%.** * )/!;;;------::::::::::::: &)/!!;;;------::::::::::::: ;;;;!!!!!///>)H%.** * )/!;;;------::::::::::::: -----;;;;;!!!//>)IH:- ## #&!!;;-----:::::::::::::: --------;;;;;!!//)& .;I*-H#&||&/ *)/!;;-----:::::::::::::: :----------;;;;!/||>//>>>>//>>)|% %|&/!;;----::::::::::::::. :::::---------;;;;!!!!!!!!!!!//>|.H: #I>/!;;-----:::::::::::::.. ::::::::----------;;;;;;;;;;!!!//)H: #| IH&*I#/;;-----:::::::::::::... ::::::::::::------------;;;;;;;!!/>)I>>)||I# H&))>////*!;;-----:::::::::::::.... ::::::::::::::::-------------;;;;;;!!!!//>|: !:|//!!!;;;;-----::::::::::::::..... ::::::::::::::::::::-------------;;;;;;!!/>)|.*#|>/!!;;;;-------::::::::::::::...... ::::::::::::::::::::::::-------------;;;;!!/>&*|I !;;;--------::::::::::::::........ :::::::::::::::::::::::::::-------------;;;!:H!!;;;--------:::::::::::::::.......... ...:::::::::::::::::::::::::::::------------------------:::::::::::::::............. .....::::::::::::::::::::::::::::::::::-----------:::::::::::::::::::............... .........::::::::::::::::::::::::::::::::::::::::::::::::::::::::................... .............::::::::::::::::::::::::::::::::::::::::::::::::.......................  ## C# using System;using System.Drawing;using System.Drawing.Imaging;using System.Threading;using System.Windows.Forms; /// <summary>/// Generates bitmap of Mandelbrot Set and display it on the form./// </summary>public class MandelbrotSetForm : Form{ const double MaxValueExtent = 2.0; Thread thread; static double CalcMandelbrotSetColor(ComplexNumber c) { // from http://en.wikipedia.org/w/index.php?title=Mandelbrot_set const int MaxIterations = 1000; const double MaxNorm = MaxValueExtent * MaxValueExtent; int iteration = 0; ComplexNumber z = new ComplexNumber(); do { z = z * z + c; iteration++; } while (z.Norm() < MaxNorm && iteration < MaxIterations); if (iteration < MaxIterations) return (double)iteration / MaxIterations; else return 0; // black } static void GenerateBitmap(Bitmap bitmap) { double scale = 2 * MaxValueExtent / Math.Min(bitmap.Width, bitmap.Height); for (int i = 0; i < bitmap.Height; i++) { double y = (bitmap.Height / 2 - i) * scale; for (int j = 0; j < bitmap.Width; j++) { double x = (j - bitmap.Width / 2) * scale; double color = CalcMandelbrotSetColor(new ComplexNumber(x, y)); bitmap.SetPixel(j, i, GetColor(color)); } } } static Color GetColor(double value) { const double MaxColor = 256; const double ContrastValue = 0.2; return Color.FromArgb(0, 0, (int)(MaxColor * Math.Pow(value, ContrastValue))); } public MandelbrotSetForm() { // form creation this.Text = "Mandelbrot Set Drawing"; this.BackColor = System.Drawing.Color.Black; this.BackgroundImageLayout = System.Windows.Forms.ImageLayout.Stretch; this.MaximizeBox = false; this.StartPosition = FormStartPosition.CenterScreen; this.FormBorderStyle = FormBorderStyle.FixedDialog; this.ClientSize = new Size(640, 640); this.Load += new System.EventHandler(this.MainForm_Load); } void MainForm_Load(object sender, EventArgs e) { thread = new Thread(thread_Proc); thread.IsBackground = true; thread.Start(this.ClientSize); } void thread_Proc(object args) { // start from small image to provide instant display for user Size size = (Size)args; int width = 16; while (width * 2 < size.Width) { int height = width * size.Height / size.Width; Bitmap bitmap = new Bitmap(width, height, PixelFormat.Format24bppRgb); GenerateBitmap(bitmap); this.BeginInvoke(new SetNewBitmapDelegate(SetNewBitmap), bitmap); width *= 2; Thread.Sleep(200); } // then generate final image Bitmap finalBitmap = new Bitmap(size.Width, size.Height, PixelFormat.Format24bppRgb); GenerateBitmap(finalBitmap); this.BeginInvoke(new SetNewBitmapDelegate(SetNewBitmap), finalBitmap); } void SetNewBitmap(Bitmap image) { if (this.BackgroundImage != null) this.BackgroundImage.Dispose(); this.BackgroundImage = image; } delegate void SetNewBitmapDelegate(Bitmap image); static void Main() { Application.Run(new MandelbrotSetForm()); }} struct ComplexNumber{ public double Re; public double Im; public ComplexNumber(double re, double im) { this.Re = re; this.Im = im; } public static ComplexNumber operator +(ComplexNumber x, ComplexNumber y) { return new ComplexNumber(x.Re + y.Re, x.Im + y.Im); } public static ComplexNumber operator *(ComplexNumber x, ComplexNumber y) { return new ComplexNumber(x.Re * y.Re - x.Im * y.Im, x.Re * y.Im + x.Im * y.Re); } public double Norm() { return Re * Re + Im * Im; }} ## C++ This generic function assumes that the image can be accessed like a two-dimensional array of colors. It may be passed a true array (in which case the Mandelbrot set will simply be drawn into that array, which then might be saved as image file), or a class which maps the subscript operator to the pixel drawing routine of some graphics library. In the latter case, there must be functions get_first_dimension and get_second_dimension defined for that type, to be found by argument dependent lookup. The code provides those functions for built-in arrays. #include <cstdlib>#include <complex> // get dimensions for arraystemplate<typename ElementType, std::size_t dim1, std::size_t dim2> std::size_t get_first_dimension(ElementType (&a)[dim1][dim2]){ return dim1;} template<typename ElementType, std::size_t dim1, std::size_t dim2> std::size_t get_second_dimension(ElementType (&a)[dim1][dim2]){ return dim2;} template<typename ColorType, typename ImageType> void draw_Mandelbrot(ImageType& image, //where to draw the image ColorType set_color, ColorType non_set_color, //which colors to use for set/non-set points double cxmin, double cxmax, double cymin, double cymax,//the rect to draw in the complex plane unsigned int max_iterations) //the maximum number of iterations{ std::size_t const ixsize = get_first_dimension(image); std::size_t const iysize = get_first_dimension(image); for (std::size_t ix = 0; ix < ixsize; ++ix) for (std::size_t iy = 0; iy < iysize; ++iy) { std::complex<double> c(cxmin + ix/(ixsize-1.0)*(cxmax-cxmin), cymin + iy/(iysize-1.0)*(cymax-cymin)); std::complex<double> z = 0; unsigned int iterations; for (iterations = 0; iterations < max_iterations && std::abs(z) < 2.0; ++iterations) z = z*z + c; image[ix][iy] = (iterations == max_iterations) ? set_color : non_set_color; }} Note this code has not been executed. ## Cixl Displays a zooming Mandelbrot using ANSI graphics.  use: cx; define: max 4.0;define: max-iter 570; let: (max-x max-y) screen-size;let: max-cx max-x 2.0 /;let: max-cy max-y 2.0 /;let: rows Stack<Str> new;let: buf Buf new;let: zoom 0 ref; func: render()() rows clear max-y 2 / { let: y; buf 0 seek max-x { let: x; let: (zx zy) 0.0 ref %%; let: cx x max-cx - zoom deref /; let: cy y max-cy - zoom deref /; let: i #max-iter ref; { let: nzx zx deref ** zy deref ** - cx +; zy zx deref *2 zy deref * cy + set zx nzx set i &-- set-call nzx ** zy deref ** + #max < i deref and } while let: c i deref % -7 bsh bor 256 mod; c {x 256 mod y 256 mod} {0 0} if-else c new-rgb buf set-bg @@s buf print } for rows buf str push } for 1 1 #out move-to rows {#out print} for rows riter {#out print} for; #out hide-cursorraw-mode let: poll Poll new;let: is-done #f ref; poll #in { #in read-char _ is-done #t set} on-read { zoom &++ set-call render poll 0 wait _ is-done deref !} while #out reset-style#out clear-screen1 1 #out move-to#out show-cursornormal-mode  ## Clojure Translation of: Perl (ns mandelbrot (:refer-clojure :exclude [+ * <]) (:use (clojure.contrib complex-numbers) (clojure.contrib.generic [arithmetic :only [+ *]] [comparison :only [<]] [math-functions :only [abs]])))(defn mandelbrot? [z] (loop [c 1 m (iterate #(+ z (* % %)) 0)] (if (and (> 20 c) (< (abs (first m)) 2) ) (recur (inc c) (rest m)) (if (= 20 c) true false)))) (defn mandelbrot [] (for [y (range 1 -1 -0.05) x (range -2 0.5 0.0315)] (if (mandelbrot? (complex x y)) "#" " "))) (println (interpose \newline (map #(apply str %) (partition 80 (mandelbrot)))))  ## COBOL EBCDIC art. IDENTIFICATION DIVISION.PROGRAM-ID. MANDELBROT-SET-PROGRAM.DATA DIVISION.WORKING-STORAGE SECTION.01 COMPLEX-ARITHMETIC. 05 X PIC S9V9(9). 05 Y PIC S9V9(9). 05 X-A PIC S9V9(6). 05 X-B PIC S9V9(6). 05 Y-A PIC S9V9(6). 05 X-A-SQUARED PIC S9V9(6). 05 Y-A-SQUARED PIC S9V9(6). 05 SUM-OF-SQUARES PIC S9V9(6). 05 ROOT PIC S9V9(6).01 LOOP-COUNTERS. 05 I PIC 99. 05 J PIC 99. 05 K PIC 999.77 PLOT-CHARACTER PIC X.PROCEDURE DIVISION.CONTROL-PARAGRAPH. PERFORM OUTER-LOOP-PARAGRAPH VARYING I FROM 1 BY 1 UNTIL I IS GREATER THAN 24. STOP RUN.OUTER-LOOP-PARAGRAPH. PERFORM INNER-LOOP-PARAGRAPH VARYING J FROM 1 BY 1 UNTIL J IS GREATER THAN 64. DISPLAY ''.INNER-LOOP-PARAGRAPH. MOVE SPACE TO PLOT-CHARACTER. MOVE ZERO TO X-A. MOVE ZERO TO Y-A. MULTIPLY J BY 0.0390625 GIVING X. SUBTRACT 1.5 FROM X. MULTIPLY I BY 0.083333333 GIVING Y. SUBTRACT 1 FROM Y. PERFORM ITERATION-PARAGRAPH VARYING K FROM 1 BY 1 UNTIL K IS GREATER THAN 100 OR PLOT-CHARACTER IS EQUAL TO '#'. DISPLAY PLOT-CHARACTER WITH NO ADVANCING.ITERATION-PARAGRAPH. MULTIPLY X-A BY X-A GIVING X-A-SQUARED. MULTIPLY Y-A BY Y-A GIVING Y-A-SQUARED. SUBTRACT Y-A-SQUARED FROM X-A-SQUARED GIVING X-B. ADD X TO X-B. MULTIPLY X-A BY Y-A GIVING Y-A. MULTIPLY Y-A BY 2 GIVING Y-A. SUBTRACT Y FROM Y-A. MOVE X-B TO X-A. ADD X-A-SQUARED TO Y-A-SQUARED GIVING SUM-OF-SQUARES. MOVE FUNCTION SQRT (SUM-OF-SQUARES) TO ROOT. IF ROOT IS GREATER THAN 2 THEN MOVE '#' TO PLOT-CHARACTER. Output: ################################################################ ################################# ############################ ################################ ########################### ############################## ## ############################ ######################## # ###################### ######################## ################## ##################### ################# #################### ############### ######## ## ##### ################ ####### # ################ ###### # ################# #################### ###### # ################# ####### # ################ ######## ## ##### ################ #################### ############### ##################### ################# ######################## ################## ######################## # ###################### ############################## ## ############################ ################################ ########################### ################################# ############################ ################################################################ ################################################################ ## Common Lisp (defpackage #:mandelbrot (:use #:cl)) (in-package #:mandelbrot) (deftype pixel () '(unsigned-byte 8))(deftype image () '(array pixel)) (defun write-pgm (image filespec) (declare (image image)) (with-open-file (s filespec :direction :output :element-type 'pixel :if-exists :supersede) (let* ((width (array-dimension image 1)) (height (array-dimension image 0)) (header (format nil "P5~A~D ~D~A255~A" #\Newline width height #\Newline #\Newline))) (loop for c across header do (write-byte (char-code c) s)) (dotimes (row height) (dotimes (col width) (write-byte (aref image row col) s)))))) (defparameter *x-max* 800)(defparameter *y-max* 800)(defparameter *cx-min* -2.5)(defparameter *cx-max* 1.5)(defparameter *cy-min* -2.0)(defparameter *cy-max* 2.0)(defparameter *escape-radius* 2)(defparameter *iteration-max* 40) (defun mandelbrot (filespec) (let ((pixel-width (/ (- *cx-max* *cx-min*) *x-max*)) (pixel-height (/ (- *cy-max* *cy-min*) *y-max*)) (image (make-array (list *y-max* *x-max*) :element-type 'pixel :initial-element 0))) (loop for y from 0 below *y-max* for cy from *cy-min* by pixel-height do (loop for x from 0 below *x-max* for cx from *cx-min* by pixel-width for iteration = (loop with c = (complex cx cy) for iteration from 0 below *iteration-max* for z = c then (+ (* z z) c) while (< (abs z) *escape-radius*) finally (return iteration)) for pixel = (round (* 255 (/ (- *iteration-max* iteration) *iteration-max*))) do (setf (aref image y x) pixel))) (write-pgm image filespec))) ## Cowgol Translation of: B include "cowgol.coh"; const xmin := -8601;const xmax := 2867;const ymin := -4915;const ymax := 4915;const maxiter := 32; const dx := (xmax-xmin)/79;const dy := (ymax-ymin)/24; var cy: int16 := ymin;while cy <= ymax loop var cx: int16 := xmin; while cx <= xmax loop var x: int32 := 0; var y: int32 := 0; var x2: int32 := 0; var y2: int32 := 0; var iter: uint8 := 0; while iter < maxiter and x2 + y2 <= 16384 loop y := ((x*y)>>11)+cy as int32; x := x2-y2+cx as int32; x2 := (x*x)>>12; y2 := (y*y)>>12; iter := iter + 1; end loop; print_char(' ' + iter); cx := cx + dx; end loop; print_nl(); cy := cy + dy;end loop; Output: !!!!!!!!!!!!!!!"""""""""""""####################################"""""""""""""""" !!!!!!!!!!!!!"""""""""#######################$$$%'+)%%%$#####""""""""""" !!!!!!!!!!!"""""""#######################%%%&&(+,)++&%$$######"""""" !!!!!!!!!"""""#######################$$%%%%&')*5:/+('&%%$$#######""" !!!!!!!!""""#####################$$%%%&&&''),@@@@@@@,'&%%%%%######## !!!!!!!"""####################%%%&'())((())*,@@@@@@/+))('&&&&)'%$$###### !!!!!!""###################$$$$%%%%%%&&&'[email protected]@=/<@@@@@@@@@@@@@@@/[email protected]%%##### !!!!!"################$$$%%%%%%%%%%&&&&'),[email protected]@@@@@@@@@@@@@@@@@@@@@@@@1(&&%$$#### !!!!"##########$$$$%%&(-(''''''''''''(*,[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@@+)-&%$$###
!!!!####%%%%%&'(*[email protected][email protected]+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4-(&%$$## !!!!#$$$$%%%%%%'''[email protected]@@@@@@@@8/[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3(%%$$$$# !!!#$$$%&&&&''()/[email protected]@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?'&%%# !!!(**+/+<523/80/[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+)'&&%%# !!!#$$%&&&&''()[email protected]@@@@@@@@@@@@@[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$# !!!!#$$$$%%%%%&'''/,[email protected]@@@@@@@@;/[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0'%%$$$$# !!!!####$$$$%%%%%&'(*-:2.,/?-5+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+(&%$$$##
!!!!"##########$%%&(-(''''(''''''((*,[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@4+).&%$$### !!!!!"################$$$%%%%%%%%%%&&&&')<,[email protected]@@@@@@@@@@@@@@@@@@@@@@@@/('&%%$#### !!!!!!""##################$$%%%%%%&&&'*[email protected]@@[email protected]@@@@@@@@@@@@@@@1,,@//9)%%##### !!!!!!!"""####################$$$$%%%&(())((()**[email protected]@@@@@/+)))'&&&')'%$$###### !!!!!!!!""""#####################$$%%%&&&''(,@@@@@@@+'&&%%%%%$$$########
!!!!!!!!!"""""#######################$$%%%%&')*[email protected]+('&%%%$$$$#######""" !!!!!!!!!!!"""""""######################$$$$%%%&&(+-).*&%$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$%%'3(%%%$$$$######"""""""""" !!!!!!!!!!!!!!!""""""""""""#####################################"""""""""""""""" ## D ### Textual Version This uses std.complex because D built-in complex numbers are deprecated. void main() { import std.stdio, std.complex; for (real y = -1.2; y < 1.2; y += 0.05) { for (real x = -2.05; x < 0.55; x += 0.03) { auto z = 0.complex; foreach (_; 0 .. 100) z = z ^^ 2 + complex(x, y); write(z.abs < 2 ? '#' : '.'); } writeln; }} Output: ....................................................................................... ....................................................................................... ....................................................................................... ....................................................................................... ....................................................................................... ....................................................................................... ....................................................................................... ................................................................##..................... .............................................................######.................... .............................................................#######................... ..............................................................######................... ..........................................................#.#.###..#.#................. ...................................................##....################.............. ..................................................###.######################.###....... ...................................................############################........ ................................................###############################........ ................................................################################....... .............................................#####################################..... ..............................................###################################...... ..............................##.####.#......####################################...... ..............................###########....####################################...... ............................###############.######################################..... ............................###############.#####################################...... ........................##.#####################################################....... ......#.#####################################################################.......... ........................##.#####################################################....... ............................###############.#####################################...... ............................###############.######################################..... ..............................###########....####################################...... ..............................##.####.#......####################################...... ..............................................###################################...... .............................................#####################################..... ................................................################################....... ................................................###############################........ ...................................................############################........ ..................................................###.######################.###....... ...................................................##....################.............. ..........................................................#.#.###..#.#................. ..............................................................######................... .............................................................#######................... .............................................................######.................... ................................................................##..................... ....................................................................................... ....................................................................................... ....................................................................................... ....................................................................................... ....................................................................................... ....................................................................................... ....................................................................................... ### More Functional Textual Version The output is similar. void main() { import std.stdio, std.complex, std.range, std.algorithm; foreach (immutable y; iota(-1.2, 1.2, 0.05)) iota(-2.05, 0.55, 0.03).map!(x => 0.complex .recurrence!((a, n) => a[n - 1] ^^ 2 + complex(x, y)) .drop(100).front.abs < 2 ? '#' : '.').writeln;} ### Graphical Version Library: QD Library: SDL Library: Phobos import qd; double lensqr(cdouble c) { return c.re * c.re + c.im * c.im; } const Limit = 150; void main() { screen(640, 480); for (int y = 0; y < screen.h; ++y) { flip; events; for (int x = 0; x < screen.w; ++x) { auto c_x = x * 1.0 / screen.w - 0.5, c_y = y * 1.0 / screen.h - 0.5, c = c_y * 2.0i + c_x * 3.0 - 1.0, z = 0.0i + 0.0, i = 0; for (; i < Limit; ++i) { z = z * z + c; if (lensqr(z) > 4) break; } auto value = cast(ubyte) (i * 255.0 / Limit); pset(x, y, rgb(value, value, value)); } } while (true) { flip; events; }} ## Dart Implementation in Google Dart works on http://try.dartlang.org/ (as of 10/18/2011) since the language is very new, it may break in the future. The implementation uses a incomplete Complex class supporting operator overloading. class Complex { double _r,_i; Complex(this._r,this._i); double get r => _r; double get i => _i; String toString() => "(r,i)"; Complex operator +(Complex other) => new Complex(r+other.r,i+other.i); Complex operator *(Complex other) => new Complex(r*other.r-i*other.i,r*other.i+other.r*i); double abs() => r*r+i*i;} void main() { double start_x=-1.5; double start_y=-1.0; double step_x=0.03; double step_y=0.1; for(int y=0;y<20;y++) { String line=""; for(int x=0;x<70;x++) { Complex c=new Complex(start_x+step_x*x,start_y+step_y*y); Complex z=new Complex(0.0, 0.0); for(int i=0;i<100;i++) { z=z*(z)+c; if(z.abs()>2) { break; } } line+=z.abs()>2 ? " " : "*"; } print(line); }} ## Dc ### ASCII output Works with: GNU Dc Works with: OpenBSD Dc This can be done in a more Dc-ish way, e.g. by moving the loop macros' definitions to the initialisations in the top instead of saving the macro definition of inner loops over and over again in outer loops.  _2.1 sx # xmin = -2.1 0.7 sX # xmax = 0.7 _1.2 sy # ymin = -1.2 1.2 sY # ymax = 1.2 32 sM # maxiter = 32 80 sW # image width 25 sH # image height 8 k # precision [ q ] sq # quitter helper macro # for h from 0 to H-10 sh[ lh lH =q # quit if H reached # for w from 0 to W-1 0 sw [ lw lW =q # quit if W reached # (w,h) -> (R,I) # | | # | ymin + h*(ymax-ymin)/(height-1) # xmin + w*(xmax-xmin)/(width-1) lX lx - lW 1 - / lw * lx + sR lY ly - lH 1 - / lh * ly + sI # iterate for (R,I) 0 sr # r:=0 0 si # i:=0 0 sa # a:=0 (r squared) 0 sb # b:=0 (i squared) 0 sm # m:=0 # do while m!=M and a+b=<4 [ lm lM =q # exit if m==M la lb + 4<q # exit if >4 2 lr * li * lI + si # i:=2*r*i+I la lb - lR + sr # r:=a-b+R lm 1 + sm # m+=1 lr 2 ^ sa # a:=r*r li 2 ^ sb # b:=i*i l0 x # loop ] s0 l0 x lm 32 + P # print "pixel" lw 1 + sw # w+=1 l1 x # loop ] s1 l1 x A P # linefeed lh 1 + sh # h+=1 l2 x # loop] s2l2 x Output: !!!!!!!!!!!!!!!"""""""""""""####################################"""""""""""""""" !!!!!!!!!!!!!"""""""""#######################$$$%'0(%%%$#####"""""""""""
