Mandelbrot set
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You are encouraged to solve this task according to the task description, using any language you may know.
- Task
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
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)
#
..
.####
. # .##.
##*###############.
#.##################
.######################.
######. #######################
##########.######################
##############################################
##########.######################
######. #######################
.######################.
#.##################
##*###############.
. # .##.
.####
..
AArch64 Assembly
Compiler: GNU Compiler Collection (v12.2.0)
The size of the drawn image is adjustable through xsize and ysize, and the precision through limit.
#include <stdio.h>
.globl main
.section .text
.macro NEWLINE
mov x0, #10
stp x9, x10, [sp, #-16]!
bl putchar
ldp x9, x10, [sp], 16
.endm
.macro PRINTCHAR p
mov x1, \p
mov x0, #64
sub x0, x0, x1
stp x9, x10, [sp, #-16]!
bl putchar
ldp x9, x10, [sp], 16
.endm
xsize .req x9
xsize_w .req w9
ysize .req x10
ysize_w .req w10
min_imag .req s8
max_imag .req s9
min_real .req s10
max_real .req s9
imag .req s11
real .req s12
step_x .req s13
step_y .req s14
zi .req s15
zr .req s16
a .req s17
b .req s18
ftemp_1 .req s19
ftemp_2 .req s20
y .req x19
y_w .req w19
x .req x20
x_w .req w20
n .req x21
limit .req x22
itemp_1 .req x23
itemp_1w .req w23
/*
redefining register names
for easier implementation
*/
main:
stp xzr, lr, [sp, #-16]!
stp d8, d9, [sp, #-16]!
stp d10, d11,[sp, #-16]!
stp d12, d13,[sp, #-16]!
stp d14, d15,[sp, #-16]!
stp x19, x20,[sp, #-16]!
stp x21, x22,[sp, #-16]!
stp x23, x24,[sp, #-16]!
mov xsize, #108
mov ysize, #72
mov limit, #32
fmov min_imag, #-1.0
fmov max_imag, #1.0
fmov min_real, #-2.0
// fmov max_real #1.0
fsub step_x, max_real, min_real
scvtf ftemp_1, xsize_w
fdiv step_x, step_x, ftemp_1
fsub step_y, max_imag, min_imag
scvtf ftemp_1, ysize_w
fdiv step_y, step_y, ftemp_1
mov y, #0
1:
cmp y, ysize
b.eq 20f
scvtf ftemp_1, y_w
fmadd imag, step_y, ftemp_1, min_imag
mov x, #0
2:
cmp x, xsize
b.eq 15f
scvtf ftemp_1, x_w
fmadd real, step_y, ftemp_1, min_real
fmov zr, real
fmov zi, imag
mov n, #0
3:
cmp n, limit
b.eq 10f
fmul a, zr, zr
fmul b, zi, zi
fadd ftemp_1, a, b
fmov ftemp_2, #4.0
fcmp ftemp_1, ftemp_2
b.gt 10f
fmul zi, zi, zr
fmov ftemp_2, #2.0
fmadd zi, zi, ftemp_2, imag
fsub zr, a, b
fadd zr, zr, real
add n, n, #1
b 3b
10:
add x, x, #1
PRINTCHAR n
b 2b
15:
add y, y, #1
NEWLINE
b 1b
20:
ldp x23, x24,[sp], 16
ldp x21, x22,[sp], 16
ldp x19, x20,[sp], 16
ldp d14, d15,[sp], 16
ldp d12, d13,[sp], 16
ldp d10, d11,[sp], 16
ldp d8, d9, [sp], 16
ldp xzr, lr, [sp], 16
ret- Output:
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" 1 889887$9;<===>>>>>>>>>>?????? @@@@@???>>>>>>>>>>>>>>>>>>>>>>>>>==========<<<<;;9242 6887/'5 31/% '/24-63 79::::929;<==>>>>>>>>>>??????? @@@@@???>>>>>>>>>>>>>>>>>>>>>>>>>>===========<<<<:899*8999887764' 467888::;;;::3;<===>>>>>>>>>>??????? @@@@@????>>>>>>>>>>>>>>>>>>>>>>>>>>>===========<<<;::::::::98862 3799::;;;;;;;<<===>>>>>>>>>>???????? @@@@@@????>>>>>>>>>>>>>>>>>>>>>>>>>>>============<<;;;;;;:::983+ 79::;;;;<<<<<====>>>>>>>>>????????? @@@@@@?????>>>>>>>>>>>>>>>>>>>>>>>>>>>============<<<;;;;;:::97' 379:;;<<<<<<<====>>>>>>>>>?????????? @@@@@@@????>>>>>>>>>>>>>>>>>>>>>>>>>>>>=============<<<;;;;::970 ,+::;<<<<<<=====>>>>>>>>>>?????????? @@@@@@@?????>>>>>>>>>>>>>>>>>>>>>>>>>>>>=============<<<<<;;:821.- 3 7:;<<<<<<======>>>>>>>>>??????????? @@@@@@@@?????>>>>>>>>>>>>>>>>>>>>>>>>>>>>=============<<<<<;;:74441 3663;<<<<<=======>>>>>>>>>???????????? @@@@@@@@??????>>>>>>>>>>>>>>>>>>>>>>>>>>>>>============<<<<<<;:7871 ,489:;<<<<=======>>>>>>>>>????????????? @@@@@@@@@??????>>>>>>>>>>>>>>>>>>>>>>>>>>>>>============<<<<<;;:9964*469:;;<<<=======>>>>>>>>>?????????????? @@@@@@@@@???????>>>>>>>>>>>>>>>>>>>>>>>>>>>>>============<<<<<;::9861479:;<<<========>>>>>>>>??????????????? @@@@@@@@@@????????>>>>>>>>>>>>>>>>>>>>>>>>>>>>>===========<<<<<;:984-047:;<<========>>>>>>>?????????????????
Ada
mandelbrot.adb:
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;
mandelbrot.ads:
with Lumen.Image;
package Mandelbrot is
function Create_Image (Width, Height : Natural) return Lumen.Image.Descriptor;
end Mandelbrot;
test_mandelbrot.adb:
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 pix
DO 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
OD
OD;
# 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 pix
DO 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))
OD
OD;
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_y0
end.
- Output:
1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111 1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211 1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222 1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222 1111111111111112222222222222333333333333333333333333333333333333222222222222222222222222222222222222222 1111111111111222222222233333333333333333333333344444456655544443333332222222222222222222222222222222222 1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222 11111111111222222333333333333333333333334444444445555679@@@@7654444443333333222222222222222222222222222 1111111112222223333333333333333333333444444444455556789@@@@98755544444433333332222222222222222222222222 1111111122223333333333333333333333344444444445556668@@@ @@@76555544444333333322222222222222222222222 1111111222233333333333333333333344444444455566667778@@ @987666555544433333333222222222222222222222 111111122333333333333333333333444444455556@@@@@99@@@@@@ @@@@@@877779@5443333333322222222222222222222 1111112233333333333333333334444455555556679@ @@@ @@@@@@ 8544333333333222222222222222222 1111122333333333333333334445555555556666789@@@ @86554433333333322222222222222222 1111123333333333333444456666555556666778@@ @ @@87655443333333332222222222222222 111123333333344444455568@887789@8777788@@@ @@@@65444333333332222222222222222 111133334444444455555668@@@@@@@@@@@@99@@@ @@765444333333333222222222222222 111133444444445555556778@@@ @@@@ @855444333333333222222222222222 11124444444455555668@99@@ @ @655444433333333322222222222222 11134555556666677789@@ @86655444433333333322222222222222 111 @@876555444433333333322222222222222 11134555556666677789@@ @86655444433333333322222222222222 11124444444455555668@99@@ @ @655444433333333322222222222222 111133444444445555556778@@@ @@@@ @855444333333333222222222222222 111133334444444455555668@@@@@@@@@@@@99@@@ @@765444333333333222222222222222 111123333333344444455568@887789@8777788@@@ @@@@65444333333332222222222222222 1111123333333333333444456666555556666778@@ @ @@87655443333333332222222222222222 1111122333333333333333334445555555556666789@@@ @86554433333333322222222222222222 1111112233333333333333333334444455555556679@ @@@ @@@@@@ 8544333333333222222222222222222 111111122333333333333333333333444444455556@@@@@99@@@@@@ @@@@@@877779@5443333333322222222222222222222 1111111222233333333333333333333344444444455566667778@@ @987666555544433333333222222222222222222222 1111111122223333333333333333333333344444444445556668@@@ @@@76555544444333333322222222222222222222222 1111111112222223333333333333333333333444444444455556789@@@@98755544444433333332222222222222222222222222 11111111111222222333333333333333333333334444444445555679@@@@7654444443333333222222222222222222222222222 1111111111112222222233333333333333333333333444444445567@@6665444444333333222222222222222222222222222222 1111111111111222222222233333333333333333333333344444456655544443333332222222222222222222222222222222222 1111111111111112222222222222333333333333333333333333333333333333222222222222222222222222222222222222222 1111111111111111222222222222222222233333333333333333333333222222222222222222222222222222222222222222222 1111111111111111112222222222222222222222222222222222222222222222222222222222222222222222222222222222222 1111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222222222211 1111111111111111111111122222222222222222222222222222222222222222222222222222222222222222222222222211111
The entry for m4 also is based on Rosetta Code's "compiler" task suite.
Amazing Hopper
El siguiente programa genera el conjunto de Mandelbrot directamente en pantalla. Ha sido adaptado desde Wikipedia.
Se ejecutó con:
rxvt -g 500x250 -fn "xft:FantasqueSansMono-Regular:pixelsize=1" -e hopper3 jm/mandel.jambo
#!/usr/bin/hopper
#include <jambo.h>
Main
Initialize '300, ancho, alto'
Set '-2,0.47,-1.12,1.12' Init 'min real, max real, min complex, max complex'
Init zero 'submaxRminR, submaxCminC'
Let ( submaxRminR := 'max real' Minus 'min real')
Let ( submaxCminC := 'maxcomplex' Minus 'mincomplex' )
Init zero 'a2,b2,a,b,ta'
Loop for (i=1, Less equal(i, ancho),++i)
Let ( ta := Add(min real, Div ( Mul( submaxRminR, Minus one(i)), Minus one(ancho) )) )
Loop for (j=1, Less equal (j, alto),++j)
Let ( b := Add( min complex, Div ( Mul (submaxCminC, Minus one(j)), Minus one(alto))) )
a=ta, a2=a, b2=b
k=1000, color=256
Loop if (Sqradd (a,b) Is less than (4), And (k) )
Add(Sqrdiff(a,b), a2),
Add(b2, Mul(2, Mul(a, b)))
Move to (b), Move to (a)
--color
--k
Back
Color back (color), Print("O")
Back
Prnl
Back
Pause
End- Output:
Arturo
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:
**
******
********
******
******** ** *
*** *****************
************************ ***
****************************
******************************
*******************************
************************************
* **********************************
** ***** * **********************************
*********** ************************************
************** ************************************
***************************************************
******************************************************
************************************************************************
******************************************************
***************************************************
************** ************************************
*********** ************************************
** ***** * **********************************
* **********************************
************************************
*******************************
******************************
****************************
************************ ***
*** *****************
******** ** *
******
********
******
**
ATS
A non-interactive program that writes a PPM image
(* The algorithm is borrowed from Wikipedia. The graphics is a
modification of the display made by the JavaScript entry. Output
from the program is a Portable Pixmap file. *)
#include "share/atspre_staload.hats"
staload "libats/libc/SATS/math.sats"
staload _ = "libats/libc/DATS/math.dats"
fn
mandel_iter {max_iter : nat}
(cx : double,
cy : double,
max_iter : int max_iter)
:<> intBtwe (0, max_iter) =
let
fun
loop {iter : nat | iter <= max_iter}
.<max_iter - iter>.
(x : double,
y : double,
iter : int iter) :<> intBtwe (0, max_iter) =
if iter = max_iter then
iter
else if 2.0 * 2.0 < (x * x) + (y * y) then
iter
else
let
val x = (x * x) - (y * y) + cx
and y = (2.0 * x * y) + cy
in
loop (x, y, succ iter)
end
in
loop (0.0, 0.0, 0)
end
fn (* Write a Portable Pixmap of the Mandelbrot set. *)
write_mandelbrot_ppm (outf : FILEref,
width : intGte 0,
height : intGte 0,
xmin : double,
xmax : double,
ymin : double,
ymax : double,
max_iter : intGte 0) : void =
let
prval [width : int] EQINT () = eqint_make_gint width
prval [height : int] EQINT () = eqint_make_gint height
macdef output (r, g, b) =
let
val r = min ($UNSAFE.cast{int} ,(r), 255)
and g = min ($UNSAFE.cast{int} ,(g), 255)
and b = min ($UNSAFE.cast{int} ,(b), 255)
in
fprint_val<uchar> (outf, $UNSAFE.cast r);
fprint_val<uchar> (outf, $UNSAFE.cast g);
fprint_val<uchar> (outf, $UNSAFE.cast b);
end
val xscale = (xmax - xmin) / g0i2f width
and yscale = (ymax - ymin) / g0i2f height
fun
loop_y {iy : nat | iy <= height}
.<height - iy>.
(iy : int iy) : void =
if iy <> height then
let
fun
loop_x {ix : nat | ix <= width}
.<width - ix>.
(ix : int ix) : void =
if ix <> width then
let
(* We want to go from top to bottom, left to right. *)
val x = xmin + (xscale * g0i2f ix)
and y = ymin + (yscale * g0i2f (height - iy))
val i = mandel_iter (x, y, max_iter)
(* We can PROVE that "i" is no greater than
"max_iter". *)
prval [i : int] EQINT () = eqint_make_gint i
prval [max_iter : int] EQINT () = eqint_make_gint max_iter
prval () = prop_verify {i <= max_iter} ()
val c = (4.0 * log (g0i2f i)) / log (g0i2f max_iter)
in
if i = max_iter then
output (0, 0, 0)
else if c < 1.0 then
output (0, 0, 255.0 * (c - 1.0))
else if c < 2.0 then
output (0, 255.0 * (c - 1.0), 255)
else
output (255.0 * (c - 2.0), 255, 255);
loop_x (succ ix)
end
in
loop_x 0;
loop_y (succ iy)
end
in
fprintln! (outf, "P6");
fprintln! (outf, width, " ", height);
fprintln! (outf, 255);
loop_y 0
end
implement
main0 () =
let
val outf = stdout_ref
val width = 1024
val height = 1024
val xmin = ~2.25
val xmax = 0.75
val ymin = ~1.5
val ymax = 1.5
val max_iter = 1000
in
write_mandelbrot_ppm (outf, width, height, xmin, xmax,
ymin, ymax, max_iter)
end- Output:
An interactive program that can write PAM images
(*-*- ATS -*-*)
(* This program requires ats2-xprelude:
https://sourceforge.net/p/chemoelectric/ats2-xprelude
Also required is the SDL2 library for C. Not everything in the SDL
interface below is used. The interface is meant to be relatively
safe. For instance, you cannot create a window or renderer without
later destroying it, and you cannot use one at all that was not
properly created. Also you cannot accidentally use an
SDL_WindowEvent as an SDL_TextInputEvent, etc.
The program uses 32+32-bit fixed point to calculate escape times.
One does not need so many bits left of the decimal point, but this
is the fixed point format available from ats2-xprelude.
There are some "FIXME" notes below that refer to a few of the ways
the program could be improved. This is a demo version of something
I am likely to expand into a better program.
Compile the program with (for example)
"myatscc mandelbrot_task_interactive.dats"
##myatsccdef=\
patscc -std=gnu2x -O3 \
-DATS_MEMALLOC_GCBDW \
`pkg-config --define-variable=PATSHOME="${PATSHOME}" \
--cflags sdl2 ats2-xprelude bdw-gc` \
`pkg-config --define-variable=PATSHOME="${PATSHOME}" \
--variable=PATSCCFLAGS ats2-xprelude` \
-o $fname($1) $1 \
`pkg-config --define-variable=PATSHOME="${PATSHOME}" \
--libs sdl2 ats2-xprelude bdw-gc`
*)
(* How to use the program:
Left click : re-center the image
Double left-click : zoom in
Double right-click : zoom out
p or P : save an image as a Portable Arbitrary Map
q or Q : quit the program
The window is resizable.
