Fractal tree: Difference between revisions

From Rosetta Code
Content added Content deleted
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[https://easylang.online/apps/fractal-tree.html Run it]
[https://easylang.online/apps/fractal-tree.html Run it]


<lang>func tree x y deg n . .
<lang># Fractal tree
#
func tree x y deg n . .
if n > 0
if n > 0
set_linewidth n * 0.4
set_linewidth n * 0.4
Line 905: Line 907:
.
.
.
.
set_timer 0
call tree 50 90 -90 10
on mouse_down
on timer
clear_screen
clear_screen
call tree 50 90 -90 10
call tree 50 90 -90 10
set_timer 1
.</lang>
.</lang>


Revision as of 16:53, 25 September 2021

Task
Fractal tree
You are encouraged to solve this task according to the task description, using any language you may know.

Generate and draw a fractal tree.

  1. Draw the trunk
  2. At the end of the trunk, split by some angle and draw two branches
  3. Repeat at the end of each branch until a sufficient level of branching is reached


Related tasks



Ada

Library: SDLAda

<lang Ada>with Ada.Numerics.Elementary_Functions;

with SDL.Video.Windows.Makers; with SDL.Video.Renderers.Makers; with SDL.Video.Rectangles; with SDL.Events.Events;

procedure Fractal_Tree is 

  Width   : constant := 600;
  Height  : constant := 600;
  Level   : constant := 13;
  Length  : constant := 130.0;
  X_Start : constant := 475.0;
  Y_Start : constant := 580.0;
  A_Start : constant := -1.54;
  Angle_1 : constant := 0.10;
  Angle_2 : constant := 0.35;
  C_1     : constant := 0.71;
  C_2     : constant := 0.87;

  Window   : SDL.Video.Windows.Window;
  Renderer : SDL.Video.Renderers.Renderer;
  Event    : SDL.Events.Events.Events;

  procedure Draw_Tree (Level  : in Natural;
                       Length : in Float;
                       Angle  : in Float;
                       X, Y   : in Float)
  is
     use SDL;
     use Ada.Numerics.Elementary_Functions;
     Pi   : constant       := Ada.Numerics.Pi;
     X_2  : constant Float := X + Length * Cos (Angle, 2.0 * Pi);
     Y_2  : constant Float := Y + Length * Sin (Angle, 2.0 * Pi);
     Line : constant SDL.Video.Rectangles.Line_Segment
       := ((C.int (X), C.int (Y)), (C.int (X_2), C.int (Y_2)));
  begin
     if Level > 0 then
        Renderer.Set_Draw_Colour (Colour => (0, 220, 0, 255));
        Renderer.Draw (Line => Line);

        Draw_Tree (Level - 1, C_1 * Length, Angle + Angle_1, X_2, Y_2);
        Draw_Tree (Level - 1, C_2 * Length, Angle - Angle_2, X_2, Y_2);
     end if;
  end Draw_Tree;

  procedure Wait is
     use type SDL.Events.Event_Types;
  begin
     loop
        while SDL.Events.Events.Poll (Event) loop
           if Event.Common.Event_Type = SDL.Events.Quit then
              return;
           end if;
        end loop;
        delay 0.100;
     end loop;
  end Wait;

begin 

  if not SDL.Initialise (Flags => SDL.Enable_Screen) then
     return;
  end if;

  SDL.Video.Windows.Makers.Create (Win      => Window,
                                   Title    => "Fractal tree",
                                   Position => SDL.Natural_Coordinates'(X => 10, Y => 10),
                                   Size     => SDL.Positive_Sizes'(Width, Height),
                                   Flags    => 0);
  SDL.Video.Renderers.Makers.Create (Renderer, Window.Get_Surface);
  Renderer.Set_Draw_Colour ((0, 0, 0, 255));
  Renderer.Fill (Rectangle => (0, 0, Width, Height));

  Draw_Tree (Level, Length, A_Start, X_Start, Y_Start);
  Window.Update_Surface;

  Wait;
  Window.Finalize;
  SDL.Finalise;

end Fractal_Tree;</lang>

Arturo

<lang rebol>width: 1000 height: 1000

trunkLength: 400 scaleFactor: 0.6 startingAngle: 1.5 * pi deltaAngle: 0.2 * pi

drawTree: function [out x y len theta][ 

   if len < 1 -> return null

   x2: x + len * cos theta
   y2: y + len * sin theta

   'out ++ ~"<line x1='|x|' y1='|y|' x2='|x2|' y2='|y2|' style='stroke: white; stroke-width:1'/>\n"

   drawTree out x2 y2 len*scaleFactor theta+deltaAngle
   drawTree out x2 y2 len*scaleFactor theta-deltaAngle

]

svg: { 

   <?xml version='1.0' encoding='utf-8' standalone='no'?>
   <!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN'
             'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'>
   <svg width='100%%' height='100%%' version='1.1'
        xmlns='http://www.w3.org/2000/svg'>
       <rect width="100%" height="100%" fill="black"/>

}

drawTree svg 0.5*width height trunkLength startingAngle 'svg ++ "</svg>"

write "fractal.svg" svg</lang>

Output:

Fractal Tree output in Arturo

AutoHotkey

Image - Link, since uploads seem to be disabled currently.

Library: GDIP

<lang AutoHotkey>#SingleInstance, Force

  1. NoEnv

SetBatchLines, -1

Uncomment if Gdip.ahk is not in your standard library
#Include, Gdip.ahk

FileOut := A_Desktop "\MyNewFile.png" TreeColor := 0xff0066ff ; ARGB TrunkWidth := 10 ; Pixels TrunkLength := 80 ; Pixels Angle := 60 ; Degrees ImageWidth := 670 ; Pixels ImageHeight := 450 ; Pixels Branches := 13 Decrease := 0.81

Angle := (Angle * 0.01745329252) / 2 , Points := {} , Points[1, "Angle"] := 0 , Points[1, "X"] := ImageWidth // 2 , Points[1, "Y"] := ImageHeight - TrunkLength

if (!pToken := Gdip_Startup()) { MsgBox, 48, Gdiplus error!, Gdiplus failed to start. Please ensure you have Gdiplus on your system. ExitApp } OnExit, Exit

pBitmap := Gdip_CreateBitmap(ImageWidth, ImageHeight) , G := Gdip_GraphicsFromImage(pBitmap) , Gdip_SetSmoothingMode(G, 4) , pBrush := Gdip_BrushCreateSolid(0xff000000) , Gdip_FillRectangle(G, pBrush, -5, -5, ImageWidth + 10, ImageHeight + 10) , Gdip_DeleteBrush(pBrush) , pPen := Gdip_CreatePen(TreeColor, TrunkWidth/Decrease) , Gdip_DrawLine(G, pPen, Points.1.X, Points.1.Y, Points.1.X, ImageHeight) , Gdip_DeletePen(pPen)

Loop, % Branches { NewPoints := {} pPen := Gdip_CreatePen(TreeColor, TrunkWidth) for Each, Point in Points { N1 := A_Index * 2 , N2 := (A_Index * 2) + 1 , NewPoints[N1, "X"] := Point.X + (TrunkLength * Sin(NewPoints[N1, "Angle"] := Point.Angle - Angle)) , NewPoints[N1, "Y"] := Point.Y - (TrunkLength * Cos(NewPoints[N1].Angle)) , NewPoints[N2, "X"] := Point.X + (TrunkLength * Sin(NewPoints[N2, "Angle"] := Point.Angle + Angle)) , NewPoints[N2, "Y"] := Point.Y - (TrunkLength * Cos(NewPoints[N2].Angle)) , Gdip_DrawLine(G, pPen, Point.X, Point.Y, NewPoints[N1].X, NewPoints[N1].Y) , Gdip_DrawLine(G, pPen, Point.X, Point.Y, NewPoints[N2].X, NewPoints[N2].Y) } TrunkWidth *= Decrease , TrunkLength *= Decrease , Points := NewPoints , Gdip_DeletePen(pPen) }

Gdip_SaveBitmapToFile(pBitmap, FileOut) , Gdip_DisposeImage(pBitmap) , Gdip_DeleteGraphics(G) Run, % FileOut