!!!!!!!!!!!"""""""#######################%%%&&(++)++&$$######"""""" !!!!!!!!!"""""#######################$$%%%%&')*@;/*('&%%$$#######""" !!!!!!!!""""#####################$$%%%&&&''),@@@@@@@+'&%%%%%########
!!!!!!!"""####################%%%&'())((())*[email protected]@@@@@.+))('&&&&+&%$$###### !!!!!!""###################$$$$%%%%%%&&&'[email protected]@@[email protected]@@@@@@@@@@@@@@/+,@//@)%%##### !!!!!"################$$$%%%%%%%%%%&&&&')[email protected]@@@@@@@@@@@@@@@@@@@@@@@@4(&&%$$#### !!!!"##########$$$$%%&(,('''''''''''((*[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@3+)4&%$$### !!!!####%%%%%&'(*[email protected]+/@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3+'&%$$## !!!!#$$$$%%%%%%'''[email protected]@@@@@@@@9/[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@<6'%%$$$$# !!!#$$$%&&&&''()[email protected]@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%#
[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@2+)'&&%%#
!!!#$$%&&&&''()[email protected]@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$# !!!!#$$$$%%%%%%'''[email protected]@@@@@@@@9/[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@<6'%%$$$$# !!!!####$$$$%%%%%&'(*[email protected]+/@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3+'&%$$$## !!!!"##########$%%&(,('''''''''''((*[email protected]@@@@@@@@@@@@@@@@@@@@@@@@@@3+)4&%$$### !!!!!"################$$$%%%%%%%%%%&&&&')[email protected]@@@@@@@@@@@@@@@@@@@@@@@@4(&&%$$#### !!!!!!""###################$$$$%%%%%%&&&'[email protected]@@[email protected]@@@@@@@@@@@@@@/+,@//@)%%##### !!!!!!!"""####################$$$$%%%&'())((())*[email protected]@@@@@.+))('&&&&+&%$$###### !!!!!!!!""""#####################$$%%%&&&''),@@@@@@@+'&%%%%%$$$$######## !!!!!!!!!"""""#######################$$%%%%&')*@;/*('&%%$$#######""" !!!!!!!!!!!"""""""#######################$$$$%%%&&(++)++&$$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$%'0(%%%$$$$#####""""""""""" !!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""  ### PGM (P5) output This is a condensed version of the ASCII output variant modified to generate a PGM (P5) image. _2.1 sx 0.7 sX _1.2 sy 1.2 sY32 sM640 sW 480 sH8 k[P5] P A PlW n 32 P lH n A PlM 1 - n A P[ q ] sq0 sh[ lh lH =q 0 sw [ lw lW =q lX lx - lW 1 - / lw * lx + sR lY ly - lH 1 - / lh * ly + sI 0 sr 0 si 0 sa 0 sb 0 sm [ lm lM =q la lb + 4<q 2 lr * li * lI + si la lb - lR + sr lm 1 + sm lr 2 ^ sa li 2 ^ sb l0 x ] s0 l0 x lm 1 - P lw 1 + sw l1 x ] s1 l1 x lh 1 + sh l2 x] s2l2 x ## DEC BASIC-PLUS Works under RSTS/E v7.0 on the simh PDP-11 emulator. For installation procedures for RSTS/E, see here. 10 X1=59\Y1=2120 I1=-1.0\I2=1.0\R1=-2.0\R2=1.030 S1=(R2-R1)/X1\S2=(I2-I1)/Y140 FOR Y=0 TO Y150 I3=I1+S2*Y60 FOR X=0 TO X170 R3=R1+S1*X\Z1=R3\Z2=I380 FOR N=0 TO 3090 A=Z1*Z1\B=Z2*Z2100 IF A+B>4.0 THEN GOTO 130110 Z2=2*Z1*Z2+I3\Z1=A-B+R3120 NEXT N130 PRINT STRING(1%,62%-N);140 NEXT X150 PRINT160 NEXT Y170 END  Output: >>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<=========== >>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<======== >>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<======= >>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<===== >>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<==== >>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<=== >=<<<<<<<<;;;:599999999886 %78:;;<<<<<<== ><<<<;;;;;:::972456-567763 +9;;<<<<<<<= ><;;;;;;::::9875& .3 *9;;;<<<<<<= >;;;;;;::997564' ' 8:;;;<<<<<<= >::988897735/ &89:;;;<<<<<<= >::988897735/ &89:;;;<<<<<<= >;;;;;;::997564' ' 8:;;;<<<<<<= ><;;;;;;::::9875& .3 *9;;;<<<<<<= ><<<<;;;;;:::972456-567763 +9;;<<<<<<<= >=<<<<<<<<;;;:599999999886 %78:;;<<<<<<== >>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<=== >>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<==== >>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<===== >>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<======= >>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<======== >>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<=========== ## Delphi See Pascal. ## DWScript Translation of: D const maxIter = 256; var x, y, i : Integer;for y:=-39 to 39 do begin for x:=-39 to 39 do begin var c := Complex(y/40-0.5, x/40); var z := Complex(0, 0); for i:=1 to maxIter do begin z := z*z + c; if Abs(z)>=4 then Break; end; if i>=maxIter then Print('#') else Print('.'); end; PrintLn('');end; ## EasyLang for y0 range 300 cy = (y0 - 150) / 120 for x0 range 300 cx = (x0 - 220) / 120 x = 0 y = 0 set_rgb 0 0 0 for n range 128 if x * x + y * y > 4 set_rgb n / 16 0 0 break 1 . h = x * x - y * y + cx y = 2 * x * y + cy x = h . move_pen x0 / 3 y0 / 3 draw_rect 0.4 0.4 .. ## eC Drawing code: void drawMandelbrot(Bitmap bmp, float range, Complex center, ColorAlpha * palette, int nPalEntries, int nIterations, float scale){ int x, y; int w = bmp.width, h = bmp.height; ColorAlpha * picture = (ColorAlpha *)bmp.picture; double logOf2 = log(2); Complex d { w > h ? range : range * w / h, h > w ? range : range * h / w }; Complex C0 { center.a - d.a/2, center.b - d.b/2 }; Complex C = C0; double delta = d.a / w; for(y = 0; y < h; y++, C.a = C0.a, C.b += delta) { for(x = 0; x < w; x++, picture++, C.a += delta) { Complex Z { }; int i; double ii = 0; bool out = false; double Za2 = Z.a * Z.a, Zb2 = Z.b * Z.b; for(i = 0; i < nIterations; i++) { double z2; Z = { Za2 - Zb2, 2*Z.a*Z.b }; Z.a += C.a; Z.b += C.b; Za2 = Z.a * Z.a, Zb2 = Z.b * Z.b; z2 = Za2 + Zb2; if(z2 >= 2*2) { ii = (double)(i + 1 - log(0.5 * log(z2)) / logOf2); out = true; break; } } if(out) { float si = (float)(ii * scale); int i0 = ((int)si) % nPalEntries; *picture = palette[i0]; } else *picture = black; } }} Interactive class with Rubberband Zoom: class Mandelbrot : Window{ caption = "Mandelbrot"; borderStyle = sizable; hasMaximize = true; hasMinimize = true; hasClose = true; clientSize = { 600, 600 }; Point mouseStart, mouseEnd; bool dragging; bool needUpdate; float scale; int nIterations; nIterations = 256; ColorAlpha * palette; int nPalEntries; Complex center { -0.75, 0 }; float range; range = 4; Bitmap bmp { }; Mandelbrot() { static ColorKey keys[] = { { navy, 0.0f }, { Color { 146, 213, 237 }, 0.198606268f }, { white, 0.3f }, { Color { 255, 255, 124 }, 0.444250882f }, { Color { 255, 100, 0 }, 0.634146333f }, { navy, 1 } }; nPalEntries = 30000; palette = new ColorAlpha[nPalEntries]; scale = nPalEntries / 175.0f; PaletteGradient(palette, nPalEntries, keys, sizeof(keys)/sizeof(keys[0]), 1.0); needUpdate = true; } ~Mandelbrot() { delete palette; } void OnRedraw(Surface surface) { if(needUpdate) { drawMandelbrot(bmp, range, center, palette, nPalEntries, nIterations, scale); needUpdate = false; } surface.Blit(bmp, 0,0, 0,0, bmp.width, bmp.height); if(dragging) { surface.foreground = lime; surface.Rectangle(mouseStart.x, mouseStart.y, mouseEnd.x, mouseEnd.y); } } bool OnLeftButtonDown(int x, int y, Modifiers mods) { mouseEnd = mouseStart = { x, y }; Capture(); dragging = true; Update(null); return true; } bool OnLeftButtonUp(int x, int y, Modifiers mods) { if(dragging) { int dx = Abs(mouseEnd.x - mouseStart.x), dy = Abs(mouseEnd.y - mouseStart.y); if(dx > 4 && dy > 4) { int w = clientSize.w, h = clientSize.h; float rangeX = w > h ? range : range * w / h; float rangeY = h > w ? range : range * h / w; center.a += ((mouseStart.x + mouseEnd.x) - w) / 2.0f * rangeX / w; center.b += ((mouseStart.y + mouseEnd.y) - h) / 2.0f * rangeY / h; range = dy > dx ? dy * range / h : dx * range / w; needUpdate = true; Update(null); } ReleaseCapture(); dragging = false; } return true; } bool OnMouseMove(int x, int y, Modifiers mods) { if(dragging) { mouseEnd = { x, y }; Update(null); } return true; } bool OnRightButtonDown(int x, int y, Modifiers mods) { range = 4; nIterations = 256; center = { -0.75, 0 }; needUpdate = true; Update(null); return true; } void OnResize(int width, int height) { bmp.Allocate(null, width, height, 0, pixelFormat888, false); needUpdate = true; Update(null); } bool OnKeyHit(Key key, unichar ch) { switch(key) { case space: case keyPadPlus: case plus: nIterations += 256; needUpdate = true; Update(null); break; } return true; }} Mandelbrot mandelbrotForm {}; ## EchoLisp  (lib 'math) ;; fractal function(lib 'plot) ;; (fractal z zc n) iterates z := z^2 + c, n times;; 100 iterations(define (mset z) (if (= Infinity (fractal 0 z 100)) Infinity z)) ;; plot function argument inside square (-2 -2), (2,2)(plot-z-arg mset -2 -2) ;; result here [http://www.echolalie.org/echolisp/help.html#fractal]  ## Elixir defmodule Mandelbrot do def set do xsize = 59 ysize = 21 minIm = -1.0 maxIm = 1.0 minRe = -2.0 maxRe = 1.0 stepX = (maxRe - minRe) / xsize stepY = (maxIm - minIm) / ysize Enum.each(0..ysize, fn y -> im = minIm + stepY * y Enum.map(0..xsize, fn x -> re = minRe + stepX * x 62 - loop(0, re, im, re, im, re*re+im*im) end) |> IO.puts end) end defp loop(n, _, _, _, _, _) when n>=30, do: n defp loop(n, _, _, _, _, v) when v>4.0, do: n-1 defp loop(n, re, im, zr, zi, _) do a = zr * zr b = zi * zi loop(n+1, re, im, a-b+re, 2*zr*zi+im, a+b) endend Mandelbrot.set Output: ??????=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<=========== ?????===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<======== ????===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<======= ???==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<===== ??==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<==== ??=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<=== ?=<<<<<<<<;;;:599999999886 %78:;;<<<<<<== ?<<<<;;;;;:::972456-567763 +9;;<<<<<<<= ?<;;;;;;::::9875& .3 *9;;;<<<<<<= ?;;;;;;::997564' ' 8:;;;<<<<<<= ?::988897735/ &89:;;;<<<<<<= ?::988897735/ &89:;;;<<<<<<= ?;;;;;;::997564' ' 8:;;;<<<<<<= ?<;;;;;;::::9875& .3 *9;;;<<<<<<= ?<<<<;;;;;:::972456-567763 +9;;<<<<<<<= ?=<<<<<<<<;;;:599999999886 %78:;;<<<<<<== ??=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<=== ??==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<==== ???==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<===== ????===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<======= ?????===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<======== ??????=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<===========  ## Erlang Translation of: Haskell Function seq_float/2 is copied from Andrew Fecheyr's GitHubGist. Using module complex from Geoff Hulette's GitHub repository Geoff Hulette's GitHub repository provides two alternative implementations which are very interesting.  -module(mandelbrot). -export([test/0]). magnitude(Z) -> R = complex:real(Z), I = complex:imaginary(Z), R * R + I * I. mandelbrot(A, MaxI, Z, I) -> case (I < MaxI) and (magnitude(Z) < 2.0) of true -> NZ = complex:add(complex:mult(Z, Z), A), mandelbrot(A, MaxI, NZ, I + 1); false -> case I of MaxI -> *; _ ->  end end. test() -> lists:map( fun(S) -> io:format("~s",[S]) end, [ [ begin Z = complex:make(X, Y), mandelbrot(Z, 50, Z, 1) end || X <- seq_float(-2, 0.5, 0.0315) ] ++ "\n" || Y <- seq_float(-1,1, 0.05) ] ), ok. % **************************************************% Copied from https://gist.github.com/andruby/241489% ************************************************** seq_float(Min, Max, Inc, Counter, Acc) when (Counter*Inc + Min) >= Max -> lists:reverse([Max|Acc]);seq_float(Min, Max, Inc, Counter, Acc) -> seq_float(Min, Max, Inc, Counter+1, [Inc * Counter + Min|Acc]).seq_float(Min, Max, Inc) -> seq_float(Min, Max, Inc, 0, []). % **************************************************  Output:  ** ****** ******** ****** ******** ** * *** ***************** ************************ *** **************************** ****************************** ****************************** ************************************ * ********************************** ** ***** * ********************************** *********** ************************************ ************** ************************************ *************************************************** ***************************************************** ***************************************************** ***************************************************** *************************************************** ************** ************************************ *********** ************************************ ** ***** * ********************************** * ********************************** ************************************ ****************************** ****************************** **************************** ************************ *** *** ***************** ******** ** * ****** ******** ****** **  ## ERRE  PROGRAM MANDELBROT !KEY!INCLUDE="PC.LIB" BEGIN SCREEN(7)GR_WINDOW(-2,1.5,2,-1.5)FOR X0=-2 TO 2 STEP 0.01 DO FOR Y0=-1.5 TO 1.5 STEP 0.01 DO X=0 Y=0 ITERATION=0 MAX_ITERATION=223 WHILE (X*X+Y*Y<=(2*2) AND ITERATION<MAX_ITERATION) DO X_TEMP=X*X-Y*Y+X0 Y=2*X*Y+Y0 X=X_TEMP ITERATION=ITERATION+1 END WHILE IF ITERATION<>MAX_ITERATION THEN C=ITERATION ELSE C=0 END IF PSET(X0,Y0,C) END FOREND FOREND PROGRAM  Note: This is a PC version which uses EGA 16-color 320x200. Graphic commands are taken from PC.LIB library. ## F# open System.Drawing open System.Windows.Formstype Complex = { re : float; im : float }let cplus (x:Complex) (y:Complex) : Complex = { re = x.re + y.re; im = x.im + y.im }let cmult (x:Complex) (y:Complex) : Complex = { re = x.re * y.re - x.im * y.im; im = x.re * y.im + x.im * y.re; } let norm (x:Complex) : float = x.re*x.re + x.im*x.im type Mandel = class inherit Form static member xPixels = 500 static member yPixels = 500 val mutable bmp : Bitmap member x.mandelbrot xMin xMax yMin yMax maxIter = let rec mandelbrotIterator z c n = if (norm z) > 2.0 then false else match n with | 0 -> true | n -> let z' = cplus ( cmult z z ) c in mandelbrotIterator z' c (n-1) let dx = (xMax - xMin) / (float (Mandel.xPixels)) let dy = (yMax - yMin) / (float (Mandel.yPixels)) in for xi = 0 to Mandel.xPixels-1 do for yi = 0 to Mandel.yPixels-1 do let c = {re = xMin + (dx * float(xi) ) ; im = yMin + (dy * float(yi) )} in if (mandelbrotIterator {re=0.;im=0.;} c maxIter) then x.bmp.SetPixel(xi,yi,Color.Azure) else x.bmp.SetPixel(xi,yi,Color.Black) done done member public x.generate () = x.mandelbrot (-1.5) 0.5 (-1.0) 1.0 200 ; x.Refresh() new() as x = {bmp = new Bitmap(Mandel.xPixels , Mandel.yPixels)} then x.Text <- "Mandelbrot set" ; x.Width <- Mandel.xPixels ; x.Height <- Mandel.yPixels ; x.BackgroundImage <- x.bmp; x.generate(); x.Show(); end let f = new Mandel()do Application.Run(f) ### Alternate version, applicable to text and GUI Basic generation code  let getMandelbrotValues width height maxIter ((xMin,xMax),(yMin,yMax)) = let mandIter (cr:float,ci:float) = let next (zr,zi) = (cr + (zr * zr - zi * zi)), (ci + (zr * zi + zi * zr)) let rec loop = function | step,_ when step=maxIter->0 | step,(zr,zi) when ((zr * zr + zi * zi) > 2.0) -> step | step,z -> loop ((step + 1), (next z)) loop (0,(0.0, 0.0)) let forPos = let dx, dy = (xMax - xMin) / (float width), (yMax - yMin) / (float height) fun y x -> mandIter ((xMin + dx * float(x)), (yMin + dy * float(y))) [0..height-1] |> List.map(fun y->[0..width-1] |> List.map (forPos y))  Text display  getMandelbrotValues 80 25 50 ((-2.0,1.0),(-1.0,1.0))|> List.map(fun row-> row |> List.map (function | 0 ->" " |_->".") |> String.concat "")|> List.iter (printfn "%s")  Results: Output: ................................................................................ ................................................................................ ................................................. ............................. ................................................ ........................... ................................................. ........................... ....................................... . ...................... ........................................ ................. .................................... .................. .................................... ................. .......................... ...... ................ ....................... ... ................ ..................... . ................ ................. ................. ................. ................. ..................... . ................ ....................... ... ................ .......................... ...... ................ .................................... ................. .................................... .................. ........................................ ................. ....................................... . ...................... ................................................. ........................... ................................................ ........................... ................................................. ............................. ................................................................................  Graphics display  open System.Drawing open System.Windows.Forms let showGraphic (colorForIter: int -> Color) (width: int) (height:int) maxIter view = new Form() |> fun frm -> frm.Width <- width frm.Height <- height frm.BackgroundImage <- new Bitmap(width,height) |> fun bmp -> getMandelbrotValues width height maxIter view |> List.mapi (fun y row->row |> List.mapi (fun x v->((x,y),v))) |> List.collect id |> List.iter (fun ((x,y),v) -> bmp.SetPixel(x,y,(colorForIter v))) bmp frm.Show() let toColor = (function | 0 -> (0,0,0) | n -> ((31 &&& n) |> fun x->(0, 18 + x * 5, 36 + x * 7))) >> Color.FromArgb showGraphic toColor 640 480 5000 ((-2.0,1.0),(-1.0,1.0))  ## Factor  ! with ("::") or without (":") generalizations:! : [a..b] ( steps a b -- a..b ) 2dup swap - 4 nrot 1 - / <range> ;:: [a..b] ( steps a b -- a..b ) a b b a - steps 1 - / <range> ; : >char ( n -- c ) dup -1 = [ drop 32 ] [ 26 mod CHAR: a + ] if ; ! iterates z' = z^2 + c, Factor does complex numbers!: iter ( c z -- z' ) dup * + ; : unbound ( c -- ? ) absq 4 > ; :: mz ( c max i z -- n ) { { [ i max >= ] [ -1 ] } { [ z unbound ] [ i ] } [ c max i 1 + c z iter mz ] } cond ; : mandelzahl ( c max -- n ) 0 0 mz ; :: mandel ( w h max -- ) h -1. 1. [a..b] ! range over y [ w -2. 1. [a..b] ! range over x [ dupd swap rect> max mandelzahl >char ] map >string print drop ! old y ] each ; 70 25 1000 mandel  Output: bbbbbbbcccccdddddddddddddddddddeeeeeeeffghjpjl feeeeedddddcccccccccccc bbbbbbccccddddddddddddddddddeeeeeeeefffghikopjhgffeeeeedddddcccccccccc bbbbbcccddddddddddddddddddeeeeeeeefffggjotx etiigfffeeeeddddddcccccccc bbbbccddddddddddddddddddeeeeeeeffgggghhjq iihgggfffeedddddddcccccc bbbccddddddddddddddddeeeeeefffghvasjjqqyqt upqlrjhhhkhfedddddddccccc bbbcdddddddddddddddeeeeffffffgghks c qnbpfmgfedddddddcccc bbcdddddddddddddeefffffffffgggipmt qhgfeedddddddccc bbdddddddddeeeefhlggggggghhhhils ljigfeedddddddcc bcddddeeeeeefffghmllkjiljjiijle yhfeedddddddcc bddeeeeeeeffffghhjoj do clmq qlgfeeedddddddc bdeeeeeefffffhiijpu sm ohffeeedddddddc beffeefgggghhjocsu higffeeedddddddc cmihgffeeedddddddd beffeefgggghhjocsu higffeeedddddddc bdeeeeeefffffhiijpu sd ohffeeedddddddc bddeeeeeeeffffghhjoj do clmq qlgfeeedddddddc bcddddeeeeeefffghmllkjiljjiijle yhfeedddddddcc bbdddddddddeeeefhlggggggghhhhils ljigfeedddddddcc bbcdddddddddddddeefffffffffgggipmt qhgfeedddddddccc bbbcdddddddddddddddeeeeffffffgghks c qnbpfmgfedddddddcccc bbbccddddddddddddddddeeeeeefffghvasjjqqyqt upqlrjhhhkhfedddddddccccc bbbbccddddddddddddddddddeeeeeeeffgggghhjq iihgggfffeedddddddcccccc bbbbbcccddddddddddddddddddeeeeeeeefffggjotx etiigfffeeeeddddddcccccccc bbbbbbccccddddddddddddddddddeeeeeeeefffghikopjhgffeeeeedddddcccccccccc bbbbbbbcccccdddddddddddddddddddeeeeeeeffghjpjl feeeeedddddcccccccccccc  ## FOCAL 1.1 S I1=-1.2; S I2=1.2; S R1=-2; S R2=.51.2 S MIT=301.3 F Y=1,24; D 21.4 Q 2.1 T !2.2 F X=1,70; D 3 3.1 S R=X*(R2-R1)/70+R13.2 S I=Y*(I2-I1)/24+I13.3 S C1=R; S C2=I3.4 F T=1,MIT; D 4 4.1 S C3=C14.2 S C1=C1*C1 - C2*C24.3 S C2=C3*C2 + C2*C34.4 S C1=C1+R4.5 S C2=C2+I4.6 I (-FABS(C1)+2)5.14.7 I (-FABS(C2)+2)5.14.8 I (MIT-T-1)6.1 5.1 S T=MIT; T "*"; R 6.1 T " "; R Output: ********************************************************************** ********************************************************************** **************************************************** ***************** ************************************************* *************** ************************************************* *************** **************************************** * ********** *************************************** * ****** ************************************* ***** ********************** **** ******* **** *********************** ** ** ********************* **** *** * ******* ********************* **** *********************** ** ** ********************** **** ******* **** ************************************* ***** *************************************** * ****** **************************************** * ********** ************************************************* *************** ************************************************* *************** **************************************************** ***************** ********************************************************************** ********************************************************************** **********************************************************************  ## Forth This uses grayscale image utilities. 