Closing the window quits the program, just as the Q key does. *)
(*------------------------------------------------------------------*)
#include "share/atspre_staload.hats"
staload UN = "prelude/SATS/unsafe.sats"
#include "xprelude/HATS/xprelude.hats"
(* To use 32+32-bit fixed point: *)
staload "xprelude/SATS/fixed32p32.sats"
staload _ = "xprelude/DATS/fixed32p32.dats"
stadef realknd = fix32p32knd
typedef real = fixed32p32
(* Actually, one could use different kinds of real number for
different algorithms: fixed point, floating point,
multiple-precision rational, interval arithmetic, ... even
continued fractions. *)
(*------------------------------------------------------------------*)
(* This is a weak choice of ATS_EXTERN_PREFIX, but will spare us from
having to do a lot of writing. *)
#define ATS_EXTERN_PREFIX ""
extern fn atexit : (() -> void) -> int = "mac#%"
%{^
#define SDL_MAIN_HANDLED 1
#include <SDL.h>
ATSinline() atstype_bool
SDL_bool2ATS (SDL_bool b)
{
return (b == SDL_FALSE) ? atsbool_false : atsbool_true;
}
%}
typedef SDL_bool = $extype"SDL_bool"
extern fn SDL_bool2ATS (b : SDL_bool) :<> bool = "mac#%"
(* - - - - - - - - - - - - - - - - - - - - - - *)
(* Housekeeping. *)
extern fn SDL_SetMainReady () : void = "mac#%"
extern fn SDL_Init (flags : uint32) : void = "mac#%"
extern fn SDL_Quit () : void = "mac#%"
(* - - - - - - - - - - - - - - - - - - - - - - *)
(* Timers. *)
extern fn SDL_Delay (ms : uint32) : void = "mac#%"
(* - - - - - - - - - - - - - - - - - - - - - - *)
(* Video handling. *)
(* Screensavers are disabled by default, except in very early versions
of SDL2. *)
extern fn SDL_DisableScreenSaver () : void = "mac#%"
extern fn SDL_EnableScreenSaver () : void = "mac#%"
extern fn SDL_IsScreenSaverEnabled () : SDL_bool = "mac#%"
absvtype SDL_Window_ptr (p : addr) = ptr p
vtypedef SDL_Window_ptr0 = [p : addr] SDL_Window_ptr p
vtypedef SDL_Window_ptr1 = [p : agz] SDL_Window_ptr p
absvtype SDL_Renderer_ptr (p : addr) = ptr p
vtypedef SDL_Renderer_ptr0 = [p : addr] SDL_Renderer_ptr p
vtypedef SDL_Renderer_ptr1 = [p : agz] SDL_Renderer_ptr p
extern castfn SDL_Window_ptr2ptr :
{p : addr} (!SDL_Window_ptr p) -<> ptr p
extern castfn SDL_Renderer_ptr2ptr :
{p : addr} (!SDL_Renderer_ptr p) -<> ptr p
macdef SDL_INIT_EVENTS = $extval (uint32, "SDL_INIT_EVENTS")
macdef SDL_INIT_TIMER = $extval (uint32, "SDL_INIT_TIMER")
macdef SDL_INIT_VIDEO = $extval (uint32, "SDL_INIT_VIDEO")
macdef SDL_WINDOWPOS_CENTERED = $extval (int, "SDL_WINDOWPOS_CENTERED")
macdef SDL_WINDOWPOS_UNDEFINED = $extval (int, "SDL_WINDOWPOS_UNDEFINED")
macdef SDL_WINDOW_OPENGL = $extval (uint32, "SDL_WINDOW_OPENGL")
macdef SDL_WINDOW_RESIZABLE = $extval (uint32, "SDL_WINDOW_RESIZABLE")
extern fn
SDL_CreateWindow (title : string,
x : int, y : int,
w : int, h : int,
flags : uint32) : SDL_Window_ptr0 = "mac#%"
extern fn
SDL_DestroyWindow : SDL_Window_ptr1 -> void = "mac#%"
fn {}
SDL_DestroyWindow_null
(window : SDL_Window_ptr null) : void =
$UN.castvwtp0{void} window
extern fn
SDL_CreateRenderer (window : !SDL_Window_ptr1,
index : int,
flags : uint32) : SDL_Renderer_ptr0 = "mac#%"
extern fn
SDL_DestroyRenderer : SDL_Renderer_ptr1 -> void = "mac#%"
fn {}
SDL_DestroyRenderer_null
(renderer : SDL_Renderer_ptr null) : void =
$UN.castvwtp0{void} renderer
extern fn
SDL_GetRendererOutputSize (renderer : !SDL_Renderer_ptr1,
w : &int? >> int,
h : &int? >> int) : int = "mac#%"
extern fn
SDL_SetRenderDrawColor (renderer : !SDL_Renderer_ptr1,
r : uint8,
g : uint8,
b : uint8,
a : uint8) : int = "mac#%"
extern fn
SDL_RenderClear (renderer : !SDL_Renderer_ptr1) : int = "mac#%"
extern fn
SDL_RenderDrawPoint (renderer : !SDL_Renderer_ptr1,
x : int,
y : int) : int = "mac#%"
extern fn
SDL_RenderPresent (renderer : !SDL_Renderer_ptr1) : void = "mac#%"
(* - - - - - - - - - - - - - - - - - - - - - - *)
(* Event handling. *)
typedef SDL_Event (t : int) =
$extype_struct"SDL_Event" of
{
type = uint32 t,
timestamp = uint32
}
typedef SDL_Event = [t : int] SDL_Event t
extern fn
SDL_PollEvent (event : &SDL_Event? >> SDL_Event)
: intBtwe (0, 1) = "mac#%"
extern fn
SDL_GetMouseState (x : &int? >> int,
y : &int? >> int) : uint32 = "mac#%"
macdef SDL_BUTTON_LMASK = $extval (uint32, "SDL_BUTTON_LMASK")
macdef SDL_BUTTON_MMASK = $extval (uint32, "SDL_BUTTON_MMASK")
macdef SDL_BUTTON_RMASK = $extval (uint32, "SDL_BUTTON_RMASK")
macdef SDL_BUTTON_X1MASK = $extval (uint32, "SDL_BUTTON_X1MASK")
macdef SDL_BUTTON_X2MASK = $extval (uint32, "SDL_BUTTON_X2MASK")
(* - - - - - - - - - - - - - *)
stacst SDL_QUIT : int
macdef SDL_QUIT = $extval (uint32 SDL_QUIT, "SDL_QUIT")
typedef SDL_QuitEvent =
$extype_struct"SDL_QuitEvent" of
{
type = uint32 SDL_QUIT,
timestamp = uint32
}
extern praxi
SDL_Event2QuitEvent_v :
{p : addr}
SDL_Event SDL_QUIT @ p -<prf>
@(SDL_QuitEvent @ p,
SDL_QuitEvent @ p -<lin,prf> SDL_Event SDL_QUIT @ p)
(* - - - - - - - - - - - - - *)
stacst SDL_WINDOWEVENT : int
macdef SDL_WINDOWEVENT = $extval (uint32 SDL_WINDOWEVENT, "SDL_WINDOWEVENT")
typedef SDL_WindowEvent =
$extype_struct"SDL_WindowEvent" of
{
type = uint32 SDL_WINDOWEVENT,
timestamp = uint32,
windowID = uint32,
event = uint8,
padding1 = uint8,
padding2 = uint8,
padding3 = uint8,
data1 = int32,
data2 = int32
}
extern praxi
SDL_Event2WindowEvent_v :
{p : addr}
SDL_Event SDL_WINDOWEVENT @ p -<prf>
@(SDL_WindowEvent @ p,
SDL_WindowEvent @ p -<lin,prf> SDL_Event SDL_WINDOWEVENT @ p)
macdef SDL_WINDOWEVENT_NONE = $extval (uint8, "SDL_WINDOWEVENT_NONE")
macdef SDL_WINDOWEVENT_SHOWN = $extval (uint8, "SDL_WINDOWEVENT_SHOWN")
macdef SDL_WINDOWEVENT_HIDDEN = $extval (uint8, "SDL_WINDOWEVENT_HIDDEN")
macdef SDL_WINDOWEVENT_EXPOSED = $extval (uint8, "SDL_WINDOWEVENT_EXPOSED")
macdef SDL_WINDOWEVENT_MOVED = $extval (uint8, "SDL_WINDOWEVENT_MOVED")
macdef SDL_WINDOWEVENT_RESIZED = $extval (uint8, "SDL_WINDOWEVENT_RESIZED")
macdef SDL_WINDOWEVENT_SIZE_CHANGED = $extval (uint8, "SDL_WINDOWEVENT_SIZE_CHANGED")
macdef SDL_WINDOWEVENT_MINIMIZED = $extval (uint8, "SDL_WINDOWEVENT_MINIMIZED")
macdef SDL_WINDOWEVENT_MAXIMIZED = $extval (uint8, "SDL_WINDOWEVENT_MAXIMIZED")
macdef SDL_WINDOWEVENT_RESTORED = $extval (uint8, "SDL_WINDOWEVENT_RESTORED")
macdef SDL_WINDOWEVENT_ENTER = $extval (uint8, "SDL_WINDOWEVENT_ENTER")
macdef SDL_WINDOWEVENT_LEAVE = $extval (uint8, "SDL_WINDOWEVENT_LEAVE")
macdef SDL_WINDOWEVENT_FOCUS_GAINED = $extval (uint8, "SDL_WINDOWEVENT_FOCUS_GAINED")
macdef SDL_WINDOWEVENT_FOCUS_LOST = $extval (uint8, "SDL_WINDOWEVENT_FOCUS_LOST")
macdef SDL_WINDOWEVENT_CLOSE = $extval (uint8, "SDL_WINDOWEVENT_CLOSE")
macdef SDL_WINDOWEVENT_TAKE_FOCUS = $extval (uint8, "SDL_WINDOWEVENT_TAKE_FOCUS")
macdef SDL_WINDOWEVENT_HIT_TEST = $extval (uint8, "SDL_WINDOWEVENT_HIT_TEST")
macdef SDL_WINDOWEVENT_ICCPROF_CHANGED = $extval (uint8, "SDL_WINDOWEVENT_ICCPROF_CHANGED")
macdef SDL_WINDOWEVENT_DISPLAY_CHANGED = $extval (uint8, "SDL_WINDOWEVENT_DISPLAY_CHANGED")
(* - - - - - - - - - - - - - *)
stacst SDL_MOUSEMOTION : int
macdef SDL_MOUSEMOTION = $extval (uint32 SDL_MOUSEMOTION, "SDL_MOUSEMOTION")
typedef SDL_MouseMotionEvent =
$extype_struct"SDL_MouseMotionEvent" of
{
type = uint32 SDL_MOUSEMOTION,
timestamp = uint32,
windowID = uint32,
which = uint32,
state = uint32,
x = int32,
y = int32,
xrel = int32,
yrel = int32
}
extern praxi
SDL_Event2MouseMotionEvent_v :
{p : addr}
SDL_Event SDL_MOUSEMOTION @ p -<prf>
@(SDL_MouseMotionEvent @ p,
SDL_MouseMotionEvent @ p -<lin,prf> SDL_Event SDL_MOUSEMOTION @ p)
(* - - - - - - - - - - - - - *)
stacst SDL_MOUSEBUTTONDOWN : int
macdef SDL_MOUSEBUTTONDOWN = $extval (uint32 SDL_MOUSEBUTTONDOWN, "SDL_MOUSEBUTTONDOWN")
stacst SDL_MOUSEBUTTONUP : int
macdef SDL_MOUSEBUTTONUP = $extval (uint32 SDL_MOUSEBUTTONUP, "SDL_MOUSEBUTTONUP")
typedef SDL_MouseButtonEvent (t : int) =
[t == SDL_MOUSEBUTTONDOWN || t == SDL_MOUSEBUTTONUP]
$extype_struct"SDL_MouseButtonEvent" of
{
type = uint32 t,
timestamp = uint32,
windowID = uint32,
which = uint32,
button = uint8,
state = uint8,
clicks = uint8,
padding1 = uint8,
x = int32,
y = int32
}
typedef SDL_MouseButtonEvent = [t : int] SDL_MouseButtonEvent t
extern praxi
SDL_Event2MouseButtonEvent_v :
{p : addr}
{t : int | t == SDL_MOUSEBUTTONDOWN || t == SDL_MOUSEBUTTONUP}
SDL_Event t @ p -<prf>
@(SDL_MouseButtonEvent t @ p,
SDL_MouseButtonEvent t @ p -<lin,prf> SDL_Event t @ p)
macdef SDL_BUTTON_LEFT = $extval (uint8, "SDL_BUTTON_LEFT")
macdef SDL_BUTTON_MIDDLE = $extval (uint8, "SDL_BUTTON_MIDDLE")
macdef SDL_BUTTON_RIGHT = $extval (uint8, "SDL_BUTTON_RIGHT")
macdef SDL_BUTTON_X1 = $extval (uint8, "SDL_BUTTON_X1")
macdef SDL_BUTTON_X2 = $extval (uint8, "SDL_BUTTON_X2")
macdef SDL_PRESSED = $extval (uint8, "SDL_PRESSED")
macdef SDL_RELEASED = $extval (uint8, "SDL_RELEASED")
(* - - - - - - - - - - - - - *)
stacst SDL_TEXTINPUT : int
macdef SDL_TEXTINPUT = $extval (uint32 SDL_TEXTINPUT, "SDL_TEXTINPUT")
#define SDL_TEXTINPUTEVENT_TEXT_SIZE 32
typedef SDL_TextInputEvent =
$extype_struct"SDL_TextInputEvent" of
{
type = uint32 SDL_TEXTINPUT,
timestamp = uint32,
windowID = uint32,
text = @[char][SDL_TEXTINPUTEVENT_TEXT_SIZE]
}
extern praxi
SDL_Event2TextInputEvent_v :
{p : addr}
SDL_Event SDL_TEXTINPUT @ p -<prf>
@(SDL_TextInputEvent @ p,
SDL_TextInputEvent @ p -<lin,prf> SDL_Event SDL_TEXTINPUT @ p)
(*------------------------------------------------------------------*)
exception bailout of string
typedef rgba = @(uint8, uint8, uint8, uint8)
val empty_scene_color =
@(g0i2u 200, g0i2u 200, g0i2u 200, g0i2u 255) : rgba
typedef rgba_array (w : int, h : int) =
matrixref (rgba, w, h)
typedef scene_computer =
{w, h : nat}
(int w, int h, real, real, real) -<cloref1>
rgba_array (w, h)
vtypedef situation (p : addr, q : addr,
w : int, h : int) =
[null < p; null < q; 0 <= w; 0 <= h]
@{window = SDL_Window_ptr p,
renderer = SDL_Renderer_ptr q,
width = int w,
height = int h,
xcenter = real,
ycenter = real,
pixels_per_unit = real,
compute_scene = scene_computer}
vtypedef situation (w : int, h : int) =
[p, q : agz]
situation (p, q, w, h)
vtypedef situation =
[w, h : nat]
situation (w, h)
fn
destroy_situation (situation : situation) : void =
begin
SDL_DestroyRenderer (situation.renderer);
SDL_DestroyWindow (situation.window)
end
fn
get_renderer_size (situation : &situation)
: [renderer_width, renderer_height : nat]
@(int renderer_width, int renderer_height) =
let
var w : int
var h : int
val status = SDL_GetRendererOutputSize (situation.renderer, w, h)
val w = g1ofg0 w and h = g1ofg0 h
in
if (status < 0) + (w < 0) + (h < 0) then
begin
destroy_situation situation;
$raise bailout "rendering error"
end
else
@(w, h)
end
fn
resize_needed (situation : &situation) : bool =
let
val @(w, h) = get_renderer_size situation
in
(w <> situation.width) + (h <> situation.height)
end
(*------------------------------------------------------------------*)
fn
compute_escape_times
{w, h : nat}
{mxtm : nat}
(width : int w,
height : int h,
xcenter : real,
ycenter : real,
pixels_per_unit : real,
max_time : uint16 mxtm)
: matrixref ([tm : nat | tm <= mxtm] uint16 tm, w, h) =
let
typedef tm = [tm : nat | tm <= mxtm] uint16 tm
val times = matrixref_make_elt<tm> (i2sz width, i2sz height,
max_time)
and ppu2 = pixels_per_unit + pixels_per_unit
fun
ij_loop {i, j : nat | i <= w; j <= h}
.<w - i, h - j>.