Exit: Gdip_Shutdown(pToken) ExitApp</lang>

BASIC

BASIC256

Asymmetric fractal tree image created by the BASIC-256 script

<lang basic256>graphsize 300,300

level = 12 : len =63 # initial values x = 230: y = 285 rotation = pi/2

A1 = pi/27 : A2 = pi/8 # constants which determine shape C1 = 0.7 : C2 = 0.85

dim xs(level+1) : dim ys(level+1) # stacks

fastgraphics color black rect 0,0,graphwidth,graphheight refresh color green gosub tree refresh imgsave "Fractal_tree_BASIC-256.png", "PNG" end

tree: xs[level] = x : ys[level] = y gosub putline if level>0 then level = level - 1 len = len*C1 rotation = rotation - A1 gosub tree len = len/C1*C2 rotation = rotation + A1 + A2 gosub tree rotation = rotation - A2 len = len/C2 level = level + 1 end if x = xs[level] : y = ys[level] return

putline: yn = -sin(rotation)*len + y xn = cos(rotation)*len + x line x,y,xn,yn x = xn : y = yn return</lang>

Run BASIC

<lang Run BASIC> 'Fractal Tree - for Run Basic - 29 Apr 2018 

'from BASIC256 - http://rosettacode.org/wiki/Fractal_tree#BASIC256
'copy this text and go to http://www.runbasic.com

WindowWidth = 500 'Run Basic max size 800 x 600 WindowHeight = 350 c = 255 '255 for white '0 for black 

graphic #w, WindowWidth, WindowHeight
#w cls("black")  'black background color
#w color(c,c,c)  'changes color to white

level = 10 ' initial values leng = 50 x = 230: y = 325 ' initial values x = 230: y = 285 pi = 3.1415 rotation = 3.1415/2

'A1 = pi/27 : A2 = pi/8 ' constants which determine shape 'C1 = 0.7 : C2 = 0.85 ' tree is drifted left

A1 = pi/9 : A2 = pi/9 ' constants which determine shape C1 = 0.85 : C2 = 0.85 ' Symmetrical Tree

dim xs(level+1) : dim ys(level+1) ' stacks

print : print "Welcome to the Run BASIC Fractal Tree Program"

  1. w color("green") 'color green

gosub [tree] 

render #w

' imgsave "Fractal_tree_BASIC-256.png", "PNG" Print "Thank you and goodbye" end

[tree] xs(level) = x : ys(level) = y gosub [putline] if level>0 then level = level - 1 leng = leng*C1 rotation = rotation - A1 gosub [tree] leng = leng/C1*C2 rotation = rotation + A1 + A2 gosub [tree] rotation = rotation - A2 leng = leng/C2 level = level + 1 end if x = xs(level) : y = ys(level) return

[putline] yn = -1*sin(rotation)*leng + y xn = cos(rotation)*leng + x 

               #w line(x,y,xn,yn)

x = xn : y = yn return 'end of code End</lang>

BBC BASIC

Output:








Works with: BBC BASIC for Windows

<lang bbcbasic> 

     Spread = 25
     Scale = 0.76
     SizeX% = 400
     SizeY% = 300
     Depth% = 10

</lang><lang bbcbasic> 

     VDU 23,22,SizeX%;SizeY%;8,16,16,128
     
     PROCbranch(SizeX%, 0, SizeY%/2, 90, Depth%)
     END

     DEF PROCbranch(x1, y1, size, angle, depth%)
     LOCAL x2, y2
     x2 = x1 + size * COSRAD(angle)
     y2 = y1 + size * SINRAD(angle)
     VDU 23,23,depth%;0;0;0;
     LINE x1, y1, x2, y2
     IF depth% > 0 THEN
       PROCbranch(x2, y2, size * Scale, angle - Spread, depth% - 1)
       PROCbranch(x2, y2, size * Scale, angle + Spread, depth% - 1)
     ENDIF
     ENDPROC</lang>

IS-BASIC

<lang IS-BASIC>100 PROGRAM "Tree.bas" 110 OPTION ANGLE DEGREES 120 GRAPHICS HIRES 2 130 SET PALETTE 0,170 140 PLOT 640,10;ANGLE 90; 150 CALL TREE(200) 160 DEF TREE(N) 170 IF N<24 THEN EXIT DEF 180 PLOT FORWARD N;RIGHT 25; 190 CALL TREE(N*.75) 200 PLOT LEFT 50; 210 CALL TREE(N*.75) 220 PLOT RIGHT 25,BACK N, 230 END DEF</lang>

C

Library: SDL
Library: SGE

or

Library: cairo

<lang c>#include <SDL/SDL.h>

  1. ifdef WITH_CAIRO
  2. include <cairo.h>
  3. else
  4. include <SDL/sge.h>
  5. endif
  6. include <cairo.h>
  7. include <stdlib.h>
  8. include <time.h>
  9. include <math.h>
  1. ifdef WITH_CAIRO
  2. define PI 3.1415926535
  3. endif
  1. define SIZE 800 // determines size of window
  2. define SCALE 5 // determines how quickly branches shrink (higher value means faster shrinking)
  3. define BRANCHES 14 // number of branches
  4. define ROTATION_SCALE 0.75 // determines how slowly the angle between branches shrinks (higher value means slower shrinking)
  5. define INITIAL_LENGTH 50 // length of first branch

double rand_fl(){ 

 return (double)rand() / (double)RAND_MAX;

}

void draw_tree(SDL_Surface * surface, double offsetx, double offsety, 

              double directionx, double directiony, double size,
              double rotation, int depth) {
  1. ifdef WITH_CAIRO
 cairo_surface_t *surf = cairo_image_surface_create_for_data( surface->pixels,
                                                              CAIRO_FORMAT_RGB24,

surface->w, surface->h, surface->pitch ); 

 cairo_t *ct = cairo_create(surf);

 cairo_set_line_width(ct, 1);
 cairo_set_source_rgba(ct, 0,0,0,1);
 cairo_move_to(ct, (int)offsetx, (int)offsety);
 cairo_line_to(ct, (int)(offsetx + directionx * size), (int)(offsety + directiony * size));
 cairo_stroke(ct);
  1. else
 sge_AALine(surface,
     (int)offsetx, (int)offsety,
     (int)(offsetx + directionx * size), (int)(offsety + directiony * size),
     SDL_MapRGB(surface->format, 0, 0, 0));
  1. endif
 if (depth > 0){
   // draw left branch
   draw_tree(surface,
       offsetx + directionx * size,
       offsety + directiony * size,
       directionx * cos(rotation) + directiony * sin(rotation),
       directionx * -sin(rotation) + directiony * cos(rotation),
       size * rand_fl() / SCALE + size * (SCALE - 1) / SCALE,
       rotation * ROTATION_SCALE,
       depth - 1);

   // draw right branch
   draw_tree(surface,
       offsetx + directionx * size,
       offsety + directiony * size,
       directionx * cos(-rotation) + directiony * sin(-rotation),
       directionx * -sin(-rotation) + directiony * cos(-rotation),
       size * rand_fl() / SCALE + size * (SCALE - 1) / SCALE,
       rotation * ROTATION_SCALE,
       depth - 1);
 }

}

void render(SDL_Surface * surface){ 

 SDL_FillRect(surface, NULL, SDL_MapRGB(surface->format, 255, 255, 255));
 draw_tree(surface,
     surface->w / 2.0,
     surface->h - 10.0,
     0.0, -1.0,
     INITIAL_LENGTH,
     PI / 8,
     BRANCHES);
 SDL_UpdateRect(surface, 0, 0, 0, 0);

}

int main(){ 

 SDL_Surface * screen;
 SDL_Event evt;

 SDL_Init(SDL_INIT_VIDEO);

 srand((unsigned)time(NULL));

 screen = SDL_SetVideoMode(SIZE, SIZE, 32, SDL_HWSURFACE);

 render(screen);
 while(1){
   if (SDL_PollEvent(&evt)){
     if(evt.type == SDL_QUIT) break;
   }
   SDL_Delay(1);
 }
 SDL_Quit();
 return 0;