500 value max-iter : mandel ( gmp F: imin imax rmin rmax -- ) 0e 0e { F: imin F: imax F: rmin F: rmax F: Zr F: Zi } dup bheight 0 do i s>f dup bheight s>f f/ imax imin f- f* imin f+ TO Zi dup bwidth 0 do i s>f dup bwidth s>f f/ rmax rmin f- f* rmin f+ TO Zr Zr Zi max-iter begin 1- dup while fover fdup f* fover fdup f* fover fover f+ 4e f< while f- Zr f+ frot frot f* 2e f* Zi f+ repeat fdrop fdrop drop 0 \ for a pretty grayscale image, replace with: 255 max-iter */ else drop 255 then fdrop fdrop over i j rot g! loop loop drop ; 80 24 graymapdup -1e 1e -2e 1e mandeldup gshowfree bye ## Fortran Works with: Fortran version 90 and later program mandelbrot implicit none integer , parameter :: rk = selected_real_kind (9, 99) integer , parameter :: i_max = 800 integer , parameter :: j_max = 600 integer , parameter :: n_max = 100 real (rk), parameter :: x_centre = -0.5_rk real (rk), parameter :: y_centre = 0.0_rk real (rk), parameter :: width = 4.0_rk real (rk), parameter :: height = 3.0_rk real (rk), parameter :: dx_di = width / i_max real (rk), parameter :: dy_dj = -height / j_max real (rk), parameter :: x_offset = x_centre - 0.5_rk * (i_max + 1) * dx_di real (rk), parameter :: y_offset = y_centre - 0.5_rk * (j_max + 1) * dy_dj integer, dimension (i_max, j_max) :: image integer :: i integer :: j integer :: n real (rk) :: x real (rk) :: y real (rk) :: x_0 real (rk) :: y_0 real (rk) :: x_sqr real (rk) :: y_sqr do j = 1, j_max y_0 = y_offset + dy_dj * j do i = 1, i_max x_0 = x_offset + dx_di * i x = 0.0_rk y = 0.0_rk n = 0 do x_sqr = x ** 2 y_sqr = y ** 2 if (x_sqr + y_sqr > 4.0_rk) then image (i, j) = 255 exit end if if (n == n_max) then image (i, j) = 0 exit end if y = y_0 + 2.0_rk * x * y x = x_0 + x_sqr - y_sqr n = n + 1 end do end do end do open (10, file = 'out.pgm') write (10, '(a/ i0, 1x, i0/ i0)') 'P2', i_max, j_max, 255 write (10, '(i0)') image close (10) end program mandelbrot ## FreeBASIC #define pix 1./120#define zero_x 320#define zero_y 240#define maxiter 250 screen 12 type complex r as double i as doubleend type operator + (x as complex, y as complex) as complex dim as complex ret ret.r = x.r + y.r ret.i = x.i + y.i return retend operator operator * (x as complex, y as complex) as complex dim as complex ret ret.r = x.r*y.r - x.i*y.i ret.i = x.r*y.i + x.i*y.r return retend operator operator abs ( x as complex ) as double return sqr(x.r*x.r + x.i*x.i)end operator dim as complex c, zdim as integer x, y, iter for x=0 to 639 for y=0 to 240 c.r = (x-zero_x)*pix c.i = (y-zero_y)*pix z.r = 0.0 z.i = 0.0 for iter=0 to maxiter z = z*z + c if abs(z)>2 then pset(x,y),iter mod 16 pset(x,480-y),iter mod 16 goto cont end if next iter pset(x,y),1 pset(x,480-y),1 cont: next ynext x while inkey=""wendend ## Frink This draws a graphical Mandelbrot set using Frink's built-in graphics and complex arithmetic.  // Maximum levels for each pixel.levels = 60 // Create a random color for each level.colors = new array[[levels]]for a = 0 to levels-1 [email protected] = new color[randomFloat[0,1], randomFloat[0,1], randomFloat[0,1]] // Make this number smaller for higher resolution.stepsize = .005 g = new graphicsg.antialiased[false] for im = -1.2 to 1.2 step stepsize{ imag = i * im for real = -2 to 1 step stepsize { C = real + imag z = 0 count = -1 do { z = z^2 + C count=count+1; } while abs[z] < 4 and count < levels g.color[[email protected]((count-1) mod levels)] g.fillRectSize[real, im, stepsize, stepsize] }} g.show[]  ## Furor  ###sysinclude X.uhff0000 sto szin300 sto maxitermaxypixel sto YRESmaxxpixel sto XRESmyscreen "Mandelbrot" @YRES @XRES graphic@YRES 2 / (#d) sto y2@YRES 2 / (#d) sto x2#g 0. @XRES (#d) 1. i: {#d#g 0. @YRES (#d) 1. {#d#d{#d}§i 400. - @x2 - @x2 /sto x{#d} @y2 - @y2 /sto yzero#d xa zero#d ya zero iter(( #d@x @xa dup* @ya dup* -+@y @xa *2 @ya *+ sto yasto xa #g inc iter@iter @maxiter >= then((>))#d ( @xa dup* @ya dup* + 4. > )))#g @iter @maxiter == { #dmyscreen {d} {d}§i @szin [][]}{ #dmyscreen {d} {d}§i #g @iter 64 * [][]}#d}#d}(( ( myscreen key? 10000 usleep )))myscreen !graphicend{ „x” }{ „x2” }{ „y” }{ „y2” }{ „xa” }{ „ya” }{ „iter” }{ „maxiter” }{ „szin” }{ „YRES” }{ „XRES” }{ „myscreen” }  ## Futhark  This example is incorrect. Please fix the code and remove this message.Details: Futhark's syntax has changed, so this example will not compile Computes escapes for each pixel, but not the colour.  default(f32) type complex = (f32, f32) fun dot(c: complex): f32 = let (r, i) = c in r * r + i * i fun multComplex(x: complex, y: complex): complex = let (a, b) = x let (c, d) = y in (a*c - b * d, a*d + b * c) fun addComplex(x: complex, y: complex): complex = let (a, b) = x let (c, d) = y in (a + c, b + d) fun divergence(depth: int, c0: complex): int = loop ((c, i) = (c0, 0)) = while i < depth && dot(c) < 4.0 do (addComplex(c0, multComplex(c, c)), i + 1) in i fun mandelbrot(screenX: int, screenY: int, depth: int, view: (f32,f32,f32,f32)): [screenX][screenY]int = let (xmin, ymin, xmax, ymax) = view let sizex = xmax - xmin let sizey = ymax - ymin in map (fn (x: int): [screenY]int => map (fn (y: int): int => let c0 = (xmin + (f32(x) * sizex) / f32(screenX), ymin + (f32(y) * sizey) / f32(screenY)) in divergence(depth, c0)) (iota screenY)) (iota screenX) fun main(screenX: int, screenY: int, depth: int, xmin: f32, ymin: f32, xmax: f32, ymax: f32): [screenX][screenY]int = mandelbrot(screenX, screenY, depth, (xmin, ymin, xmax, ymax))  ## Fōrmulæ In this page you can see the solution of this task. Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text (more info). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition. The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code. ## GLSL Uses smooth coloring.  const int MaxIterations = 1000;const vec2 Focus = vec2(-0.51, 0.54);const float Zoom = 1.0; vec3color(int iteration, float sqLengthZ) { // If the point is within the mandlebrot set // just color it black if(iteration == MaxIterations) return vec3(0.0); // Else we give it a smoothed color float ratio = (float(iteration) - log2(log2(sqLengthZ))) / float(MaxIterations); // Procedurally generated colors return mix(vec3(1.0, 0.0, 0.0), vec3(1.0, 1.0, 0.0), sqrt(ratio));} voidmainImage(out vec4 fragColor, in vec2 fragCoord) { // C is the aspect-ratio corrected UV coordinate. vec2 c = (-1.0 + 2.0 * fragCoord / iResolution.xy) * vec2(iResolution.x / iResolution.y, 1.0); // Apply scaling, then offset to get a zoom effect c = (c * exp(-Zoom)) + Focus; vec2 z = c; int iteration = 0; while(iteration < MaxIterations) { // Precompute for efficiency float zr2 = z.x * z.x; float zi2 = z.y * z.y; // The larger the square length of Z, // the smoother the shading if(zr2 + zi2 > 32.0) break; // Complex multiplication, then addition z = vec2(zr2 - zi2, 2.0 * z.x * z.y) + c; ++iteration; } // Generate the colors fragColor = vec4(color(iteration, dot(z,z)), 1.0); // Apply gamma correction fragColor.rgb = pow(fragColor.rgb, vec3(0.5));}  ## gnuplot The output from gnuplot is controlled by setting the appropriate values for the options terminal and output. set terminal pngset output 'mandelbrot.png' The following script draws an image of the number of iterations it takes to escape the circle with radius rmax with a maximum of nmax. rmax = 2nmax = 100complex (x, y) = x * {1, 0} + y * {0, 1}mandelbrot (z, z0, n) = n == nmax || abs (z) > rmax ? n : mandelbrot (z ** 2 + z0, z0, n + 1)set samples 200set isosamples 200set pm3d mapset size squaresplot [-2 : .8] [-1.4 : 1.4] mandelbrot (complex (0, 0), complex (x, y), 0) notitle Output: ## Go Text Prints an 80-char by 41-line depiction. package main import "fmt"import "math/cmplx" func mandelbrot(a complex128) (z complex128) { for i := 0; i < 50; i++ { z = z*z + a } return} func main() { for y := 1.0; y >= -1.0; y -= 0.05 { for x := -2.0; x <= 0.5; x += 0.0315 { if cmplx.Abs(mandelbrot(complex(x, y))) < 2 { fmt.Print("*") } else { fmt.Print(" ") } } fmt.Println("") }} Graphical .png image package main import ( "fmt" "image" "image/color" "image/draw" "image/png" "math/cmplx" "os") const ( maxEsc = 100 rMin = -2. rMax = .5 iMin = -1. iMax = 1. width = 750 red = 230 green = 235 blue = 255) func mandelbrot(a complex128) float64 { i := 0 for z := a; cmplx.Abs(z) < 2 && i < maxEsc; i++ { z = z*z + a } return float64(maxEsc-i) / maxEsc} func main() { scale := width / (rMax - rMin) height := int(scale * (iMax - iMin)) bounds := image.Rect(0, 0, width, height) b := image.NewNRGBA(bounds) draw.Draw(b, bounds, image.NewUniform(color.Black), image.ZP, draw.Src) for x := 0; x < width; x++ { for y := 0; y < height; y++ { fEsc := mandelbrot(complex( float64(x)/scale+rMin, float64(y)/scale+iMin)) b.Set(x, y, color.NRGBA{uint8(red * fEsc), uint8(green * fEsc), uint8(blue * fEsc), 255}) } } f, err := os.Create("mandelbrot.png") if err != nil { fmt.Println(err) return } if err = png.Encode(f, b); err != nil { fmt.Println(err) } if err = f.Close(); err != nil { fmt.Println(err) }} ## Haskell Translation of: Ruby import Data.Boolimport Data.Complex (Complex((:+)), magnitude) mandelbrot :: RealFloat a => Complex a -> Complex amandelbrot a = iterate ((a +) . (^ 2)) 0 !! 50 main :: IO ()main = mapM_ putStrLn [ [ bool ' ' '*' (2 > magnitude (mandelbrot (x :+ y))) | x <- [-2,-1.9685 .. 0.5] ] | y <- [1,0.95 .. -1] ] Save the code to file m.hs and run : runhaskell m.hs  Output:  ** ****** ******** ****** ******** ** * *** ***************** ************************ *** **************************** ****************************** ****************************** ************************************ * ********************************** ** ***** * ********************************** *********** ************************************ ************** ************************************ *************************************************** ***************************************************** *********************************************************************** ***************************************************** *************************************************** ************** ************************************ *********** ************************************ ** ***** * ********************************** * ********************************** ************************************ ****************************** ****************************** **************************** ************************ *** *** ***************** ******** ** * ****** ******** ****** **  ## Haxe This version compiles for flash version 9 or greater. The compilation command is haxe -swf mandelbrot.swf -main Mandelbrot class Mandelbrot extends flash.display.Sprite{ inline static var MAX_ITER = 255; public static function main() { var w = flash.Lib.current.stage.stageWidth; var h = flash.Lib.current.stage.stageHeight; var mandelbrot = new Mandelbrot(w, h); flash.Lib.current.stage.addChild(mandelbrot); mandelbrot.drawMandelbrot(); } var image:flash.display.BitmapData; public function new(width, height) { super(); var bitmap:flash.display.Bitmap; image = new flash.display.BitmapData(width, height, false); bitmap = new flash.display.Bitmap(image); this.addChild(bitmap); } public function drawMandelbrot() { image.lock(); var step_x = 3.0 / (image.width-1); var step_y = 2.0 / (image.height-1); for (i in 0...image.height) { var ci = i * step_y - 1.0; for (j in 0...image.width) { var k = 0; var zr = 0.0; var zi = 0.0; var cr = j * step_x - 2.0; while (k <= MAX_ITER && (zr*zr + zi*zi) <= 4) { var temp = zr*zr - zi*zi + cr; zi = 2*zr*zi + ci; zr = temp; k ++; } paint(j, i, k); } } image.unlock(); } inline function paint(x, y, iter) { var color = iter > MAX_ITER? 0 : iter * 0x100; image.setPixel(x, y, color); }} ## Huginn #! /bin/shexec huginn -E "{0}" "{@}"#! huginn import Algorithms as algo;import Mathematics as math;import Terminal as term; mandelbrot( x, y ) { c = math.Complex( x, y ); z = math.Complex( 0., 0. ); s = -1; for ( i : algo.range( 50 ) ) { z = z * z + c; if ( | z | > 2. ) { s = i; break; } } return ( s );} main( argv_ ) { imgSize = term_size( argv_ ); yRad = 1.2; yScale = 2. * yRad / real( imgSize[0] ); xScale = 3.3 / real( imgSize[1] ); glyphTab = [ ".", ":", "-", "+", "+" ].resize( 12, "*" ).resize( 26, "%" ).resize( 50, "@" ).push( " " ); for ( y : algo.range( imgSize[0] ) ) { line = ""; for ( x : algo.range( imgSize[1] ) ) { line += glyphTab[ mandelbrot( xScale * real( x ) - 2.3, yScale * real( y ) - yRad ) ]; } print( line + "\n" ); } return ( 0 );} term_size( argv_ ) { lines = 25; columns = 80; if ( size( argv_ ) == 3 ) { lines = integer( argv_[1] ); columns = integer( argv_[2] ); } else { lines = term.lines(); columns = term.columns(); if ( ( lines % 2 ) == 0 ) { lines -= 1; } } lines -= 1; columns -= 1; return ( ( lines, columns ) );} Output: ........................:::::::::::::::::::------------------------------------------------------:::::::::::::::::::::::::::::::::::: ......................::::::::::::::::------------------------------------++++++++++++++++++++---------:::::::::::::::::::::::::::::: ....................:::::::::::::-----------------------------------+++++++++++++*******+++++++++++--------:::::::::::::::::::::::::: ...................:::::::::::----------------------------------++++++++++++++++****%%******++++++++++---------:::::::::::::::::::::: .................:::::::::----------------------------------++++++++++++++++++++******% %****++++++++++++---------::::::::::::::::::: ................::::::::---------------------------------+++++++++++++++++++++******%%%%%*****+++++++++++++----------:::::::::::::::: ...............::::::---------------------------------++++++++++++++++++++*****%%%%% @%%%@***++++++++++++++----------:::::::::::::: ..............:::::--------------------------------++++++++++++++++++***********@% @%******+++++++++++++-----------::::::::::: .............::::-------------------------------+++++++++++++++++****************@ %%***************+++++------------::::::::: ............:::------------------------------+++++++++++++++++****@%%%****%@@%@% %%@ @%%%% %*% ********%**++++------------:::::::: ...........:::----------------------------+++++++++++++++++********% @%@@ %%%**%@%%@@**+++++------------:::::: ..........:::-------------------------+++++++++++++++++++**********% @ %%***++++++------------::::: ..........:----------------------+++++++++++++++++++++*********%%%% %%******++++++------------:::: .........:-----------------++++++++**************************** %*****+++++-------------::: .........----------+++++++++++++++****%********%%*********** @%% % %%**++++++-------------:: ........:------++++++++++++++++++*******%@@%%**%% %%%*******%% %%***+++++++-------------: ........---+++++++++++++++++++++********%@ @%%%**% %%***+++++++-------------: .......:-+++++++++++++++++++++*******%%%% @%% @****++++++++------------- .......-+++++++++++++***********%**@*%@ % %***+++++++++------------- .......++++++*******************%% @ %*****+++++++++------------- ....... %%******++++++++++------------- .......++++++*******************%% @ %*****+++++++++------------- .......-+++++++++++++***********%**@*%@ % %***+++++++++------------- .......:-+++++++++++++++++++++*******%%%% @%% @****++++++++------------- ........---+++++++++++++++++++++********%@ @%%%**% %%***+++++++-------------: ........:------++++++++++++++++++*******%@@%%**%% %%%*******%% %%***+++++++-------------: .........----------+++++++++++++++****%********%%*********** @%% % %%**++++++-------------:: .........:-----------------++++++++**************************** %*****+++++-------------::: ..........:----------------------+++++++++++++++++++++*********%%%% %%******++++++------------:::: ..........:::-------------------------+++++++++++++++++++**********% @ %%***++++++------------::::: ...........:::----------------------------+++++++++++++++++********% @%@@ %%%**%@%%@@**+++++------------:::::: ............:::------------------------------+++++++++++++++++****@%%%****%@@%@% %%@ @%%%% %*% ********%**++++------------:::::::: .............::::-------------------------------+++++++++++++++++****************@ %%***************+++++------------::::::::: ..............:::::--------------------------------++++++++++++++++++***********@% @%******+++++++++++++-----------::::::::::: ...............::::::---------------------------------++++++++++++++++++++*****%%%%% @%%%@***++++++++++++++----------:::::::::::::: ................::::::::---------------------------------+++++++++++++++++++++******%%%%%*****+++++++++++++----------:::::::::::::::: .................:::::::::----------------------------------++++++++++++++++++++******% %****++++++++++++---------::::::::::::::::::: ...................:::::::::::----------------------------------++++++++++++++++****%%******++++++++++---------:::::::::::::::::::::: ....................:::::::::::::-----------------------------------+++++++++++++*******+++++++++++--------:::::::::::::::::::::::::: ......................::::::::::::::::------------------------------------++++++++++++++++++++---------::::::::::::::::::::::::::::::  ## Icon and Unicon link graphics procedure main() width := 750 height := 600 limit := 100 WOpen("size="||width||","||height) every x:=1 to width & y:=1 to height do { z:=complex(0,0) c:=complex(2.5*x/width-2.0,(2.0*y/height-1.0)) j:=0 while j<limit & cAbs(z)<2.0 do { z := cAdd(cMul(z,z),c) j+:= 1 } Fg(mColor(j,limit)) DrawPoint(x,y) } WriteImage("./mandelbrot.gif") WDone()end procedure mColor(x,limit) max_color := 2^16-1 color := integer(max_color*(real(x)/limit)) return(if x=limit then "black" else color||","||color||",0")end record complex(r,i) procedure cAdd(x,y) return complex(x.r+y.r,x.i+y.i)end procedure cMul(x,y) return complex(x.r*y.r-x.i*y.i,x.r*y.i+x.i*y.r)end procedure cAbs(x) return sqrt(x.r*x.r+x.i*x.i)end  This example is in need of improvement: The example is correct; however, Unicon implemented additional graphical features and a better example may be possible. ## IDL IDL - Interactive Data Language (free implementation: GDL - GNU Data Language http://gnudatalanguage.sourceforge.net)  PRO Mandelbrot,xRange,yRange,xPixels,yPixels,iterations xPixelstartVec = Lindgen( xPixels) * Float(xRange[1]-xRange[0]) /  xPixels + xRange[0]yPixelstartVec = Lindgen( yPixels) * Float(YRANGE[1]-yrange[0]) / yPixels + yRange[0] constArr = Complex( Rebin( xPixelstartVec, xPixels, yPixels), Rebin( Transpose(yPixelstartVec), xPixels, yPixels)) valArr = ComplexArr( xPixels, yPixels) res = IntArr( xPixels, yPixels) oriIndex = Lindgen( Long(xPixels) * yPixels) FOR i = 0, iterations-1 DO BEGIN ; only one loop needed ; calculation for whole array at once valArr = valArr^2 - constArr whereIn = Where( Abs( valArr) LE 4.0d, COMPLEMENT=whereOut) IF whereIn[0] EQ -1 THEN BREAK valArr = valArr[ whereIn] constArr = constArr[ whereIn] IF whereOut[0] NE -1 THEN BEGIN res[ oriIndex[ whereOut]] = i+1 oriIndex = oriIndex[ whereIn] ENDIFENDFOR tv,res ; open a window and show the result END Mandelbrot,[-1.,2.3],[-1.3,1.3],640,512,200 END  from the command line:  GDL>.run mandelbrot  or  GDL> Mandelbrot,[-1.,2.3],[-1.3,1.3],640,512,200  ## Inform 7 "Mandelbrot" The story headline is "A Non-Interactive Set". Include Glimmr Drawing Commands by Erik Temple. [Q20 fixed-point or floating-point: see definitions below]Use floating-point math. Finished is a room. The graphics-window is a graphics g-window spawned by the main-window.The position is g-placeabove. When play begins: let f10 be 10 as float; now min re is ( -20 as float ) fdiv f10; now max re is ( 6 as float ) fdiv f10; now min im is ( -12 as float ) fdiv f10; now max im is ( 12 as float ) fdiv f10; now max iterations is 100; add color g-Black to the palette; add color g-Red to the palette; add hex "#FFA500" to the palette; add color g-Yellow to the palette; add color g-Green to the palette; add color g-Blue to the palette; add hex "#4B0082" to the palette; add hex "#EE82EE" to the palette; open up the graphics-window. Min Re is a number that varies.Max Re is a number that varies.Min Im is a number that varies.Max Im is a number that varies. Max Iterations is a number that varies. Min X is a number that varies.Max X is a number that varies.Min Y is a number that varies.Max Y is a number that varies. The palette is a list of numbers that varies. [vertically mirrored version]Window-drawing rule for the graphics-window when max im is fneg min im: clear the graphics-window; let point be { 0, 0 }; now min X is 0 as float; now min Y is 0 as float; let mX be the width of the graphics-window minus 1; let mY be the height of the graphics-window minus 1; now max X is mX as float; now max Y is mY as float; let L be the column order with max mX; repeat with X running through L: now entry 1 in point is X; repeat with Y running from 0 to mY / 2: now entry 2 in point is Y; let the scaled point be the complex number corresponding to the point; let V be the Mandelbrot result for the scaled point; let C be the color corresponding to V; if C is 0, next; draw a rectangle (C) in the graphics-window at the point with size 1 by 1; now entry 2 in point is mY - Y; draw a rectangle (C) in the graphics-window at the point with size 