(i : int i,
j : int j) :<!refwrt> void =
if i = width then
()
else if j = height then
ij_loop (succ i, 0)
else
let
val cx = xcenter + (g0i2f ((i + i) - width) / ppu2)
and cy = ycenter + (g0i2f (height - (j + j)) / ppu2)
fun
tm_loop {tm : nat | tm <= mxtm}
.<mxtm - tm>.
(x : real,
y : real,
xx : real,
yy : real,
tm : uint16 tm)
:<> [tm1 : nat | tm1 <= mxtm] uint16 tm1 =
if tm = max_time then
tm
else if g0i2f 4 < xx + yy then
tm
else
let
val x = xx - yy + cx and y = ((x + x) * y) + cy
val xx = x * x and yy = y * y
in
tm_loop (x, y, xx, yy, succ tm)
end
val tm = tm_loop (g0i2f 0, g0i2f 0,
g0i2f 0, g0i2f 0,
g1i2u 0)
in
times[i, height, j] := tm;
ij_loop (i, succ j)
end
in
ij_loop (0, 0);
times
end
fn
the_durn_simplest_scene_computer
{w, h : nat}
(width : int w,
height : int h,
xcenter : real,
ycenter : real,
pixels_per_unit : real)
:<cloref1> rgba_array (w, h) =
let
val escape_times =
compute_escape_times (width, height, xcenter, ycenter,
pixels_per_unit, g1i2u 255)
and points = matrixref_make_elt<rgba> (i2sz width, i2sz height,
empty_scene_color)
fn {}
time2rgba {tm : nat | tm <= 255}
(tm : uint16 tm) : rgba =
let
val v = (g0u2u (g1i2u 255 - tm)) : uint8
in
@(v, v, v, g0i2u 255)
end
fun
loop {i, j : nat | i <= w; j <= h}
.<w - i, h - j>.
(i : int i,
j : int j) : void =
if i = width then
()
else if j = height then
loop (succ i, 0)
else
begin
points[i, height, j] :=
time2rgba escape_times[i, height, j];
loop (i, succ j)
end
in
loop (0, 0);
points
end
(*------------------------------------------------------------------*)
(* Writing an image to a Portable Arbitrary Map. *)
fn
write_rgba_points_as_pam
{w, h : nat}
(outf : FILEref,
width : int w,
height : int h,
points : rgba_array (w, h)) : void =
let
fun
loop {i, j : nat | i <= w; j <= h}
.<h - j, w - i>.
(i : int i,
j : int j) : void =
if j = height then
()
else if i = width then
loop (0, succ j)
else
let
val @(r, g, b, a) = points[i, height, j]
in
fprint! (outf, int2uchar0 (g0u2i r));
fprint! (outf, int2uchar0 (g0u2i g));
fprint! (outf, int2uchar0 (g0u2i b));
fprint! (outf, int2uchar0 (g0u2i a));
loop (succ i, j)
end
in
(* Portable Arbitrary Map:
https://netpbm.sourceforge.net/doc/pam.html *)
fprintln! (outf, "P7");
fprintln! (outf, "WIDTH ", width);
fprintln! (outf, "HEIGHT ", height);
fprintln! (outf, "DEPTH 4");
fprintln! (outf, "MAXVAL 255");
fprintln! (outf, "TUPLTYPE RGB_ALPHA");
fprintln! (outf, "ENDHDR");
loop (0, 0)
end
(* For this demo, simply number the images, starting at 1 on each run
of the program. *)
val image_number : ref uint = ref 1U
fn
write_image {w, h : nat}
(width : int w,
height : int h,
points : rgba_array (w, h)) : void =
let
val filename =
strptr2string (string_append ("mandelbrot-image-",
tostring_val<uint> !image_number,
".pam"))
in
case+ fileref_open_opt (filename, file_mode_w) of
| ~ None_vt () =>
println! ("ERROR: could not open ", filename, " for writing.")
| ~ Some_vt outf =>
begin
write_rgba_points_as_pam (outf, width, height, points);
fileref_close (outf);
println! ("SUCCESS: wrote ", filename);
!image_number := succ !image_number
end
end
(*------------------------------------------------------------------*)
val initial_width : intGte 0 = 400
val initial_height : intGte 0 = 400
val initial_xcenter : real = g0f2f ~0.75
val initial_ycenter : real = g0f2f 0.0
val initial_pixels_per_unit : real = g0f2f 150.0
val initial_scene_computer : scene_computer =
the_durn_simplest_scene_computer
(* Zoom factor could be adjustable, but is not in this simple demo. *)
val zoom_factor : real = g0f2f 2.0
val min_pixels_per_unit : real = g0f2f 10.0
fn
set_render_rgba (renderer : !SDL_Renderer_ptr1,
rgba : rgba) : int =
let
val @(r, g, b, a) = rgba
in
SDL_SetRenderDrawColor (renderer, r, g, b, a)
end
fn
draw_scene {w, h : nat}
(renderer : !SDL_Renderer_ptr1,
width : int w,
height : int h,
points : rgba_array (w, h)) : void =
let
prval () = mul_gte_gte_gte {w, h} ()
fun
loop {i, j : nat | i <= w; j <= h}
.<w - i, h - j>.
(renderer : !SDL_Renderer_ptr1,
i : int i,
j : int j) : void =
if i = width then
()
else if j = height then
loop (renderer, succ i, 0)
else
let
val rgba = points[i, height, j]
val _ = set_render_rgba (renderer, rgba)
val _ = SDL_RenderDrawPoint (renderer, i, j)
in
loop (renderer, i, succ j)
end
in
ignoret (set_render_rgba (renderer, empty_scene_color));
ignoret (SDL_RenderClear (renderer));
loop (renderer, 0, 0);
end
fnx
situation_changed
{w, h : nat}
(situation : &situation (w, h) >> situation,
event : &SDL_Event? >> SDL_Event) : void =
let
val compute_scene = situation.compute_scene
val points =
compute_scene (situation.width, situation.height,
situation.xcenter, situation.ycenter,
situation.pixels_per_unit)
in
SDL_Delay (g0i2u 16);
event_loop (situation, points, event)
end
and
event_loop {w, h : nat}
(situation : &situation (w, h) >> situation,
points : rgba_array (w, h),
event : &SDL_Event? >> SDL_Event) : void =
let
macdef quit_the_event_loop =
()
macdef present_the_scene =
present_scene (situation, points, event)
macdef deal_with_changed_situation =
situation_changed (situation, event)
macdef write_an_image =
write_image (situation.width, situation.height, points);
in
if resize_needed situation then
let
val @(w, h) = get_renderer_size situation
in
situation.width := w;
situation.height := h;
deal_with_changed_situation
end
else
let
in
draw_scene (situation.renderer,
situation.width, situation.height,
points);
case+ SDL_PollEvent (event) of
| 0 => present_the_scene
| 1 =>
if event.type = SDL_QUIT then
quit_the_event_loop
else if event.type = SDL_WINDOWEVENT then
let
prval @(pf, fpf) = SDL_Event2WindowEvent_v (view@ event)
prval () = view@ event := pf
val window_event = event
prval () = view@ event := fpf (view@ event)
in
if window_event.event = SDL_WINDOWEVENT_SIZE_CHANGED then
deal_with_changed_situation
else if window_event.event = SDL_WINDOWEVENT_CLOSE then
quit_the_event_loop
else
present_the_scene
end
else if event.type = SDL_MOUSEBUTTONDOWN then
let
prval @(pf, fpf) = SDL_Event2MouseButtonEvent_v (view@ event)
prval () = view@ event := pf
val button_event = event
prval () = view@ event := fpf (view@ event)
in
if button_event.button = SDL_BUTTON_LEFT then
begin
if button_event.clicks = g0i2u 1 then
let (* Re-center. *)
val x = g0i2i button_event.x
and y = g0i2i button_event.y
and w = situation.width
and h = situation.height
and ppu = situation.pixels_per_unit
val ppu2 = ppu + ppu
in
situation.xcenter :=
situation.xcenter + (g0i2f (x + x - w) / ppu2);
situation.ycenter :=
situation.ycenter + (g0i2f (h - y - y) / ppu2);
deal_with_changed_situation
end
else
let (* Zoom in. *)
val new_ppu = situation.pixels_per_unit * zoom_factor
in
situation.pixels_per_unit := new_ppu;
deal_with_changed_situation
end
end
else if button_event.button = SDL_BUTTON_RIGHT then
begin
if button_event.clicks = g0i2u 1 then
present_the_scene
else
let (* Zoom out *)
val new_ppu = situation.pixels_per_unit / zoom_factor
in
if min_pixels_per_unit <= new_ppu then
situation.pixels_per_unit := new_ppu;
deal_with_changed_situation
end
end
else
present_the_scene
end
else if event.type = SDL_TEXTINPUT then
let
prval @(pf, fpf) = SDL_Event2TextInputEvent_v (view@ event)
prval () = view@ event := pf
var text_event = event
prval () = view@ event := fpf (view@ event)
macdef text = text_event.text
in
case+ @(text[0], text[1]) of
| @('q', '\0') => quit_the_event_loop
| @('Q', '\0') => quit_the_event_loop
| @('p', '\0') =>
begin
write_an_image;
present_the_scene
end
| @('P', '\0') =>
begin
write_an_image;
present_the_scene
end
| _ => present_the_scene
end
else
present_the_scene
end
end
and
present_scene {w, h : nat}
(situation : &situation (w, h) >> situation,
points : rgba_array (w, h),
event : &SDL_Event? >> SDL_Event) : void =
begin
SDL_RenderPresent (situation.renderer);
SDL_Delay (g0i2u 16);
event_loop (situation, points, event)
end
fn
run_program () : void =
let
(* FIXME: For best form, we should also set up a signal handler
that runs SDL_Quit, so the display does not get stuck in an
undesired state even if the program crashes. For instance,
there could be a signaled divide by zero or overflow event. And
we are at least changing whether the screensaver is enabled. *)
val _ = atexit SDL_Quit
val () = SDL_Init (SDL_INIT_EVENTS
lor SDL_INIT_TIMER
lor SDL_INIT_VIDEO)
(* FIXME: Find out whether the screensaver was enabled BEFORE we
started SDL2, and set SDL2 to whichever setting it was. *)
val () = SDL_EnableScreenSaver ()
val window = SDL_CreateWindow ("mandelbrot_task_interactive",
SDL_WINDOWPOS_CENTERED,
SDL_WINDOWPOS_CENTERED,
initial_width, initial_height,
SDL_WINDOW_RESIZABLE)
val p_window = SDL_Window_ptr2ptr window
prval () = lemma_ptr_param p_window
in
if iseqz p_window then
begin
SDL_DestroyWindow_null window;
$raise bailout "failed to initialize a window"
end
else
let
val renderer = SDL_CreateRenderer (window, ~1, g0i2u 0)
val p_renderer = SDL_Renderer_ptr2ptr renderer
prval () = lemma_ptr_param p_renderer
in
if iseqz p_renderer then
begin
SDL_DestroyRenderer_null renderer;
SDL_DestroyWindow window;
$raise bailout "failed to initialize a renderer"
end
else
let
var situation : situation =
@{window = window,
renderer = renderer,
width = initial_width,
height = initial_height,
xcenter = initial_xcenter,
ycenter = initial_ycenter,
pixels_per_unit = initial_pixels_per_unit,
compute_scene = initial_scene_computer}
var event : SDL_Event?
in
situation_changed (situation, event);
destroy_situation situation
end
end
end
implement
main () =
try
begin
SDL_SetMainReady ();
run_program ();
0
end
with
| ~ bailout msg =>
begin
println! ("Error: ", msg);
1
end
(*------------------------------------------------------------------*)- Output:
A snapshot image of part of the set:
AutoHotkey
Max_Iteration := 256
Width := Height := 400
File := "MandelBrot." Width ".bmp"
Progress, b2 w400 fs9, Creating Colours ...
Gosub, CreateColours
Gosub, CreateBitmap
Progress, Off
Gui, -Caption
Gui, Margin, 0, 0
Gui, Add, Picture,, %File%
Gui, Show,, MandelBrot
Return
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.
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:
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'+)%%%$$$$$#####"""""""""""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(+,)++&%$$$$$$######""""""
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*5:/+('&%%$$$$$$#######"""
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),@@@@@@@,'&%%%%%$$$$########
!!!!!!!"""####################$$$$$$$$%%%&'())((())*,@@@@@@/+))('&&&&)'%$$######
!!!!!!""###################$$$$$%%%%%%&&&'+.@@=/<@@@@@@@@@@@@@@@/++@..93%%$#####
!!!!!"################$$$%%%%%%%%%%&&&&'),+2@@@@@@@@@@@@@@@@@@@@@@@@@1(&&%$$####
!!!!"##########$$$$$%%&(-(''''''''''''(*,5@@@@@@@@@@@@@@@@@@@@@@@@@@@@+)-&%$$###
!!!!####$$$$$$$$%%%%%&'(*-@1.+.@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4-(&%$$$##
!!!!#$$$$$$$$$%%%%%%'''++.6@@@@@@@@@8/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3(%%$$$$#
!!!#$$$$$$$%&&&&''()/-5.5@@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?'&%%$$$$#
!!!(**+/+<523/80/46@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+)'&&%%$$$$#
!!!#$$$$$$$%&&&&''().-2.@@@@@@@@@@@@@@?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$#
!!!!#$$$$$$$$$%%%%%&'''/,.7@@@@@@@@@;/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0'%%$$$$#
!!!!####$$$$$$$$%%%%%&'(*-:2.,/?-5+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+(&%$$$##
!!!!"##########$$$$$%%&(-(''''(''''''((*,4@@@@@@@@@@@@@@@@@@@@@@@@@@@4+).&%$$###
!!!!!"################$$$%%%%%%%%%%&&&&')<,4@@@@@@@@@@@@@@@@@@@@@@@@@/('&%%$####
!!!!!!""##################$$$$$$%%%%%%&&&'*.@@@0@@@@@@@@@@@@@@@@1,,@//9)%%$#####
!!!!!!!"""####################$$$$$$$$%%%&(())((()**-@@@@@@/+)))'&&&')'%$$######
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''(,@@@@@@@+'&&%%%%%$$$########
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*7@0+('&%%%$$$$$#######"""
!!!!!!!!!!!"""""""######################$$$$$$$$$%%%&&(+-).*&%$$$$$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$%%'3(%%%$$$$$######""""""""""
!!!!!!!!!!!!!!!""""""""""""#####################################""""""""""""""""
bc
Producing a PGM image.