}</lang>

C++

<lang cpp>

  1. include <windows.h>
  2. include <string>
  3. include <math.h>

//-------------------------------------------------------------------------------------------------- using namespace std;

//-------------------------------------------------------------------------------------------------- const float PI = 3.1415926536f;

//-------------------------------------------------------------------------------------------------- class myBitmap { public: 

   myBitmap() : pen( NULL ) {}
   ~myBitmap()
   {

DeleteObject( pen ); DeleteDC( hdc ); DeleteObject( bmp ); 

   }

   bool create( int w, int h )
   {

BITMAPINFO bi; void *pBits; ZeroMemory( &bi, sizeof( bi ) ); bi.bmiHeader.biSize = sizeof( bi.bmiHeader ); bi.bmiHeader.biBitCount = sizeof( DWORD ) * 8; bi.bmiHeader.biCompression = BI_RGB; bi.bmiHeader.biPlanes = 1; bi.bmiHeader.biWidth = w; bi.bmiHeader.biHeight = -h;

HDC dc = GetDC( GetConsoleWindow() ); bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 ); if( !bmp ) return false;

hdc = CreateCompatibleDC( dc ); SelectObject( hdc, bmp ); ReleaseDC( GetConsoleWindow(), dc );

width = w; height = h;

return true; 

   }

   void setPenColor( DWORD clr )
   {

if( pen ) DeleteObject( pen ); pen = CreatePen( PS_SOLID, 1, clr ); SelectObject( hdc, pen ); 

   }

   void saveBitmap( string path )
   {

BITMAPFILEHEADER fileheader; BITMAPINFO infoheader; BITMAP bitmap; DWORD* dwpBits; DWORD wb; HANDLE file;

GetObject( bmp, sizeof( bitmap ), &bitmap );

dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight]; ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) ); ZeroMemory( &infoheader, sizeof( BITMAPINFO ) ); ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );

infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8; infoheader.bmiHeader.biCompression = BI_RGB; infoheader.bmiHeader.biPlanes = 1; infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader ); infoheader.bmiHeader.biHeight = bitmap.bmHeight; infoheader.bmiHeader.biWidth = bitmap.bmWidth; infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );

fileheader.bfType = 0x4D42; fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER ); fileheader.bfSize = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;

GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );

file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, NULL ); WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL ); WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL ); WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL ); CloseHandle( file );

delete [] dwpBits; 

   }

   HDC getDC()     { return hdc; }
   int getWidth()  { return width; }
   int getHeight() { return height; }

private: 

   HBITMAP bmp;
   HDC	    hdc;
   HPEN    pen;
   int     width, height;

}; //-------------------------------------------------------------------------------------------------- class vector2 { public: 

   vector2() { x = y = 0; }
   vector2( int a, int b ) { x = a; y = b; }
   void set( int a, int b ) { x = a; y = b; }
   void rotate( float angle_r )
   {

float _x = static_cast<float>( x ), _y = static_cast<float>( y ), s = sinf( angle_r ), c = cosf( angle_r ), a = _x * c - _y * s, b = _x * s + _y * c;

x = static_cast<int>( a ); y = static_cast<int>( b ); 

   }

   int x, y;

}; //-------------------------------------------------------------------------------------------------- class fractalTree { public: 

   fractalTree()		      { _ang = DegToRadian( 24.0f ); }
   float DegToRadian( float degree ) { return degree * ( PI / 180.0f ); }

   void create( myBitmap* bmp )
   {

_bmp = bmp; float line_len = 130.0f;

vector2 sp( _bmp->getWidth() / 2, _bmp->getHeight() - 1 ); MoveToEx( _bmp->getDC(), sp.x, sp.y, NULL ); sp.y -= static_cast<int>( line_len ); LineTo( _bmp->getDC(), sp.x, sp.y);

drawRL( &sp, line_len, 0, true ); drawRL( &sp, line_len, 0, false ); 

   }

private: 

   void drawRL( vector2* sp, float line_len, float a, bool rg )
   {

line_len *= .75f; if( line_len < 2.0f ) return;

MoveToEx( _bmp->getDC(), sp->x, sp->y, NULL ); vector2 r( 0, static_cast<int>( line_len ) ); 

       if( rg ) a -= _ang;
       else a += _ang;

r.rotate( a ); r.x += sp->x; r.y = sp->y - r.y;

LineTo( _bmp->getDC(), r.x, r.y );

drawRL( &r, line_len, a, true ); drawRL( &r, line_len, a, false ); 

   }

   myBitmap* _bmp;
   float     _ang;

}; //-------------------------------------------------------------------------------------------------- int main( int argc, char* argv[] ) { 

   ShowWindow( GetConsoleWindow(), SW_MAXIMIZE );

   myBitmap bmp;
   bmp.create( 640, 512 );
   bmp.setPenColor( RGB( 255, 255, 0 ) );

   fractalTree tree;
   tree.create( &bmp );

   BitBlt( GetDC( GetConsoleWindow() ), 0, 20, 648, 512, bmp.getDC(), 0, 0, SRCCOPY );

   bmp.saveBitmap( "f://rc//fracTree.bmp" );

   system( "pause" );

   return 0;

} //-------------------------------------------------------------------------------------------------- </lang>

Ceylon

Translation of: Java
Library: Swing
Library: AWT

Be sure to import java.desktop and ceylon.numeric in your module.ceylon file. <lang ceylon>import javax.swing {

JFrame { exitOnClose } } import java.awt {

Color { white, black }, Graphics } import ceylon.numeric.float {

cos, toRadians, sin }

shared void run() { 

   value fractalTree = object extends JFrame("fractal tree") {
       
       background = black;
       setBounds(100, 100, 800, 600);
       resizable = false;
       defaultCloseOperation = exitOnClose;
       
       shared actual void paint(Graphics g) {

           void drawTree(Integer x1, Integer y1, Float angle, Integer depth) {
               if (depth <= 0) {
                   return;
               }
               value x2 = x1 + (cos(toRadians(angle)) * depth * 10.0).integer;
               value y2 = y1 + (sin(toRadians(angle)) * depth * 10.0).integer;
               g.drawLine(x1, y1, x2, y2);
               drawTree(x2, y2, angle - 20, depth - 1);
               drawTree(x2, y2, angle + 20, depth - 1);
           }
           
           g.color = white;
           drawTree(400, 500, -90.0, 9);
       }
   };
   
   fractalTree.visible = true;

}</lang>

Clojure

Translation of: Java
Library: Swing
Library: AWT

<lang Clojure>(import '[java.awt Color Graphics] 'javax.swing.JFrame)

(defn deg-to-radian [deg] (* deg Math/PI 1/180)) (defn cos-deg [angle] (Math/cos (deg-to-radian angle))) (defn sin-deg [angle] (Math/sin (deg-to-radian angle)))

(defn draw-tree [^Graphics g, x y angle depth] 

 (when (pos? depth)
   (let [x2 (+ x (int (* depth 10 (cos-deg angle))))

y2 (+ y (int (* depth 10 (sin-deg angle))))] 

     (.drawLine g x y x2 y2)
     (draw-tree g x2 y2 (- angle 20) (dec depth))
     (recur     g x2 y2 (+ angle 20) (dec depth)))))

(defn fractal-tree [depth] 

 (doto (proxy [JFrame] []

(paint [g] (.setColor g Color/BLACK) (draw-tree g 400 500 -90 depth))) 

   (.setBounds 100 100 800 600)
   (.setResizable false)
   (.setDefaultCloseOperation JFrame/DISPOSE_ON_CLOSE)
   (.show)))

(fractal-tree 9)</lang>

Common Lisp

Library: lispbuilder-sdl
Translation of: Clojure

<lang lisp>;; (require :lispbuilder-sdl)

(defun deg-to-radian (deg) 

 "converts degrees to radians"
 (* deg pi 1/180))

(defun cos-deg (angle) 

 "returns cosin of the angle expressed in degress"
 (cos (deg-to-radian angle)))