1 by 1; yield to VM; rule succeeds. [slower non-mirrored version]Window-drawing rule for the graphics-window: clear the graphics-window; let point be { 0, 0 }; now min X is 0 as float; now min Y is 0 as float; let mX be the width of the graphics-window minus 1; let mY be the height of the graphics-window minus 1; now max X is mX as float; now max Y is mY as float; let L be the column order with max mX; repeat with X running through L: now entry 1 in point is X; repeat with Y running from 0 to mY: now entry 2 in point is Y; let the scaled point be the complex number corresponding to the point; let V be the Mandelbrot result for the scaled point; let C be the color corresponding to V; if C is 0, next; draw a rectangle (C) in the graphics-window at the point with size 1 by 1; yield to VM; rule succeeds. To decide which list of numbers is column order with max (N - number): let L be a list of numbers; let L2 be a list of numbers; let D be 64; let rev be false; while D > 0: let X be 0; truncate L2 to 0 entries; while X <= N: if D is 64 or X / D is odd, add X to L2; increase X by D; if rev is true: reverse L2; let rev be false; otherwise: let rev be true; add L2 to L; let D be D / 2; decide on L. To decide which list of numbers is complex number corresponding to (P - list of numbers): let R be a list of numbers; extend R to 2 entries; let X be entry 1 in P as float; let X be (max re fsub min re) fmul (X fdiv max X); let X be X fadd min re; let Y be entry 2 in P as float; let Y be (max im fsub min im) fmul (Y fdiv max Y); let Y be Y fadd min im; now entry 1 in R is X; now entry 2 in R is Y; decide on R. To decide which number is Mandelbrot result for (P - list of numbers): let c_re be entry 1 in P; let c_im be entry 2 in P; let z_re be 0 as float; let z_im be z_re; let threshold be 4 as float; let runs be 0; while 1 is 1: [ z = z * z ] let r2 be z_re fmul z_re; let i2 be z_im fmul z_im; let ri be z_re fmul z_im; let z_re be r2 fsub i2; let z_im be ri fadd ri; [ z = z + c ] let z_re be z_re fadd c_re; let z_im be z_im fadd c_im; let norm be (z_re fmul z_re) fadd (z_im fmul z_im); increase runs by 1; if norm is greater than threshold, decide on runs; if runs is max iterations, decide on 0. To decide which number is color corresponding to (V - number): let L be the number of entries in the palette; let N be the remainder after dividing V by L; decide on entry (N + 1) in the palette. Section - Fractional numbers (for Glulx only) To decide which number is (N - number) as float: (- (numtof({N})) -).To decide which number is (N - number) fadd (M - number): (- (fadd({N}, {M})) -).To decide which number is (N - number) fsub (M - number): (- (fsub({N}, {M})) -).To decide which number is (N - number) fmul (M - number): (- (fmul({N}, {M})) -).To decide which number is (N - number) fdiv (M - number): (- (fdiv({N}, {M})) -).To decide which number is fneg (N - number): (- (fneg({N})) -).To yield to VM: (- glk_select_poll(gg_event); -). Use Q20 fixed-point math translates as (- Constant Q20_MATH; -).Use floating-point math translates as (- Constant FLOAT_MATH; -). Include (-#ifdef Q20_MATH;! Q11.20 format: 1 sign bit, 11 integer bits, 20 fraction bits[ numtof n r; @shiftl n 20 r; return r; ];[ fadd n m; return n+m; ];[ fsub n m; return n-m; ];[ fmul n m; n = n +$$1000000000; @sshiftr n 10 n; m = m + $$1000000000; @sshiftr m 10 m; return n * m; ]; [ fdiv n m; @sshiftr m 20 m; return n / m; ];[ fneg n; return -n; ];#endif; #ifdef FLOAT_MATH;[ numtof f; @"S2:400" f f; return f; ];[ fadd n m; @"S3:416" n m n; return n; ];[ fsub n m; @"S3:417" n m n; return n; ];[ fmul n m; @"S3:418" n m n; return n; ];[ fdiv n m; @"S3:419" n m n; return n; ];[ fneg n; @bitxor n 80000000 n; return n; ];#endif;-). Newer Glulx interpreters provide 32-bit floating-point operations, but this solution also supports fixed-point math which is more widely supported and accurate enough for a zoomed-out view. Inform 6 inclusions are used for the low-level math functions in either case. The rendering process is extremely slow, since the graphics system is not optimized for pixel-by-pixel drawing, so this solution includes an optimization for vertical symmetry (as in the default view) and also includes extra logic to draw the lines in a more immediately useful order. ## J The characteristic function of the Mandelbrot can be defined as follows: mcf=. (<: 2:)@|@(] ((*:@] + [)^:((<: 2:)@|@])^:1000) 0:) NB. 1000 iterations test The Mandelbrot set can be drawn as follows: domain=. |[email protected]|:@({[email protected][ + ] *~ j./&i.&>/@[email protected](1j1 + ] %~ -~/@[))&>/ load 'viewmat'viewmat mcf "0 @ domain (_2j_1 1j1) ; 0.01 NB. Complex interval and resolution A smaller version, based on a black&white implementation of viewmat (and paraphrased, from html markup to wiki markup), is shown here:  viewmat mcf "0 @ domain (_2j_1 1j1) ; 0.1 NB. Complex interval and resolution The output is HTML-heavy and can be found here (split out to make editing this page easier). ## Java Library: Swing Library: AWT import java.awt.Graphics;import java.awt.image.BufferedImage;import javax.swing.JFrame; public class Mandelbrot extends JFrame { private final int MAX_ITER = 570; private final double ZOOM = 150; private BufferedImage I; private double zx, zy, cX, cY, tmp; public Mandelbrot() { super("Mandelbrot Set"); setBounds(100, 100, 800, 600); setResizable(false); setDefaultCloseOperation(EXIT_ON_CLOSE); I = new BufferedImage(getWidth(), getHeight(), BufferedImage.TYPE_INT_RGB); for (int y = 0; y < getHeight(); y++) { for (int x = 0; x < getWidth(); x++) { zx = zy = 0; cX = (x - 400) / ZOOM; cY = (y - 300) / ZOOM; int iter = MAX_ITER; while (zx * zx + zy * zy < 4 && iter > 0) { tmp = zx * zx - zy * zy + cX; zy = 2.0 * zx * zy + cY; zx = tmp; iter--; } I.setRGB(x, y, iter | (iter << 8)); } } } @Override public void paint(Graphics g) { g.drawImage(I, 0, 0, this); } public static void main(String[] args) { new Mandelbrot().setVisible(true); }} ### Interactive Library: AWT Library: Swing import static java.awt.Color.HSBtoRGB;import static java.awt.Color.black;import static java.awt.event.KeyEvent.VK_BACK_SLASH;import static java.awt.event.KeyEvent.VK_ESCAPE;import static java.awt.image.BufferedImage.TYPE_INT_RGB;import static java.lang.Integer.signum;import static java.lang.Math.abs;import static java.lang.Math.max;import static java.lang.Math.min;import static java.lang.System.currentTimeMillis;import static java.util.Locale.ROOT; import java.awt.Dimension;import java.awt.Graphics;import java.awt.Insets;import java.awt.event.KeyAdapter;import java.awt.event.KeyEvent;import java.awt.event.MouseAdapter;import java.awt.event.MouseEvent;import java.awt.image.BufferedImage;import java.util.function.Consumer;import java.util.function.Predicate; import javax.swing.JFrame; /* * click: point to center * ctrl-click: point to origin * drag: point to mouse release point * ctrl-drag: point to origin + zoom * back-slash: back to previous point * esc: back to previous zoom point - zoom */ public class Mandelbrot extends JFrame { private static final long serialVersionUID = 1L; private Insets insets; private int width, height; private double widthHeightRatio; private int minX, minY; private double Zoom; private int mpX, mpY, mdX, mdY; private boolean isCtrlDown, ctrl; private Stack stack = new Stack(); private BufferedImage image; private boolean newImage = true; public static void main(String[] args) { new Mandelbrot(800, 600); // (800, 600), (1024, 768), (1600, 900), (1920, 1080) //new Mandelbrot(800, 600, 4.5876514379235943e-09, -0.6092161175392330, -0.4525577210859453); //new Mandelbrot(800, 600, 5.9512354925205320e-10, -0.6092146769531246, -0.4525564820098262); //new Mandelbrot(800, 600, 6.7178527589983420e-08, -0.7819036465400592, -0.1298363433443265); //new Mandelbrot(800, 600, 4.9716091454775210e-09, -0.7818800036717134, -0.1298044093748981); //new Mandelbrot(800, 600, 7.9333341281639390e-06, -0.7238770725243187, -0.2321214232559487); /* new Mandelbrot(800, 600, new double[][] { {5.0000000000000000e-03, -2.6100000000000000, -1.4350000000000000}, // done! {3.5894206549118390e-04, -0.7397795969773300, -0.4996473551637279}, // done! {3.3905106941862460e-05, -0.6270410477828043, -0.4587021918164572}, // done! {6.0636337351945460e-06, -0.6101531446039512, -0.4522561221394852}, // done! {1.5502741161769430e-06, -0.6077214060084073, -0.4503995886987711}, // done! }); //*/ } public Mandelbrot(int width, int height) { this(width, height, .005, -2.61, -1.435); } public Mandelbrot(int width, int height, double Zoom, double r, double i) { this(width, height, new double[] {Zoom, r, i}); } public Mandelbrot(int width, int height, double[] ... points) { super("Mandelbrot Set"); setResizable(false); setDefaultCloseOperation(EXIT_ON_CLOSE); Dimension screen = getToolkit().getScreenSize(); setBounds( rint((screen.getWidth() - width) / 2), rint((screen.getHeight() - height) / 2), width, height ); addMouseListener(mouseAdapter); addMouseMotionListener(mouseAdapter); addKeyListener(keyAdapter); Point point = stack.push(points); this.Zoom = point.Zoom; this.minX = point.minX; this.minY = point.minY; setVisible(true); insets = getInsets(); this.width = width -= insets.left + insets.right; this.height = height -= insets.top + insets.bottom; widthHeightRatio = (double) width / height; } private int rint(double d) { return (int) Math.rint(d); // half even } private void repaint(boolean newImage) { this.newImage = newImage; repaint(); } private MouseAdapter mouseAdapter = new MouseAdapter() { public void mouseClicked(MouseEvent e) { stack.push(false); if (!ctrl) { minX -= width / 2 ; minY -= height / 2; } minX += e.getX() - insets.left; minY += e.getY() - insets.top; ctrl = false; repaint(true); } public void mousePressed(MouseEvent e) { mpX = e.getX(); mpY = e.getY(); ctrl = isCtrlDown; } public void mouseDragged(MouseEvent e) { if (!ctrl) return; setMdCoord(e); repaint(); } private void setMdCoord(MouseEvent e) { int dx = e.getX() - mpX; int dy = e.getY() - mpY; mdX = mpX + max(abs(dx), rint(abs(dy) * widthHeightRatio) * signum(dx)); mdY = mpY + max(abs(dy), rint(abs(dx) / widthHeightRatio) * signum(dy)); acceptIf(insets.left, ge(mdX), setMdXY); acceptIf(insets.top, ge(mdY), setMdYX); acceptIf(insets.left+width-1, le(mdX), setMdXY); acceptIf(insets.top+height-1, le(mdY), setMdYX); } private void acceptIf(int value, Predicate<Integer> p, Consumer<Integer> c) { if (p.test(value)) c.accept(value); } private Predicate<Integer> ge(int md) { return v-> v >= md; } private Predicate<Integer> le(int md) { return v-> v <= md; } private Consumer<Integer> setMdXY = v-> mdY = mpY + rint(abs((mdX=v)-mpX) / widthHeightRatio) * signum(mdY-mpY); private Consumer<Integer> setMdYX = v-> mdX = mpX + rint(abs((mdY=v)-mpY) * widthHeightRatio) * signum(mdX-mpX); public void mouseReleased(MouseEvent e) { if (e.getX() == mpX && e.getY() == mpY) return; stack.push(ctrl); if (!ctrl) { minX += mpX - (mdX = e.getX()); minY += mpY - (mdY = e.getY()); } else { setMdCoord(e); if (mdX < mpX) { int t=mpX; mpX=mdX; mdX=t; } if (mdY < mpY) { int t=mpY; mpY=mdY; mdY=t; } minX += mpX - insets.left; minY += mpY - insets.top; double rZoom = (double) width / abs(mdX - mpX); minX *= rZoom; minY *= rZoom; Zoom /= rZoom; } ctrl = false; repaint(true); } }; private KeyAdapter keyAdapter = new KeyAdapter() { public void keyPressed(KeyEvent e) { isCtrlDown = e.isControlDown(); } public void keyReleased(KeyEvent e) { isCtrlDown = e.isControlDown(); } public void keyTyped(KeyEvent e) { char c = e.getKeyChar(); boolean isEsc = c == VK_ESCAPE; if (!isEsc && c != VK_BACK_SLASH) return; repaint(stack.pop(isEsc)); } }; private class Point { public boolean type; public double Zoom; public int minX; public int minY; Point(boolean type, double Zoom, int minX, int minY) { this.type = type; this.Zoom = Zoom; this.minX = minX; this.minY = minY; } } private class Stack extends java.util.Stack<Point> { private static final long serialVersionUID = 1L; public Point push(boolean type) { return push(type, Zoom, minX, minY); } public Point push(boolean type, double ... point) { double Zoom = point[0]; return push(type, Zoom, rint(point[1]/Zoom), rint(point[2]/Zoom)); } public Point push(boolean type, double Zoom, int minX, int minY) { return push(new Point(type, Zoom, minX, minY)); } public Point push(double[] ... points) { Point lastPoint = push(false, points[0]); for (int i=0, e=points.length-1; i<e; i+=1) { double[] point = points[i]; lastPoint = push(point[0] != points[i+1][0], point); done(printPoint(lastPoint)); } return lastPoint; } public boolean pop(boolean type) { for (;;) { if (empty()) return false; Point d = super.pop(); Zoom = d.Zoom; minX = d.minX; minY = d.minY; if (!type || d.type) return true; } } } @Override public void paint(Graphics g) { if (newImage) newImage(); g.drawImage(image, insets.left, insets.top, this); //g.drawLine(insets.left+width/2, insets.top+0, insets.left+width/2, insets.top+height); //g.drawLine(insets.left+0, insets.top+height/2, insets.left+width, insets.top+height/2); if (!ctrl) return; g.drawRect(min(mpX, mdX), min(mpY, mdY), abs(mpX - mdX), abs(mpY - mdY)); } private void newImage() { long milli = printPoint(); image = new BufferedImage(width, height, TYPE_INT_RGB); int maxX = minX + width; int maxY = minY + height; for (int x = minX; x < maxX; x+=1) { double r = x * Zoom; for (int y = minY; y < maxY; y+=1) { double i = y * Zoom; //System.out.printf("%+f%+fi\n", r, i); // 0f 1/6f 1/3f 1/2f 2/3f 5/6f //straight -> red yellow green cian blue magenta <- reverse image.setRGB(x-minX, y-minY, color(r, i, 360, false, 2/3f)); } } newImage = false; done(milli); } private long printPoint() { return printPoint(Zoom, minX, minY); } private long printPoint(Point point) { return printPoint(point.Zoom, point.minX, point.minY); } private long printPoint(double Zoom, int minX, int minY) { return printPoint(Zoom, minX*Zoom, minY*Zoom); } private long printPoint(Object ... point) { System.out.printf(ROOT, "{%.16e, %.16g, %.16g},", point); return currentTimeMillis(); } private void done(long milli) { milli = currentTimeMillis() - milli; System.out.println(" // " + milli + "ms done!"); } private int color(double r0, double i0, int max, boolean straight, float shift) { int n = -1; double r=0, i=0, r2=0, i2=0; do { i = r*(i+i) + i0; r = r2-i2 + r0; r2 = r*r; i2 = i*i; } while (++n < max && r2 + i2 < 4); return n == max ? black.getRGB() : HSBtoRGB(shift + (float) (straight ? n : max-n) / max * 11/12f + (straight ? 0f : 1/12f), 1, 1) ; }} ## JavaScript Works with: Firefox version 3.5.11 This needs the canvas tag of HTML 5 (it will not run on IE8 and lower or old browsers). The code can be run directly from the Javascript console in modern browsers by copying and pasting it. function mandelIter(cx, cy, maxIter) { var x = 0.0; var y = 0.0; var xx = 0; var yy = 0; var xy = 0; var i = maxIter; while (i-- && xx + yy <= 4) { xy = x * y; xx = x * x; yy = y * y; x = xx - yy + cx; y = xy + xy + cy; } return maxIter - i;} function mandelbrot(canvas, xmin, xmax, ymin, ymax, iterations) { var width = canvas.width; var height = canvas.height; var ctx = canvas.getContext('2d'); var img = ctx.getImageData(0, 0, width, height); var pix = img.data; for (var ix = 0; ix < width; ++ix) { for (var iy = 0; iy < height; ++iy) { var x = xmin + (xmax - xmin) * ix / (width - 1); var y = ymin + (ymax - ymin) * iy / (height - 1); var i = mandelIter(x, y, iterations); var ppos = 4 * (width * iy + ix); if (i > iterations) { pix[ppos] = 0; pix[ppos + 1] = 0; pix[ppos + 2] = 0; } else { var c = 3 * Math.log(i) / Math.log(iterations - 1.0); if (c < 1) { pix[ppos] = 255 * c; pix[ppos + 1] = 0; pix[ppos + 2] = 0; } else if ( c < 2 ) { pix[ppos] = 255; pix[ppos + 1] = 255 * (c - 1); pix[ppos + 2] = 0; } else { pix[ppos] = 255; pix[ppos + 1] = 255; pix[ppos + 2] = 255 * (c - 2); } } pix[ppos + 3] = 255; } } ctx.putImageData(img, 0, 0);} var canvas = document.createElement('canvas');canvas.width = 900;canvas.height = 600; document.body.insertBefore(canvas, document.body.childNodes[0]); mandelbrot(canvas, -2, 1, -1, 1, 1000); Output: with default parameters: ### ES6/WebAssembly With ES6 and WebAssembly, the program can run faster. Of course, this requires a compiled WASM file, but one can easily build one for instance with the WebAssembly explorer var mandelIter;fetch("./mandelIter.wasm") .then(res => { if (res.ok) return res.arrayBuffer(); throw new Error('Unable to fetch WASM.'); }) .then(bytes => { return WebAssembly.compile(bytes); }) .then(module => { return WebAssembly.instantiate(module); }) .then(instance => { WebAssembly.instance = instance; draw(); }) function mandelbrot(canvas, xmin, xmax, ymin, ymax, iterations) { // ... var i = WebAssembly.instance.exports.mandelIter(x, y, iterations); // ...} function draw() { // canvas initialization if necessary // ... mandelbrot(canvas, -2, 1, -1, 1, 1000); // ...} ## jq Thumbnail of SVG produced by jq program Works with: jq version 1.4 The Mandelbrot function as defined here is similar to the JavaScript implementation but generates SVG. The resulting picture is the same. Preliminaries # SVG STUFF def svg(id; width; height): "<svg width='\(width // "100%")' height='\(height // "100%") ' id='\(id)' xmlns='http://www.w3.org/2000/svg'>"; def pixel(x;y;r;g;b;a): "<circle cx='\(x)' cy='\(y)' r='1' fill='rgb(\(r|floor),\(g|floor),\(b|floor))' />"; # "UNTIL" # As soon as "condition" is true, then emit . and stop: def do_until(condition; next): def u: if condition then . else (next|u) end; u;   def Mandeliter( cx; cy; maxiter ): # [i, x, y, x^2+y^2] [ maxiter, 0.0, 0.0, 0.0 ] | do_until( .[0] == 0 or .[3] > 4; .[1] as x | .[2] as y | (x * y) as xy | (x * x) as xx | (y * y) as yy | [ (.[0] - 1), # i (xx - yy + cx), # x (xy + xy + cy), # y (xx+yy) # xx+yy ] ) | maxiter - .[0]; # width and height should be specified as the number of pixels.# obj == { xmin: _, xmax: _, ymin: _, ymax: _ }def Mandelbrot( obj; width; height; iterations ): def pixies: range(0; width) as ix | (obj.xmin + ((obj.xmax - obj.xmin) * ix / (width - 1))) as x | range(0; height) as iy | (obj.ymin + ((obj.ymax - obj.ymin) * iy / (height - 1))) as y | Mandeliter( x; y; iterations ) as i | if i == iterations then pixel(ix; iy; 0; 0; 0; 255) else (3 * (i|log)/((iterations - 1.0)|log)) as c # redness | if c < 1 then pixel(ix;iy; 255*c; 0; 0; 255) elif c < 2 then pixel(ix;iy; 255; 255*(c-1); 0; 255) else pixel(ix;iy; 255; 255; 255*(c-2); 255) end end; svg("mandelbrot"; "100%"; "100%"), pixies, "</svg>"; Example:  Mandelbrot( {"xmin": -2, "xmax": 1, "ymin": -1, "ymax":1}; 900; 600; 1000 )  Execution:   jq -n -r -f mandelbrot.jq > mandelbrot.svg  The output can be viewed in a web browser such as Chrome, Firefox, or Safari. ## Julia Generates an ASCII representation: function mandelbrot(a) z = 0 for i=1:50 z = z^2 + a end return zend for y=1.0:-0.05:-1.0 for x=-2.0:0.0315:0.5 abs(mandelbrot(complex(x, y))) < 2 ? print("*") : print(" ") end println()end This generates a PNG image file: using Images @inline function hsv2rgb(h, s, v) c = v * s x = c * (1 - abs(((h/60) % 2) - 1)) m = v - c r,g,b = if h < 60 (c, x, 0) elseif h < 120 (x, c, 0) elseif h < 180 (0, c, x) elseif h < 240 (0, x, c) elseif h < 300 (x, 0, c) else (c, 0, x) end (r + m), (b + m), (g + m)end function mandelbrot() w = 1600 h = 1200 zoom = 0.5 moveX = -0.5 moveY = 0 maxIter = 30 img = Array{RGB{Float64},2}(undef,h,w) for x in 1:w for y in 1:h i = maxIter z = c = Complex( (2*x - w) / (w * zoom) + moveX, (2*y - h) / (h * zoom) + moveY ) while abs(z) < 2 && (i -= 1) > 0 z = z^2 + c end r,g,b = hsv2rgb(i / maxIter * 360, 1, i / maxIter) img[y,x] = RGB{Float64}(r, g, b) end end return imgend img = mandelbrot()save("mandelbrot.png", img) ### Mandelbrot Set with Julia Animation This is just a translation of the corresponding R section. using Plotsgr(aspect_ratio=:equal, legend=false, dpi=250) d = 800 # pixel density (= image width)h = 600 # image height A = range(-1, 1, length=d+1)' .* ones(h + 1)B = ones(d + 1)' .* range(-h/d, h/d, length=h+1) C = 2.0 * (A + B * im) .- 0.5Z = zero(C) anim = Animation()for k = 1:20 global Z = Z .^ 2 + C heatmap(exp.(-abs.(Z)), c=:jet) frame(anim)end gif(anim, "Mandelbrot_animation.gif", fps=1) ### Normalized Iteration Count, Distance Estimation and Mercator Maps This is just a translation of the corresponding Python section. using Plotsgr(aspect_ratio=:equal, legend=false, dpi=250) d, h = 800, 600 # pixel density (= image width) and image heightn, r = 200, 500 # number of iterations and escape radius (r > 2) x = range(0, 2, length=d+1)y = range(0, 2 * h / d, length=h+1) A, B = (x .- 1)' .* ones(h + 1), ones(d + 1)' .* (y .- h / d)C = 2.0 * (A + B * im) .- 0.5 Z, dZ = zero(C), zero(C)T, D = zeros(size(C)), zeros(size(C)) for k = 1:n M = abs.(Z) .< r Z[M], dZ[M] = Z[M] .^ 2 + C[M], 2 * Z[M] .* dZ[M] .+ 1 T[M] = T[M] .+ 1end heatmap(T .^ 0.1, c=:jet)savefig("Mandelbrot_set_1.png") N = abs.(Z) .> r # normalized iteration countT[N] = T[N] - log2.(log.(abs.(Z[N])) / log(r)) heatmap(T .^ 0.1, c=:jet)savefig("Mandelbrot_set_2.png") N = abs.(Z) .> 2 # exterior distance estimationD[N] = 0.5 * log.(abs.(Z[N])) .* abs.(Z[N]) ./ abs.(dZ[N]) heatmap(D .^ 0.1, c=:jet)savefig("Mandelbrot_set_3.png") A small change in the above code allows Mercator maps of the Mandelbrot set. using Plotsgr(aspect_ratio=:equal, legend=false, dpi=250) d, h = 400, 2200 # pixel density (= image width) and image heightn, r = 800, 1000 # number of iterations and escape radius (r > 2) x = range(0, 2, length=d+1)y = range(0, 2 * h / d, length=h+1) A, B = (x * pi)' .* ones(h + 1), ones(d + 1)' .* (y * pi)C = 2.0 * exp.((A + B * im) * im) .