To work properly, this needs to run with the environment variable BC_LINE_LENGTH set to 0.
max_iter = 50
width = 400; height = 401
scale = 10
xmin = -2; xmax = 1/2
ymin = -5/4; ymax = 5/4
define mandelbrot(c_re, c_im) {
auto i
# z = 0
z_re = 0; z_im = 0
z2_re = 0; z2_im = 0
for (i=0; i<max_iter; i++) {
# z *= z
z_im = 2*z_re*z_im
z_re = z2_re - z2_im
# z += c
z_re += c_re
z_im += c_im
# z2 = z.*z
z2_re = z_re*z_re
z2_im = z_im*z_im
if (z2_re + z2_im > 4) return i
}
return 0
}
print "P2\n", width, " ", height, "\n255\n"
for (i = 0; i < height; i++) {
y = ymin + (ymax - ymin) / height * i
for (j = 0; j < width; j++) {
x = xmin + (xmax - xmin) / width * j
tmp_scale = scale
scale = 0
m = (255 * mandelbrot(x, y) + max_iter + 1) / max_iter
print m
if ( j < width - 1 ) print " "
scale = tmp_scale
}
print "\n"
}
quit
BASIC
AmigaBASIC
SCREEN 1,320,200,5,1
WINDOW 2,"Mandelbrot",,0,1
maxIteration = 100
xmin = -2
xmax = 1
ymin = -1.5
ymax = 1.5
xs = 300
ys = 180
st = .01 ' use e.g. st = .05 for a coarser but faster picture
' and perhaps also lower maxIteration = 10 or so
xp = xs / (xmax - xmin) * st
yp = 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
NEXT
NEXT
' endless loop, use Run -> Stop from the menu to stop program
WHILE (1)
WEND
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 HGR2
20 XC = -0.5 : REM CENTER COORD X
30 YC = 0 : REM " " Y
40 S = 2 : REM SCALE
45 IT = 20 : REM ITERATIONS
50 XR = S * (280 / 192): REM TOTAL RANGE OF X
60 YR = S : REM " " " Y
70 X0 = XC - (XR/2) : REM MIN VALUE OF X
80 X1 = XC + (XR/2) : REM MAX " " X
90 Y0 = YC - (YR/2) : REM MIN " " Y
100 Y1 = YC + (YR/2) : REM MAX " " Y
110 XM = XR / 279 : REM SCALING FACTOR FOR X
120 YM = YR / 191 : REM " " " Y
130 FOR YI = 0 TO 3 : REM INTERLEAVE
140 FOR YS = 0+YI TO 188+YI STEP 4 : REM Y SCREEN COORDINATE
145 HCOLOR=3 : HPLOT 0,YS TO 279,YS
150 FOR XS = 0 TO 278 STEP 2 : REM X SCREEN COORDINATE
170 X = XS * XM + X0 : REM TRANSL SCREEN TO TRUE X
180 Y = YS * YM + Y0 : REM TRANSL SCREEN TO TRUE Y
190 ZX = 0
200 ZY = 0
210 XX = 0
220 YY = 0
230 FOR I = 0 TO IT
240 ZY = 2 * ZX * ZY + Y
250 ZX = XX - YY + X
260 XX = ZX * ZX
270 YY = ZY * ZY
280 C = IT-I
290 IF XX+YY >= 4 GOTO 301
300 NEXT I
301 IF C >= 8 THEN C = C - 8 : GOTO 301
310 HCOLOR = C : HPLOT XS, YS TO XS+1, YS
320 NEXT XS
330 NEXT YS
340 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 279
301 C = (C - INT(C/2)*2)*3
310 HCOLOR = C: HPLOT XS, YS
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:VDU5
20D%=100 : REM adjust for speed/precision
30FORX%=0 TO 1279 STEP8
40FORY%=0 TO 1023 STEP4
50MANDEL (Y%-512)/256, (X%-640)/256
51REM (not sure why X and Y need to be swapped to correct orientation)
60GCOL0,C%
70PLOT69,X%,Y%
80NEXT
90NEXT
BASIC256
fastgraphics
graphsize 384,384
refresh
kt = 319 : m = 4.0
xmin = -2.1 : xmax = 0.6 : ymin = -1.35 : ymax = 1.35
dx = (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
refresh
next x
imgsave "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%
Commander X16 BASIC
10 CLS
20 SCREEN $80
30 FOR X=1 TO 199:
40 FOR Y=1 TO 99:
50 LET I=0
60 LET CX=(X-100)/50
70 LET CY=(Y-100)/50
80 LET VX=0
90 LET VY=0
100 REM START OF THE CALCULATION LOOP
110 LET I=I+1
120 LET X2 = VX*VX
130 LET Y2 = VY*VY
140 LET VY = CY + (VX+VX)*VY
150 LET VX = CX + X2-Y2
160 IF I<32 AND (X2+Y2)<4 THEN GOTO 100
170 LET YR = 199-Y
180 PSET X,Y,I
190 PSET X,YR,I
200 :NEXT:NEXTCommodore BASIC
The standard version 2.0 of BASIC that came with the VIC-20 and C-64 had no built-in support for graphics (though you could use POKE statements to put values in the VIC chip's registers and the RAM being used for video). However, Commodore sold add-on cartridges that provided such support, which was also included in later versions of BASIC (3.5 on the C-16 and Plus/4, 7.0 on the C-128). In all of these cases the programs are very slow; rendering the Mandelbrot set even with the escape threshold set to just 20 iterations takes hours. The fastest is the VIC-20, because it has only a 160x160-pixel bitmap display.
VIC-20 with Super Expander cartridge
Runs in about 90 minutes.
100 TH=20:REM ESCAPE THRESHOLD IN ITERATIONS
110 COLOR 1,3,0,0:GRAPHIC 2:TH=20
120 FOR PY=0 TO 80
130 : SY=INT(PY*6.4)
140 : IM=1.12-PY/160*2.24
150 : FOR PX=0 TO 160
160 : SX=INT(PX*6.4)
170 : RE=PX/160*2.47-2
180 : X=0:Y=0:IT=0
190 : XT=X*X-Y*Y+RE
200 : Y = 2*X*Y+IM
210 : X=XT
220 : IT=IT+1
230 : IF(X*X+Y*Y<=4)AND(IT<TH) THEN 190
240 : IF IT<TH THEN 270
250 : DRAW 1,SX,SY TO SX,SY
260 : DRAW 1,SX,1024-SY TO SX,1024-SY
270 : NEXT PX
280 NEXT PY
290 GET K$:IF K$="" THEN 290
300 GRAPHIC 4
C-64 with Super Expander 64
Runs in about 4.5 hours.
100 TH=20:REM ESCAPE THRESHOLD IN ITERATIONS
110 COLOR 6,0,0,0,6:GRAPHIC 2,1
120 FOR PY=0 TO 100
140 : IM=1.12-PY/200*2.24
150 : FOR PX=0 TO 319
170 : RE=PX/320*2.47-2
180 : X=0:Y=0:IT=0
190 : XT=X*X-Y*Y+RE
200 : Y = 2*X*Y+IM
210 : X=XT
220 : IT=IT+1
230 : IF(X*X+Y*Y<=4)AND(IT<TH) THEN 190
240 : IF IT<TH THEN 270
250 : DRAW 1,PX,PY
260 : DRAW 1,PX,200-PY
270 : NEXT PX
280 NEXT PY
290 GET K$:IF K$="" THEN 290
300 GRAPHIC 0
Commodore-16 / 116 / Plus/4
Despite the faster clock on the TED systems compared to the C-64, this takes almost six hours to run.
100 TH=20:REM ESCAPE THRESHOLD IN ITERATIONS
110 COLOR 0,2:COLOR 1,1:GRAPHIC 1,1
120 FOR PY=0 TO 100
130 : IM = 1.12-PY*2.24/200
140 : FOR PX=0 TO 319
150 : RE=PX/320*2.47-2
160 : X=0:Y=0:IT=0
170 : DO WHILE (X*X+Y*Y<=4) AND (IT<TH)
180 : XT = X*X-Y*Y+RE
190 : Y = 2*X*Y+IM
200 : X = XT
210 : IT = IT +1
220 : LOOP
230 : IF IT=TH THEN DRAW 1,PX,PY:DRAW 1,PX,199-PY
240 : NEXT PX
250 NEXT PY
260 GETKEY K$
270 GRAPHIC 0
Commodore 128 (40-column display)
With the switch to FAST (2MHz) mode, this runs in about 2.5 hours, but you get to stare at a blank screen until it's done rendering. Without that switch it takes about 5.5 hours, splitting the difference between the Super Expander 64 and Plus/4 versions.
100 TH=20:REM ESCAPE THRESHOLD IN ITERATIONS
110 COLOR 0,12:GRAPHIC 1,1:COLOR 1,1:GRAPHIC0:FAST
120 FOR PY=0 TO 100
130 : IM = 1.12-PY*2.24/200
140 : FOR PX=0 TO 319
150 : RE=PX/320*2.47-2
160 : X=0:Y=0:IT=0
170 : DO WHILE (X*X+Y*Y<=4) AND (IT<TH)
180 : XT = X*X-Y*Y+RE
190 : Y = 2*X*Y+IM
200 : X = XT
210 : IT = IT +1
220 : LOOP
230 : IF IT=TH THEN DRAW 1,PX,PY:DRAW 1,PX,199-PY
240 : NEXT PX
250 NEXT PY
260 SLOW:GRAPHIC 1
270 GETKEY K$
280 GRAPHIC 0
Commodore 128 (80-column display)
This uses BASIC 8 to create a 640x200 render on the C-128's 80-column display. The doubled resolution comes with a commensurate increase in run time; this takes about 5h20m using FAST 2MHz mode.
100 TH=20:REM ESCAPE THRESHOLD IN ITERATIONS
110 @MODE,0:@COLOR,15,0,0:@SCREEN,0,0:@CLEAR,0:FAST
120 FOR PY=0 TO 100
130 : IM = 1.12-PY*2.24/200
140 : FOR PX=0 TO 639
150 : RE=PX/640*2.47-2
160 : X=0:Y=0:IT=0
170 : DO WHILE (X*X+Y*Y<=4) AND (IT<20)
180 : XT = X*X-Y*Y+RE
190 : Y = 2*X*Y+IM
200 : X = XT
210 : IT = IT +1
220 : LOOP
230 : IF IT=20 THEN @DOT,PX,PY,0:@DOT,PX,199-PY,0
240 : NEXT PX
250 NEXT PY
260 GETKEY K$
270 @TEXT
- Output:
Screen shots of all of the above running in the VICE emulator can be found here.
Commodore PET
Here's a version using mostly ASCII and some PETSCII (could probably improve the tile set for PETSCII) inspired by the Perl solution. Designed for a PET with an 80-column display.
100 TH=20:REM ESCAPE THRESHOLD IN ITERATIONS
110 CH$=" .:-=+*#@"+CHR$(255)
120 FOR Y=1 TO -1 STEP -0.08
130 : FOR X = -2 TO 0.5 STEP 0.0315
140 : GOSUB 200:IF I=20 THEN PRINT CHR$(18);" ";CHR$(146);:GOTO 160
150 : PRINT MID$(CH$,I/2+1,1);
160 : NEXT X:IF PEEK(198) THEN PRINT
170 NEXT Y
180 GET K$:IF K$=""THEN 180
190 END
200 CX=X:CY=Y:ZX=X:ZY=Y
210 FOR I=1 TO TH
220 : TX=ZX*ZX-ZY*ZY
230 : TY=ZX*ZY*2
240 : ZX = TX + CX
250 : ZY = TY + CY
260 : IF ZX*ZX+ZY*ZY > 4 THEN 280
270 NEXT I
280 IF I>TH THEN I=TH
290 RETURN
- Output:
VICE screenshot here.
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=21
20 I1=-1.0\I2=1.0\R1=-2.0\R2=1.0
30 S1=(R2-R1)/X1\S2=(I2-I1)/Y1
40 FOR Y=0 TO Y1
50 I3=I1+S2*Y
60 FOR X=0 TO X1
70 R3=R1+S1*X\Z1=R3\Z2=I3
80 FOR N=0 TO 30
90 A=Z1*Z1\B=Z2*Z2
100 IF A+B>4.0 THEN GOTO 130
110 Z2=2*Z1*Z2+I3\Z1=A-B+R3
120 NEXT N
130 PRINT STRING$(1%,62%-N);
140 NEXT X
150 PRINT
160 NEXT Y
170 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:;;;;<<<<===========
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 double
end 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 ret
end 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 ret
end operator
operator abs ( x as complex ) as double
return sqr(x.r*x.r + x.i*x.i)
end operator
dim as complex c, z
dim 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 y
next x
while inkey=""
wend
end
GW-BASIC
10 SCALE# = 1/60 : ZEROX = 160
20 ZEROY = 100 : MAXIT = 32
30 SCREEN 1
40 FOR X = 0 TO 2*ZEROX - 1
50 CR# = (X-ZEROX)*SCALE#
60 FOR Y = 0 TO ZEROY
70 CI# = (ZEROY-Y)*SCALE#
80 ZR# = 0
90 ZI# = 0
100 FOR I = 1 TO MAXIT
110 BR# = CR# + ZR#*ZR# - ZI#*ZI#
120 ZI# = CI# + 2*ZR#*ZI#
130 ZR# = BR#
140 IF ZR#*ZR# + ZI#*ZI# > 4 THEN GOTO 170
150 NEXT I
160 GOTO 190
170 PSET (X, Y), 1 + (I MOD 3)
180 PSET (X, 2*ZEROY-Y), 1+(I MOD 3)
190 NEXT Y
200 NEXT X
Liberty BASIC
Any words of description go outside of lang tags.
nomainwin
WindowWidth =440
WindowHeight =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
next
next
#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; " "; yScreen
end sub
[quit]
close #w
endLocomotive Basic
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 639
3 FOR yp = 0 TO 399
4 x = 0 : y = 0
5 x0 = xp / 213 - 2 : y0 = yp / 200 - 1
6 iteration = 0
7 maxIteration = 100
8 WHILE (x * x + y * y <= (2 * 2) AND iteration < maxIteration)
9 xtemp = x * x - y * y + x0
10 y = 2 * x * y + y0
11 x = xtemp
12 iteration = iteration + 1
13 WEND
14 IF iteration <> maxIteration THEN c = iteration ELSE c = 0
15 PLOT xp, yp, c MOD 16
16 NEXT
17 NEXT
Microsoft Small Basic
GraphicsWindow.Show()
size = 500
half = 250
GraphicsWindow.Width = size * 1.5
GraphicsWindow.Height = size
GraphicsWindow.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
EndFor
EndForMicrosoft Super Extended Color BASIC (Tandy Color Computer 3)
1 REM MANDELBROT SET - TANDY COCO 3
2 POKE 65497,1
10 HSCREEN 2
20 HCLS
30 X1=319:Y1=191
40 I1=-1.0:I2=1.0:R1=-2:R2=1.0
50 S1=(R2-R1)/X1:S2=(I2-I1)/Y1
60 FOR Y=0 TO Y1
70 I3=I1+S2*Y
80 FOR X=0 TO X1
90 R3=R1+S1*X:Z1=R3:Z2=I3
100 FOR N=0 TO 30
110 A=Z1*Z1:B=Z2*Z2
120 IF A+B>4.0 GOTO 150
130 Z2=2*Z1*Z2+I3:Z1=A-B+R3
140 NEXT N
150 HSET(X,Y,N-16*INT(N/16))
160 NEXT X
170 NEXT Y
180 GOTO 180MSX Basic
100 SCREEN 2
110 CLS
120 x1 = 256 : y1 = 192
130 i1 = -1 : i2 = 1
140 r1 = -2 : r2 = 1
150 s1 = (r2-r1)/x1 : s2 = (i2-i1)/y1
160 FOR y = 0 TO y1
170 i3 = i1+s2*y
180 FOR x = 0 TO x1
190 r3 = r1+s1*x
200 z1 = r3 : z2 = i3
210 FOR n = 0 TO 30
220 a = z1*z1 : b = z2*z2
230 IF a+b > 4 GOTO 270
240 z2 = 2*z1*z2+i3
250 z1 = a-b+r3
260 NEXT n
270 PSET (x,y),n-16*INT(n/16)
280 NEXT x
290 NEXT y
300 GOTO 300
- Output:
Nascom BASIC
In fact, it is based on the ZX81 version, but some optimizations are done to shorten the execution time (though they lengthen the code):
- The variables
X2andY2forXA*XAandYA*YArespectively are introduced in order to calculate the squares only once. - The value of
Xdoes not depend onJ, so it is calculated before theFOR Jloop. - The symmetry of the shape is taken into account in order to calculate symmetric values only once. It is the most significant optimization. The case
X=0(corresponding to the line 22 on the screen grid) is treated separately.
Only a fragment of the shape is drawn because of low resolution of block graphics. Like in the ZX81 version, you can adjust the constants in lines 40 and 70 to zoom in on a particular area, if you like.