(defun sin-deg (angle) 

 "returns sin of the angle expressed in degress"
 (sin (deg-to-radian angle)))

(defun draw-tree (surface x y angle depth) 

 "draws a branch of the tree on the sdl-surface"
 (when (plusp depth)
   (let ((x2 (+ x (round (* depth 10 (cos-deg angle)))))

(y2 (+ y (round (* depth 10 (sin-deg angle)))))) 

     (sdl:draw-line-* x y x2 y2 :surface surface :color sdl:*green*)
     (draw-tree surface x2 y2 (- angle 20) (1- depth))
     (draw-tree surface x2 y2 (+ angle 20) (1- depth)))))

(defun fractal-tree (depth) 

 "shows a window with a fractal tree"
 (sdl:with-init ()
   (sdl:window 800 600 :title-caption "fractal-tree")
   (sdl:clear-display sdl:*black*)
   (draw-tree sdl:*default-surface* 400 500 -90 depth)
   (sdl:update-display)
   (sdl:with-events ()
     (:video-expose-event ()

(sdl:update-display)) 

     (:quit-event ()

t))))

(fractal-tree 9) </lang>

D

SVG Version

Translation of: Raku

<lang d>import std.stdio, std.math;

enum width = 1000, height = 1000; // Image dimension. enum length = 400; // Trunk size. enum scale = 6.0 / 10; // Branch scale relative to trunk.

void tree(in double x, in double y, in double length, in double angle) { 

   if (length < 1)
       return;
   immutable x2 = x + length * angle.cos;
   immutable y2 = y + length * angle.sin;
   writefln("<line x1='%f' y1='%f' x2='%f' y2='%f' " ~
            "style='stroke:black;stroke-width:1'/>", x, y, x2, y2);
   tree(x2, y2, length * scale, angle + PI / 5);
   tree(x2, y2, length * scale, angle - PI / 5);

}

void main() { 

   "<svg width='100%' height='100%' version='1.1'
    xmlns='http://www.w3.org/2000/svg'>".writeln;
   tree(width / 2.0, height, length, 3 * PI / 2);
   "</svg>".writeln;

}</lang>

Turtle Version

This uses the turtle module from the Dragon Curve task, and the module from the Grayscale Image task.

Translation of: Logo

<lang d>import grayscale_image, turtle;

void tree(Color)(Image!Color img, ref Turtle t, in uint depth, 

                in real step, in real scale, in real angle) {
   if (depth == 0) return;
   t.forward(img, step);
   t.right(angle);
   img.tree(t, depth - 1, step * scale, scale, angle);
   t.left(2 * angle);
   img.tree(t, depth - 1, step * scale, scale, angle);
   t.right(angle);
   t.forward(img, -step);

}

void main() { 

   auto img = new Image!Gray(330, 300);
   auto t = Turtle(165, 270, -90);
   img.tree(t, 10, 80, 0.7, 30);
   img.savePGM("fractal_tree.pgm");

}</lang>

Alternative version

Translation of: Java

Using DFL. <lang d>import dfl.all; import std.math;

class FractalTree: Form { 

   private immutable DEG_TO_RAD = PI / 180.0;

   this() {
       width = 600;
       height = 500;
       text = "Fractal Tree";
       backColor = Color(0xFF, 0xFF, 0xFF);
       startPosition = FormStartPosition.CENTER_SCREEN;
       formBorderStyle = FormBorderStyle.FIXED_DIALOG;
       maximizeBox = false;
   }

   private void drawTree(Graphics g, Pen p, int x1, int y1, double angle, int depth) {
       if (depth == 0) return;
       int x2 = x1 + cast(int) (cos(angle * DEG_TO_RAD) * depth * 10.0);
       int y2 = y1 + cast(int) (sin(angle * DEG_TO_RAD) * depth * 10.0);
       g.drawLine(p, x1, y1, x2, y2);
       drawTree(g, p, x2, y2, angle - 20, depth - 1);
       drawTree(g, p, x2, y2, angle + 20, depth - 1);
   }
   
   protected override void onPaint(PaintEventArgs ea){
       super.onPaint(ea);
       Pen p = new Pen(Color(0, 0xAA, 0));
       drawTree(ea.graphics, p, 300, 450, -90, 9);
   }

}

int main() { 

   int result = 0; 
   try {
       Application.run(new FractalTree);
   } catch(Exception e) {
       msgBox(e.msg, "Fatal Error", MsgBoxButtons.OK, MsgBoxIcon.ERROR);        
       result = 1;
   }   
   return result;

}</lang>

EasyLang

Run it

<lang># Fractal tree

func tree x y deg n . . 

 if n > 0
   set_linewidth n * 0.4
   move_pen x y
   x += cos deg * n * 1.3 * (randomf + 0.5)
   y += sin deg * n * 1.3 * (randomf + 0.5)
   draw_line x y
   call tree x y deg - 20 n - 1
   call tree x y deg + 20 n - 1
 .

. set_timer 0 on timer 

 clear_screen
 call tree 50 90 -90 10
 set_timer 1

.</lang>

F#

Translation of: Raku

<lang fsharp>let (cos, sin, pi) = System.Math.Cos, System.Math.Sin, System.Math.PI

let (width, height) = 1000., 1000. // image dimension let scale = 6./10. // branch scale relative to trunk let length = 400. // trunk size

let rec tree x y length angle = 

   if length >= 1. then
       let (x2, y2) = x + length * (cos angle),  y + length * (sin angle)
       printfn "<line x1='%f' y1='%f' x2='%f' y2='%f' style='stroke:rgb(0,0,0);stroke-width:1'/>"
           x y x2 y2
       tree x2 y2 (length*scale) (angle + pi/5.)
       tree x2 y2 (length*scale) (angle - pi/5.)

printfn "<?xml version='1.0' encoding='utf-8' standalone='no'?> <!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN' 'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'> <svg width='100%%' height='100%%' version='1.1' xmlns='http://www.w3.org/2000/svg'>" tree (width/2.) height length (3.*pi/2.) printfn "</svg>"</lang>

Fantom

<lang fantom> using fwt using gfx

class FractalCanvas : Canvas { 

 new make () : super() {}

 Void drawTree (Graphics g, Int x1, Int y1, Int angle, Int depth)
 {
   if (depth == 0) return
   Int x2 := x1 + (angle.toFloat.toRadians.cos * depth * 10.0).toInt;
   Int y2 := y1 + (angle.toFloat.toRadians.sin * depth * 10.0).toInt;
   g.drawLine(x1, y1, x2, y2);
   drawTree(g, x2, y2, angle - 20, depth - 1);
   drawTree(g, x2, y2, angle + 20, depth - 1);
 }

 override Void onPaint (Graphics g)
 {
   drawTree (g, 400, 500, -90, 9)
 }

}

class FractalTree { 

 public static Void main ()
 {
   Window
   {
     title = "Fractal Tree"
     size = Size(800, 600)
     FractalCanvas(),
   }.open
 }

} </lang>

FreeBASIC

Translation of: BBC BASIC

<lang freebasic>' version 17-03-2017 ' compile with: fbc -s gui

Const As Double deg2rad = Atn(1) / 45 Dim Shared As Double scale = 0.76 Dim Shared As Double spread = 25 * deg2rad ' convert degree's to rad's

Sub branch(x1 As ULong, y1 As ULong, size As ULong, angle As Double, depth As ULong) 

   Dim As ULong x2, y2

   x2 = x1 + size * Cos(angle)
   y2 = y1 + size * Sin(angle)

   Line (x1,y1) - (x2,y2), 2  ' palette color green
   If depth > 0 Then
       branch(x2, y2, size * scale, angle - spread, depth -1)
       branch(x2, y2, size * scale, angle + spread, depth -1)
   End If

End Sub

' ------=< MAIN >=-----

Dim As Double angle = -90 * deg2rad ' make sure that the tree grows up Dim As ULong SizeX = 800 Dim As ULong SizeY = SizeX * 3 \ 4 Dim As Double size = SizeY \ 4 Dim As ULong depth = 11