- 0.74366367740001 .+ 0.131863214401 * im Z, dZ = zero(C), zero(C)T, D = zeros(size(C)), zeros(size(C)) for k = 1:n M = abs.(Z) .< r Z[M], dZ[M] = Z[M] .^ 2 + C[M], 2 * Z[M] .* dZ[M] .+ 1 T[M] = T[M] .+ 1end heatmap(-T' .^ 0.1, c=:nipy_spectral)savefig("Mercator_map_1.png") N = abs.(Z) .> r # normalized iteration countT[N] = T[N] - log2.(log.(abs.(Z[N])) / log(r)) heatmap(-T' .^ 0.1, c=:nipy_spectral)savefig("Mercator_map_2.png") N = abs.(Z) .> 2 # exterior distance estimationD[N] = 0.5 * log.(abs.(Z[N])) .* abs.(Z[N]) ./ abs.(dZ[N]) heatmap(D' .^ 0.1, c=:nipy_spectral)savefig("Mercator_map_3.png") ## Kotlin Translation of: Java // version 1.1.2 import java.awt.Graphicsimport java.awt.image.BufferedImageimport javax.swing.JFrame class Mandelbrot: JFrame("Mandelbrot Set") { companion object { private const val MAX_ITER = 570 private const val ZOOM = 150.0 } private val img: BufferedImage init { setBounds(100, 100, 800, 600) isResizable = false defaultCloseOperation = EXIT_ON_CLOSE img = BufferedImage(width, height, BufferedImage.TYPE_INT_RGB) for (y in 0 until height) { for (x in 0 until width) { var zx = 0.0 var zy = 0.0 val cX = (x - 400) / ZOOM val cY = (y - 300) / ZOOM var iter = MAX_ITER while (zx * zx + zy * zy < 4.0 && iter > 0) { val tmp = zx * zx - zy * zy + cX zy = 2.0 * zx * zy + cY zx = tmp iter-- } img.setRGB(x, y, iter or (iter shl 7)) } } } override fun paint(g: Graphics) { g.drawImage(img, 0, 0, this) }} fun main(args: Array<String>) { Mandelbrot().isVisible = true} ## LabVIEW Works with: LabVIEW version 8.0 Full Development Suite ## Lang5  : d2c(*,*) 2 compress 'c dress ; # Make a complex number. : iterate(c) [0 0](c) "dup * over +" steps reshape execute ; : print_line(*) "#*+-. " "" split swap subscript "" join . "\n" . ; 75 iota 45 - 20 / # x coordinates29 iota 14 - 10 / # y cordinates'd2c outer # Make complex matrix. 10 'steps set # How many iterations? iterate abs int 5 min 'print_line apply # Compute & print  ## Lasso  define mandelbrotBailout => 16define mandelbrotMaxIterations => 1000 define mandelbrotIterate(x, y) => { local(cr = #y - 0.5, ci = #x, zi = 0.0, zr = 0.0, i = 0, temp, zr2, zi2) { ++#i; #temp = #zr * #zi #zr2 = #zr * #zr #zi2 = #zi * #zi #zi2 + #zr2 > mandelbrotBailout? return #i #i > mandelbrotMaxIterations? return 0 #zr = #zr2 - #zi2 + #cr #zi = #temp + #temp + #ci currentCapture->restart }()} define mandelbrotTest() => { local(x, y = -39.0) { stdout('\n') #x = -39.0 { mandelbrotIterate(#x / 40.0, #y / 40.0) == 0? stdout('*') | stdout(' '); ++#x #x <= 39.0? currentCapture->restart }(); ++#y #y <= 39.0? currentCapture->restart }() stdout('\n')} mandelbrotTest  Output:  * * * * * *** ***** ***** *** * ********* ************* *************** ********************* ********************* ******************* ******************* ******************* ******************* *********************** ******************* ******************* ********************* ******************* ******************* ***************** *************** ************* ********* * *************** *********************** * ************************* * ***************************** * ******************************* * ********************************* *********************************** *************************************** *** ***************************************** *** ************************************************* *********************************************** ********************************************* ********************************************* *********************************************** *********************************************** *************************************************** ************************************************* ************************************************* *************************************************** *************************************************** * *************************************************** * ***** *************************************************** ***** ****** *************************************************** ****** ******* *************************************************** ******* *********************************************************************** ********* *************************************************** ********* ****** *************************************************** ****** ***** *************************************************** ***** *************************************************** *************************************************** *************************************************** *************************************************** ************************************************* ************************************************* *************************************************** *********************************************** *********************************************** ******************************************* ***************************************** ********************************************* **** ****************** ****************** **** *** **************** **************** *** * ************** ************** * *********** *********** ** ***** ***** ** * * * *  ## LIL From the source distribution. Produces a PBM, not shown here. ## A mandelbrot generator that outputs a PBM file. This can be used to measure# performance differences between LIL versions and measure performance# bottlenecks (although keep in mind that LIL is not supposed to be a fast# language, but a small one which depends on C for the slow parts - in a real# program where for some reason mandelbrots are required, the code below would# be written in C). The code is based on the mandelbrot test for the Computer# Language Benchmarks Game at http://shootout.alioth.debian.org/## In my current computer (Intel Core2Quad Q9550 @ 2.83GHz) running x86 Linux# the results are (using the default 256x256 size):## 2m3.634s - commit 1c41cdf89f4c1e039c9b3520c5229817bc6274d0 (Jan 10 2011)## To test call## time ./lil mandelbrot.lil > mandelbrot.pbm## with an optimized version of lil (compiled with CFLAGS=-O3 make).# set width [expr argv]if not width { set width 256 }set height widthset bit_num 0set byte_acc 0set iter 50set limit 2.0 write "P4\n{width} {height}\n" for {set y 0} {y < height} {inc y} { for {set x 0} {x < width} {inc x} { set Zr 0.0 Zi 0.0 Tr 0.0 Ti 0.0 set Cr [expr 2.0 * x / width - 1.5] set Ci [expr 2.0 * y / height - 1.0] for {set i 0} {i < iter && Tr + Ti <= limit * limit} {inc i} { set Zi [expr 2.0 * Zr * Zi + Ci] set Zr [expr Tr - Ti + Cr] set Tr [expr Zr * Zr] set Ti [expr Zi * Zi] } set byte_acc [expr byte_acc << 1] if [expr Tr + Ti <= limit * limit] { set byte_acc [expr byte_acc | 1] } inc bit_num if [expr bit_num == 8] { writechar byte_acc set byte_acc 0 set bit_num 0 } {if [expr x == width - 1] { set byte_acc [expr 8 - width % 8] writechar byte_acc set byte_acc 0 set bit_num 0 }} }} ## Logo Works with: UCB Logo to mandelbrot :left :bottom :side :size cs setpensize [1 1] make "inc :side/:size make "zr :left repeat :size [ make "zr :zr + :inc make "zi :bottom pu setxy repcount - :size/2 minus :size/2 pd repeat :size [ make "zi :zi + :inc setpencolor count.color calc :zr :zi fd 1 ] ]end to count.color :count ;op (list :count :count :count) if :count > 256 [op 0] ; black if :count > 128 [op 7] ; white if :count > 64 [op 5] ; magenta if :count > 32 [op 6] ; yellow if :count > 16 [op 4] ; red if :count > 8 [op 2] ; green if :count > 4 [op 1] ; blue op 3 ; cyanend to calc :zr :zi [:count 0] [:az 0] [:bz 0] if :az*:az + :bz*:bz > 4 [op :count] if :count > 256 [op :count] op (calc :zr :zi (:count + 1) (:zr + :az*:az - :bz*:bz) (:zi + 2*:az*:bz))end mandelbrot -2 -1.25 2.5 400 ## Lua ### Graphical Needs LÖVE 2D Engine Zoom in: drag the mouse; zoom out: right click  local maxIterations = 250local minX, maxX, minY, maxY = -2.5, 2.5, -2.5, 2.5local miX, mxX, miY, mxYfunction remap( x, t1, t2, s1, s2 ) local f = ( x - t1 ) / ( t2 - t1 ) local g = f * ( s2 - s1 ) + s1 return g;endfunction drawMandelbrot() local pts, a, as, za, b, bs, zb, cnt, clr = {} for j = 0, hei - 1 do for i = 0, wid - 1 do a = remap( i, 0, wid, minX, maxX ) b = remap( j, 0, hei, minY, maxY ) cnt = 0; za = a; zb = b while( cnt < maxIterations ) do as = a * a - b * b; bs = 2 * a * b a = za + as; b = zb + bs if math.abs( a ) + math.abs( b ) > 16 then break end cnt = cnt + 1 end if cnt == maxIterations then clr = 0 else clr = remap( cnt, 0, maxIterations, 0, 255 ) end pts[1] = { i, j, clr, clr, 0, 255 } love.graphics.points( pts ) end endendfunction startFractal() love.graphics.setCanvas( canvas ); love.graphics.clear() love.graphics.setColor( 255, 255, 255 ) drawMandelbrot(); love.graphics.setCanvas()endfunction love.load() wid, hei = love.graphics.getWidth(), love.graphics.getHeight() canvas = love.graphics.newCanvas( wid, hei ) startFractal()endfunction love.mousepressed( x, y, button, istouch ) if button == 1 then startDrag = true; miX = x; miY = y else minX = -2.5; maxX = 2.5; minY = minX; maxY = maxX startFractal() startDrag = false endendfunction love.mousereleased( x, y, button, istouch ) if startDrag then local l if x > miX then mxX = x else l = x; mxX = miX; miX = l end if y > miY then mxY = y else l = y; mxY = miY; miY = l end miX = remap( miX, 0, wid, minX, maxX ) mxX = remap( mxX, 0, wid, minX, maxX ) miY = remap( miY, 0, hei, minY, maxY ) mxY = remap( mxY, 0, hei, minY, maxY ) minX = miX; maxX = mxX; minY = miY; maxY = mxY startFractal() endendfunction love.draw() love.graphics.draw( canvas )end  ### ASCII -- Mandelbrot set in Lua 6/15/2020 dblocal charmap = { [0]=" ", ".", ":", "-", "=", "+", "*", "#", "%", "@" }for y = -1.3, 1.3, 0.1 do for x = -2.1, 1.1, 0.04 do local zi, zr, i = 0, 0, 0 while i < 100 do if (zi*zi+zr*zr >= 4) then break end zr, zi, i = zr*zr-zi*zi+x, 2*zr*zi+y, i+1 end io.write(charmap[i%10]) end print()end Output: ...............::::::::::::::::::---------------:::::::::::::::::::::::::::::::: .............:::::::::::---------------------------------::::::::::::::::::::::: ...........::::::::---------------------======+#@#++=====-----:::::::::::::::::: ..........::::::--------------------=======+++**@[email protected]@*+=====-----::::::::::::::: ........:::::--------------------========++++*#@@#=:%#*++=====------:::::::::::: .......:::--------------------========+++***#%: .:#*+++++===-------::::::::: ......:::------------------=======+++#%@%%%@@ :# %[email protected]@%#***%*+==------:::::::: .....::-----------------====++++++**# = =% %-.*+=#%+==-------:::::: .....:--------------==+++++++++****%:.*+ *%*++==-------::::: ....:--------=====+*#=%##########%%.** [email protected] +===-------:::: ....---========++++*#@:=*:[email protected]+ [email protected]@ := @ #*===--------::: ...--=======+++++*##%.=: @+. @##+====--------:: ...=======****##% .-=% *#*+====--------:: [email protected]:: :: % :@#*++====--------:: ...=======****##% .-=% *#*+====--------:: ...--=======+++++*##%.=: @+. @##+====--------:: ....---========++++*#@:=*:[email protected]+ [email protected]@ := @ #*===--------::: ....:--------=====+*#=%##########%%.** [email protected] +===-------:::: .....:--------------==+++++++++****%:.*+ *%*++==-------::::: .....::-----------------====++++++**# = =% %-.*+=#%+==-------:::::: ......:::------------------=======+++#%@%%%@@ :# %[email protected]@%#***%*+==------:::::::: .......:::--------------------========+++***#%: .:#*+++++===-------::::::::: ........:::::--------------------========++++*#@@#=:%#*++=====------:::::::::::: ..........::::::--------------------=======+++**@[email protected]@*+=====-----::::::::::::::: ...........::::::::---------------------======+#@#++=====-----:::::::::::::::::: .............:::::::::::---------------------------------::::::::::::::::::::::: ...............::::::::::::::::::---------------:::::::::::::::::::::::::::::::: ## M2000 Interpreter Console is a bitmap so we can plot on it. A subroutine plot different size of pixels so we get Mandelbrot image at final same size for 32X26 for a big pixel of 16x16 pixels to 512x416 for a 1:1 pixel. Iterations for each pixel set to 25. Module can get left top corner as twips, and the size factor from 1 to 16 (size of output is 512x416 pixels for any factor).  Module Mandelbrot(x=0&,y=0&,z=1&) { If z<1 then z=1 If z>16 then z=16 Const iXmax=32*z Const iYmax=26*z Def single Cx, Cy, CxMin=-2.05, CxMax=0.85, CyMin=-1.2, CyMax=1.2 Const PixelWidth=(CxMax-CxMin)/iXmax, iXm=(iXmax-1)*PixelWidth Const PixelHeight=(CyMax-CyMin)/iYmax,Ph2=PixelHeight/2 Const Iteration=25 Const EscRadious=2.5, ER2=EscRadious**2 Def single preview preview=iXmax*twipsX*(z/16) Def long yp, xp, dx, dy, dx1, dy1 Let dx=twipsx*(16/z), dx1=dx-1 Let dy=twipsy*(16/z), dy1=dy-1 yp=y For iY=0 to (iYmax-1)*PixelHeight step PixelHeight { Cy=CyMin+iY xp=x if abs(Cy)<Ph2 Then Cy=0 For iX=0 to iXm Step PixelWidth { Let Cx=CxMin+iX,Zx=0,Zy=0,Zx2=Zx**2,Zy2=Zy**2 For It=Iteration to 1 {Let Zy=2*Zx*Zy+Cy,Zx=Zx2-Zy2+Cx,Zx2=Zx**2,Zy2=Zy**2 :if Zx2+Zy2>ER2 Then exit } if it>13 then {it-=13} else.if it=0 then SetPixel(xp,yp,0): xp+=dx : continue it*=10:SetPixel(xp,yp,color(it, it,255)) :xp+=dx } : yp+=dy } Sub SetPixel() move number, number: fill dx1, dy1, number End Sub}Cls 1,0sz=(1,2,4,8,16)i=each(sz)While i { Mandelbrot 250*twipsx,100*twipsy, array(i)}  Version 2 without Subroutine. Also there is a screen refresh every 2 seconds.  Module Mandelbrot(x=0&,y=0&,z=1&) { If z<1 then z=1 If z>16 then z=16 Const iXmax=32*z Const iYmax=26*z Def single Cx, Cy, CxMin=-2.05, CxMax=0.85, CyMin=-1.2, CyMax=1.2 Const PixelWidth=(CxMax-CxMin)/iXmax, iXm=(iXmax-1)*PixelWidth Const PixelHeight=(CyMax-CyMin)/iYmax,Ph2=PixelHeight/2 Const Iteration=25 Const EscRadious=2.5, ER2=EscRadious**2 Def single preview preview=iXmax*twipsX*(z/16) Def long yp, xp, dx, dy, dx1, dy1 Let dx=twipsx*(16/z), dx1=dx-1 Let dy=twipsy*(16/z), dy1=dy-1 yp=y Refresh 2000 For iY=0 to (iYmax-1)*PixelHeight step PixelHeight { Cy=CyMin+iY xp=x if abs(Cy)<Ph2 Then Cy=0 move xp, yp For iX=0 to iXm Step PixelWidth { Let Cx=CxMin+iX,Zx=0,Zy=0,Zx2=Zx**2,Zy2=Zy**2 For It=Iteration to 1 {Let Zy=2*Zx*Zy+Cy,Zx=Zx2-Zy2+Cx,Zx2=Zx**2,Zy2=Zy**2 :if Zx2+Zy2>ER2 Then exit } if it>13 then {it-=13} else.if it=0 then fill dx1, dy1, 0: Step 0,-dy1: continue it*=10:fill dx1, dy1, color(it, it,255): Step 0,-dy1 } : yp+=dy } }Cls 1,0sz=(1,2,4,8,16)i=each(sz)While i { Mandelbrot 250*twipsx,100*twipsy, array(i)}  ## Maple ImageTools:-Embed(Fractals[EscapeTime]:-Mandelbrot(500, -2.0-1.35*I, .7+1.35*I, output = layer1)); ## Mathematica / Wolfram Language The implementation could be better. But this is a start... eTime[c_, maxIter_Integer: 100] := [email protected][#^2 + c &, 0, [email protected]# <= 2 &, 1, maxIter] - 1 DistributeDefinitions[eTime];mesh = ParallelTable[eTime[x + I*y, 1000], {y, 1.2, -1.2, -0.01}, {x, -1.72, 1, 0.01}];ReliefPlot[mesh, Frame -> False] Faster version: cf = With[{ mandel = Block[{z = #, c = #}, [email protected][If[Abs[z] > 2, [email protected]]; z = z^2 + c, {i, 100}]] & }, Compile[{},Table[mandel[y + x I], {x, -1, 1, 0.005}, {y, -2, 0.5, 0.005}]] ];ArrayPlot[cf[]]  Built-in function: MandelbrotSetPlot[] ## Mathmap filter mandelbrot (gradient coloration) c=ri:(xy/xy:[X,X]*1.5-xy:[0.5,0]); z=ri:[0,0]; # initial value z0 = 0 # iteration of z iter=0; while abs(z)<2 && iter<31 do z=z*z+c; # z(n+1) = fc(zn) iter=iter+1 end; coloration(iter/32) # color of pixel end  ## MATLAB This solution uses the escape time algorithm to determine the coloring of the coordinates on the complex plane. The code can be reduced to a single line via vectorization after the Escape Time Algorithm function definition, but the code becomes unnecessarily obfuscated. Also, this code uses a lot of memory. You will need a computer with a lot of memory to compute the set with high resolution. function [theSet,realAxis,imaginaryAxis] = mandelbrotSet(start,gridSpacing,last,maxIteration) %Define the escape time algorithm function escapeTime = escapeTimeAlgorithm(z0) escapeTime = 0; z = 0; while( (abs(z)<=2) && (escapeTime < maxIteration) ) z = (z + z0)^2; escapeTime = escapeTime + 1; end end %Define the imaginary axis imaginaryAxis = (imag(start):imag(gridSpacing):imag(last)); %Define the real axis realAxis = (real(start):real(gridSpacing):real(last)); %Construct the complex plane from the real and imaginary axes complexPlane = meshgrid(realAxis,imaginaryAxis) + meshgrid(imaginaryAxis(end:-1:1),realAxis)'.*i; %Apply the escape time algorithm to each point in the complex plane theSet = arrayfun(@escapeTimeAlgorithm, complexPlane); %Draw the set pcolor(realAxis,imaginaryAxis,theSet); shading flat; end To use this function you must specify the: 1. lower left hand corner of the complex plane from which to start the image, 2. the grid spacing in both the imaginary and real directions, 3. the upper right hand corner of the complex plane at which to end the image and 4. the maximum iterations for the escape time algorithm. For example: 1. Lower Left Corner: -2.05-1.2i 2. Grid Spacing: 0.004+0.0004i 3. Upper Right Corner: 0.45+1.2i 4. Maximum Iterations: 500 Sample usage: mandelbrotSet(-2.05-1.2i,0.004+0.0004i,0.45+1.2i,500); ## Metapost prologues:=3;outputtemplate:="%j-%c.svg";outputformat:="svg"; def mandelbrot(expr maxX, maxY) = max_iteration := 500; color col[]; for i := 0 upto max_iteration: t := i / max_iteration; col[i] = (t,t,t); endfor; for px := 0 upto maxX: for py := 0 upto maxY: xz := px * 3.5 / maxX - 2.5; % (-2.5,1) yz := py * 2 / maxY - 1; % (-1,1) x := 0; y := 0; iteration := 0; forever: exitunless ((x*x + y*y < 4) and (iteration < max_iteration)); xtemp := x*x - y*y + xz; y := 2*x*y + yz; x := xtemp; iteration := iteration + 1; endfor; draw (px,py) withpen pencircle withcolor col[iteration]; endfor; endfor;enddef; beginfig(1); mandelbrot(200, 150);endfig; end Sample usage: mpost -numbersystem="double" mandelbrot.mp ## MiniScript ZOOM = 100MAX_ITER = 40gfx.clear color.blackfor y in range(0,200) for x in range(0,300) zx = 0 zy = 0 cx = (x - 200) / ZOOM cy = (y - 100) / ZOOM for iter in range(MAX_ITER) if zx*zx + zy*zy > 4 then break tmp = zx * zx - zy * zy + cx zy = 2 * zx * zy + cy zx = tmp end for if iter then gfx.setPixel x, y, rgb(255-iter*6, 0, iter*6) end if end forend for (Will upload an output image as soon as image uploading is fixed.) ## Modula-3 MODULE Mandelbrot EXPORTS Main; IMPORT Wr, Stdio, Fmt, Word; CONST m = 50; limit2 = 4.0; TYPE UByte = BITS 8 FOR [0..16_FF]; VAR width := 200; height := 200; bitnum: CARDINAL := 0; byteacc: UByte := 0; isOverLimit: BOOLEAN; Zr, Zi, Cr, Ci, Tr, Ti: REAL; BEGIN Wr.PutText(Stdio.stdout, "P4\n" & Fmt.Int(width) & " " & Fmt.Int(height) & "\n"); FOR y := 0 TO height - 1 DO FOR x := 0 TO width - 1 DO Zr := 0.0; Zi := 0.0; Cr := 2.0 * FLOAT(x) / FLOAT(width) - 1.5; Ci := 2.0 * FLOAT(y) / FLOAT(height) - 1.0; FOR i := 1 TO m + 1 DO Tr := Zr*Zr - Zi*Zi + Cr; Ti := 2.0*Zr*Zi + Ci; Zr := Tr; Zi := Ti; isOverLimit := Zr*Zr + Zi*Zi > limit2; IF isOverLimit THEN EXIT; END; END; IF isOverLimit THEN byteacc := Word.Xor(Word.LeftShift(byteacc, 1), 16_00); ELSE byteacc := Word.Xor(Word.LeftShift(byteacc, 1), 16_01); END; INC(bitnum); IF bitnum = 8 THEN Wr.PutChar(Stdio.stdout, VAL(byteacc, CHAR)); byteacc := 0; bitnum := 0; ELSIF x = width - 1 THEN byteacc := Word.LeftShift(byteacc, 8 - (width MOD 8)); Wr.PutChar(Stdio.stdout, VAL(byteacc, CHAR)); byteacc := 0; bitnum := 0 END; Wr.Flush(Stdio.stdout); END; END;END Mandelbrot. ## MySQL See http://arbitraryscrawl.blogspot.co.uk/2012/06/fractsql.html for an explanation.  -- Table to contain all the data pointsCREATE TABLE points ( c_re DOUBLE, c_im DOUBLE, z_re DOUBLE DEFAULT 0, z_im DOUBLE DEFAULT 0, znew_re DOUBLE DEFAULT 0, znew_im DOUBLE DEFAULT 0, steps INT DEFAULT 0, active CHAR DEFAULT 1); DELIMITER | -- Iterate over all the points in the table 'points'CREATE PROCEDURE itrt (IN n INT)BEGIN label: LOOP UPDATE points SET znew_re=POWER(z_re,2)-POWER(z_im,2)+c_re, znew_im=2*z_re*z_im+c_im, steps=steps+1 WHERE active=1; UPDATE points SET z_re=znew_re, z_im=znew_im, active=IF(POWER(z_re,2)+POWER(z_im,2)>4,0,1) WHERE active=1; SET n = n - 1; IF n > 0 THEN ITERATE label; END IF; LEAVE label; END LOOP label;END| -- Populate the table 'points'CREATE PROCEDURE populate ( r_min DOUBLE, r_max DOUBLE, r_step DOUBLE, i_min DOUBLE, i_max DOUBLE, i_step DOUBLE)BEGIN DELETE FROM points; SET @rl = r_min; SET @a = 0; rloop: LOOP SET @im = i_min; SET @b = 0; iloop: LOOP INSERT INTO points (c_re, c_im) VALUES (@rl, @im); SET @b=@b+1; SET @im=i_min + @b * i_step; IF @im < i_max THEN ITERATE iloop; END IF; LEAVE iloop; END LOOP iloop; SET @a=@a+1; SET @rl=r_min + @a * r_step; IF @rl < r_max THEN ITERATE rloop; END IF; LEAVE rloop; END LOOP rloop;END| DELIMITER ; -- Choose size and resolution of graph-- R_min, R_max, R_step, I_min, I_max, I_stepCALL populate( -2.5, 1.5, 0.005, -2, 2, 0.005 ); -- Calculate 50 iterationsCALL itrt( 50 ); -- Create the image (/tmp/image.ppm)-- Note, MySQL will not over-write an existing file and you may need-- administrator access to delete or move itSELECT @xmax:=COUNT(c_re) INTO @xmax FROM points GROUP BY c_im LIMIT 1;SELECT @ymax:=COUNT(c_im) INTO @ymax FROM points GROUP BY c_re LIMIT 1;SET group_concat_max_len=11*@xmax*@ymax;SELECT 'P3', @xmax, @ymax, 200, GROUP_CONCAT( CONCAT( IF( active=1, 0, 55+MOD(steps, 200) ), ' ', IF( active=1, 0, 55+MOD(POWER(steps,3), 200) ), ' ', IF( active=1, 0, 55+MOD(POWER(steps,2), 200) ) ) ORDER BY c_im ASC, c_re ASC SEPARATOR ' ' ) INTO OUTFILE '/tmp/image.ppm' FROM points;  ## Nim ### Textual version Translation of: Python import complex proc inMandelbrotSet(c: Complex, maxEscapeIterations = 50): bool = result = true; var z: Complex for i in 0..maxEscapeIterations: z = z * z + c if abs2(z) > 4: return false iterator steps(start, step: float, numPixels: int): float = for i in 0..numPixels: yield start + i.float * step proc mandelbrotImage(yStart, yStep, xStart, xStep: float, height, width: int): string = for y in steps(yStart, yStep, height): for x in steps(xStart, xStep, width): result.add(if complex(x, y).inMandelbrotSet: '*' else: ' ') result.add('\n') echo mandelbrotImage(1.0, -0.05, -2.0, 0.0315, 40, 80) Output:  ** ****** ******** ****** ******** ** * *** ***************** ************************ *** **************************** ****************************** ****************************** ************************************ * ********************************** ** ***** * ********************************** *********** ************************************ ************** ************************************ *************************************************** ***************************************************** ************************************************************************ ***************************************************** *************************************************** ************** ************************************ *********** ************************************ ** ***** * ********************************** * ********************************** ************************************ ****************************** ****************************** **************************** ************************ *** *** ***************** ******** ** * ****** ******** ****** **  ### Graphical version Translation of: Julia Library: imageman import math, complex, lenientopsimport imageman const W = 800 H = 600 Zoom = 0.5 MoveX = -0.5 MoveY = 0.0 MaxIter = 30 func hsvToRgb(h, s, v: float): array[3, float] = let c = v * s let x = c * (1 - abs(((h / 60) mod 2) - 1)) let m = v - c let (r, g, b) = if h < 60: (c, x, 0.0) elif h < 120: (x, c, 0.0) elif h < 180: (0.0, c, x) elif h < 240: (0.0, x, c) elif x < 300: (x, 0.0, c) else: (c, 0.0, x) result = [r + m, g + m, b + m] var img = initImage[ColorRGBF64](W, H)for x in 1..W: for y in 1..H: var i = MaxIter - 1 let c = complex((2 * x - W) / (W * Zoom) + MoveX, (2 * y - H) / (H * Zoom) + MoveY) var z = c while abs(z) < 2 and i > 0: z = z * z + c dec i let color = hsvToRgb(i / MaxIter * 360, 1, i / MaxIter) img[x - 1, y - 1] = ColorRGBF64(color) img.savePNG("mandelbrot.png", compression = 9) ## OCaml #load "graphics.cma";; let mandelbrot xMin xMax yMin yMax xPixels yPixels maxIter = let rec mandelbrotIterator z c n = if (Complex.norm z) > 2.0 then false else match n with | 0 -> true | n -> let z' = Complex.add (Complex.mul z z) c in mandelbrotIterator z' c (n-1) in Graphics.open_graph (" "^(string_of_int xPixels)^"x"^(string_of_int yPixels)); let dx = (xMax -. xMin) /. (float_of_int xPixels) and dy = (yMax -. yMin) /. (float_of_int yPixels) in for xi = 0 to xPixels - 1 do for yi = 0 to yPixels - 1 do let c = {Complex.re = xMin +. (dx *. float_of_int xi); Complex.im = yMin +. (dy *. float_of_int yi)} in if (mandelbrotIterator Complex.zero c maxIter) then (Graphics.set_color Graphics.white; Graphics.plot xi yi ) else (Graphics.set_color Graphics.black; Graphics.plot xi yi ) done done;; mandelbrot (-1.5) 0.5 (-1.0) 1.0 500 500 200;; ## Octave This code runs rather slowly and produces coloured Mandelbrot set by accident (output image). #! /usr/bin/octave -qfglobal width = 200;global height = 200;maxiter = 100; z0 = 0;global cmax = 1 + i;global cmin = -2 - i; function cs = pscale(c) global cmax; global cmin; global width; global height; persistent px = (real(cmax-cmin))/width; persistent py = (imag(cmax-cmin))/height; cs = real(cmin) + px*real(c) + i*(imag(cmin) + py*imag(c));endfunction ms = zeros(width, height);for x = 0:width-1 for y = 0:height-1 z0 = 0; c = pscale(x+y*i); for ic = 1:maxiter z1 = z0^2 + c; if ( abs(z1) > 2 ) break; endif z0 = z1; endfor ms(x+1, y+1) = ic/maxiter; endforendfor saveimage("mandel.ppm", round(ms .* 255).', "ppm"); ## Ol  (define x-size 59)(define y-size 21)(define min-im -1)(define max-im 1)(define min-re -2)(define max-re 1) (define step-x (/ (- max-re min-re) x-size))(define step-y (/ (- max-im min-im) y-size)) (for-each (lambda (y) (let ((im (+ min-im (* step-y y)))) (for-each (lambda (x) (let*((re (+ min-re (* step-x x))) (zr (inexact re)) (zi (inexact im))) (let loop ((n 0) (zi zi) (zr zr)) (let ((a (* zr zr)) (b (* zi zi))) (cond ((> (+ a b) 4) (display (string (- 62 n)))) ((= n 30) (display (string (- 62 n)))) (else (loop (+ n 1) (+ (* 2 zr zi) im) (- (+ a re) b)))))))) (iota x-size)) (print))) (iota y-size))  Output: >>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<========== >>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<======= >>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<====== >>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<==== >>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<=== >>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<== >=<<<<<<<<;;;:599999999886 %78:;;<<<<<<= ><<<<;;;;;:::972456-567763 +9;;<<<<<<< ><;;;;;;::::9875& .3 *9;;;<<<<<< >;;;;;;::997564' ' 8:;;;<<<<<< >::988897735/ &89:;;;<<<<<< >::988897735/ &89:;;;<<<<<< >;;;;;;::997564' ' 8:;;;<<<<<< ><;;;;;;::::9875& .3 *9;;;<<<<<< ><<<<;;;;;:::972456-567763 +9;;<<<<<<< >=<<<<<<<<;;;:599999999886 %78:;;<<<<<<= >>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<== >>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<=== >>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<==== >>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<====== >>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<=======  ## OpenEdge/Progress DEFINE VARIABLE print_str AS CHAR NO-UNDO INIT ''.DEFINE VARIABLE X1 AS DECIMAL NO-UNDO INIT 50.DEFINE VARIABLE Y1 AS DECIMAL NO-UNDO INIT 21.DEFINE VARIABLE X AS DECIMAL NO-UNDO.DEFINE VARIABLE Y AS DECIMAL NO-UNDO.DEFINE VARIABLE N AS DECIMAL NO-UNDO.DEFINE VARIABLE I3 AS DECIMAL NO-UNDO.DEFINE VARIABLE R3 AS DECIMAL NO-UNDO.DEFINE VARIABLE Z1 AS DECIMAL NO-UNDO.DEFINE VARIABLE Z2 AS DECIMAL NO-UNDO.DEFINE VARIABLE A AS DECIMAL NO-UNDO.DEFINE VARIABLE B AS DECIMAL NO-UNDO.DEFINE VARIABLE I1 AS DECIMAL NO-UNDO INIT -1.0.DEFINE VARIABLE I2 AS DECIMAL NO-UNDO INIT 1.0.DEFINE VARIABLE R1 AS DECIMAL NO-UNDO INIT -2.0.DEFINE VARIABLE R2 AS DECIMAL NO-UNDO INIT 1.0.DEFINE VARIABLE S1 AS DECIMAL NO-UNDO.DEFINE VARIABLE S2 AS DECIMAL NO-UNDO. S1 = (R2 - R1) / X1.S2 = (I2 - I1) / Y1.DO Y = 0 TO Y1 - 1: I3 = I1 + S2 * Y. DO X = 0 TO X1 - 1: R3 = R1 + S1 * X. Z1 = R3. Z2 = I3. DO N = 0 TO 29: A = Z1 * Z1. B = Z2 * Z2. IF A + B > 4.0 THEN LEAVE. Z2 = 2 * Z1 * Z2 + I3. Z1 = A - B + R3. END. print_str = print_str + CHR(62 - N). END. print_str = print_str + '~n'.END. OUTPUT TO "C:\Temp\out.txt".MESSAGE print_str.OUTPUT CLOSE.  Example : ## PARI/GP Define function mandelbrot(): mandelbrot() = { forstep(y=-1, 1, 0.05, forstep(x=-2, 0.5, 0.0315, print1(((c)->my(z=c);for(i=1,20,z=z*z+c;if(abs(z)>2,return(" ")));"#")(x+y*I))); print());} Output: gp > mandelbrot() # # ### # ######## ######### ###### ## ## ############ # ### ################### # ############################# ############################ ################################ ################################ #################################### # # # ################################### ########### ################################### ########### ##################################### ############## #################################### #################################################### ###################################################### ######################################################################### ###################################################### #################################################### ############## #################################### ########### ##################################### ########### ################################### # # ################################### #################################### # ################################ ################################ ############################ ############################# ### ################### # ## ## ############ # ###### ######### ######## # ### # #  ## Pascal Translation of: C program mandelbrot; {IFDEF FPC} {MODE DELPHI} {ENDIF} const ixmax = 800; iymax = 800; cxmin = -2.5; cxmax = 1.5; cymin = -2.0; cymax = 2.0; maxcolorcomponentvalue = 255; maxiteration = 200; escaperadius = 2; type colortype = record red : byte; green : byte; blue : byte; end; var ix, iy : integer; cx, cy : real; pixelwidth : real = (cxmax - cxmin) / ixmax; pixelheight : real = (cymax - cymin) / iymax; filename : string = 'new1.ppm'; comment : string = '# '; outfile : textfile; color : colortype; zx, zy : real; zx2, zy2 : real; iteration : integer; er2 : real = (escaperadius * escaperadius); begin {I-} assign(outfile, filename); rewrite(outfile); if ioresult <> 0 then begin {IFDEF FPC} writeln(stderr, 'Unable to open output file: ', filename); {ELSE} writeln('ERROR: Unable to open output file: ', filename); {ENDIF} exit; end; writeln(outfile, 'P6'); writeln(outfile, ' ', comment); writeln(outfile, ' ', ixmax); writeln(outfile, ' ', iymax); writeln(outfile, ' ', maxcolorcomponentvalue); for iy := 1 to iymax do begin cy := cymin + (iy - 1)*pixelheight; if abs(cy) < pixelheight / 2 then cy := 0.0; for ix := 1 to ixmax do begin cx := cxmin + (ix - 1)*pixelwidth; zx := 0.0; zy := 0.0; zx2 := zx*zx; zy2 := zy*zy; iteration := 0; while (iteration < maxiteration) and (zx2 + zy2 < er2) do begin zy := 2*zx*zy + cy; zx := zx2 - zy2 + cx; zx2 := zx*zx; zy2 := zy*zy; iteration := iteration + 1; end; if iteration = maxiteration then begin color.red := 0; color.green := 0; color.blue := 0; end else begin color.red := 255; color.green := 255; color.blue := 255; end; write(outfile, chr(color.red), chr(color.green), chr(color.blue)); end; end; close(outfile);end. ## Perl translation / optimization of the ruby solution use Math::Complex; sub mandelbrot { my (z, c) = @_[0,0]; for (1 .. 20) { z = z * z + c; return _ if abs z > 2; }} for (my y = 1; y >= -1; y -= 0.05) { for (my x = -2; x <= 0.5; x += 0.0315) {print mandelbrot(x + y * i) ? ' ' : '#'} print "\n"} ## Phix Ascii This is included in the distribution (with some extra validation) as demo\mandle.exw ---- Mandlebrot set in ascii art demo.-- constant b=" .:,;!/>)|&IH%*#"atom r, i, c, C, z, Z, t, k for y=30 to 0 by -1 do C = y*0.1-1.5 puts(1,'\n') for x=0 to 74 do c = x*0.04-2 z = 0 Z = 0 r = c i = C k = 0 while k<112 do t = z*z-Z*Z+r Z = 2*z*Z+i z = t if z*z+Z*Z>10 then exit end if k += 1 end while puts(1,b[remainder(k,16)+1]) end for end for Graphical This is included in the distribution as demo\arwendemo\mandel.exw include arwen.ewinclude ..\arwen\dib256.ew constant HelpText = "Left-click drag with the mouse to move the image.\n"& " (the image is currently only redrawn on mouseup).\n"& "Right-click-drag with the mouse to select a region to zoom in to.\n"& "Use the mousewheel to zoom in and out (nb: can be slow).\n"& "Press F2 to select iterations, higher==more detail but slower.\n"& "Resize the window as you please, but note that going fullscreen, \n"& "especially at high iteration, may mean a quite long draw time.\n"& "Press Escape to close the window." procedure Help() void = messageBox("Mandelbrot Set",HelpText,MB_OK)end procedure integer cWidth = 520 -- client area widthinteger cHeight = 480 -- client area height constant Main = create(Window, "Mandelbrot Set", 0, 0, 50, 50, cWidth+16, cHeight+38, 0), mainHwnd = getHwnd(Main), mainDC = getPrivateDC(Main), mIter = create(Menu, "", 0, 0, 0,0,0,0,0), iterHwnd = getHwnd(mIter), mIter50 = create(MenuItem,"50 (fast, low detail)", 0, mIter, 0,0,0,0,0), mIter100 = create(MenuItem,"100 (default)", 0, mIter, 0,0,0,0,0), mIter500 = create(MenuItem,"500", 0, mIter, 0,0,0,0,0), mIter1000 = create(MenuItem,"1000 (slow, high detail)",0, mIter, 0,0,0,0,0), m50to1000 = {mIter50,mIter100,mIter500,mIter1000}, i50to1000 = { 50, 100, 500, 1000} integer mainDib = 0 constant whitePen = c_func(xCreatePen, {0,1,BrightWhite})constant NULL_BRUSH = 5, NullBrushID = c_func(xGetStockObject,{NULL_BRUSH}) atom t0integer iteratom x0, y0 -- top-left coords to drawatom scale -- controls width/zoom procedure init() x0 = -2 y0 = -1.25 scale = 2.5/cHeight iter = 100 void = c_func(xSelectObject,{mainDC,whitePen}) void = c_func(xSelectObject,{mainDC,NullBrushID})end procedureinit() function in_set(atom x, atom y)atom u,t if x>-0.75 then u = x-0.25 t = u*u+y*y return ((2*t+u)*(2*t+u)>t) else return ((x+1)*(x+1)+y*y)>0.0625 end ifend function function pixel_colour(atom x0, atom y0, integer iter)integer count = 1atom x = 0, y = 0 while (count<=iter) and (x*x+y*y<4) do count += 1 {x,y} = {x*x-y*y+x0,2*x*y+y0} end while if count<=iter then return count end if return 0end function procedure mandel(atom x0, atom y0, atom scale)atom x,yinteger c t0 = time() y = y0 for yi=1 to cHeight do x = x0 for xi=1 to cWidth do c = 0 -- default to black if in_set(x,y) then c = pixel_colour(x,y,iter) end if setDibPixel(mainDib, xi, yi, c) x += scale end for y += scale end forend procedure integer firsttime = 1integer drawBox = 0integer drawTime = 0 procedure newDib()sequence pal if mainDib!=0 then {} = deleteDib(mainDib) end if mainDib = createDib(cWidth, cHeight) pal = repeat({0,0,0},256) for i=2 to 256 do pal[i][1] = i*5 pal[i][2] = 0 pal[i][3] = i*10 end for setDibPalette(mainDib, 1, pal) mandel(x0,y0,scale) drawTime = 2end procedure procedure reDraw() setText(Main,"Please Wait...") mandel(x0,y0,scale) drawTime = 2 repaintWindow(Main,False)end procedure procedure zoom(integer z) while z do if z>0 then scale /= 1.1 z -= 1 else scale *= 1.1 z += 1 end if end while reDraw()end procedure integer dx=0,dy=0 -- mouse down coordsinteger mx=0,my=0 -- mouse move/up coords function mainHandler(integer id, integer msg, atom wParam, object lParam)integer x, y -- scratch varsatom scale10 if msg=WM_SIZE then -- (also activate/firsttime) {{},{},x,y} = getClientRect(Main) if firsttime or cWidth!=x or cHeight!=y then scale *= cWidth/x {cWidth, cHeight} = {x,y} newDib() firsttime = 0 end if elsif msg=WM_PAINT then copyDib(mainDC, 0, 0, mainDib) if drawBox then void = c_func(xRectangle, {mainDC, dx, dy, mx, my}) end if if drawTime then if drawTime=2 then setText(Main,sprintf("Mandelbrot Set [generated in %gs]",time()-t0)) else setText(Main,"Mandelbrot Set") end if drawTime -= 1 end if elsif msg=WM_CHAR then if wParam=VK_ESCAPE then closeWindow(Main) elsif wParam='+' then zoom(+1) elsif wParam='-' then zoom(-1) end if elsif msg=WM_LBUTTONDOWN or msg=WM_RBUTTONDOWN then {dx,dy} = lParam elsif msg=WM_MOUSEMOVE then if and_bits(wParam,MK_LBUTTON) then {mx,my} = lParam -- minus dx,dy (see WM_LBUTTONUP) -- DEV maybe a timer to redraw, but probably too slow... -- (this is where we need a background worker thread, -- ideally one we can direct to abandon what it is -- currently doing and start work on new x,y instead) elsif and_bits(wParam,MK_RBUTTON) then {mx,my} = lParam drawBox = 1 repaintWindow(Main,False) end if elsif msg=WM_MOUSEWHEEL then wParam = floor(wParam/#10000) if wParam>=#8000 then -- sign bit set wParam-=#10000 end if wParam = floor(wParam/120) -- (gives +/-1, usually) zoom(wParam) elsif msg=WM_LBUTTONUP then {mx,my} = lParam drawBox = 0 x0 += (dx-mx)*scale y0 += (dy-my)*scale reDraw() elsif msg=WM_RBUTTONUP then {mx,my} = lParam drawBox = 0 if mx!=dx and my!=dy then x0 += min(mx,dx)*scale y0 += min(my,dy)*scale scale *= (abs(mx-dx))/cHeight reDraw() end if elsif msg=WM_KEYDOWN then if wParam=VK_F1 then Help() elsif wParam=VK_F2 then {x,y} = getWindowRect(Main) void = c_func(xTrackPopupMenu, {iterHwnd,TPM_LEFTALIGN,x+20,y+40,0,mainHwnd,NULL}) elsif find(wParam,{VK_UP,VK_DOWN,VK_LEFT,VK_RIGHT}) then drawBox = 0 scale10 = scale*10 if wParam=VK_UP then y0 += scale10 elsif wParam=VK_DOWN then y0 -= scale10 elsif wParam=VK_LEFT then x0 += scale10 elsif wParam=VK_RIGHT then x0 -= scale10 end if reDraw() end if elsif msg=WM_COMMAND then id = find(id,m50to1000) if id!=0 then iter = i50to1000[id] reDraw() end if end if return 0end functionsetHandler({Main,mIter50,mIter100,mIter500,mIter1000}, routine_id("mainHandler")) WinMain(Main,SW_NORMAL)void = deleteDib(0) ## PHP Works with: PHP version 5.3.5 Sample output min_x=-2;max_x=1;min_y=-1;max_y=1; dim_x=400;dim_y=300; im = @imagecreate(dim_x, dim_y) or die("Cannot Initialize new GD image stream");header("Content-Type: image/png");black_color = imagecolorallocate(im, 0, 0, 0);white_color = imagecolorallocate(im, 255, 255, 255); for(y=0;y<=dim_y;y++) { for(x=0;x<=dim_x;x++) { c1=min_x+(max_x-min_x)/dim_x*x; c2=min_y+(max_y-min_y)/dim_y*y; z1=0; z2=0; for(i=0;i<100;i++) { new1=z1*z1-z2*z2+c1; new2=2*z1*z2+c2; z1=new1; z2=new2; if(z1*z1+z2*z2>=4) { break; } } if(i<100) { imagesetpixel (im, x, y, white_color); } }} imagepng(im);imagedestroy(im);  ## PicoLisp (scl 6) (let Ppm (make (do 300 (link (need 400)))) (for (Y . Row) Ppm (for (X . @) Row (let (ZX 0 ZY 0 CX (*/ (- X 250) 1.0 150) CY (*/ (- Y 150) 1.0 150) C 570) (while (and (> 4.0 (+ (*/ ZX ZX 1.0) (*/ ZY ZY 1.0))) (gt0 C)) (let Tmp (- (*/ ZX ZX 1.0) (*/ ZY ZY 1.0) (- CX)) (setq ZY (+ (*/ 2 ZX ZY 1.0) CY) ZX Tmp ) ) (dec 'C) ) (set (nth Ppm Y X) (list 0 C C)) ) ) ) (out "img.ppm" (prinl "P6") (prinl 400 " " 300) (prinl 255) (for Y Ppm (for X Y (apply wr X))) ) ) ## PostScript %!PS-Adobe-2.0%%BoundingBox: 0 0 300 200%%EndComments/origstate save def/ld {load def} bind def/m /moveto ld /g /setgray ld/dot { currentpoint 1 0 360 arc fill } bind def%%EndProlog% param/maxiter 200 def% complex manipulation/complex { 2 array astore } def/real { 0 get } def/imag { 1 get } def/cmul { /a exch def /b exch def a real b real mul a imag b imag mul sub a real b imag mul a imag b real mul add 2 array astore} def/cadd { aload pop 3 -1 roll aload pop 3 -1 roll add 3 1 roll add exch 2 array astore} def/cconj { aload pop neg 2 array astore } def/cabs2 { dup cconj cmul 0 get} def% mandel200 100 translate-200 1 100 { /x exch def -100 1 100 { /y exch def /z0 0.0 0.0 complex def 0 1 maxiter { /iter exch def x 100 div y 100 div complex z0 z0 cmul cadd dup /z0 exch def cabs2 4 gt {exit} if } for iter maxiter div g x y m dot } for} for%showpageorigstate restore%%EOF ## PowerShell  x = y = i = j = r = -16colors = [Enum]::GetValues([System.ConsoleColor]) while((y++) -lt 15){ for(x=0; (x++) -lt 84; Write-Host " " -BackgroundColor (colors[k -band 15]) -NoNewline) { i = k = r = 0 do { j = r * r - i * i -2 + x / 25 i = 2 * r * i + y / 10 r = j } while ((j * j + i * i) -lt 11 -band (k++) -lt 111) } Write-Host}  ## Processing Click on an area to zoom in. Choose areas with multiple colors for interesting zooming. double x, y, zr, zi, zr2, zi2, cr, ci, n;double zmx1, zmx2, zmy1, zmy2, f, di, dj;double fn1, fn2, fn3, re, gr, bl, xt, yt, i, j; void setup() { size(500, 500); di = 0; dj = 0; f = 10; fn1 = random(20); fn2 = random(20); fn3 = random(20); zmx1 = int(width / 4); zmx2 = 2; zmy1 = int(height / 4); zmy2 = 2;} void draw() { if (i <= width) i++; x = (i + di)/ zmx1 - zmx2; for ( j = 0; j <= height; j++) { y = zmy2 - (j + dj) / zmy1; zr = 0; zi = 0; zr2 = 0; zi2 = 0; cr = x; ci = y; n = 1; while (n < 200 && (zr2 + zi2) < 4) { zi2 = zi * zi; zr2 = zr * zr; zi = 2 * zi * zr + ci; zr = zr2 - zi2 + cr; n++; } re = (n * fn1) % 255; gr = (n * fn2) % 255; bl = (n * fn3) % 255; stroke((float)re, (float)gr, (float)bl); point((float)i, (float)j); }} void mousePressed() { background(200); xt = mouseX; yt = mouseY; di = di + xt - float(width / 2); dj = dj + yt - float(height / 2); zmx1 = zmx1 * f; zmx2 = zmx2 * (1 / f); zmy1 = zmy1 * f; zmy2 = zmy2 * (1 / f); di = di * f; dj = dj * f; i = 0; j = 0;} The sketch can be run online : here. ### Processing Python mode Click on an area to zoom in. Choose areas with multiple colors for interesting zooming. i = di = dj = 0fn1, fn2, fn3 = random(20), random(20), random(20)f = 10 def setup(): global zmx1, zmx2, zmy1, zmy2 size(500, 500) zmx1 = int(width / 4) zmx2 = 2 zmy1 = int(height / 4) zmy2 = 2 def draw(): global i if i <= width: i += 1 x = float(i + di) / zmx1 - zmx2 for j in range(height + 1): y = zmy2 - float(j + dj) / zmy1 zr = zi = zr2 = zi2 = 0 cr, ci = x, y n = 1 while n < 200 and (zr2 + zi2) < 4: zi2 = zi * zi zr2 = zr * zr zi = 2 * zi * zr + ci zr = zr2 - zi2 + cr n += 1 re = (n * fn1) % 255 gr = (n * fn2) % 255 bl = (n * fn3) % 255 stroke(re, gr, bl) point(i, j) def mousePressed(): global zmx1, zmx2, zmy1, zmy2, di, dj global i, j background(200) xt, yt = mouseX, mouseY di = di + xt - width / 2. dj = dj + yt - height / 2. zmx1 = zmx1 * f zmx2 = zmx2 * (1. / f) zmy1 = zmy1 * f zmy2 = zmy2 * (1. / f) di, dj = di * f, dj * f i = j = 0 ## Prolog SWI-Prolog has a graphic interface XPCE : :- use_module(library(pce)). mandelbrot :- new(D, window('Mandelbrot Set')), send(D, size, size(700, 650)), new(Img, image(@nil, width := 700, height := 650, kind := pixmap)), forall(between(0,699, I), ( forall(between(0,649, J), ( get_RGB(I, J, R, G, B), R1 is (R * 256) mod 65536, G1 is (G * 256) mod 65536, B1 is (B * 256) mod 65536, send(Img, pixel(I, J, colour(@default, R1, G1, B1))))))), new(Bmp, bitmap(Img)), send(D, display, Bmp, point(0,0)), send(D, open). get_RGB(X, Y, R, G, B) :- CX is (X - 350) / 150, CY is (Y - 325) / 150, Iter = 570, compute_RGB(CX, CY, 0, 0, Iter, It), IterF is It \/ It << 15, R is IterF >> 16, Iter1 is IterF - R << 16, G is Iter1 >> 8, B is Iter1 - G << 8. compute_RGB(CX, CY, ZX, ZY, Iter, IterF) :- ZX * ZX + ZY * ZY < 4, Iter > 0, !, Tmp is ZX * ZX - ZY * ZY + CX, ZY1 is 2 * ZX * ZY + CY, Iter1 is Iter - 1, compute_RGB(CX, CY, Tmp, ZY1, Iter1, IterF). compute_RGB(_CX, _CY, _ZX, _ZY, Iter, Iter). Example : ## PureBasic PureBasic forum: discussion EnableExplicit #Window1 = 0#Image1 = 0#ImgGadget = 0 #max_iteration = 64#width = 800#height = 600Define.d x0 ,y0 ,xtemp ,cr, ciDefine.i i, n, x, y ,Event ,color Dim Color.l (255)For n = 0 To 63 Color( 0 + n ) = RGB( n*4+128, 4 * n, 0 ) Color( 64 + n ) = RGB( 64, 255, 4 * n ) Color( 128 + n ) = RGB( 64, 255 - 4 * n , 255 ) Color( 192 + n ) = RGB( 64, 0, 255 - 4 * n )Next If OpenWindow(#Window1, 0, 0, #width, #height, "'Mandelbrot set' PureBasic Example", #PB_Window_SystemMenu ) If CreateImage(#Image1, #width, #height) ImageGadget(#ImgGadget, 0, 0, #width, #height, ImageID(#Image1)) For y.i = 1 To #height -1 StartDrawing(ImageOutput(#Image1)) For x.i = 1 To #width -1 x0 = 0 y0 = 0; cr = (x / #width)*2.5 -2 ci = (y / #height)*2.5 -1.25 i = 0 While (x0*x0 + y0*y0 <= 4.0) And i < #max_iteration i +1 xtemp = x0*x0 - y0*y0 + cr y0 = 2*x0*y0 + ci x0 = xtemp Wend If i >= #max_iteration Plot(x, y, 0 ) Else Plot(x, y, Color(i & 255)) EndIf Next StopDrawing() SetGadgetState(#ImgGadget, ImageID(#Image1)) Repeat Event = WindowEvent() If Event = #PB_Event_CloseWindow End EndIf Until Event = 0 Next EndIf Repeat Event = WaitWindowEvent() Until Event = #PB_Event_CloseWindow EndIf Example: ## Python Translation of the ruby solution # Python 3.0+ and 2.5+try: from functools import reduceexcept: pass def mandelbrot(a): return reduce(lambda z, _: z * z + a, range(50), 0) def step(start, step, iterations): return (start + (i * step) for i in range(iterations)) rows = (("*" if abs(mandelbrot(complex(x, y))) < 2 else " " for x in step(-2.0, .0315, 80)) for y in step(1, -.05, 41)) print("\n".join("".join(row) for row in rows))  A more "Pythonic" version of the code:  import math def mandelbrot(z , c , n=40): if abs(z) > 1000: return float("nan") elif n > 0: return mandelbrot(z ** 2 + c, c, n - 1) else: return z ** 2 + c print("\n".join(["".join(["#" if not math.isnan(mandelbrot(0, x + 1j * y).real) else " " for x in [a * 0.02 for a in range(-80, 30)]]) for y in [a * 0.05 for a in range(-20, 20)]]) )  Finally, we can also use Matplotlib to visualize the Mandelbrot set with Python: Library: matplotlib Library: NumPy from pylab import *from numpy import NaN def m(a): z = 0 for n in range(1, 100): z = z**2 + a if abs(z) > 2: return n return NaN X = arange(-2, .5, .002)Y = arange(-1, 1, .002)Z = zeros((len(Y), len(X))) for iy, y in enumerate(Y): print (iy, "of", len(Y)) for ix, x in enumerate(X): Z[iy,ix] = m(x + 1j * y) imshow(Z, cmap = plt.cm.prism, interpolation = 'none', extent = (X.min(), X.max(), Y.min(), Y.max()))xlabel("Re(c)")ylabel("Im(c)")savefig("mandelbrot_python.svg")show() Another Numpy version using masks to avoid (explicit) nested loops. Runs about 16x faster for the same resolution. import matplotlib.pyplot as pltimport numpy as np npts = 300max_iter = 100 X = np.linspace(-2, 1, 2 * npts)Y = np.linspace(-1, 1, npts) #broadcast X to a square arrayC = X[:, None] + 1J * Y#initial value is always zeroZ = np.zeros_like(C) exit_times = max_iter * np.ones(C.shape, np.int32)mask = exit_times > 0 for k in range(max_iter): Z[mask] = Z[mask] * Z[mask] + C[mask] mask, old_mask = abs(Z) < 2, mask #use XOR to detect the area which has changed exit_times[mask ^ old_mask] = k plt.imshow(exit_times.T, cmap=plt.cm.prism, extent=(X.min(), X.max(), Y.min(), Y.max()))plt.show() ### Normalized Iteration Count, Distance Estimation and Mercator Maps Actually the same, but without optimizations and therefore better suited for teaching. The escape time, normalized iteration count and exterior distance estimation algorithms are used with NumPy and complex matrices (see Wikipedia: Plotting algorithms for the Mandelbrot set and Syntopia: Distance Estimated 3D Fractals (V): The Mandelbulb & Different DE Approximations). Finally, the Mandelbrot set is also printed with a scatter plot which will be misused later for a nice effect. import numpy as npimport matplotlib.pyplot as plt d, h = 800, 600 # pixel density (= image width) and image heightn, r = 100, 500 # number of iterations and escape radius (r > 2) x = np.linspace(0, 2, num=d+1)y = np.linspace(0, 2 * h / d, num=h+1) A, B = np.meshgrid(x - 1, y - h / d)C = 2.0 * (A + B * 1j) - 0.5 Z, dZ = np.zeros_like(C), np.zeros_like(C)T, D = np.zeros(C.shape), np.zeros(C.shape) for k in range(n): M = abs(Z) < r Z[M], dZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1 T[M] = T[M] + 1 plt.imshow(T ** 0.1, cmap=plt.cm.twilight_shifted)plt.savefig("Mandelbrot_set_1.png", dpi=250) N = abs(Z) > r # normalized iteration countT[N] = T[N] - np.log2(np.log(abs(Z[N])) / np.log(r)) plt.imshow(T ** 0.1, cmap=plt.cm.twilight_shifted)plt.savefig("Mandelbrot_set_2.png", dpi=250) N = abs(Z) > 2 # exterior distance estimationD[N] = 0.5 * np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N]) plt.imshow(D ** 0.1, cmap=plt.cm.twilight_shifted)plt.savefig("Mandelbrot_set_3.png", dpi=250) X, Y = C.real, C.imagS = 150 * 2 / d # scaling depends on figsize fig, ax = plt.subplots(figsize=(8, 6))ax.scatter(X, Y, s=S**2, c=D**0.1, cmap=plt.cm.twilight_shifted)plt.savefig("Mandelbrot_plot.png", dpi=250) A small change in the above code allows Mercator maps of the Mandelbrot set (see David Madore: Mandelbrot set images and videos and Anders Sandberg: Mercator Mandelbrot Maps). The maximum magnification is exp(2*pi*h/d) = exp(2*pi*5.5) = 535.5^5.5 = 10^15, which is also the maximum for 64-bit arithmetic. Note that Anders Sandberg uses a different scaling. He uses 10^(3*h/d) = 1000^(h/d) instead of exp(2*pi*h/d) = 535.5^(h/d), so his images appear somewhat compressed in comparison (but not much, because 1000^5 = 10^15 = 535.5^5.5). With the same pixel density and the same maximum magnification, the difference in height between the maps is only about 10 percent. By misusing a scatter plot, it is possible to create zoom images of the Mandelbrot set. import numpy as npimport matplotlib.pyplot as plt d, h = 400, 2200 # pixel density (= image width) and image heightn, r = 800, 1000 # number of iterations and escape radius (r > 2) x = np.linspace(0, 2, num=d+1)y = np.linspace(0, 2 * h / d, num=h+1) A, B = np.meshgrid(x * np.pi, y * np.pi)C = 1.5 * np.exp((A + B * 1j) * 1j) - 0.74366367740001 + 0.131863214401 * 1j Z, dZ = np.zeros_like(C), np.zeros_like(C)T, D = np.zeros(C.shape), np.zeros(C.shape) for k in range(n): M = abs(Z) < r Z[M], dZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1 T[M] = T[M] + 1 plt.imshow(T.T ** 0.1, cmap=plt.cm.nipy_spectral_r)plt.savefig("Mercator_map_1.png", dpi=250) N = abs(Z) > r # normalized iteration countT[N] = T[N] - np.log2(np.log(abs(Z[N])) / np.log(r)) plt.imshow(T.T ** 0.1, cmap=plt.cm.nipy_spectral_r)plt.savefig("Mercator_map_2.png", dpi=250) N = abs(Z) > 2 # exterior distance estimationD[N] = 0.5 * np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N]) plt.imshow(D.T ** 0.1, cmap=plt.cm.nipy_spectral)plt.savefig("Mercator_map_3.png", dpi=250) X, Y = C.real, C.imagS = 150 * 2 / d * np.pi * np.exp(-B) # scaling depends on figsize fig, ax = plt.subplots(2, 2, figsize=(16, 16))ax[0, 0].scatter(X[0:300], Y[0:300], s=S[0:300]**2, c=D[0:300]**0.5, cmap=plt.cm.nipy_spectral)ax[0, 1].scatter(X[100:400], Y[100:400], s=S[0:300]**2, c=D[100:400]**0.4, cmap=plt.cm.nipy_spectral)ax[1, 0].scatter(X[200:500], Y[200:500], s=S[0:300]**2, c=D[200:500]**0.3, cmap=plt.cm.nipy_spectral)ax[1, 1].scatter(X[300:600], Y[300:600], s=S[0:300]**2, c=D[300:600]**0.2, cmap=plt.cm.nipy_spectral)plt.savefig("Mandelbrot_zoom.png", dpi=250) ## R iterate.until.escape <- function(z, c, trans, cond, max=50, response=dwell) { #we iterate all active points in the same array operation, #and keeping track of which points are still iterating. active <- seq_along(z) dwell <- z dwell[] <- 0 for (i in 1:max) { z[active] <- trans(z[active], c[active]); survived <- cond(z[active]) dwell[active[!survived]] <- i active <- active[survived] if (length(active) == 0) break } eval(substitute(response))} re = seq(-2, 1, len=500)im = seq(-1.5, 1.5, len=500)c <- outer(re, im, function(x,y) complex(real=x, imaginary=y))x <- iterate.until.escape(array(0, dim(c)), c, function(z,c)z^2+c, function(z)abs(z) <= 2, max=100)image(x) ### Mandelbrot Set with R Animation Modified Mandelbrot set animation by Jarek Tuszynski, PhD. (see: Wikipedia: R (programming_language) and R Tricks: Mandelbrot Set with R Animation) #install.packages("caTools") # install external package (if missing)library(caTools) # external package providing write.gif functionjet.colors <- colorRampPalette(c("red", "blue", "#007FFF", "cyan", "#7FFF7F", "yellow", "#FF7F00", "red", "#7F0000"))dx <- 800 # define widthdy <- 600 # define heightC <- complex(real = rep(seq(-2.5, 1.5, length.out = dx), each = dy), imag = rep(seq(-1.5, 1.5, length.out = dy), dx))C <- matrix(C, dy, dx) # reshape as square matrix of complex numbersZ <- 0 # initialize Z to zeroX <- array(0, c(dy, dx, 20)) # initialize output 3D arrayfor (k in 1:20) { # loop with 20 iterations Z <- Z^2 + C # the central difference equation X[, , k] <- exp(-abs(Z)) # capture results}write.gif(X, "Mandelbrot.gif", col = jet.colors, delay = 100) ## Racket  #lang racket (require racket/draw) (define (iterations a z i) (define z′ (+ (* z z) a)) (if (or (= i 255) (> (magnitude z′) 2)) i (iterations a z′ (add1 i)))) (define (iter->color i) (if (= i 255) (make-object color% "black") (make-object color% (* 5 (modulo i 15)) (* 32 (modulo i 7)) (* 8 (modulo i 31))))) (define (mandelbrot width height) (define target (make-bitmap width height)) (define dc (new bitmap-dc% [bitmap target])) (for* ([x width] [y height]) (define real-x (- (* 3.0 (/ x width)) 2.25)) (define real-y (- (* 2.5 (/ y height)) 1.25)) (send dc set-pen (iter->color (iterations (make-rectangular real-x real-y) 0 0)) 1 'solid) (send dc draw-point x y)) (send target save-file "mandelbrot.png" 'png)) (mandelbrot 300 200)  ## Raku (formerly Perl 6) Works with: rakudo version 2016-05-01 Variant of a Mandelbrot script from the Raku ecosystem. Produces a Portable Pixel Map to STDOUT. Redirect into a file to save it. Converted to a .png file for display here. constant @color_map = map ~*.comb(/../).map({:16(_)}), < 000000 0000fc 4000fc 7c00fc bc00fc fc00fc fc00bc fc007c fc0040 fc0000 fc4000fc7c00 fcbc00 fcfc00 bcfc00 7cfc00 40fc00 00fc00 00fc40 00fc7c 00fcbc 00fcfc00bcfc 007cfc 0040fc 7c7cfc 9c7cfc bc7cfc dc7cfc fc7cfc fc7cdc fc7cbc fc7c9cfc7c7c fc9c7c fcbc7c fcdc7c fcfc7c dcfc7c bcfc7c 9cfc7c 7cfc7c 7cfc9c 7cfcbc7cfcdc 7cfcfc 7cdcfc 7cbcfc 7c9cfc b4b4fc c4b4fc d8b4fc e8b4fc fcb4fc fcb4e8fcb4d8 fcb4c4 fcb4b4 fcc4b4 fcd8b4 fce8b4 fcfcb4 e8fcb4 d8fcb4 c4fcb4 b4fcb4b4fcc4 b4fcd8 b4fce8 b4fcfc b4e8fc b4d8fc b4c4fc 000070 1c0070 380070 540070700070 700054 700038 70001c 700000 701c00 703800 705400 707000 547000 3870001c7000 007000 00701c 007038 007054 007070 005470 003870 001c70 383870 443870543870 603870 703870 703860 703854 703844 703838 704438 705438 706038 707038607038 547038 447038 387038 387044 387054 387060 387070 386070 385470 384470505070 585070 605070 685070 705070 705068 705060 705058 705050 705850 706050706850 707050 687050 607050 587050 507050 507058 507060 507068 507070 506870506070 505870 000040 100040 200040 300040 400040 400030 400020 400010 400000401000 402000 403000 404000 304000 204000 104000 004000 004010 004020 004030004040 003040 002040 001040 202040 282040 302040 382040 402040 402038 402030402028 402020 402820 403020 403820 404020 384020 304020 284020 204020 204028204030 204038 204040 203840 203040 202840 2c2c40 302c40 342c40 3c2c40 402c40402c3c 402c34 402c30 402c2c 40302c 40342c 403c2c 40402c 3c402c 34402c 30402c2c402c 2c4030 2c4034 2c403c 2c4040 2c3c40 2c3440 2c3040>; constant MAX_ITERATIONS = 50;my width = my height = +(@*ARGS[0] // 31); sub cut(Range r, UInt n where n > 1) { r.min, * + (r.max - r.min) / (n - 1) ... r.max} my @re = cut(-2 .. 1/2, height);my @im = cut( 0 .. 5/4, width div 2 + 1) X* 1i; sub mandelbrot(Complex z is copy, Complex c) { for 1 .. MAX_ITERATIONS { z = z*z + c; return _ if z.abs > 2; } return 0;} say "P3";say "width height";say "255"; for @re -> re { put @color_map[|.reverse, |.[1..*]][^width] given my @ = map &mandelbrot.assuming(0i, *), re «+« @im;} Alternately, a more modern, faster version. use Image::PNG::Portable; my (w, h) = 800, 800;my out = Image::PNG::Portable.new: :width(w), :height(h); my maxIter = 150; my @re = scale(-2.05 .. 1.05, h);my @im = scale( -11/8 .. 11/8, w) X* 1i; race for ^(w div 2) -> x { ^h .map: -> y { my i = (mandelbrot( @re[y] + @im[x] ) / maxIter) ** .25; my @hsv = hsv2rgb(i, 1, ?i).rotate; out.set: x, y, |@hsv; out.set: w - 1 - x, y, |@hsv; }} out.write: 'Mandelbrot-set-perl6.png'; sub scale (Range r,Int n) { r.min, * + (r.max - r.min) / (n - 1) ... r.max } sub mandelbrot(Complex c) { my z = c; for ^maxIter { z = z * z + c; .return if z.abs > 2; } 0} sub hsv2rgb ( h, s, v ){ state %cache; %cache{"h|s|v"} //= do { my c = v * s; my x = c * (1 - abs( ((h*6) % 2) - 1 ) ); my m = v - c; [(do given h { when 0..^1/6 { c, x, 0 } when 1/6..^1/3 { x, c, 0 } when 1/3..^1/2 { 0, c, x } when 1/2..^2/3 { 0, x, c } when 2/3..^5/6 { x, 0, c } when 5/6..1 { c, 0, x } } ).map: ((*+m) * 255).Int] }} See Mandelbrot-set-perl6.png (offsite .png image) ## REXX ### version 1 Translation of: AWK This REXX version doesn't depend on the ASCII sequence of glyphs; an internal character string was used that mimics a part of the ASCII glyph sequence. /*REXX program generates and displays a Mandelbrot set as an ASCII art character image.*/@ = '>=<;:9876543210/.-,+*)(''&%#"!' /*the characters used in the display. */Xsize = 59; minRE = -2; maxRE = +1; stepX = (maxRE-minRE) / XsizeYsize = 21; minIM = -1; maxIM = +1; stepY = (maxIM-minIM) / Ysize do y=0 for ysize; im=minIM + stepY*y = do x=0 for Xsize; re=minRE + stepX*x; zr=re; zi=im do n=0 for 30; a=zr**2; b=zi**2; if a+b>4 then leave zi=zr*zi*2 + im; zr=a-b+re end /*n*/ = || substr(@, n+1, 1) /*append number (as a char) to  string*/ end /*x*/ say  /*display a line of character output.*/ end /*y*/ /*stick a fork in it, we're all done. */ output using the internal defaults: >>>>>>=====<<<<<<<<<<<<<<<;;;;;;:::96032:;;;;<<<<========== >>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<======= >>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<====== >>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<==== >>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<=== >>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<== >=<<<<<<<<;;;:599999999886 %78:;;<<<<<<= ><<<<;;;;;:::972456-567763 +9;;<<<<<<< ><;;;;;;::::9875& .3 *9;;;<<<<<< >;;;;;;::997564' ' 8:;;;<<<<<< >::988897735/ &89:;;;<<<<<< >::988897735/ &89:;;;<<<<<< >;;;;;;::997564' ' 8:;;;<<<<<< ><;;;;;;::::9875& .3 *9;;;<<<<<< ><<<<;;;;;:::972456-567763 +9;;<<<<<<< >=<<<<<<<<;;;:599999999886 %78:;;<<<<<<= >>=<<<<<<<<<<<;;;::::::999752 *79:;<<<<<<== >>==<<<<<<<<<<<<<;;;;::::996. &2 45335:;<<<<<<=== >>>==<<<<<<<<<<<<<<<;;;;;;:98888764 5789999:;;<<<<<==== >>>>===<<<<<<<<<<<<<<<;;;;;;;::9974 (.9::::;;<<<<<====== >>>>>===<<<<<<<<<<<<<<<<;;;;;;;:::873*079::;;;;<<<<<=======  ### version 2 This REXX version uses glyphs that are "darker" (with a white background) around the output's peripheral. /*REXX program generates and displays a Mandelbrot set as an ASCII art character image.*/@ = '█▓▒░@9876543210=.-,+*)(·&%#"!' /*the characters used in the display. */Xsize = 59; minRE = -2; maxRE = +1; stepX = (maxRE-minRE) / XsizeYsize = 21; minIM = -1; maxIM = +1; stepY = (maxIM-minIM) / Ysize do y=0 for ysize; im=minIM + stepY*y = do x=0 for Xsize; re=minRE + stepX*x; zr=re; zi=im do n=0 for 30; a=zr**2; b=zi**2; if a+b>4 then leave zi=zr*zi*2 + im; zr=a-b+re end /*n*/ = || substr(@, n+1, 1) /*append number (as a char) to  string*/ end /*x*/ say  /*display a line of character output.*/ end /*y*/ /*stick a fork in it, we're all done. */ output using the internal defaults: ██████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@@@[email protected]░░░░▒▒▒▒▓▓▓▓▓▓▓▓▓▓ █████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@@873*[email protected]@░░░░▒▒▒▒▒▓▓▓▓▓▓▓ ████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@9974 ([email protected]@@@░░▒▒▒▒▒▓▓▓▓▓▓ ███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@98888764 [email protected]░░▒▒▒▒▒▓▓▓▓ ██▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░@@@@996. &2 [email protected]░▒▒▒▒▒▒▓▓▓ ██▓▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@999752 *[email protected]░▒▒▒▒▒▒▓▓ █▓▒▒▒▒▒▒▒▒░░░@599999999886 %[email protected]░░▒▒▒▒▒▒▓ █▒▒▒▒░░░░░@@@972456-567763 +9░░▒▒▒▒▒▒▒ █▒░░░░░░@@@@9875& .3 *9░░░▒▒▒▒▒▒ █░░░░░░@@997564· · [email protected]░░░▒▒▒▒▒▒ █@@988897735= &[email protected]░░░▒▒▒▒▒▒ █@@988897735= &[email protected]░░░▒▒▒▒▒▒ █░░░░░░@@997564· · [email protected]░░░▒▒▒▒▒▒ █▒░░░░░░@@@@9875& .3 *9░░░▒▒▒▒▒▒ █▒▒▒▒░░░░░@@@972456-567763 +9░░▒▒▒▒▒▒▒ █▓▒▒▒▒▒▒▒▒░░░@599999999886 %[email protected]░░▒▒▒▒▒▒▓ ██▓▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@999752 *[email protected]░▒▒▒▒▒▒▓▓ ██▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░@@@@996. &2 [email protected]░▒▒▒▒▒▒▓▓▓ ███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@98888764 [email protected]░░▒▒▒▒▒▓▓▓▓ ████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@9974 ([email protected]@@@░░▒▒▒▒▒▓▓▓▓▓▓ █████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@@873*[email protected]@░░░░▒▒▒▒▒▓▓▓▓▓▓▓  ### version 3 This REXX version produces a larger output (it uses the full width of the terminal screen (less one), and the height is one-half of the width. /*REXX program generates and displays a Mandelbrot set as an ASCII art character image.*/@ = '█▓▒░@9876543210=.-,+*)(·&%#"!' /*the characters used in the display. */parse arg Xsize Ysize . /*obtain optional arguments from the CL*/if Xsize=='' then Xsize=linesize() - 1 /*X: the (usable) linesize (minus 1).*/if Ysize=='' then Ysize=Xsize%2 + (Xsize//2==1) /*Y: half the linesize (make it even).*/minRE = -2; maxRE = +1; stepX = (maxRE-minRE) / XsizeminIM = -1; maxIM = +1; stepY = (maxIM-minIM) / Ysize do y=0 for ysize; im=minIM + stepY*y = do x=0 for Xsize; re=minRE + stepX*x; zr=re; zi=im do n=0 for 30; a=zr**2; b=zi**2; if a+b>4 then leave zi=zr*zi*2 + im; zr=a-b+re end /*n*/ = || substr(@, n+1, 1) /*append number (as a char) to  string*/ end /*x*/ say  /*display a line of character output.*/ end /*y*/ /*stick a fork in it, we're all done. */ output using the internal defaults: ████████▓▓▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░@@@@985164([email protected]░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓▓▓▓ ███████▓▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@@@[email protected]░░░░░░▒▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓▓ ███████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@@[email protected]@@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓ ██████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@@985 2. [email protected]@@@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓ █████▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@999874 *[email protected]@@@@░░░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓▓ █████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@999998873 [email protected]@@@@░░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓ ████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@98888888764 #[email protected]@░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓ ████▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@@@9343,665 322= [email protected]░░▒▒▒▒▒▒▒▒▓▓▓▓▓ ███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@@@@@9986 + 32 ,56554)[email protected]░▒▒▒▒▒▒▒▒▒▓▓▓▓ ███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░@@@@@@@999863 + 2· ",[email protected]░░▒▒▒▒▒▒▒▒▓▓▓▓ ███▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@@@@@9998763  [email protected]@░▒▒▒▒▒▒▒▒▒▓▓▓ ██▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@@@@@999986.2  [email protected]@░░▒▒▒▒▒▒▒▒▒▓▓ ██▓▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@[email protected]@@99999887 [email protected]░░▒▒▒▒▒▒▒▒▒▓▓ ██▒▒▒▒▒▒▒▒▒▒░░░░░@@9717888877888888763. [email protected]░░░▒▒▒▒▒▒▒▒▒▓ █▓▒▒▒▒▒▒░░░░░░░@@@996)566761467777762 [email protected]░░░▒▒▒▒▒▒▒▒▒▓ █▓▒▒▒▒░░░░░░░░@@@@99763 & 42&..366651· [email protected]░░░░▒▒▒▒▒▒▒▒▓ █▒▒▒░░░░░░░░@@@@@@98864* )  343 [email protected]░░░░▒▒▒▒▒▒▒▒▒ █▒▒░░░░░░░░@@@@@@988753. 11 #[email protected]░░░░▒▒▒▒▒▒▒▒▒ █▒░░░░░░░░@@@@@9877650 - [email protected]░░░░▒▒▒▒▒▒▒▒▒ █░░░░░░░░@9999887%413+ % &[email protected]@░░░░▒▒▒▒▒▒▒▒▒ █░@@@@@89999888763 % ( [email protected]@░░░░▒▒▒▒▒▒▒▒▒ █@@99872676676422 [email protected]@░░░░▒▒▒▒▒▒▒▒▒ █@@99872676676422 [email protected]@░░░░▒▒▒▒▒▒▒▒▒ █░@@@@@89999888763 % ( [email protected]@░░░░▒▒▒▒▒▒▒▒▒ █░░░░░░░░@9999887%413+ % &[email protected]@░░░░▒▒▒▒▒▒▒▒▒ █▒░░░░░░░░@@@@@9877650 - [email protected]░░░░▒▒▒▒▒▒▒▒▒ █▒▒░░░░░░░░@@@@@@988753. 