10 REM Mandelbrot set
20 CLS
30 FOR I=0 TO 95
40 LET X=(I-78)/48
50 REM ** When X<>0
60 FOR J=1 TO 22
70 LET Y=(22-J)/30
80 LET XA=0:X2=0
90 LET YA=0:Y2=0
100 LET ITER=0
110 LET XTEMP=X2-Y2+X
120 LET YA=2*XA*YA+Y:Y2=YA*YA
130 LET XA=XTEMP:X2=XA*XA
140 LET ITER=ITER+1
150 IF X2+Y2<=4 AND ITER<200 THEN 110
160 IF ITER=200 THEN SET(I,J):SET(I,44-J)
170 NEXT J
180 REM ** When X=0
190 LET XA=0:X2=0
200 LET ITER=0
210 LET XA=X2+X:X2=XA*XA
220 LET ITER=ITER+1
230 IF X2<=4 AND ITER<200 THEN 210
240 IF ITER=200 THEN SET(I,22)
250 NEXT I
290 REM ** Set up machine code INKEY$ command
300 IF PEEK(1)<>0 THEN RESTORE 510
310 DOKE 4100,3328:FOR A=3328 TO 3342 STEP 2
320 READ B:DOKE A,B:NEXT A
400 SCREEN 1,15
410 PRINT "Hit any key to exit.";
420 A=USR(0):IF A<0 THEN 420
430 CLS
440 END
490 REM ** Data for machine code INKEY$
500 DATA 25055,1080,-53,536,-20665,3370,-5664,0
510 DATA 27085,14336,-13564,6399,18178,10927
520 DATA -8179,233
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=21
20 I1=-1.0\I2=1.0\R1=-2.0\R2=1.0
30 S1=(R2-R1)/X1\S2=(I2-I1)/Y1
40 FOR Y=0 TO Y1
50 I3=I1+S2*Y
60 FOR X=0 TO X1
70 R3=R1+S1*X\Z1=R3\Z2=I3
80 FOR N=0 TO 30
90 A=Z1*Z1\B=Z2*Z2
100 IF A+B>4.0 GOTO 130
110 Z2=2*Z1*Z2+I3\Z1=A-B+R3
120 NEXT N
130 PRINT CHR$(62-N);
140 NEXT X
150 PRINT
160 NEXT Y
170 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:;;;;<<<<===========
PureBasic
PureBasic forum: discussion
EnableExplicit
#Window1 = 0
#Image1 = 0
#ImgGadget = 0
#max_iteration = 64
#width = 800
#height = 600
Define.d x0 ,y0 ,xtemp ,cr, ci
Define.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:
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 13
WINDOW (-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
NEXT
NEXT
Quite BASIC
1000 REM Mandelbrot Set Project
1010 REM Quite BASIC Math Project
1015 REM 'http://www.quitebasic.com/prj/math/mandelbrot/
1020 REM ------------------------
1030 CLS
1040 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 palette
2010 GOSUB 3000
2020 REM L is the maximum iterations to try
2030 LET L = 100
2040 FOR I = 0 TO 100
2050 FOR J = 0 TO 100
2060 REM Map from pixel coordinates (I,J) to math (U,V)
2060 LET U = I / 50 - 1.5
2070 LET V = J / 50 - 1
2080 LET X = U
2090 LET Y = V
2100 LET N = 0
2110 REM Inner iteration loop starts here
2120 LET R = X * X
2130 LET Q = Y * Y
2140 IF R + Q > 4 OR N >= L THEN GOTO 2190
2150 LET Y = 2 * X * Y + V
2160 LET X = R - Q + U
2170 LET N = N + 1
2180 GOTO 2120
2190 REM Compute the color to plot
2200 IF N < 10 THEN LET C = "black" ELSE LET C = P[ROUND(8 * (N-10) / (L-10))]
2210 PLOT I, J, C
2220 NEXT J
2230 NEXT I
2240 END
3000 REM Subroutine -- Set up Palette
3010 ARRAY P
3020 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 RETURNRun 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 600
WindowHeight = 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"; guess
cls
[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 = 3/440
cc = 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 ?
next
next
'#w flush() 'what is flush? RunBasic uses the render command.
render #w
input "OK, hit enter to continue"; guess
cls
a = a + 0.75
b = b + 0.75
if 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; " "; yScreen
end sub
[quit]
'cls
print
print "This is a Mandelbrot Graph output from www.runbasic.com"
render #w
print "All done, good bye."
endSinclair ZX81 BASIC
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+Y
100 LET XA=XTEMP
110 LET ITER=ITER+1
120 IF XA*XA+YA*YA<=4 AND ITER<200 THEN GOTO 80
130 IF ITER=200 THEN PLOT I, J
140 NEXT J
150 NEXT I
SmileBASIC
Generates the points at random, gradually building up the image.
X = RNDF()*4-2
Y = RNDF()*4-2@N
N = N+16
I = X+S*S-T*T
T = Y+S*T*2
S = I
IF N < #L&&S*S+T*T < 4 GOTO @N
GPSET X*50+99, Y*50+99, RGB(99 XOR N,N,N)
EXEC.Alternative, based on the QBasic and other BASIC samples.
The 3DS screen is 400 x 240 pixels. SmileBASIC doesn't have +=, -=, etc. but there are INC and DEC statements.
OPTION STRICT
VAR XP, YP, X, Y, X0, Y0, X2, Y2
VAR NEXT_X, IT, C
FOR XP = -200 TO 199
FOR YP = -120 TO 119
X = 0: Y = 0
X0 = XP / 100: Y0 = YP / 100
IT = 0
X2 = X * X: Y2 = Y * Y
WHILE X2 + Y2 <= 4 AND IT < 100
NEXT_X = X2 - Y2 + X0
Y = 2 * X * Y + Y0
X = NEXT_X
X2 = X * X: Y2 = Y * Y
INC IT
WEND
IF IT == 100 THEN C = 0 ELSE C = IT
GPSET XP + 200, YP + 120, RGB((C * 3) MOD 200 + 50, FLOOR(C * 1.2) + 20, C)
NEXT
NEXT
TI-Basic Color
ClrDraw
~2->Xmin:1->Xmax:~1->Ymin:1->Ymax
AxesOff
FnOff
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
End
EndTrue BASIC
SET WINDOW 0, 256, 0, 192
LET x1 = 256/2
LET y1 = 192/2
LET i1 = -1
LET i2 = 1
LET r1 = -2
LET r2 = 1
LET s1 = (r2-r1) / x1
LET s2 = (i2-i1) / y1
FOR y = 0 TO y1 STEP .05
LET i3 = i1 + s2 * y
FOR x = 0 TO x1 STEP .05
LET r3 = r1 + s1 * x
LET z1 = r3
LET z2 = i3
FOR n = 0 TO 30
LET a = z1 * z1
LET b = z2 * z2
IF a+b > 4 THEN EXIT FOR
LET z2 = 2 * z1 * z2 + i3
LET z1 = a - b + r3
NEXT n
SET COLOR n - 16*INT(n/16)
PLOT POINTS: x,y
NEXT x
NEXT y
END
Visual BASIC for Applications on Excel
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 = 256
x = 0
y = 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 = i
End FunctionFile: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
Yabasic
open window 640, 320
wid = 4
xcenter = -1: ycenter = 0
ms = 0
for xcoord = 0 to 639
for ycoord = 0 to 160
ms = 0
ca =(xcoord-320)/640*wid+xcenter
cb =(ycoord-160)/640*wid+ycenter
x = 0: y=0
for t = 1 to 20
xnew = x*x-y*y+ca
ynew = 2*x*y+cb
x=xnew:y=ynew
magnitudesquared=x*x+y*y
ms = magnitudesquared
if (magnitudesquared > 100) break
//if(magnitudesquared < 100) then : color 0,0,0 : dot xcoord, ycoord : end if
next t
ms = ms+1
if(ms > 250) then
color 32,64,mod(ms,255)
dot xcoord, ycoord
dot xcoord, 320- ycoord
elseif (ms > 150) then
color mod(ms,255),64,32
dot xcoord, ycoord
dot xcoord, 320-ycoord
else
color 0,0,0
dot xcoord, ycoord
dot xcoord, 320-ycoord
end if
next ycoord
next xcoordBefunge
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:
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}{zzzzzzzzyyyyyxxwttuutqe Dj $uxy
}zzzzzzzzyxxxxxwwvuppnpn ` twxy
}yyyxxwvwwwxwvvvrtppc Y auwxxy
dqtvwxyy
}yyyxxwvwwwxwvvvrtppc Y auwxxy
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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 bx
use 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 += dAn example plot from the longer version:
Brainf***
A mandelbrot set fractal viewer in brainf*ck written by Erik Bosman
+++++++++++++[->++>>>+++++>++>+<<<<<<]>>>>>++++++>--->>>>>>>>>>+++++++++++++++[[
>>>>>>>>>]+[<<<<<<<<<]>>>>>>>>>-]+[>>>>>>>>[-]>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>[-]+
<<<<<<<+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>>>+>>>>>>>>>>>>>>>>>>>>>>>>>>
>+<<<<<<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+[>>>>>>[>>>>>>>[-]>>]<<<<<<<<<[<<<<<<<<<]>>
>>>>>[-]+<<<<<<++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>>+<<<<<<+++++++[-[->>>
>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>>+<<<<<<<<<<<<<<<<[<<<<<<<<<]>>>[[-]>>>>>>[>>>>>
>>[-<<<<<<+>>>>>>]<<<<<<[->>>>>>+<<+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>
[>>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<+<<]>>>>>>>>]<<<<<<<<<[<<<<<<<
<<]>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<<<]>>>>>>>>>+++++++++++++++[[
>>>>>>>>>]+>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[
>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>[-<<<<+>>>>]<<<<[->>>>+<<<<<[->>[
-<<+>>]<<[->>+>>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<
<<[>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<
[>[-]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+<<<<<<<<<]>>>>>
>>>>[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+
<<<<<<[->>>[-<<<+>>>]<<<[->>>+>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>
>>>>>>>]<<<<<<<<<[>>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<<]>>[->>>>>>>>>+<<<<<<<<<]<<
+>>>>>>>>]<<<<<<<<<[>[-]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<
<]<+<<<<<<<<<]>>>>>>>>>[>>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>
>>>>>]<<<<<<<<<-<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+>>>>>>>>>>>>>>>>>>>>>+<<<[<<<<<<
<<<]>>>>>>>>>[>>>[-<<<->>>]+<<<[->>>->[-<<<<+>>>>]<<<<[->>>>+<<<<<<<<<<<<<[<<<<<
<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>[-<<<<->>>>]+<<<<[->>>>-<[-<<<+>>>]<<<[->
>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<
<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]<<<<<<<[->+>>>-<<<<]>>>>>>>>>+++++++++++++++++++
+++++++>>[-<<<<+>>>>]<<<<[->>>>+<<[-]<<]>>[<<<<<<<+<[-<+>>>>+<<[-]]>[-<<[->+>>>-
<<<<]>>>]>>>>>>>>>>>>>[>>[-]>[-]>[-]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-]>>>>>>[>>>>>
[-<<<<+>>>>]<<<<[->>>>+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>[-<<<<<<<<
<+>>>>>>>>>]>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>>>>>>]+>[-
]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[>+>>>>>>>>]<<<
<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<<<[->>[-<<+>>]<
<[->>+>+<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>[->>>>
>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[>[-]<->>>
[-<<<+>[<->-<<<<<<<+>>>>>>>]<[->+<]>>>]<<[->>+<<]<+<<<<<<<<<]>>>>>>>>>[>>>>>>[-<
<<<<+>>>>>]<<<<<[->>>>>+<<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>+>>>>>>>>
]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<<<[->>[-<<+
>>]<<[->>+>>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>
[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[>[-
]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+<<<<<<<<<]>>>>>>>>>
[>>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>]>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>++++++++
+++++++[[>>>>>>>>>]<<<<<<<<<-<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[>>>>>>>>[-<<<<<<<+
>>>>>>>]<<<<<<<[->>>>>>>+<<<<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>>[
-]>>>]<<<<<<<<<[<<<<<<<<<]>>>>+>[-<-<<<<+>>>>>]>[-<<<<<<[->>>>>+<++<<<<]>>>>>[-<
<<<<+>>>>>]<->+>]<[->+<]<<<<<[->>>>>+<<<<<]>>>>>>[-]<<<<<<+>>>>[-<<<<->>>>]+<<<<
[->>>>->>>>>[>>[-<<->>]+<<[->>->[-<<<+>>>]<<<[->>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]
+>>>>>>[>>>>>>>>>]>+<]]+>>>[-<<<->>>]+<<<[->>>-<[-<<+>>]<<[->>+<<<<<<<<<<<[<<<<<
<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<<<
[<<<<<<<<<]>>>>[-<<<<+>>>>]<<<<[->>>>+>>>>>[>+>>[-<<->>]<<[->>+<<]>>>>>>>>]<<<<<
<<<+<[>[->>>>>+<<<<[->>>>-<<<<<<<<<<<<<<+>>>>>>>>>>>[->>>+<<<]<]>[->>>-<<<<<<<<<
<<<<<+>>>>>>>>>>>]<<]>[->>>>+<<<[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>>+<<<]<<
<<<<<<<<<<]>>>>[-]<<<<]>>>[-<<<+>>>]<<<[->>>+>>>>>>[>+>[-<->]<[->+<]>>>>>>>>]<<<
<<<<<+<[>[->>>>>+<<<[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>[->>>>+<<<<]>]<[->>>>-<<<<<<<
<<<<<<<+>>>>>>>>>>]<]>>[->>>+<<<<[->>>>-<<<<<<<<<<<<<<+>>>>>>>>>>]>]<[->>>>+<<<<
]<<<<<<<<<<<]>>>>>>+<<<<<<]]>>>>[-<<<<+>>>>]<<<<[->>>>+>>>>>[>>>>>>>>>]<<<<<<<<<
[>[->>>>>+<<<<[->>>>-<<<<<<<<<<<<<<+>>>>>>>>>>>[->>>+<<<]<]>[->>>-<<<<<<<<<<<<<<
+>>>>>>>>>>>]<<]>[->>>>+<<<[->>>-<<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>>+<<<]<<<<<<<
<<<<<]]>[-]>>[-]>[-]>>>>>[>>[-]>[-]>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>[-<
<<<+>>>>]<<<<[->>>>+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[
[>>>>>>>>>]+>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+
[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>[-<<<<+>>>>]<<<<[->>>>+<<<<<[->>
[-<<+>>]<<[->>+>+<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<
<[>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[
>[-]<->>>[-<<<+>[<->-<<<<<<<+>>>>>>>]<[->+<]>>>]<<[->>+<<]<+<<<<<<<<<]>>>>>>>>>[
>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>]>
>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>[-]>>>>+++++++++++++++[[>>>>>>>>>]<<<<<<<<<-<<<<<
<<<<[<<<<<<<<<]>>>>>>>>>-]+[>>>[-<<<->>>]+<<<[->>>->[-<<<<+>>>>]<<<<[->>>>+<<<<<
<<<<<<<<[<<<<<<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>[-<<<<->>>>]+<<<<[->>>>-<[-
<<<+>>>]<<<[->>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>
>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-<<<+>>>]<<<[->>>+>>>>>>[>+>>>
[-<<<->>>]<<<[->>>+<<<]>>>>>>>>]<<<<<<<<+<[>[->+>[-<-<<<<<<<<<<+>>>>>>>>>>>>[-<<
+>>]<]>[-<<-<<<<<<<<<<+>>>>>>>>>>>>]<<<]>>[-<+>>[-<<-<<<<<<<<<<+>>>>>>>>>>>>]<]>
[-<<+>>]<<<<<<<<<<<<<]]>>>>[-<<<<+>>>>]<<<<[->>>>+>>>>>[>+>>[-<<->>]<<[->>+<<]>>
>>>>>>]<<<<<<<<+<[>[->+>>[-<<-<<<<<<<<<<+>>>>>>>>>>>[-<+>]>]<[-<-<<<<<<<<<<+>>>>
>>>>>>>]<<]>>>[-<<+>[-<-<<<<<<<<<<+>>>>>>>>>>>]>]<[-<+>]<<<<<<<<<<<<]>>>>>+<<<<<
]>>>>>>>>>[>>>[-]>[-]>[-]>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-]>[-]>>>>>[>>>>>>>[-<<<<<