ScreenRes SizeX, SizeY, 8 WindowTitle ("Fractal Tree")

branch(SizeX\2, SizeY, size, angle, depth)

' empty keyboard buffer While InKey <> "" : Wend windowtitle ("Fractal Tree, hit any key to end program") Sleep End</lang>

Frege

Works with: Frege version 3.23.888-g4e22ab6

<lang frege>module FractalTree where

import Java.IO import Prelude.Math

data AffineTransform = native java.awt.geom.AffineTransform where 

 native new :: () -> STMutable s AffineTransform
 native clone :: Mutable s AffineTransform -> STMutable s AffineTransform
 native rotate :: Mutable s AffineTransform -> Double -> ST s ()
 native scale :: Mutable s AffineTransform -> Double -> Double -> ST s ()
 native translate :: Mutable s AffineTransform -> Double -> Double -> ST s ()

data BufferedImage = native java.awt.image.BufferedImage where 

 pure native type_3byte_bgr "java.awt.image.BufferedImage.TYPE_3BYTE_BGR" :: Int
 native new :: Int -> Int -> Int -> STMutable s BufferedImage
 native createGraphics :: Mutable s BufferedImage -> STMutable s Graphics2D

data Color = pure native java.awt.Color where 

 pure native black "java.awt.Color.black" :: Color
 pure native green "java.awt.Color.green" :: Color
 pure native white "java.awt.Color.white" :: Color
 pure native new :: Int -> Color

data BasicStroke = pure native java.awt.BasicStroke where 

 pure native new :: Float -> BasicStroke

data RenderingHints = native java.awt.RenderingHints where 

 pure native key_antialiasing "java.awt.RenderingHints.KEY_ANTIALIASING" :: RenderingHints_Key
 pure native value_antialias_on "java.awt.RenderingHints.VALUE_ANTIALIAS_ON" :: Object

data RenderingHints_Key = pure native java.awt.RenderingHints.Key

data Graphics2D = native java.awt.Graphics2D where 

 native drawLine :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
 native drawOval :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
 native fillRect :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
 native setColor :: Mutable s Graphics2D -> Color -> ST s ()
 native setRenderingHint :: Mutable s Graphics2D -> RenderingHints_Key -> Object -> ST s ()
 native setStroke :: Mutable s Graphics2D -> BasicStroke -> ST s ()
 native setTransform :: Mutable s Graphics2D -> Mutable s AffineTransform -> ST s ()

data ImageIO = mutable native javax.imageio.ImageIO where 

 native write "javax.imageio.ImageIO.write" :: MutableIO BufferedImage -> String -> MutableIO File -> IO Bool throws IOException

drawTree :: Mutable s Graphics2D -> Mutable s AffineTransform -> Int -> ST s () drawTree g t i = do 

 let len = 10 -- ratio of length to thickness
     shrink = 0.75
     angle = 0.3 -- radians
     i' = i - 1
 g.setTransform t
 g.drawLine 0 0 0 len
 when (i' > 0) $ do
   t.translate 0 (fromIntegral len)
   t.scale shrink shrink
   rt <- t.clone
   t.rotate angle
   rt.rotate (-angle)
   drawTree g t i'
   drawTree g rt i'

main = do 

 let width = 900
     height = 800
     initScale = 20
     halfWidth = fromIntegral width / 2
 buffy <- BufferedImage.new width height BufferedImage.type_3byte_bgr
 g <- buffy.createGraphics
 g.setRenderingHint RenderingHints.key_antialiasing RenderingHints.value_antialias_on
 g.setColor Color.black
 g.fillRect 0 0 width height
 g.setColor Color.green
 t <- AffineTransform.new ()
 t.translate halfWidth (fromIntegral height)
 t.scale initScale initScale
 t.rotate pi
 drawTree g t 16
 f <- File.new "FractalTreeFrege.png"
 void $ ImageIO.write buffy "png" f</lang>

Output is here due to Is file uploading blocked forever?

Frink

<lang Frink> // Draw Fractal Tree in Frink

// Define the tree function FractalTree[x1, y1, angleval, lengthval, graphicsobject] := { 

  if lengthval > 1
  {
     // Define current line end points (x2 and y2)
     x2 = x1 + ((cos[angleval degrees]) * lengthval)
     y2 = y1 + ((sin[angleval degrees]) * lengthval)
     // Draw line - notice that graphicsobject is the graphics object passed into the function.
     graphicsobject.line[x1,y1,x2,y2]

     // Calculate branches. You can change the lengthval multiplier factor and angleval summand to create different trees
     FractalTree[x2, y2, angleval - 20, lengthval * 0.7, graphicsobject]
     FractalTree[x2, y2, angleval + 20, lengthval * 0.7, graphicsobject]
  }

}

// Create graphics object g = new graphics

// Start the recursive function. In Frink, a -90° angle moves from the bottom of the screen to the top. FractalTree[0, 0, -90, 30, g]

// Show the final tree g.show[] </lang>

Go

png converted from output ppm

<lang go>package main

// Files required to build supporting package raster are found in: // * Bitmap // * Grayscale image // * Xiaolin Wu's line algorithm // * Write a PPM file

import ( 

   "math"
   "raster"

)

const ( 

   width  = 400
   height = 300
   depth  = 8
   angle  = 12
   length = 50
   frac   = .8

)

func main() { 

   g := raster.NewGrmap(width, height)
   ftree(g, width/2, height*9/10, length, 0, depth)
   g.Bitmap().WritePpmFile("ftree.ppm")

}

func ftree(g *raster.Grmap, x, y, distance, direction float64, depth int) { 

   x2 := x + distance*math.Sin(direction*math.Pi/180)
   y2 := y - distance*math.Cos(direction*math.Pi/180)
   g.AaLine(x, y, x2, y2)
   if depth > 0 {
       ftree(g, x2, y2, distance*frac, direction-angle, depth-1)
       ftree(g, x2, y2, distance*frac, direction+angle, depth-1)
   }

}</lang>

Haskell

An elegant yet universal monoidal solution.

Library: Gloss

<lang haskell>import Graphics.Gloss

type Model = [Picture -> Picture]

fractal :: Int -> Model -> Picture -> Picture fractal n model pict = pictures $ take n $ iterate (mconcat model) pict

tree1 _ = fractal 10 branches $ Line [(0,0),(0,100)] 

 where branches = [ Translate 0 100 . Scale 0.75 0.75 . Rotate 30 
                  , Translate 0 100 . Scale 0.5 0.5 . Rotate (-30) ]

main = animate (InWindow "Tree" (800, 800) (0, 0)) white $ tree1 . (* 60)</lang>

The solution gives rise to a variety of fractal geometric structures. Each one can be used by substituting tree1 in the main function by the desired one. <lang haskell>--animated tree tree2 t = fractal 8 branches $ Line [(0,0),(0,100)] 

 where branches = [ Translate 0 100 . Scale 0.75 0.75 . Rotate t
                  , Translate 0 100 . Scale 0.6 0.6 . Rotate 0
                  , Translate 0 100 . Scale 0.5 0.5 . Rotate (-2*t) ]

--animated fractal clock circles t = fractal 10 model $ Circle 100 

 where model = [ Translate 0 50 . Scale 0.5 0.5 . Rotate t
               , Translate 0 (-50) . Scale 0.5 0.5 . Rotate (-2*t) ]

--Pythagoras tree pithagor _ = fractal 10 model $ rectangleWire 100 100 

 where model = [ Translate 50 100 . Scale s s . Rotate 45
               , Translate (-50) 100 . Scale s s . Rotate (-45)]
       s = 1/sqrt 2

--Sierpinski pentagon pentaflake _ = fractal 5 model $ pentagon 

 where model =  map copy [0,72..288]
       copy a = Scale s s . Rotate a . Translate 0 x
       pentagon = Line [ (sin a, cos a) | a <- [0,2*pi/5..2*pi] ]
       x = 2*cos(pi/5)
       s = 1/(1+x)</lang>

Alternative solution

Using the method of the J contribution.