11 #[email protected]░░░░▒▒▒▒▒▒▒▒▒ █▒▒▒░░░░░░░░@@@@@@98864* )  343 [email protected]░░░░▒▒▒▒▒▒▒▒▒ █▓▒▒▒▒░░░░░░░░@@@@99763 & 42&..366651· [email protected]░░░░▒▒▒▒▒▒▒▒▓ █▓▒▒▒▒▒▒░░░░░░░@@@996)566761467777762 [email protected]░░░▒▒▒▒▒▒▒▒▒▓ ██▒▒▒▒▒▒▒▒▒▒░░░░░@@9717888877888888763. [email protected]░░░▒▒▒▒▒▒▒▒▒▓ ██▓▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@[email protected]@@99999887 [email protected]░░▒▒▒▒▒▒▒▒▒▓▓ ██▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@@@@@999986.2  [email protected]@░░▒▒▒▒▒▒▒▒▒▓▓ ███▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░@@@@@@@@@@9998763  [email protected]@░▒▒▒▒▒▒▒▒▒▓▓▓ ███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░@@@@@@@999863 + 2· ",[email protected]░░▒▒▒▒▒▒▒▒▓▓▓▓ ███▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░@@@@@9986 + 32 ,56554)[email protected]░▒▒▒▒▒▒▒▒▒▓▓▓▓ ████▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░@@@@9343,665 322= [email protected]░░▒▒▒▒▒▒▒▒▓▓▓▓▓ ████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@98888888764 #[email protected]@░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓ █████▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@999998873 [email protected]@@@@░░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓ █████▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@999874 *[email protected]@@@@░░░░▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓▓ ██████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@@985 2. [email protected]@@@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓ ███████▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░@@@@[email protected]@@░░░░░░▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓ ███████▓▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░@@@@[email protected]░░░░░░▒▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▓▓  This REXX program makes use of linesize REXX program (or BIF) which is used to determine the screen width (or linesize) of the terminal (console). The LINESIZE.REX REXX program is included here ──► LINESIZE.REX. ## Ring  load "guilib.ring" new qapp { win1 = new qwidget() { setwindowtitle("Mandelbrot set") setgeometry(100,100,500,500) label1 = new qlabel(win1) { setgeometry(10,10,400,400) settext("") } new qpushbutton(win1) { setgeometry(200,400,100,30) settext("draw") setclickevent("draw()") } show() } exec() } func draw p1 = new qpicture() color = new qcolor() { setrgb(0,0,255,255) } pen = new qpen() { setcolor(color) setwidth(1) } new qpainter() { begin(p1) setpen(pen) x1=300 y1=250 i1=-1 i2=1 r1=-2 r2=1 s1=(r2-r1)/x1 s2=(i2-i1)/y1 for y=0 to y1 i3=i1+s2*y for x=0 to x1 r3=r1+s1*x z1=r3 z2=i3 for n=0 to 30 a=z1*z1 b=z2*z2 if a+b>4 exit ok z2=2*z1*z2+i3 z1=a-b+r3 next if n != 31 drawpoint(x,y) ok next next endpaint() } label1 { setpicture(p1) show() }  Output: ## Ruby Text only, prints an 80-char by 41-line depiction. Found here. require 'complex' def mandelbrot(a) Array.new(50).inject(0) { |z,c| z*z + a }end (1.0).step(-1,-0.05) do |y| (-2.0).step(0.5,0.0315) do |x| print mandelbrot(Complex(x,y)).abs < 2 ? '*' : ' ' end putsend Translation of: Tcl # frozen_string_literal: true require_relative 'raster_graphics' class RGBColour def self.mandel_colour(i) self.new( 16*(i % 15), 32*(i % 7), 8*(i % 31) ) endend class Pixmap def self.mandelbrot(width, height) mandel = Pixmap.new(width,height) pb = ProgressBar.new(width) if DEBUG width.times do |x| height.times do |y| x_ish = Float(x - width*11/15) / (width/3) y_ish = Float(y - height/2) / (height*3/10) mandel[x,y] = RGBColour.mandel_colour(mandel_iters(x_ish, y_ish)) end pb.update(x) if DEBUG end pb.close if DEBUG mandel end def self.mandel_iters(cx,cy) x = y = 0.0 count = 0 while Math.hypot(x,y) < 2 and count < 255 x, y = (x**2 - y**2 + cx), (2*x*y + cy) count += 1 end count endend Pixmap.mandelbrot(300,300).save('mandel.ppm') Library: RubyGems Library: JRubyArt JRubyArt is a port of processing to ruby  # frozen_string_literal: true def setup sketch_title 'Mandelbrot' load_pixels no_loopend def draw grid(900, 600) do |x, y| const = Complex( map1d(x, (0...900), (-3..1.5)), map1d(y, (0...600), (-1.5..1.5)) ) pixels[x + y * 900] = color( constrained_map(mandel(const, 20), (5..20), (255..0)) ) end update_pixelsend def mandel(z, max) score = 0 const = z while score < max # z = z^2 + c z *= z z += const break if z.abs > 2 score += 1 end scoreend def settings size(900, 600)end  ## Rust Dependencies: image, num-complex extern crate image;extern crate num_complex; use std::fs::File;use num_complex::Complex; fn main() { let max_iterations = 256u16; let img_side = 800u32; let cxmin = -2f32; let cxmax = 1f32; let cymin = -1.5f32; let cymax = 1.5f32; let scalex = (cxmax - cxmin) / img_side as f32; let scaley = (cymax - cymin) / img_side as f32; // Create a new ImgBuf let mut imgbuf = image::ImageBuffer::new(img_side, img_side); // Calculate for each pixel for (x, y, pixel) in imgbuf.enumerate_pixels_mut() { let cx = cxmin + x as f32 * scalex; let cy = cymin + y as f32 * scaley; let c = Complex::new(cx, cy); let mut z = Complex::new(0f32, 0f32); let mut i = 0; for t in 0..max_iterations { if z.norm() > 2.0 { break; } z = z * z + c; i = t; } *pixel = image::Luma([i as u8]); } // Save image imgbuf.save("fractal.png").unwrap();} ## Sass/SCSS  canvasWidth: 200;canvasHeight: 200;iterations: 20;xCorner: -2;yCorner: -1.5;zoom: 3;data: ()!global;@mixin plot (x,y,count){ index: (y * canvasWidth + x) * 4; r: count * -12 + 255; g: count * -12 + 255; b: count * -12 + 255; data: append(data, x + px y + px 0 rgb(r,g,b), comma)!global;} @for x from 1 to canvasWidth { @for y from 1 to canvasHeight { count: 0; size: 0; cx: xCorner + ((x * zoom) / canvasWidth); cy: yCorner + ((y * zoom) / canvasHeight); zx: 0; zy: 0; @while count < iterations and size <= 4 { count: count + 1; temp: (zx * zx) - (zy * zy); zy: (2 * zx * zy) + cy; zx: temp + cx; size: (zx * zx) + (zy * zy); } @include plot(x, y, count); }}.set { height: 1px; width: 1px; position: absolute; top: 50%; left: 50%; transform: translate(canvasWidth*0.5px, canvasWidth*0.5px); box-shadow: data;}  ## Scala Works with: Scala version 2.8 Uses RgbBitmap from Basic Bitmap Storage task and Complex number class from this programming task. import org.rosettacode.ArithmeticComplex._import java.awt.Color object Mandelbrot{ def generate(width:Int =600, height:Int =400)={ val bm=new RgbBitmap(width, height) val maxIter=1000 val xMin = -2.0 val xMax = 1.0 val yMin = -1.0 val yMax = 1.0 val cx=(xMax-xMin)/width val cy=(yMax-yMin)/height for(y <- 0 until bm.height; x <- 0 until bm.width){ val c=Complex(xMin+x*cx, yMin+y*cy) val iter=itMandel(c, maxIter, 4) bm.setPixel(x, y, getColor(iter, maxIter)) } bm } def itMandel(c:Complex, imax:Int, bailout:Int):Int={ var z=Complex() for(i <- 0 until imax){ z=z*z+c; if(z.abs > bailout) return i } imax; } def getColor(iter:Int, max:Int):Color={ if (iter==max) return Color.BLACK var c=3*math.log(iter)/math.log(max-1.0) if(c<1) new Color((255*c).toInt, 0, 0) else if(c<2) new Color(255, (255*(c-1)).toInt, 0) else new Color(255, 255, (255*(c-2)).toInt) }} Read–eval–print loop import scala.swing._import javax.swing.ImageIconval imgMandel=Mandelbrot.generate()val mainframe=new MainFrame(){title="Test"; visible=true contents=new Label(){icon=new ImageIcon(imgMandel.image)}} ## Scheme This implementation writes an image of the Mandelbrot set to a plain pgm file. The set itself is drawn in white, while the exterior is drawn in black. (define x-centre -0.5)(define y-centre 0.0)(define width 4.0)(define i-max 800)(define j-max 600)(define n 100)(define r-max 2.0)(define file "out.pgm")(define colour-max 255)(define pixel-size (/ width i-max))(define x-offset (- x-centre (* 0.5 pixel-size (+ i-max 1))))(define y-offset (+ y-centre (* 0.5 pixel-size (+ j-max 1)))) (define (inside? z) (define (*inside? z-0 z n) (and (< (magnitude z) r-max) (or (= n 0) (*inside? z-0 (+ (* z z) z-0) (- n 1))))) (*inside? z 0 n)) (define (boolean->integer b) (if b colour-max 0)) (define (pixel i j) (boolean->integer (inside? (make-rectangular (+ x-offset (* pixel-size i)) (- y-offset (* pixel-size j)))))) (define (plot) (with-output-to-file file (lambda () (begin (display "P2") (newline) (display i-max) (newline) (display j-max) (newline) (display colour-max) (newline) (do ((j 1 (+ j 1))) ((> j j-max)) (do ((i 1 (+ i 1))) ((> i i-max)) (begin (display (pixel i j)) (newline)))))))) (plot) ## Scratch ## Seed7  include "seed7_05.s7i"; include "float.s7i"; include "complex.s7i"; include "draw.s7i"; include "keybd.s7i"; # Display the Mandelbrot set, that are points z[0] in the complex plane # for which the sequence z[n+1] := z[n] ** 2 + z[0] (n >= 0) is bounded. # Since this program is computing intensive it should be compiled with # hi comp -O2 mandelbr const integer: pix is 200; const integer: max_iter is 256; var array color: colorTable is max_iter times black; const func integer: iterate (in complex: z0) is func result var integer: iter is 1; local var complex: z is complex.value; begin z := z0; while sqrAbs(z) < 4.0 and # not diverged iter < max_iter do # not converged z *:= z; z +:= z0; incr(iter); end while; end func; const proc: displayMandelbrotSet (in complex: center, in float: zoom) is func local var integer: x is 0; var integer: y is 0; var complex: z0 is complex.value; begin for x range -pix to pix do for y range -pix to pix do z0 := center + complex(flt(x) * zoom, flt(y) * zoom); point(x + pix, y + pix, colorTable[iterate(z0)]); end for; end for; end func; const proc: main is func local const integer: num_pix is 2 * pix + 1; var integer: col is 0; begin screen(num_pix, num_pix); clear(curr_win, black); KEYBOARD := GRAPH_KEYBOARD; for col range 1 to pred(max_iter) do colorTable[col] := color(65535 - (col * 5003) mod 65535, (col * 257) mod 65535, (col * 2609) mod 65535); end for; displayMandelbrotSet(complex(-0.75, 0.0), 1.3 / flt(pix)); DRAW_FLUSH; readln(KEYBOARD); end func;  Original source: [1] ## SenseTalk put 0 into oReal # Real originput 0 into oImag # Imaginary originput 0.5 into mag # Magnification put oReal - .8 / mag into leftRealput oImag + .5 / mag into topImagput 1 / 200 / mag into inc put [ (0,255,255), # aqua (0,0,255), # blue (255,0,255), # fuchsia (128,128,128), # gray (0,128,0), # green (0,255,0), # lime (128,0,0), # maroon (0,0,128), # navy (128,128,0), # olive (128,0,128), # purple (255,0,0), # red (192,192,192), # silver (0,128,128), # teal (255,255,255), # white (255,255,0) # yellow] into colors put "mandelbrot.ppm" into myFile open file myFile for writingwrite "P3" & return to file myFile # PPM file magic numberwrite "320 200" & return to file myFile # Width and heightwrite "255" & return to file myFile # Max value in color channels put topImag into cImagrepeat with each item in 1 .. 200 put leftReal into cReal repeat with each item in 1 .. 320 put 0 into zReal put 0 into zImag put 0 into count put 0 into size repeat at least once until size > 2 or count = 100 put zReal squared + zImag squared * -1 into newZreal put zReal * zImag + zReal * zImag into newZimag put newZreal + cReal into zReal put newZimag + cImag into zImag put sqrt(zReal squared + zImag squared) into size add 1 to count end repeat if size > 2 then # Outside the set - colorize put item count mod 15 + 1 of colors into color write color joined by " " to file myFile write return to file myFile else # Inside the set - black write "0 0 0" & return to file myFile end if add inc to cReal end repeat subtract inc from cImagend repeat close file myFile  ## SequenceL SequenceL Code for Computing and Coloring: import <Utilities/Complex.sl>;import <Utilities/Sequence.sl>;import <Utilities/Math.sl>; COLOR_STRUCT ::= (R: int(0), G: int(0), B: int(0));rgb(r(0), g(0), b(0)) := (R: r, G: g, B: b); RESULT_STRUCT ::= (FinalValue: Complex(0), Iterations: int(0));makeResult(val(0), iters(0)) := (FinalValue: val, Iterations: iters); zSquaredOperation(startingNum(0), currentNum(0)) := complexAdd(startingNum, complexMultiply(currentNum, currentNum)); zSquared(minX(0), maxX(0), resolutionX(0), minY(0), maxY(0), resolutionY(0), maxMagnitude(0), maxIters(0))[Y,X] := let stepX := (maxX - minX) / resolutionX; stepY := (maxY - minY) / resolutionY; currentX := X * stepX + minX; currentY := Y * stepY + minY; in operateUntil(zSquaredOperation, makeComplex(currentX, currentY), makeComplex(currentX, currentY), maxMagnitude, 0, maxIters) foreach Y within 0 ... (resolutionY - 1), X within 0 ... (resolutionX - 1); operateUntil(operation(0), startingNum(0), currentNum(0), maxMagnitude(0), currentIters(0), maxIters(0)) := let operated := operation(startingNum, currentNum); in makeResult(currentNum, maxIters) when currentIters >= maxIters else makeResult(currentNum, currentIters) when complexMagnitude(currentNum) >= maxMagnitude else operateUntil(operation, startingNum, operated, maxMagnitude, currentIters + 1, maxIters); //region Smooth Coloring COLOR_COUNT := size(colorSelections); colorRange := range(0, 255, 1); colors := let first[i] := rgb(0, 0, i) foreach i within colorRange; second[i] := rgb(i, i, 255) foreach i within colorRange; third[i] := rgb(255, 255, i) foreach i within reverse(colorRange); fourth[i] := rgb(255, i, 0) foreach i within reverse(colorRange); fifth[i] := rgb(i, 0, 0) foreach i within reverse(colorRange); red[i] := rgb(i, 0, 0) foreach i within colorRange; redR[i] := rgb(i, 0, 0) foreach i within reverse(colorRange); green[i] := rgb(0, i, 0) foreach i within colorRange; greenR[i] :=rgb(0, i, 0) foreach i within reverse(colorRange); blue[i] := rgb(0, 0, i) foreach i within colorRange; blueR[i] := rgb(0, 0, i) foreach i within reverse(colorRange); in //red ++ redR ++ green ++ greenR ++ blue ++ blueR; first ++ second ++ third ++ fourth ++ fifth; //first ++ fourth; colorSelections := range(1, size(colors), 30); getSmoothColorings(zSquaredResult(2), maxIters(0))[Y,X] := let current := zSquaredResult[Y,X]; zn := complexMagnitude(current.FinalValue); nu := ln(ln(zn) / ln(2)) / ln(2); result := abs(current.Iterations + 1 - nu); index := floor(result); rem := result - index; color1 := colorSelections[(index mod COLOR_COUNT) + 1]; color2 := colorSelections[((index + 1) mod COLOR_COUNT) + 1]; in rgb(0, 0, 0) when current.Iterations = maxIters else colors[color1] when color2 < color1 else colors[floor(linearInterpolate(color1, color2, rem))]; linearInterpolate(v0(0), v1(0), t(0)) := (1 - t) * v0 + t * v1; //endregion C++ Driver Code: Library: CImg #include "SL_Generated.h"#include "../../../ThirdParty/CImg/CImg.h" using namespace std;using namespace cimg_library; int main(int argc, char ** argv){ int cores = 0; Sequence<Sequence<_sl_RESULT_STRUCT> > computeResult; Sequence<Sequence<_sl_COLOR_STRUCT> > colorResult; sl_init(cores); int maxIters = 1000; int imageWidth = 1920; int imageHeight = 1200; double maxMag = 256; double xmin = -2.5; double xmax = 1.0; double ymin = -1.0; double ymax = 1.0; CImg<unsigned char> visu(imageWidth, imageHeight, 1, 3); CImgDisplay draw_disp(visu, "Mandelbrot Fractal in SequenceL"); bool redraw = true; SLTimer t; double computeTime; double colorTime; double renderTime; while(!draw_disp.is_closed()) { if(redraw) { redraw = false; t.start(); sl_zSquared(xmin, xmax, imageWidth, ymin, ymax, imageHeight, maxMag, maxIters, cores, computeResult); t.stop(); computeTime = t.getTime(); t.start(); sl_getSmoothColorings(computeResult, maxIters, cores, colorResult); t.stop(); colorTime = t.getTime(); t.start(); visu.fill(0); for(int i = 1; i <= colorResult.size(); i++) { for(int j = 1; j <= colorResult[i].size(); j++) { visu(j-1,i-1,0,0) = colorResult[i][j].R; visu(j-1,i-1,0,1) = colorResult[i][j].G; visu(j-1,i-1,0,2) = colorResult[i][j].B; } } visu.display(draw_disp); t.stop(); renderTime = t.getTime(); draw_disp.set_title("X:[%f, %f] Y:[%f, %f] | Mandelbrot Fractal in SequenceL | Compute Time: %f | Color Time: %f | Render Time: %f | Total FPS: %f", xmin, xmax, ymin, ymax, cores, computeTime, colorTime, renderTime, 1 / (computeTime + colorTime + renderTime)); } draw_disp.wait(); double xdiff = (xmax - xmin); double ydiff = (ymax - ymin); double xcenter = ((1.0 * draw_disp.mouse_x()) / imageWidth) * xdiff + xmin; double ycenter = ((1.0 * draw_disp.mouse_y()) / imageHeight) * ydiff + ymin; if(draw_disp.button()&1) { redraw = true; xmin = xcenter - (xdiff / 4); xmax = xcenter + (xdiff / 4); ymin = ycenter - (ydiff / 4); ymax = ycenter + (ydiff / 4); } else if(draw_disp.button()&2) { redraw = true; xmin = xcenter - xdiff; xmax = xcenter + xdiff; ymin = ycenter - ydiff; ymax = ycenter + ydiff; } } sl_done(); return 0;} Output: ## Sidef func mandelbrot(z) { var c = z { z = (z*z + c) z.abs > 2 && return true } * 20 return false} for y range(1, -1, -0.05) { for x in range(-2, 0.5, 0.0315) { print(mandelbrot(x + y.i) ? ' ' : '#') } print "\n"} ## Simula Translation of: Scheme BEGIN REAL XCENTRE, YCENTRE, WIDTH, RMAX, XOFFSET, YOFFSET, PIXELSIZE; INTEGER N, IMAX, JMAX, COLOURMAX; TEXT FILENAME; CLASS COMPLEX(RE,IM); REAL RE,IM;; REF(COMPLEX) PROCEDURE ADD(A,B); REF(COMPLEX) A,B; ADD :- NEW COMPLEX(A.RE + B.RE, A.IM + B.IM); REF(COMPLEX) PROCEDURE SUB(A,B); REF(COMPLEX) A,B; SUB :- NEW COMPLEX(A.RE - B.RE, A.IM - B.IM); REF(COMPLEX) PROCEDURE MUL(A,B); REF(COMPLEX) A,B; MUL :- NEW COMPLEX(A.RE * B.RE - A.IM * B.IM, A.RE * B.IM + A.IM * B.RE); REF(COMPLEX) PROCEDURE DIV(A,B); REF(COMPLEX) A,B; BEGIN REAL TMP; TMP := B.RE * B.RE + B.IM * B.IM; DIV :- NEW COMPLEX((A.RE * B.RE + A.IM * B.IM) / TMP, (A.IM * B.RE - A.RE * B.IM) / TMP); END DIV; REF(COMPLEX) PROCEDURE RECTANGULAR(RE,IM); REAL RE,IM; RECTANGULAR :- NEW COMPLEX(RE,IM); REAL PROCEDURE MAGNITUDE(CX); REF(COMPLEX) CX; MAGNITUDE := SQRT(CX.RE**2 + CX.IM**2); BOOLEAN PROCEDURE INSIDEP(Z); REF(COMPLEX) Z; BEGIN BOOLEAN PROCEDURE INSIDE(Z0,Z,N); REAL N; REF(COMPLEX) Z,Z0; INSIDE := MAGNITUDE(Z) < RMAX AND THEN N = 0 OR ELSE INSIDE(Z0, ADD(Z0,MUL(Z,Z)), N-1); INSIDEP := INSIDE(Z, NEW COMPLEX(0,0), N); END INSIDEP; INTEGER PROCEDURE BOOL2INT(B); BOOLEAN B; BOOL2INT := IF B THEN COLOURMAX ELSE 0; INTEGER PROCEDURE PIXEL(I,J); INTEGER I,J; PIXEL := BOOL2INT(INSIDEP(RECTANGULAR(XOFFSET + PIXELSIZE * I, YOFFSET - PIXELSIZE * J))); PROCEDURE PLOT; BEGIN REF (OUTFILE) OUTF; INTEGER J,I; OUTF :- NEW OUTFILE(FILENAME); OUTF.OPEN(BLANKS(132)); OUTF.OUTTEXT("P2"); OUTF.OUTIMAGE; OUTF.OUTINT(IMAX,0); OUTF.OUTIMAGE; OUTF.OUTINT(JMAX,0); OUTF.OUTIMAGE; OUTF.OUTINT(COLOURMAX,0); OUTF.OUTIMAGE; FOR J := 1 STEP 1 UNTIL JMAX DO BEGIN FOR I := 1 STEP 1 UNTIL IMAX DO BEGIN OUTF.OUTINT(PIXEL(I,J),0); OUTF.OUTIMAGE; END; END; OUTF.CLOSE; END PLOT; XCENTRE := -0.5; YCENTRE := 0.0; WIDTH := 4.0; IMAX := 800; JMAX := 600; N := 100; RMAX := 2.0; FILENAME :- "out.pgm"; COLOURMAX := 255; PIXELSIZE := WIDTH / IMAX; XOFFSET := XCENTRE - (0.5 * PIXELSIZE * (IMAX + 1)); YOFFSET := YCENTRE + (0.5 * PIXELSIZE * (JMAX + 1)); OUTTEXT("OUTPUT WILL BE WRITTEN TO "); OUTTEXT(FILENAME); OUTIMAGE; PLOT;END; ## Spin Works with: BST/BSTC Works with: FastSpin/FlexSpin Works with: HomeSpun Works with: OpenSpin con _clkmode = xtal1+pll16x _clkfreq = 80_000_000 xmin=-8601 ' int(-2.1*4096) xmax=2867 ' int( 0.7*4096) ymin=-4915 ' int(-1.2*4096) ymax=4915 ' int( 1.2*4096) maxiter=25 obj ser : "FullDuplexSerial" pub main | c,cx,cy,dx,dy,x,y,x2,y2,iter ser.start(31, 30, 0, 115200) dx:=(xmax-xmin)/79 dy:=(ymax-ymin)/24 cy:=ymin repeat while cy=<ymax cx:=xmin repeat while cx=<xmax x:=0 y:=0 x2:=0 y2:=0 iter:=0 repeat while iter=<maxiter and x2+y2=<16384 y:=((x*y)~>11)+cy x:=x2-y2+cx iter+=1 x2:=(x*x)~>12 y2:=(y*y)~>12 cx+=dx ser.tx(iter+32) cy+=dy ser.str(string(13,10)) waitcnt(_clkfreq+cnt) ser.stop Output: !!!!!!!!!!!!!!!"""""""""""""####################################"""""""""""""""" !!!!!!!!!!!!!"""""""""#######################$$$%'+)%%%$#####"""""""""""
!!!!!!!!!!!"""""""#######################%%%&&(+,)++&%$$######"""""" !!!!!!!!!"""""#######################$$%%%%&')*5:/+('&%%$$#######""" !!!!!!!!""""#####################$$%%%&&&''),:::::::,'&%%%%%########
!!!!!!!"""####################%%%&'())((())*,::::::/+))('&&&&)'%$$###### !!!!!!""###################$$$$%%%%%%&&&'+.:::/::::::::::::::::/++:..93%%##### !!!!!"################$$$%%%%%%%%%%&&&&'),+2:::::::::::::::::::::::::1(&&%$$#### !!!!"##########$$$$%%&(-(''''''''''''(*,5::::::::::::::::::::::::::::+)-&%$$### !!!!####%%%%%&'(*-:1.+.:-4+))**:::::::::::::::::::::::::::::::4-(&%$$## !!!!#$$$$%%%%%%'''++.6:::::::::8/0::::::::::::::::::::::::::::::::3(%%$$$$# !!!#$$$%&&&&''()/-5.5::::::::::::::::::::::::::::::::::::::::::::::'&%%#
!!!(**+/+:523/80/46::::::::::::::::::::::::::::::::::::::::::::::::4+)'&&%%#
!!!#$$%&&&&''().-2.:::::::::::::::::::::::::::::::::::::::::::::::'&%%$$$$# !!!!#$$$$%%%%%&'''/,.7::::::::::/0::::::::::::::::::::::::::::::::0'%%$$$$# !!!!####$$$$%%%%%&'(*-:2.,/:-5+))**:::::::::::::::::::::::::::::::4+(&%$$$## !!!!"##########$%%&(-(''''(''''''((*,4:::::::::::::::::::::::::::4+).&%$$### !!!!!"################$$$%%%%%%%%%%&&&&'):,4:::::::::::::::::::::::::/('&%%$####
!!!!!!""##################$$%%%%%%&&&'*.:::0::::::::::::::::1,,://9)%%##### !!!!!!!"""####################$$$$%%%&(())((()**-::::::/+)))'&&&')'%$$######
!!!!!!!!""""#####################$$%%%&&&''(,:::::::+'&&%%%%%$$$######## !!!!!!!!!"""""#######################$$%%%%&')*7:0+('&%%%$$$$#######""" !!!!!!!!!!!"""""""######################$$$$%%%&&(+-).*&%$$######"""""" !!!!!!!!!!!!!"""""""""#######################$$%%'3(%%%$$$######""""""""""
!!!!!!!!!!!!!!!""""""""""""#####################################""""""""""""""""


## SPL

w,h = #.scrsize()sfx = -2.5; sfy = -2*h/w; fs = 4/w#.aaoff()> y, 1...h  > x, 1...w    fx = sfx + x*fs; fy = sfy + y*fs    #.drawpoint(x,y,color(fx,fy):3)  <<color(x,y)=  zr = x; zi = y; n = 0; maxn = 150  > zr*zr+zi*zi<4 & n<maxn    zrn = zr*zr-zi*zi+x; zin = 2*zr*zi+y    zr = zrn; zi = zin; n += 1  <  ? n=maxn, <= 0,0,0  <= #.hsv2rgb(n/maxn*360,1,1):3.

## Tcl

Library: Tk

This code makes extensive use of Tk's built-in photo image system, which provides a 32-bit RGBA plotting surface that can be then quickly drawn in any number of places in the application. It uses a computational color scheme that was easy to code...

Output:

## XSLT

The fact that you can create an image of the Mandelbrot Set with XSLT is sometimes under-appreciated. However, it has been discussed extensively on the internet so is best reproduced here, and the code can be executed directly in your browser at that site.

 <?xml version="1.0" encoding="UTF-8"?><xsl:stylesheet`