<+>>>>>>]<<<<<<[->>>>>>+<<<<+<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>+>[-<-<<<<+>>>>
>]>>[-<<<<<<<[->>>>>+<++<<<<]>>>>>[-<<<<<+>>>>>]<->+>>]<<[->>+<<]<<<<<[->>>>>+<<
<<<]+>>>>[-<<<<->>>>]+<<<<[->>>>->>>>>[>>>[-<<<->>>]+<<<[->>>-<[-<<+>>]<<[->>+<<
<<<<<<<<<[<<<<<<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>[-<<->>]+<<[->>->[-<<<+>>>]<
<<[->>>+<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<
<<<<<<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-<<<+>>>]<<<[->>>+>>>>>>[>+>[-<->]<[->+
<]>>>>>>>>]<<<<<<<<+<[>[->>>>+<<[->>-<<<<<<<<<<<<<+>>>>>>>>>>[->>>+<<<]>]<[->>>-
<<<<<<<<<<<<<+>>>>>>>>>>]<]>>[->>+<<<[->>>-<<<<<<<<<<<<<+>>>>>>>>>>]>]<[->>>+<<<
]<<<<<<<<<<<]>>>>>[-]>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<<<]]>>>>[-<<<<+>
>>>]<<<<[->>>>+>>>>>[>+>>[-<<->>]<<[->>+<<]>>>>>>>>]<<<<<<<<+<[>[->>>>+<<<[->>>-
<<<<<<<<<<<<<+>>>>>>>>>>>[->>+<<]<]>[->>-<<<<<<<<<<<<<+>>>>>>>>>>>]<<]>[->>>+<<[
->>-<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>+<<]<<<<<<<<<<<<]]>>>>[-]<<<<]>>>>[-<<<<+>>
>>]<<<<[->>>>+>[-]>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+<<+<<<<<]>>>>>>>>>[>>>>>>
>>>]<<<<<<<<<[>[->>>>+<<<[->>>-<<<<<<<<<<<<<+>>>>>>>>>>>[->>+<<]<]>[->>-<<<<<<<<
<<<<<+>>>>>>>>>>>]<<]>[->>>+<<[->>-<<<<<<<<<<<<<+>>>>>>>>>>>]<]>[->>+<<]<<<<<<<<
<<<<]]>>>>>>>>>[>>[-]>[-]>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>[-]>[-]>>>>>[>>>>>[-<<<<+
>>>>]<<<<[->>>>+<<<+<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>>[-<<<<<+>>>>>
]<<<<<[->>>>>+<<<+<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>
>>>>>]+>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]>[-]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+[>+>>
>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>[-<<<<+>>>>]<<<<[->>>>+<<<<<[->>[-<<+
>>]<<[->>+>>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>
[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<]>[->>>>>>>>>+<<<<<<<<<]<+>>>>>>>>]<<<<<<<<<[>[-
]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+<<<<<<<<<]>>>>>>>>>
[>+>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>->>>>>[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<
<<[->>>[-<<<+>>>]<<<[->>>+>+<<<<]+>>>>>>>>>]<<<<<<<<[<<<<<<<<<]]>>>>>>>>>[>>>>>>
>>>]<<<<<<<<<[>>[->>>>>>>>>+<<<<<<<<<]<<<<<<<<<<<]>>[->>>>>>>>>+<<<<<<<<<]<<+>>>
>>>>>]<<<<<<<<<[>[-]<->>>>[-<<<<+>[<->-<<<<<<+>>>>>>]<[->+<]>>>>]<<<[->>>+<<<]<+
<<<<<<<<<]>>>>>>>>>[>>>>[-<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<+>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>]>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>+++++++++++++++[[>>>>>>>>
>]<<<<<<<<<-<<<<<<<<<[<<<<<<<<<]>>>>>>>>>-]+>>>>>>>>>>>>>>>>>>>>>+<<<[<<<<<<<<<]
>>>>>>>>>[>>>[-<<<->>>]+<<<[->>>->[-<<<<+>>>>]<<<<[->>>>+<<<<<<<<<<<<<[<<<<<<<<<
]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>[-<<<<->>>>]+<<<<[->>>>-<[-<<<+>>>]<<<[->>>+<
<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>
>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>->>[-<<<<+>>>>]<<<<[->>>>+<<[-]<<]>>]<<+>>>>[-<<<<
->>>>]+<<<<[->>>>-<<<<<<.>>]>>>>[-<<<<<<<.>>>>>>>]<<<[-]>[-]>[-]>[-]>[-]>[-]>>>[
>[-]>[-]>[-]>[-]>[-]>[-]>>>]<<<<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>[-]>>>>]<<<<<<<<<
[<<<<<<<<<]>+++++++++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>+>>>>>>>>>+<<<<<<<<
<<<<<<[<<<<<<<<<]>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+[-]>>[>>>>>>>>>]<<<<<
<<<<[>>>>>>>[-<<<<<<+>>>>>>]<<<<<<[->>>>>>+<<<<<<<[<<<<<<<<<]>>>>>>>[-]+>>>]<<<<
<<<<<<]]>>>>>>>[-<<<<<<<+>>>>>>>]<<<<<<<[->>>>>>>+>>[>+>>>>[-<<<<->>>>]<<<<[->>>
>+<<<<]>>>>>>>>]<<+<<<<<<<[>>>>>[->>+<<]<<<<<<<<<<<<<<]>>>>>>>>>[>>>>>>>>>]<<<<<
<<<<[>[-]<->>>>>>>[-<<<<<<<+>[<->-<<<+>>>]<[->+<]>>>>>>>]<<<<<<[->>>>>>+<<<<<<]<
+<<<<<<<<<]>>>>>>>-<<<<[-]+<<<]+>>>>>>>[-<<<<<<<->>>>>>>]+<<<<<<<[->>>>>>>->>[>>
>>>[->>+<<]>>>>]<<<<<<<<<[>[-]<->>>>>>>[-<<<<<<<+>[<->-<<<+>>>]<[->+<]>>>>>>>]<<
<<<<[->>>>>>+<<<<<<]<+<<<<<<<<<]>+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>+<<<
<<[<<<<<<<<<]>>>>>>>>>[>>>>>[-<<<<<->>>>>]+<<<<<[->>>>>->>[-<<<<<<<+>>>>>>>]<<<<
<<<[->>>>>>>+<<<<<<<<<<<<<<<<[<<<<<<<<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>>>>[-<
<<<<<<->>>>>>>]+<<<<<<<[->>>>>>>-<<[-<<<<<+>>>>>]<<<<<[->>>>>+<<<<<<<<<<<<<<[<<<
<<<<<<]>>>[-]+>>>>>>[>>>>>>>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<
<<[<<<<<<<<<]>>>>[-]<<<+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>-<<<<<[<<<<<<<
<<]]>>>]<<<<.>>>>>>>>>>[>>>>>>[-]>>>]<<<<<<<<<[<<<<<<<<<]>++++++++++[-[->>>>>>>>
>+<<<<<<<<<]>>>>>>>>>]>>>>>+>>>>>>>>>+<<<<<<<<<<<<<<<[<<<<<<<<<]>>>>>>>>[-<<<<<<
<<+>>>>>>>>]<<<<<<<<[->>>>>>>>+[-]>[>>>>>>>>>]<<<<<<<<<[>>>>>>>>[-<<<<<<<+>>>>>>
>]<<<<<<<[->>>>>>>+<<<<<<<<[<<<<<<<<<]>>>>>>>>[-]+>>]<<<<<<<<<<]]>>>>>>>>[-<<<<<
<<<+>>>>>>>>]<<<<<<<<[->>>>>>>>+>[>+>>>>>[-<<<<<->>>>>]<<<<<[->>>>>+<<<<<]>>>>>>
>>]<+<<<<<<<<[>>>>>>[->>+<<]<<<<<<<<<<<<<<<]>>>>>>>>>[>>>>>>>>>]<<<<<<<<<[>[-]<-
>>>>>>>>[-<<<<<<<<+>[<->-<<+>>]<[->+<]>>>>>>>>]<<<<<<<[->>>>>>>+<<<<<<<]<+<<<<<<
<<<]>>>>>>>>-<<<<<[-]+<<<]+>>>>>>>>[-<<<<<<<<->>>>>>>>]+<<<<<<<<[->>>>>>>>->[>>>
>>>[->>+<<]>>>]<<<<<<<<<[>[-]<->>>>>>>>[-<<<<<<<<+>[<->-<<+>>]<[->+<]>>>>>>>>]<<
<<<<<[->>>>>>>+<<<<<<<]<+<<<<<<<<<]>+++++[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>
+>>>>>>>>>>>>>>>>>>>>>>>>>>>+<<<<<<[<<<<<<<<<]>>>>>>>>>[>>>>>>[-<<<<<<->>>>>>]+<
<<<<<[->>>>>>->>[-<<<<<<<<+>>>>>>>>]<<<<<<<<[->>>>>>>>+<<<<<<<<<<<<<<<<<[<<<<<<<
<<]>>>>[-]+>>>>>[>>>>>>>>>]>+<]]+>>>>>>>>[-<<<<<<<<->>>>>>>>]+<<<<<<<<[->>>>>>>>
-<<[-<<<<<<+>>>>>>]<<<<<<[->>>>>>+<<<<<<<<<<<<<<<[<<<<<<<<<]>>>[-]+>>>>>>[>>>>>>
>>>]>[-]+<]]+>[-<[>>>>>>>>>]<<<<<<<<]>>>>>>>>]<<<<<<<<<[<<<<<<<<<]>>>>[-]<<<++++
+[-[->>>>>>>>>+<<<<<<<<<]>>>>>>>>>]>>>>>->>>>>>>>>>>>>>>>>>>>>>>>>>>-<<<<<<[<<<<
<<<<<]]>>>]- 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'
The following version should work on architectures (such as x86/x86-64) that allow unaligned pointers.
#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;
}
Here is a variant that hopefully will work on a broader range of architectures, although it has been tested only on x86-64.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <GL/glut.h>
#include <GL/gl.h>
#include <GL/glu.h>
void set_texture();
unsigned char *tex;
int gwin;
GLuint texture;
int width, height;
int old_width, old_height;
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()
{
glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_REPLACE);
glBindTexture(GL_TEXTURE_2D, texture);
glBegin(GL_QUADS);
glTexCoord2d(0, 0);
glVertex2i(0, 0);
glTexCoord2d(1, 0);
glVertex2i(width, 0);
glTexCoord2d(1, 1);
glVertex2i(width, height);
glTexCoord2d(0, 1);
glVertex2i(0, height);
glEnd();
glFlush();
glFinish();
}
int dump = 1;
void screen_dump()
{
char fn[100];
sprintf(fn, "screen%03d.ppm", dump++);
FILE *fp = fopen(fn, "w");
fprintf(fp, "P6\n%d %d\n255\n", width, height);
for (int i = height - 1; i >= 0; i -= 1) {
for (int j = 0; j < width; j += 1) {
fwrite(&tex[((i * width) + j) * 4], 1, 3, fp);
}
}
fclose(fp);
printf("%s written\n", fn);
}
void keypress(unsigned char key,[[maybe_unused]]
int x,[[maybe_unused]]
int y)
{
switch (key) {
case 'q':
glFinish();
glutDestroyWindow(gwin);
break;
case 27:
scale = 1. / 256;
cx = -.6;
cy = 0;
set_texture();
break;
case 'r':
color_rotate = (color_rotate + 1) % 6;
set_texture();
break;
case '>':
case '.':
max_iter += 128;
if (max_iter > 1 << 15)
max_iter = 1 << 15;
printf("max iter: %d\n", max_iter);
set_texture();
break;
case '<':
case ',':
max_iter -= 128;
if (max_iter < 128)
max_iter = 128;
printf("max iter: %d\n", max_iter);
set_texture();
break;
case 'c':
saturation = 1 - saturation;
set_texture();
break;
case 's':
screen_dump();
break;
case 'z':
max_iter = 4096;
set_texture();
break;
case 'x':
max_iter = 128;
set_texture();
break;
case ' ':
invert = !invert;
set_texture();
break;
default:
set_texture();
break;
}
}
#define VAL 255
void hsv_to_rgba(int hue, int min, int max, unsigned char *px)
{
unsigned char r;
unsigned char g;
unsigned char b;
if (min == max)
max = min + 1;
if (invert)
hue = max - (hue - min);
if (!saturation) {
r = 255 * (max - hue) / (max - min);
g = r;
b = r;
} else {
double h =
fmod(color_rotate + 1e-4 + 4.0 * (hue - min) / (max - min), 6);
double c = VAL * saturation;
double X = c * (1 - fabs(fmod(h, 2) - 1));
r = 0;
g = 0;
b = 0;
switch ((int) h) {
case 0:
r = c;
g = X;
break;
case 1:
r = X;
g = c;
break;
case 2:
g = c;
b = X;
break;
case 3:
g = X;
b = c;
break;
case 4:
r = X;
b = c;
break;
default:
r = c;
b = X;
break;
}
}
/* Using an alpha channel neatly solves the problem of aligning
* rows on 4-byte boundaries (at the expense of memory, of
* course). */
px[0] = r;
px[1] = g;
px[2] = b;
px[3] = 255; /* Alpha channel. */
}
void calc_mandel()
{
int i, j, iter, min, max;
double x, y, zx, zy, zx2, zy2;
unsigned short *hsv = malloc(width * height * sizeof(unsigned short));
min = max_iter;
max = 0;
for (i = 0; i < height; i++) {
y = (i - height / 2) * scale + cy;
for (j = 0; j < width; j++) {
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 = 0;
zy = 0;
zx2 = 0;
zy2 = 0;
while (iter < max_iter && zx2 + zy2 < 4) {
zy = 2 * zx * zy + y;
zx = zx2 - zy2 + x;
zx2 = zx * zx;
zy2 = zy * zy;
iter += 1;
}
if (iter < min)
min = iter;
if (iter > max)
max = iter;
hsv[(i * width) + j] = iter;
}
}
for (i = 0; i < height; i += 1) {
for (j = 0; j < width; j += 1) {
unsigned char *px = tex + (((i * width) + j) * 4);
hsv_to_rgba(hsv[(i * width) + j], min, max, px);
}
}
free(hsv);
}
void alloc_tex()
{
if (tex == NULL || width != old_width || height != old_height) {
free(tex);
tex = malloc(height * width * 4 * sizeof(unsigned char));
memset(tex, 0, height * width * 4 * sizeof(unsigned char));
old_width = width;
old_height = height;
}
}
void set_texture()
{
alloc_tex();
calc_mandel();
glEnable(GL_TEXTURE_2D);
glBindTexture(GL_TEXTURE_2D, texture);
glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, width, height,
0, GL_RGBA, GL_UNSIGNED_BYTE, tex);
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((double) x) * 1e-16
&& scale > fabs((double) 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_RGBA);
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)
{
tex = NULL;
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;
}
// local variables:
// mode: C
// c-file-style: "k&r"
// c-basic-offset: 4
// end:
(PLEASE FIXME: Does resizing work correctly, in either version?)
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!!;;;--------:::::::::::::::..........
...:::::::::::::::::::::::::::::------------------------:::::::::::::::.............
.....::::::::::::::::::::::::::::::::::-----------:::::::::::::::::::...............
.........::::::::::::::::::::::::::::::::::::::::::::::::::::::::...................
.............::::::::::::::::::::::::::::::::::::::::::::::::.......................
Fixed point 16 bit arithmetic
/**
ascii Mandelbrot using 16 bits of fixed point integer maths with a selectable fractional precision in bits.
This is still only 16 bits mathc and allocating more than 6 bits of fractional precision leads to an overflow that adds noise to the plot..
This code frequently casts to short to ensure we're not accidentally benefitting from GCC promotion from short 16 bits to int.
gcc fixedPoint.c -lm
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <stdint.h>
#include <string.h>
short s(short i);
short toPrec(double f, int bitsPrecision);
int main(int argc, char* argv[])
{
// chosen to match https://www.youtube.com/watch?v=DC5wi6iv9io
int width = 32; // basic width of a zx81
int height = 22; // basic width of a zx81
int zoom=3; // bigger with finer detail ie a smaller step size - leave at 1 for 32x22
// params
short bitsPrecision = 6;
printf("PRECISION=%d\n", bitsPrecision);
short X1 = toPrec(3.5,bitsPrecision) / zoom;
short X2 = toPrec(2.25,bitsPrecision) ;
short Y1 = toPrec(3,bitsPrecision)/zoom ; // horiz pos
short Y2 = toPrec(1.5,bitsPrecision) ; // vert pos
short LIMIT = toPrec(4,bitsPrecision);
// fractal
//char * chr = ".:-=X$#@.";
char * chr = "abcdefghijklmnopqr ";
//char * chr = ".,'~=+:;[/<&?oxOX#.";
short maxIters = strlen(chr);
short py=0;
while (py < height*zoom) {
short px=0;
while (px < width*zoom) {
short x0 = s(s(px*X1) / width) - X2;
short y0 = s(s(py*Y1) / height) - Y2;
short x=0;
short y=0;
short i=0;
short xSqr;
short ySqr;
while (i < maxIters) {
xSqr = s(x * x) >> bitsPrecision;
ySqr = s(y * y) >> bitsPrecision;
// Breakout if sum is > the limit OR breakout also if sum is negative which indicates overflow of the addition has occurred
// The overflow check is only needed for precisions of over 6 bits because for 7 and above the sums come out overflowed and negative therefore we always run to maxIters and we see nothing.