Library: HGL

<lang haskell>import Graphics.HGL.Window import Graphics.HGL.Run import Control.Arrow import Control.Monad import Data.List

enumBase :: Int -> Int -> Int enumBase n = mapM (enumFromTo 0). replicate n. pred

psPlus (a,b) (p,q) = (a+p, b+q)

toInt :: Double -> Int toInt = fromIntegral.round

intPoint = toInt *** toInt

pts n = 

 map (map (intPoint.psPlus (100,0)). ((0,300):). scanl1 psPlus. ((r,300):). zipWith (\h a -> (h*cos a, h*sin a)) rs) hs
 where
   [r,h,sr,sh] = [50, pi/5, 0.9, 0.75]
   rs   = take n $ map (r*) $ iterate(*sr) sr
   lhs  = map (map (((-1)**).fromIntegral)) $ enumBase n 2
   rhs  = take n $ map (h*) $ iterate(*sh) 1
   hs   = map (scanl1 (+). zipWith (*)rhs) lhs

fractalTree :: Int -> IO () fractalTree n = 

  runWindow "Fractal Tree" (500,600)
   (\w -> setGraphic w (overGraphics ( map polyline $ pts (n-1))) >> getKey w)

main = fractalTree 10</lang>

Icon and Unicon

<lang Icon>procedure main() WOpen("size=800,600", "bg=black", "fg=white") | stop("*** cannot open window") drawtree(400,500,-90,9) WDone() end

link WOpen

procedure drawtree(x,y,angle,depth) if depth > 0 then { 

  x2 := integer(x + cos(dtor(angle)) * depth * 10)
  y2 := integer(y + sin(dtor(angle)) * depth * 10)
  DrawLine(x,y,x2,y2)   
  drawtree(x2,y2,angle-20, depth-1)
  drawtree(x2,y2,angle+20, depth-1)
  }

return end</lang>

Library: Icon Programming Library

WOpen provides graphics I/O

Translation of: Java

J

<lang j>require'gl2'

L0=: 50 NB. initial length A0=: 1r8p1 NB. initial angle: pi divided by 8 dL=: 0.9 NB. shrink factor for length dA=: 0.75 NB. shrink factor for angle N=: 14 NB. number of branches

L=: L0*dL^1+i.N NB. lengths of line segments

NB. relative angles of successive line segments A=: A0*(dA^i.N) +/\@:*("1) _1 ^ #:i.2 ^ N

NB. end points for each line segment P=: 0 0+/\@,"2 +.*.inv (L0,0),"2 L,"0"1 A

P_C_paint=: gllines_jgl2_ bind (10 + ,/"2 P-"1<./,/P) wd 0 :0 

pc P closeok;
xywh 0 0 250 300;
cc C isigraph rightmove bottommove;
pas 0 0;
pshow;

)</lang>

See the talk page for some implementation notes.

Java

Library: Swing
Library: AWT

<lang java>import java.awt.Color; import java.awt.Graphics; import javax.swing.JFrame;

public class FractalTree extends JFrame { 

   public FractalTree() {
       super("Fractal Tree");
       setBounds(100, 100, 800, 600);
       setResizable(false);
       setDefaultCloseOperation(EXIT_ON_CLOSE);
   }

   private void drawTree(Graphics g, int x1, int y1, double angle, int depth) {
       if (depth == 0) return;
       int x2 = x1 + (int) (Math.cos(Math.toRadians(angle)) * depth * 10.0);
       int y2 = y1 + (int) (Math.sin(Math.toRadians(angle)) * depth * 10.0);
       g.drawLine(x1, y1, x2, y2);
       drawTree(g, x2, y2, angle - 20, depth - 1);
       drawTree(g, x2, y2, angle + 20, depth - 1);
   }

   @Override
   public void paint(Graphics g) {
       g.setColor(Color.BLACK);
       drawTree(g, 400, 500, -90, 9);
   }

   public static void main(String[] args) {
       new FractalTree().setVisible(true);
   }

}</lang>

JavaScript

Implementation using HTML5 canvas element to draw tree structure. <lang JavaScript><html> <body> <canvas id="canvas" width="600" height="500"></canvas>

<script type="text/javascript"> var elem = document.getElementById('canvas'); var context = elem.getContext('2d');

context.fillStyle = '#C0C0C0'; context.lineWidth = 1;

var deg_to_rad = Math.PI / 180.0; var depth = 9;

function drawLine(x1, y1, x2, y2, brightness){ 

 context.moveTo(x1, y1);
 context.lineTo(x2, y2);

}

function drawTree(x1, y1, angle, depth){ 

 if (depth !== 0){
   var x2 = x1 + (Math.cos(angle * deg_to_rad) * depth * 10.0);
   var y2 = y1 + (Math.sin(angle * deg_to_rad) * depth * 10.0);
   drawLine(x1, y1, x2, y2, depth);
   drawTree(x2, y2, angle - 20, depth - 1);
   drawTree(x2, y2, angle + 20, depth - 1);
 }

}

context.beginPath(); drawTree(300, 500, -90, depth); context.closePath(); context.stroke(); </script>

</body> </html></lang>

jq

The following generates SVG, which can be viewed by following the link below. <lang jq># width and height define the outer dimensions;

  1. len defines the trunk size;
  2. scale defines the branch length relative to the trunk;

def main(width; height; len; scale): 

 def PI: (1|atan)*4;

 def precision(n):
   def pow(k): . as $in | reduce range(0;k) as $i (1; .*$in);
   if . < 0 then - (-. | precision(n))
   else 
     (10|pow(n)) as $power
   | (. * 10 * $power) | floor as $x | ($x % 10) as $r
   | ((if $r < 5 then $x else $x + 5 end) / 10 | floor) / $power
   end;

 def p2: precision(2);

 def tree(x; y; len; angle):
   if len < 1 then empty
   else
     (x + len * (angle|cos)) as $x2 
   | (y + len * (angle|sin)) as $y2
   | (if len < 10 then 1 else 2 end) as $swidth
   | (if len < 10 then "blue" else "black" end) as $stroke
   | "<line x1='\(x|p2)' y1='\(y|p2)' x2='\($x2|p2)' y2='\($y2|p2)' style='stroke:\($stroke); stroke-width:\($swidth)'/>",
     tree($x2; $y2; len * scale; angle + PI / 5),
     tree($x2; $y2; len * scale; angle - PI / 5)
   end
 ;

 "<svg width='100%' height='100%' version='1.1'
       xmlns='http://www.w3.org/2000/svg'>",
       tree(width / 2; height; len; 3 * PI / 2),
 "</svg>"

main(1000; 1000; 400; 6/10)</lang>

Output:

$ jq -r -n -r -f Fractal_tree_svg.jq > Fractal_tree.svg

Fractal_tree.svg

Julia

Translation of: F#

<lang julia> const width = height = 1000.0 const trunklength = 400.0 const scalefactor = 0.6 const startingangle = 1.5 * pi const deltaangle = 0.2 * pi

function tree(fh, x, y, len, theta) 

  if len >= 1.0
      x2 = x + len * cos(theta)
      y2 = y + len * sin(theta)
      write(fh, "<line x1='$x' y1='$y' x2='$x2' y2='$y2' style='stroke:rgb(0,0,0);stroke-width:1'/>\n")
      tree(fh, x2, y2, len * scalefactor, theta + deltaangle)
      tree(fh, x2, y2, len * scalefactor, theta - deltaangle)
   end

end

outsvg = open("tree.svg", "w") write(outsvg, 

   """<?xml version='1.0' encoding='utf-8' standalone='no'?>
   <!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN'
   'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'>
   <svg width='100%%' height='100%%' version='1.1'
   xmlns='http://www.w3.org/2000/svg'>\n""")

tree(outsvg, 0.5 * width, height, trunklength, startingangle)

write(outsvg, "</svg>\n") # view file tree.svg in browser </lang>

Kotlin

Translation of: Java

<lang scala>// version 1.1.2

import java.awt.Color import java.awt.Graphics import javax.swing.JFrame

class FractalTree : JFrame("Fractal Tree") { 

   init {
       background = Color.black
       setBounds(100, 100, 800, 600)
       isResizable = false
       defaultCloseOperation = EXIT_ON_CLOSE
   }

   private fun drawTree(g: Graphics, x1: Int, y1: Int, angle: Double, depth: Int) {
       if (depth == 0) return
       val x2 = x1 + (Math.cos(Math.toRadians(angle)) * depth * 10.0).toInt()
       val y2 = y1 + (Math.sin(Math.toRadians(angle)) * depth * 10.0).toInt()
       g.drawLine(x1, y1, x2, y2)
       drawTree(g, x2, y2, angle - 20, depth - 1)
       drawTree(g, x2, y2, angle + 20, depth - 1)
   }

   override fun paint(g: Graphics) {
       g.color = Color.white
       drawTree(g, 400, 500, -90.0, 9)
   }

}

fun main(args: Array<String>) { 

   FractalTree().isVisible = true

}</lang>

Lambdatalk

<lang Lisp> 1) defining the function tree:

{def tree 

{lambda {:e     // last branch length
         :s     // trunks length
         :k     // ratio between two following branches
         :a     // rotate left
         :b}    // rotate right
 {if {< :s :e}
  then 
  else M:s T:a
       {tree :e {* :k :s} :k :a :b}
       T-{+ :a :b}
       {tree :e {* :k :s} :k :a :b}
       T:b M-:s }}}

2) Calling this function generates a sequence of commands mooving a pen: • Tθ rotates the drawing direction "θ" degrees from the previous one • and Md draws a segment "d" pixels in this direction.

{def T {tree 1 190 {/ 2 3} 15 45}}

and produces 40995 words beginning with:

M190 T15 M126.66666666666666 T15 M84.44444444444443 T15 M56.29629629629628 T15 M37.53086419753085 T15 M25.020576131687235 T15 

M16.680384087791488 T15 M11.120256058527659 T15 M7.413504039018439 T15 M4.942336026012292 T15 M3.2948906840081946 ...

3) These words are sent to a the turtle lambdatalk primitive which is a graphic device translating the sequence of Md and Tθ into a sequence of SVG points x0 y0 x1 y1 ... xn yn which will feed the points attribute of a polyline SVG element:

{svg {@ width="580px" height="580px" style="box-shadow:0 0 8px #000;"} 

 {polyline
  {@ points="{turtle 230 570 180 {T}}"
     fill="transparent" stroke="#fff" stroke-width="1"

}}}

This is an abstract of the output:

<svg width="580px" height="580px" style="box-shadow:0 0 8px #000;"> 

 <polyline points="230 580 230 380 195 251 151 174 109 132 75 113 49 106 32 106 21 109 ...  
                   ... 413 286 324 286 230 380 230 580 " 
          fill="transparent" stroke="#888" stroke-width="1">
 </polyline>

</svg>

The complete ouput can be seen displayed in http://lambdaway.free.fr/lambdawalks/?view=fractal_tree </lang>

Liberty BASIC

LB includes Logo-type turtle commands, so can be drawn that way as well as that shown here. <lang lb> 

NoMainWin

sw = 640 : sh = 480 WindowWidth = sw+8 : WindowHeight = sh+31 UpperLeftX = (DisplayWidth -sw)/2 UpperLeftY = (DisplayHeight-sh)/2 Open"Fractal Tree" For Graphics_nf_nsb As #g

  1. g "Down; Color darkgreen; TrapClose halt"

h$ = "#g"

'initial assignments initAngle = Acs(-1)*1.5 'radian equivalent of 270 degrees 

   theta = 29 * (Acs(-1)/180) 'convert 29 degrees to radians
  length = 110 'length in pixels
   depth = 25   'max recursion depth
   'draw the tree
   Call tree h$, 320, 470, initAngle, theta, length, depth
   #g "Flush; when leftButtonDown halt" 'L-click to exit
   Wait

Sub halt handle$ 

   Close #handle$
   End

End Sub

Sub tree h$, x, y, initAngle, theta, length, depth 

   Scan
   newX = Cos(initAngle) * length + x
   newY = Sin(initAngle) * length + y
   #h$ "Line ";x;" ";y;" ";newX;" ";newY
   length = length * .78
   depth = depth - 1
   If depth > 0 Then
       Call tree h$, newX, newY, initAngle-theta, theta, length, depth
       Call tree h$, newX, newY, initAngle+theta, theta, length, depth
   End If

End Sub </lang>

Lingo

<lang lingo>---------------------------------------- -- Creates an image of a fractal tree -- @param {integer} width -- @param {integer} height -- @param {integer} fractalDepth -- @param {integer|float} initSize -- @param {float} spreadAngle -- @param {float} [scaleFactor=1.0] -- @return {image}

on fractalTree (width, height, fractalDepth, initSize, spreadAngle, scaleFactor) 

 if voidP(scaleFactor) then scaleFactor = 1.0
 img = image(width, height, 24)
 img.fill(img.rect, rgb(0,0,0))
 _drawTree(img, width/2, height, -PI/2, fractalDepth, initSize, spreadAngle, scaleFactor)
 return img

end

on _drawTree (img, x1, y1, angle, depth, size, spreadAngle, scaleFactor) 

 if (depth) then
   x2 = x1 + cos(angle)*depth*size
   y2 = y1 + sin(angle)*depth*size
   img.draw(x1, y1, x2, y2, [#color:rgb(255,255,255)])
   _drawTree(img, x2, y2, angle-spreadAngle, depth-1, size*ScaleFactor, spreadAngle, scaleFactor)
   _drawTree(img, x2, y2, angle+spreadAngle, depth-1, size*ScaleFactor, spreadAngle, scaleFactor)
 end if

end</lang> Usage: <lang lingo>fractalDepth = 10 initSize = 7.0 spreadAngle = 35*PI/180 scaleFactor = 0.95 img = fractalTree(480, 380, fractalDepth, initSize, spreadAngle, scaleFactor)</lang>

<lang logo>to tree :depth :length :scale :angle 

 if :depth=0 [stop]
 setpensize round :depth/2
 forward :length
 right :angle
 tree :depth-1 :length*:scale :scale :angle
 left 2*:angle
 tree :depth-1 :length*:scale :scale :angle
 right :angle
 back :length

end

clearscreen tree 10 80 0.7 30</lang>

Lua

Bitmap

Needs LÖVE 2D Engine <lang lua> g, angle = love.graphics, 26 * math.pi / 180 wid, hei = g.getWidth(), g.getHeight() function rotate( x, y, a ) 

 local s, c = math.sin( a ), math.cos( a )
 local a, b = x * c - y * s, x * s + y * c
 return a, b

end function branches( a, b, len, ang, dir ) 

 len = len * .76
 if len < 5 then return end
 g.setColor( len * 16, 255 - 2 * len , 0 )
 if dir > 0 then ang = ang - angle
 else ang = ang + angle 
 end
 local vx, vy = rotate( 0, len, ang )
 vx = a + vx; vy = b - vy
 g.line( a, b, vx, vy )
 branches( vx, vy, len, ang, 1 )
 branches( vx, vy, len, ang, 0 )

end function createTree() 

 local lineLen = 127
 local a, b = wid / 2, hei - lineLen
 g.setColor( 160, 40 , 0 )
 g.line( wid / 2, hei, a, b )
 branches( a, b, lineLen, 0, 1 ) 
 branches( a, b, lineLen, 0, 0 )

end function love.load() 

 canvas = g.newCanvas( wid, hei )
 g.setCanvas( canvas )
 createTree()
 g.setCanvas()

end function love.draw() 

 g.draw( canvas )

end </lang>

ASCII

Using the Bitmap class and text renderer from here, then extending... <lang lua>function Bitmap:tree(x, y, angle, depth, forkfn, lengfn) 

 if depth <= 0 then return end
 local fork, leng = forkfn(), lengfn()
 local x2 = x + depth * leng * math.cos(angle)
 local y2 = y - depth * leng * math.sin(angle)
 self:line(math.floor(x), math.floor(y), math.floor(x2), math.floor(y2))
 self:tree(x2, y2, angle+fork, depth-1, forkfn, lengfn)
 self:tree(x2, y2, angle-fork, depth-1, forkfn, lengfn)

end

bitmap = Bitmap(128*3,128) bitmap:tree( 64, 120, math.pi/2, 8, function() return 0.3 end, function() return 3 end) bitmap:tree(192, 120, math.pi/2, 8, function() return 0.6 end, function() return 2.5 end) bitmap:tree(320, 120, math.pi/2, 8, function() return 0.2+math.random()*0.3 end, function() return 2.0+math.random()*2.0 end) bitmap:render({[0x000000]='.', [0xFFFFFFFF]='█'})</lang>