// By including the overflow break out we can see the fractal again though with noise.
if ((xSqr + ySqr) >= LIMIT || (xSqr+ySqr) < 0) {
break;
}
short xt = xSqr - ySqr + x0;
y = s(s(s(x * y) >> bitsPrecision) * 2) + y0;
x=xt;
i = i + 1;
}
i = i - 1;
printf("%c", chr[i]);
px = px + 1;
}
printf("\n");
py = py + 1;
}
}
// convert decimal value to a fixed point value in the given precision
short toPrec(double f, int bitsPrecision) {
short whole = ((short)floor(f) << (bitsPrecision));
short part = (f-floor(f))*(pow(2,bitsPrecision));
short ret = whole + part;
return ret;
}
// convenient casting
short s(short i) {
return i;
}
$ gcc fixedPoint.c -lm && ./a.out PRECISION=6 aaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcdcccbbbbbb aaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccddcbbbbb aaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbegfcdbbb aaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdccedbb aaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdcccb aaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbcfdddcccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdded aaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbcccccddfcccccccccccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccc aaaaaaaaaaaaaaaaaabbbbbbbbbbbbbcccccdeccccccccccccccccccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbcc aaaaaaaaaaaaaaaaabbbbbbbbbbfcccccddeccccccccccccccccdddddeeeddddccccccbbbbbbbbbbbbbbbbbbbbbbbbbe aaaaaaaaaaaaaaaabbbbbbbbbbcccccdddccccccccccccccdeddddeefigeeeddddecccccbbbbbbbbbbbbbbbbbbbbbbbb aaaaaaaaaaaaaaaabbbbbbbecccccdddcccccccccccccdddddddddeefhmgfffddddedcccccbbbbbbbbbbbbbbbbbbbbbb aaaaaaaaaaaaaaabbbbbbbcccccccdcccccccccccccccdgddddddfeefgjpijjfdddddedccccccbbbbbbbbbbbbbbbbbbb aaaaaaaaaaaaaaabbbbbccccccdedccccccccccccccdddddddddeeefgkj ojgfedddddeccccccbbbbbbbbbbbbbbbbbbb aaaaaaaaaaaaaabbbbbcccccegeccccccccccccccdeedddddddeeeeghhkp hgheefddddecccccccbbbbbbbbbbbbbbbbb aaaaaaaaaaaaabbbbccccceddcccccccccccccccfddddddddeeeeefmlkr ihheeeedddddgccccccbbbbbbbbbbbbbbbb aaaaaaaaaaaaabbbccccddfcccccccccccccccedddddddddeeegffhnp rpjffeeeiddddcccccccbbbbbbbbbbbbbbb aaaaaaaaaaaabbbcccddecccccccccccccccddddddddddeeffffgghm jgffeeeegdddccccccccbbbbbbbbbbbbb aaaaaaaaaaabbbccdedccccccccccccccccdddddddddeefffffgghil khggffffeeeddccccccccbbbbbbbbbbbb aaaaaaaaaaabbccdeccccccccccccccccddddddddeeef ijjhhhkijlo qkihjhgffgngeddcccccccbbbbbbbbbbbb aaaaaaaaaabbcddccccccccccccccccdddddddfeeeefgjq lkk p n khhhiqifedcccccccdbbbbbbbbbbb aaaaaaaaaabbccccccccccccccccccddddddefeeeeffgilq plk rrqgeddcccccccdbbbbbbbbbb aaaaaaaaaabdccccccccccccccccdddhegeeeeeefffghiq mfeeddcccccccdbbbbbbbbb aaaaaaaaaaccccccccccccccccdddeeeeeeeeeeffffhjklp phfeeddcccccccdcbbbbbbbb aaaaaaaaabcccccccccccccddddegeeeeeeeeeffffhppp jgggedddccccccccbbbbbbbb aaaaaaaaabccccccccccddddeefpifffffffffggggik hgfedddcccccccdcbbbbbbb aaaaaaaaaccccccceddddddeeifl hgggjrhggggghj p qjnfdddcccccccdcbbbbbbb aaaaaaaabccccddedddddefeefghqnokkloqiqhhhik ifdddcccccccdcbbbbbbb aaaaaaaaccceddddddddgfeeffghir o n qmjiijo igfedddcccccccccbbbbbb aaaaaaaaccddedddddeeeeeefgghkq lll lgfddddcccccccdcbbbbbb aaaaaaaacddddddddeeeeeefhgjol rn geddddcccccccdcbbbbbb aaaaaaaaedddddddeeeffggojjll hfeddddeccccccdcbbbbbb aaaaaaaaddddddefffffggmkopmop ngfefdddfccccccdcbbbbbb aaaaaaaaeeffgihggiihikk hfeefdddeccccccddbbbbbb aaaaaaaa kigfgefdddecccccceebbbbbb aaaaaaaaeeffhgjggghhhklqm ligfhefdddeccccccddbbbbbb aaaaaaaaddddddefffffgggirq hffefdddeccccccdebbbbbb aaaaaaaahdddddddeefgfggilkjk hfeedddeccccccddbbbbbb aaaaaaaacddddddddeeeeeefhhhkl lfefdddeccccccdcbbbbbb aaaaaaaaccddedddddefeeeeffgijo on qfedddcccccccdcbbbbbb aaaaaaaabcceddddddddegeeefggik r kko jhfedddcccccccdcbbbbbb aaaaaaaabccccddddddddefeeefijmk jkp kmiijlq qhfedddcccccccccbbbbbb aaaaaaaaacccccccdddddddeeefh hhghi kjggghil r geddcccccccdcbbbbbbb aaaaaaaaabccccccccccdddddefgnfgffghggggggghjm lj feddcccccccdcbbbbbbb aaaaaaaaabccccccccccccccdddeffggeeeefffffggm igfefddcccccccdbbbbbbbb aaaaaaaaaaccccccccccccccccdddeeeeeeeeeeffffhjm kgfeddcccccccdcbbbbbbbb aaaaaaaaaabdccccccccccccccccdddfeeeeeeeegffgiikq feeddcccccccebbbbbbbbb aaaaaaaaaabbccccccccccccccccccdddddegeeeegffgho p nheeddcccccchfbbbbbbbbb aaaaaaaaaabbbddcccccccccccccccccdddddeeeeeefhm l ki jlnjeddcccccccdbbbbbbbbbb aaaaaaaaaaabbccecccccccccccccccccdddddddfeeefir jii npm k ohgggineedcccccccdbbbbbbbbbbb aaaaaaaaaaabbbccdddccccccccccccccccddddddddeeefggggggiik mjhhgfffffedddcccccccbbbbbbbbbbbb aaaaaaaaaaaabbbcccedfcccccccccccccccdddddddddeegffffgghp hgffgeeeedddccccccccbbbbbbbbbbbb aaaaaaaaaaaabbbbccccdddcccccccccccccccgdddddddddeegffgil ggfeeeeddddcccccccbbbbbbbbbbbbbb aaaaaaaaaaaaabbbbbccccdddccccccccccccccfeddddddddeeeefgi l nkqgeeegeddddcccccccbbbbbbbbbbbbbbb aaaaaaaaaaaaabbbbbbcccccdedccccccccccccccdedddddddeeeeeghik khhfeefdddddeccccccbbbbbbbbbbbbbbbb aaaaaaaaaaaaaabbbbbbccccccdddcccccccccccccddedddddddeeefigil jggfedddddddcccccbbbbbbbbbbbbbbbbbb aaaaaaaaaaaaaaabbbbbbbcccccccdccccccccccccccdefdddddeeeffhlliimfdddddedccccccbbbbbbbbbbbbbbbbbbb aaaaaaaaaaaaaaaabbbbbbbccccccdddccccccccccccccdddddddeeefg jggheddddedccccccbbbbbbbbbbbbbbbbbbbb aaaaaaaaaaaaaaaabbbbbbbbbccccccdddccccccccccccccdedddddefgiffeeddddeccccccbbbbbbbbbbbbbbbbbbbbbb aaaaaaaaaaaaaaaaabbbbbbbbbbecccccdeeccccccccccccccceddddeffegddddgcccccbbbbbbbbbbbbbbbbbbbbbbbbb aaaaaaaaaaaaaaaaaabbbbbbbbbbbbcccccdddcccccccccccccccccddddddddccccccbbbbbbbbbbbbbbbbbbbbbbbbbbc aaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbccccddeccccccccccccccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbed aaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbccceddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccd aaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbdcccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbecccc aaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccdebb aaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdfccbbb aaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcgdccbbbb
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 arrays
template<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.
A Simple version in CPP. Definitely not as crazy good as the ASCII one in C above.
#include <stdio.h>
int f(float X, float Y, float x, float y, int n){
return (x*x+y*y<4 && n<100)?1+f(X, Y, x*x-y*y+X, 2*x*y+Y, n+1):0;
}
main(){
for(float j=1; j>=-1; j-=.015)
for(float i=-2, x; i<=.5; i+=.015, x=f(i, j, 0, 0, 0))
printf("%c%s", x<10?' ':x<20?'.':x<50?':':x<80?'*':'#', i>-2?" ":"\n");
}
C3
This program produces a BMP as output.
module mandelbrot;
extern fn int atoi(char *s);
extern fn int printf(char *s, ...);
extern fn void putchar(int c);
fn void main(int argc, char **argv)
{
int w = atoi(argv[1]);
int h = w;
const LIMIT = 2.0;
const SQUARE_LIMIT = LIMIT * LIMIT;
printf("P4\n%d %d\n", w, h);
int iter = 50;
int bit_num = 0;
char byte_acc = 0;
for (double y = 0; y < h; y++)
{
for (double x = 0; x < w; x++)
{
double zr;
double zi;
double ti;
double tr;
double cr = (2.0 * x / w - 1.5);
double ci = (2.0 * y / h - 1.0);
for (int i = 0; i < iter && (tr + ti <= SQUARE_LIMIT); i++)
{
zi = 2.0 * zr * zi + ci;
zr = tr - ti + cr;
tr = zr * zr;
ti = zi * zi;
}
byte_acc <<= 1;
if (tr + ti <= SQUARE_LIMIT) byte_acc |= 0x01;
++bit_num;
if (bit_num == 8)
{
putchar(byte_acc);
byte_acc = 0;
bit_num = 0;
}
else if (x == w - 1)
{
byte_acc <<= (8 - w % 8);
putchar(byte_acc);
byte_acc = 0;
bit_num = 0;
}
}
}
}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-cursor
raw-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 _
$is-done deref !
} while
#out reset-style
#out clear-screen
1 1 #out move-to
#out show-cursor
normal-modeClojure
Inspired by the Ruby and Perl below
(defn complex-add
[[a0 b0] [a1 b1]]
[(+ a0 a1) (+ b0 b1)])
(defn complex-square
[[a b]]
[(- (* a a) (* b b)) (* 2 a b)])
(defn complex-abs
[[a b]]
(Math/sqrt (+ (* a a) (* b b))))
(defn f
[z c]
(complex-add z (complex-square c)))
(defn mandelbrot?
[z]
(> 2 (complex-abs (nth (iterate (partial f z) [0 0]) 20))))
(doseq [y (range 1 -1 -0.05)]
(doseq [x (range -2 0.5 0.0315)]
(print (if (mandelbrot? [(double x) (double y)]) "*" " ")))
(println ""))
- Output:
harold@freeside:~/src/mandelbrot$ clj -M mandelbrot.clj
*
* *** *
********
*********
******
** ** ************ *
*** ******************* * *
*****************************
****************************
********************************
********************************
************************************ *
* * ***********************************
*********** ***********************************
************ **************************************
************** ************************************
****************************************************
*******************************************************
************************************************************************
*******************************************************
****************************************************
************** ************************************
************ **************************************
*********** ***********************************
* * ***********************************
************************************ *
********************************
********************************
****************************
*****************************
*** ******************* * *
** ** ************ *
******
*********
********
* *** *
*
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
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:
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'+)%%%$$$$$#####"""""""""""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(+,)++&%$$$$$$######""""""
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*5:/+('&%%$$$$$$#######"""
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),@@@@@@@,'&%%%%%$$$$########
!!!!!!!"""####################$$$$$$$$%%%&'())((())*,@@@@@@/+))('&&&&)'%$$######
!!!!!!""###################$$$$$%%%%%%&&&'+.@@=/<@@@@@@@@@@@@@@@/++@..93%%$#####
!!!!!"################$$$%%%%%%%%%%&&&&'),+2@@@@@@@@@@@@@@@@@@@@@@@@@1(&&%$$####
!!!!"##########$$$$$%%&(-(''''''''''''(*,5@@@@@@@@@@@@@@@@@@@@@@@@@@@@+)-&%$$###
!!!!####$$$$$$$$%%%%%&'(*-@1.+.@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4-(&%$$$##
!!!!#$$$$$$$$$%%%%%%'''++.6@@@@@@@@@8/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3(%%$$$$#
!!!#$$$$$$$%&&&&''()/-5.5@@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?'&%%$$$$#
!!!(**+/+<523/80/46@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+)'&&%%$$$$#
!!!#$$$$$$$%&&&&''().-2.@@@@@@@@@@@@@@?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$#
!!!!#$$$$$$$$$%%%%%&'''/,.7@@@@@@@@@;/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0'%%$$$$#
!!!!####$$$$$$$$%%%%%&'(*-:2.,/?-5+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+(&%$$$##
!!!!"##########$$$$$%%&(-(''''(''''''((*,4@@@@@@@@@@@@@@@@@@@@@@@@@@@4+).&%$$###
!!!!!"################$$$%%%%%%%%%%&&&&')<,4@@@@@@@@@@@@@@@@@@@@@@@@@/('&%%$####
!!!!!!""##################$$$$$$%%%%%%&&&'*.@@@0@@@@@@@@@@@@@@@@1,,@//9)%%$#####
!!!!!!!"""####################$$$$$$$$%%%&(())((()**-@@@@@@/+)))'&&&')'%$$######
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''(,@@@@@@@+'&&%%%%%$$$########
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*7@0+('&%%%$$$$$#######"""
!!!!!!!!!!!"""""""######################$$$$$$$$$%%%&&(+-).*&%$$$$$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$%%'3(%%%$$$$$######""""""""""
!!!!!!!!!!!!!!!""""""""""""#####################################""""""""""""""""
Craft Basic
define max = 15, w = 640, h = 480
define py = 0, px = 0, sx = 0, sy = 0
define xx = 0, xy = 0
bgcolor 0, 0, 0
cls graphics
fill on
do
let px = 0
do
let sy = (py - h / 2) / 150
let sx = (px - w / 2) / 150
let i = 0
let x = 0
let y = 0
let xy = x * x + y * y
do
let xx = x * x - y * y + sx + .1
let y = 2 * x * y + sy
let x = xx
let i = i + 1
loop i < max and xy < 4
wait
fgcolor 220 + i * x, 220 + i * y, 230 + i * xy
rect px, py, 4, 4
let px = px + 4
loop px < w
let py = py + 4
loop py < h
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
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 Dart, works on https://dartpad.dev The implementation uses an incomplete Complex class supporting operator overloading.
class Complex {
double _r, _i;
Complex(this._r, this._i);
get r => _r;
get i => _i;
toString() => "($r,$i)";
operator +(Complex other) => Complex(r + other.r, i + other.i);
operator *(Complex other) =>
Complex(r * other.r - i * other.i, r * other.i + other.r * i);
abs() => r * r + i * i;
}
void main() {
const startX = -1.5;
const startY = -1.0;
const stepX = 0.03;
const stepY = 0.1;
for (int y = 0; y < 20; y++) {
String line = "";
for (int x = 0; x < 70; x++) {
var c = Complex(startX + stepX * x, startY + stepY * y);
var z = 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
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-1
0 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
] s2
l2 x- Output:
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'0(%%%$$$$$#####"""""""""""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(++)++&$$$$$$$######""""""
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*@;/*('&%%$$$$$$#######"""
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),@@@@@@@+'&%%%%%$$$$########
!!!!!!!"""####################$$$$$$$$%%%&'())((())*-@@@@@@.+))('&&&&+&%$$######
!!!!!!""###################$$$$$%%%%%%&&&'+.@@@08@@@@@@@@@@@@@@@/+,@//@)%%$#####
!!!!!"################$$$%%%%%%%%%%&&&&')-+7@@@@@@@@@@@@@@@@@@@@@@@@@4(&&%$$####
!!!!"##########$$$$$%%&(,('''''''''''((*-5@@@@@@@@@@@@@@@@@@@@@@@@@@@3+)4&%$$###
!!!!####$$$$$$$$%%%%%&'(*-@1.+/@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3+'&%$$$##
!!!!#$$$$$$$$$%%%%%%'''++.7@@@@@@@@@9/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@<6'%%$$$$#
!!!#$$$$$$$%&&&&''().-2.6@@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$#
!!!@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@2+)'&&%%$$$$#
!!!#$$$$$$$%&&&&''().-2.6@@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$#
!!!!#$$$$$$$$$%%%%%%'''++.7@@@@@@@@@9/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@<6'%%$$$$#
!!!!####$$$$$$$$%%%%%&'(*-@1.+/@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3+'&%$$$##
!!!!"##########$$$$$%%&(,('''''''''''((*-5@@@@@@@@@@@@@@@@@@@@@@@@@@@3+)4&%$$###
!!!!!"################$$$%%%%%%%%%%&&&&')-+7@@@@@@@@@@@@@@@@@@@@@@@@@4(&&%$$####
!!!!!!""###################$$$$$%%%%%%&&&'+.@@@08@@@@@@@@@@@@@@@/+,@//@)%%$#####
!!!!!!!"""####################$$$$$$$$%%%&'())((())*-@@@@@@.+))('&&&&+&%$$######
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),@@@@@@@+'&%%%%%$$$$########
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*@;/*('&%%$$$$$$#######"""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(++)++&$$$$$$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'0(%%%$$$$$#####"""""""""""
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
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 sY
32 sM
640 sW 480 sH
8 k
[P5] P A P
lW n 32 P lH n A P
lM 1 - n A P
[ q ] sq
0 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
] s2
l2 x
Delphi
See Pascal.
DWScript
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
res = 4
maxiter = 200
#
# better but slower:
# res = 8
# maxiter = 300
#
#
mid = res * 50
center_x = 3 * mid / 2
center_y = mid
scale = mid
#
background 000
textsize 2
#
fastfunc iter cx cy maxiter .
while xx + yy < 4 and it < maxiter
y = 2 * x * y + cy
x = xx - yy + cx
xx = x * x
yy = y * y
it += 1
.
return it
.
proc draw . .
clear
for scr_y = 0 to 2 * mid - 1
cy = (scr_y - center_y) / scale
for scr_x = 0 to 2 * mid - 1
cx = (scr_x - center_x) / scale
it = iter cx cy maxiter
if it < maxiter
color3 it / 20 it / 100 it / 150
move scr_x / res scr_y / res
rect 1 / res 1 / res
.
.
.
color 990
move 1 1
text "Short press to zoom in, long to zoom out"
.
on mouse_down
time0 = systime
.
on mouse_up
center_x += mid - mouse_x * res
center_y += mid - mouse_y * res
if systime - time0 < 0.3
center_x -= mid - center_x
center_y -= mid - center_y
scale *= 2
else
center_x += (mid - center_x) * 3 / 4
center_y += (mid - center_y) * 3 / 4
scale /= 4
.
draw
.
draw
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)
end
end
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:;;;;<<<<===========
Emacs Lisp
Text mode
; === Mandelbrot ============================================
(setq mandel-size (cons 76 34))
(setq xmin -2)
(setq xmax .5)
(setq ymin -1.2)
(setq ymax 1.2)
(setq max-iter 20)
(defun mandel-iter-point (x y)
"Run the actual iteration for each point."
(let ((xp 0)
(yp 0)
(it 0)
(xt 0))
(while (and (< (+ (* xp xp) (* yp yp)) 4) (< it max-iter))
(setq xt (+ (* xp xp) (* -1 yp yp) x))
(setq yp (+ (* 2 xp yp) y))
(setq xp xt)
(setq it (1+ it)))
it))
(defun mandel-iter (p)
"Return string for point based on whether inside/outside the set."
(let ((it (mandel-iter-point (car p) (cdr p))))
(if (= it max-iter) "*" "-")))
(defun mandel-pos (x y)
"Convert screen coordinates to input coordinates."
(let ((xp (+ xmin (* (- xmax xmin) (/ (float x) (car mandel-size)))))
(yp (+ ymin (* (- ymax ymin) (/ (float y) (cdr mandel-size))))))
(cons xp yp)))
(defun mandel ()
"Plot the Mandelbrot set."
(dotimes (y (cdr mandel-size))
(dotimes (x (car mandel-size))
(if (= x 0)
(insert(format "\n%s" (mandel-iter (mandel-pos x y))))
(insert(format "%s" (mandel-iter (mandel-pos x y))))))))
(mandel)
- Output:
---------------------------------------------------------------------------- ---------------------------------------------------------------------------- ---------------------------------------------------------------------------- ---------------------------------------------------------*------------------ ---------------------------------------------------------------------------- ----------------------------------------------------**--***--*-------------- -----------------------------------------------------********--------------- ------------------------------------------------------*******--------------- --------------------------------------------*-*--******************--------- --------------------------------------------****************************---- -----------------------------------------*-****************************----- -----------------------------------------*******************************---- ---------------------------------------************************************- --------------------------**--**-*-----**********************************--- -------------------------***********---************************************- ------------------*-----**************************************************-- -------------------*****************************************************---- -*********************************************************************------ -------------------*****************************************************---- ------------------*-----**************************************************-- -------------------------***********---************************************- --------------------------**--**-*-----**********************************--- ---------------------------------------************************************- -----------------------------------------*******************************---- -----------------------------------------*-****************************----- --------------------------------------------****************************---- --------------------------------------------*-*--******************--------- ------------------------------------------------------*******--------------- -----------------------------------------------------********--------------- ----------------------------------------------------**--***--*-------------- ---------------------------------------------------------------------------- ---------------------------------------------------------*------------------ ---------------------------------------------------------------------------- ----------------------------------------------------------------------------
Graphical version
With a few modifications (mandel-size, mandel-iter, string-to-image, mandel-pic), the code above can also render the Mandelbrot fractal to an XPM image and display it directly in the buffer. (You might have to scroll up in Emacs after the function has run to see its output.)
; === Graphical Mandelbrot ============================================
(setq mandel-size (cons 320 300))
(setq xmin -2)
(setq xmax .5)
(setq ymin -1.2)
(setq ymax 1.2)
(setq max-iter 20)
(defun mandel-iter-point (x y)
"Run the actual iteration for each point."
(let ((xp 0)
(yp 0)
(it 0)
(xt 0))
(while (and (< (+ (* xp xp) (* yp yp)) 4) (< it max-iter))
(setq xt (+ (* xp xp) (* -1 yp yp) x))
(setq yp (+ (* 2 xp yp) y))
(setq xp xt)
(setq it (1+ it)))
it))
(defun mandel-iter (p)
"Return string for point based on whether inside/outside the set."
(let ((it (mandel-iter-point (car p) (cdr p))))
(if (= it max-iter) "*" (if (cl-oddp it) "+" "-"))))
(defun mandel-pos (x y)
"Convert screen coordinates to input coordinates."
(let ((xp (+ xmin (* (- xmax xmin) (/ (float x) (car mandel-size)))))
(yp (+ ymin (* (- ymax ymin) (/ (float y) (cdr mandel-size))))))
(cons xp yp)))
(defun string-to-image (str)
"Convert image data string to XPM image."
(create-image (concat (format "/* XPM */
static char * mandel[] = {
\"%i %i 3 1\",
\"+ c #ff0000\",
\"- c #0000ff\",
\"* c #000000\"," (car mandel-size) (cdr mandel-size))
str "};") 'xpm t))
(defun mandel-pic ()
"Plot the Mandelbrot set."
(setq all "")
(dotimes (y (cdr mandel-size))
(setq line "")
(dotimes (x (car mandel-size))
(setq line (concat line (mandel-iter (mandel-pos x y)))))
(setq all (concat all "\"" line "\",\n")))
(insert-image (string-to-image all)))
(mandel-pic)
Erlang
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 FOR
END FOR
END PROGRAMNote: 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.Forms
type 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
Fennel
#!/usr/bin/env fennel
(fn mandelzahl [cr ci max i tr ti tr2 ti2]
"Calculates the Mandelbrot escape number of a complex point c"
(if (>= i max) -1
(>= (+ tr2 ti2) 4) i
(let [(tr ti) (values (+ (- tr2 ti2) cr)
(+ (* tr ti 2) ci))]
(mandelzahl cr ci max (+ i 1)
tr ti (* tr tr) (* ti ti)))))
(fn mandel [w h max]
"Entry point, generate a 'graphical' representation of the Mandelbrot set"
(for [y -1.0 1.0 (/ 2.0 h)]
(var line {})
(for [x -2.0 1.0 (/ 3.0 w)]
(let [mz (mandelzahl x y max 0 0 0 0 0)]
(tset line (+ (length line) 1)
(or (and (< mz 0) " ")
(string.char (+ (string.byte :a) (% mz 26)))))))
(print (table.concat line))))
(fn arg-def [pos default]
"A helper fn to extract command line parameter with defaults"
(or (tonumber (and arg (. arg pos))) default))
(let [width (arg-def 1 140)
height (arg-def 2 50)
max (arg-def 3 1e5)]
(mandel width height max))
FOCAL
1.1 S I1=-1.2; S I2=1.2; S R1=-2; S R2=.5
1.2 S MIT=30
1.3 F Y=1,24; D 2
1.4 Q
2.1 T !
2.2 F X=1,70; D 3
3.1 S R=X*(R2-R1)/70+R1
3.2 S I=Y*(I2-I1)/24+I1
3.3 S C1=R; S C2=I
3.4 F T=1,MIT; D 4
4.1 S C3=C1
4.2 S C1=C1*C1 - C2*C2
4.3 S C2=C3*C2 + C2*C3
4.4 S C1=C1+R
4.5 S C2=C2+I
4.6 I (-FABS(C1)+2)5.1
4.7 I (-FABS(C2)+2)5.1
4.8 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 graymap
dup -1e 1e -2e 1e mandel
This is a completely integer version without local variables, which uses 4tH's native graphics library.
include lib/graphics.4th \ graphics support is needed
640 pic_width ! \ width of the image
480 pic_height ! \ height of the image
create shade \ map the shades of the image
' black , \ this is the colorscheme
' blue ,
' cyan ,
' green ,
' yellow ,
' red ,
' magenta ,
' blue ,
' cyan ,
' green ,
' yellow ,
' white ,
does> swap cells + @c execute ; \ loop through the shades available
color_image \ we're making a color image
15121 -15120 do \ do y-coordinate
15481 -21000 do \ do x-coordinate
j 0 0 0 ( l u v i)
200 0 do \ get color
>r
over dup 10 / * 1000 / \ calculate X and Y
over dup 10 / * 1000 / \ if X+Y > 40000
over over + r> swap 40000 > \ use the color in the loop
if
drop drop drop i 11 min leave
else \ otherwise try the next one
j swap >r - - >r * 5000 / over + r> swap r>
then
loop \ drop all parameters and set the shade
shade drop drop drop \ now set the proper pixel
j 15120 + 63 / i 21000 + 57 / set_pixel
57 +loop \ we're scaling the x-coordinate
63 +loop \ we're scaling the y-coordinate
s" mandelbt.ppm" save_image \ done, save the image
dup gshow
free bye
Fortran
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
bs
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
colors@a = new color[randomFloat[0,1], randomFloat[0,1], randomFloat[0,1]]
// Make this number smaller for higher resolution.
stepsize = .005
g = new graphics
g.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[colors@((count-1) mod levels)]
g.fillRectSize[real, im, stepsize, stepsize]
}
}
g.show[]Furor
###sysinclude X.uh
$ff0000 sto szin
300 sto maxiter
maxypixel sto YRES
maxxpixel sto XRES
myscreen "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 y
zero#d xa zero#d ya zero iter
(( #d
@x @xa dup* @ya dup* -+
@y @xa *2 @ya *+ sto ya
sto xa #g inc iter
@iter @maxiter >= then((>))
#d ( @xa dup* @ya dup* + 4. > )))
#g @iter @maxiter == { #d
myscreen {d} {d}§i @szin [][]
}{ #d
myscreen {d} {d}§i #g @iter 64 * [][]
}
#d}
#d}
(( ( myscreen key? 10000 usleep )))
myscreen !graphic
end
{ „x” }
{ „x2” }
{ „y” }
{ „y2” }
{ „xa” }
{ „ya” }
{ „iter” }
{ „maxiter” }
{ „szin” }
{ „YRES” }
{ „XRES” }
{ „myscreen” }
Futhark
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))
FutureBasic
_xmin = -8601
_xmax = 2867
_ymin = -4915
_ymax = 4915
_maxiter = 32
_dx = ( _xmax - _xmin ) / 79
_dy = ( _ymax - _ymin ) / 24
void local fn MandelbrotSet
printf @"\n"
SInt32 cy = _ymin
while ( cy <= _ymax )
SInt32 cx = _xmin
while ( cx <= _xmax )
SInt32 x = 0
SInt32 y = 0
SInt32 x2 = 0
SInt32 y2 = 0
SInt32 iter = 0
while ( iter < _maxiter )
if ( x2 + y2 > 16384 ) then break
y = ( ( x * y ) >> 11 ) + (SInt32)cy
x = x2 - y2 + (SInt32)cx
x2 = ( x * x ) >> 12
y2 = ( y * y ) >> 12
iter++
wend
print fn StringWithFormat( @"%3c", iter + 32 );
cx += _dx
wend
printf @"\n"
cy += _dy
wend
end fn
window 1, @"Mandelbrot Set", ( 0, 0, 820, 650 )
WindowSetBackgroundColor( 1, fn ColorBlack )
text @"Impact", 10.0, fn ColorWithRGB( 1.000, 0.800, 0.000, 1.0 )
fn MandelbrotSet
HandleEvents- Output:
!!!!!!!!!!!!!!!"""""""""""""####################################""""""""""""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$$%'+)%%%$$$$$#####"""""""""""
!!!!!!!!!!!"""""""#######################$$$$$$$$%%%&&(+,)++&%$$$$$$######""""""
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*5:/+('&%%$$$$$$#######"""
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''),@@@@@@@,'&%%%%%$$$$########
!!!!!!!"""####################$$$$$$$$%%%&'())((())*,@@@@@@/+))('&&&&)'%$$######
!!!!!!""###################$$$$$%%%%%%&&&'+.@@=/<@@@@@@@@@@@@@@@/++@..93%%$#####
!!!!!"################$$$%%%%%%%%%%&&&&'),+2@@@@@@@@@@@@@@@@@@@@@@@@@1(&&%$$####
!!!!"##########$$$$$%%&(-(''''''''''''(*,5@@@@@@@@@@@@@@@@@@@@@@@@@@@@+)-&%$$###
!!!!####$$$$$$$$%%%%%&'(*-@1.+.@-4+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4-(&%$$$##
!!!!#$$$$$$$$$%%%%%%'''++.6@@@@@@@@@8/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@3(%%$$$$#
!!!#$$$$$$$%&&&&''()/-5.5@@@@@@@@@@@@@>@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?'&%%$$$$#
!!!(**+/+<523/80/46@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+)'&&%%$$$$#
!!!#$$$$$$$%&&&&''().-2.@@@@@@@@@@@@@@?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'&%%$$$$#
!!!!#$$$$$$$$$%%%%%&'''/,.7@@@@@@@@@;/0@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0'%%$$$$#
!!!!####$$$$$$$$%%%%%&'(*-:2.,/?-5+))**@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@4+(&%$$$##
!!!!"##########$$$$$%%&(-(''''(''''''((*,4@@@@@@@@@@@@@@@@@@@@@@@@@@@4+).&%$$###
!!!!!"################$$$%%%%%%%%%%&&&&')<,4@@@@@@@@@@@@@@@@@@@@@@@@@/('&%%$####
!!!!!!""##################$$$$$$%%%%%%&&&'*.@@@0@@@@@@@@@@@@@@@@1,,@//9)%%$#####
!!!!!!!"""####################$$$$$$$$%%%&(())((()**-@@@@@@/+)))'&&&')'%$$######
!!!!!!!!""""#####################$$$$$$$$$$%%%&&&''(,@@@@@@@+'&&%%%%%$$$########
!!!!!!!!!"""""#######################$$$$$$$$$$%%%%&')*7@0+('&%%%$$$$$#######"""
!!!!!!!!!!!"""""""######################$$$$$$$$$%%%&&(+-).*&%$$$$$$######""""""
!!!!!!!!!!!!!"""""""""#######################$$$$$$%%'3(%%%$$$$$######""""""""""
!!!!!!!!!!!!!!!""""""""""""#####################################"""""""""""""""
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. 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 storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website.
In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.
Solution
We need first to generate a color palette, this is, a list of colors:
The following function draw the Mandelbrot set:
Test Case 1. Grayscale palette
Test case 2. Black & white palette
GLSL
Uses smooth coloring.
const int MaxIterations = 1000;
const vec2 Focus = vec2(-0.51, 0.54);
const float Zoom = 1.0;
vec3
color(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));
}
void
mainImage(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 png
set 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 = 2
nmax = 100
complex (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 200
set