Output:

Shown at 25% scale: 

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Mathematica / Wolfram Language

<lang Mathematica>fractalTree[ 

 pt : {_, _}, \[Theta]orient_: \[Pi]/2, \[Theta]sep_: \[Pi]/9, 
 depth_Integer: 9] := Module[{pt2},
 If[depth == 0, Return[]];
 pt2 = pt + {Cos[\[Theta]orient], Sin[\[Theta]orient]}*depth;
 DeleteCases[
  Flatten@{
    Line[{pt, pt2}],
    fractalTree[pt2, \[Theta]orient - \[Theta]sep, \[Theta]sep, 
     depth - 1],
    fractalTree[pt2, \[Theta]orient + \[Theta]sep, \[Theta]sep, 
     depth - 1]
    },
  Null
  ]
 ]

Graphics[fractalTree[{0, 0}, \[Pi]/2, \[Pi]/9]] </lang>

NetRexx

Translation of: Java
Library: Swing
Library: AWT

<lang NetRexx>/* NetRexx */ options replace format comments java crossref symbols binary

import java.awt.Color import java.awt.Graphics import javax.swing.JFrame

class RFractalTree public extends JFrame 

 properties constant
   isTrue  = (1 == 1)
   isFalse = \isTrue
 -- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
 method RFractalTree() public
   super('Fractal Tree')
   setBounds(100, 100, 800, 600)
   setResizable(isFalse)
   setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE)
   return
 -- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
 method drawTree(g = Graphics, x1 = int, y1 = int, angle = double, depth = int) private
   if depth \= 0 then do
     x2 = x1 + (int Math.cos(Math.toRadians(angle)) * depth * 10.0)
     y2 = y1 + (int Math.sin(Math.toRadians(angle)) * depth * 10.0)
     g.drawLine(x1, y1, x2, y2)
     drawTree(g, x2, y2, angle - 20, depth - 1)
     drawTree(g, x2, y2, angle + 20, depth - 1)
     end
   return
 -- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
 method paint(g = Graphics) public
   g.setColor(Color.BLACK)
   drawTree(g, 400, 500, -90, 9)
   return
 -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 method main(args = String[])public static
   RFractalTree().setVisible(isTrue)
   return

</lang>

Nim

Translation of: Julia

<lang Nim> import math import strformat

const 

 Width = 1000
 Height = 1000
 TrunkLength = 400
 ScaleFactor = 0.6
 StartingAngle = 1.5 * PI
 DeltaAngle = 0.2 * PI

proc drawTree(outfile: File; x, y, len, theta: float) = 

 if len >= 1:
   let x2 = x + len * cos(theta)
   let y2 = y + len * sin(theta)
   outfile.write(
     fmt"<line x1='{x}' y1='{y}' x2='{x2}' y2='{y2}' style='stroke:white;stroke-width:1'/>\n")
   outfile.drawTree(x2, y2, len * ScaleFactor, theta + DeltaAngle)
   outFile.drawTree(x2, y2, len * ScaleFactor, theta - DeltaAngle)

let outsvg = open("tree.svg", fmWrite) outsvg.write("""<?xml version='1.0' encoding='utf-8' standalone='no'?> 

               <!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN'
               'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'>
               <svg width='100%%' height='100%%' version='1.1'
               xmlns='http://www.w3.org/2000/svg'>\n
               <rect width="100%" height="100%" fill="black"/>\n""")

outsvg.drawTree(0.5 * Width, Height, TrunkLength, StartingAngle) outsvg.write("</svg>\n") # View file tree.svg in browser.

</lang>

OCaml

Library: ocaml-cairo

<lang ocaml>#directory "+cairo"

  1. load "bigarray.cma"
  2. load "cairo.cma"

let img_name = "/tmp/fractree.png" let width = 480 let height = 640

let level = 9 let line_width = 4.0

let color = (1.0, 0.5, 0.0)

let pi = 4.0 *. atan 1.0

let angle_split = pi *. 0.12 let angle_rand = pi *. 0.12

let () = 

 Random.self_init();
 let surf = Cairo.image_surface_create Cairo.FORMAT_RGB24 ~width ~height in
 let ctx = Cairo.create surf in
 Cairo.set_antialias ctx Cairo.ANTIALIAS_SUBPIXEL;
 Cairo.set_line_cap ctx Cairo.LINE_CAP_ROUND;

 let draw_line (x,y) (dx,dy) =
   Cairo.move_to ctx x  (float height -. y);
   Cairo.line_to ctx dx (float height -. dy);
   Cairo.stroke ctx;
 in
 let set_color (r,g,b) v =
   Cairo.set_source_rgb ctx ~red:(r *. v) ~green:(g *. v) ~blue:(b *. v);
 in
 let trans_pos (x,y) len angle =
   let _x = cos angle
   and _y = sin angle in
   (x +. (_x *. len),
    y +. (_y *. len))
 in

 let rec loop ~level ~pos ~line_width ~line_len
              ~angle ~angle_split ~angle_rand ~intc =
   if level > 0 then begin
     (* draw the current segment *)
     Cairo.set_line_width ctx line_width;
     set_color color intc;
     let pos_to = trans_pos pos line_len angle in
     draw_line pos pos_to;
     (* evolution of the parameters *)
     let line_width = line_width *. 0.8
     and line_len   = line_len   *. 0.62
     and angle_split = angle_split *. 1.02
     and angle_rand  = angle_rand  *. 1.02
     and intc = intc *. 0.9
     in
     let next_loop =
       loop ~level:(pred level) ~pos:pos_to ~intc
            ~line_width ~line_len ~angle_split ~angle_rand
     in
     (* split *)
     let angle_left  = angle +. angle_split +. Random.float angle_rand
     and angle_right = angle -. angle_split -. Random.float angle_rand
     in
     next_loop ~angle:angle_left;
     next_loop ~angle:angle_right
   end
 in

 let pos = (float width *. 0.5, float height *. 0.1)
 and line_len = float height *. 0.3
 in
 loop ~level ~pos ~angle:(pi /. 2.0)
      ~angle_split ~angle_rand
      ~line_width ~line_len ~intc:1.0;

 Cairo_png.surface_write_to_file surf img_name
 (*Cairo_png.surface_write_to_channel surf stdout*)</lang>

PARI/GP

Output FracTree1.png
Output FracTree2.png
Output FracTree3.png

This version with recursion, in general, is a translation of JavaScript version. Some tweaks and options were added to make it reusable and outputting different size of a tree.

Translation of: JavaScript
Works with: PARI/GP version 2.7.4 and above

<lang parigp> \\ Fractal tree (w/recursion) \\ 4/10/16 aev plotline(x1,y1,x2,y2)={plotmove(0, x1,y1);plotrline(0,x2-x1,y2-y1);}

plottree(x,y,a,d)={ my(x2,y2,d2r=Pi/180.0,a1=a*d2r,d1); if(d<=0, return();); if(d>0, d1=d*10.0; 

   x2=x+cos(a1)*d1;
   y2=y+sin(a1)*d1;
   plotline(x,y,x2,y2);
   plottree(x2,y2,a-20,d-1);
   plottree(x2,y2,a+20,d-1),
   return();
 );

}

FractalTree(depth,size)={ my(dx=1,dy=0,ttlb="Fractal Tree, depth ",ttl=Str(ttlb,depth)); print1(" *** ",ttl); print(", size ",size); plotinit(0); plotcolor(0,6); \\green plotscale(0, -size,size, 0,size); plotmove(0, 0,0); plottree(0,0,90,depth); plotdraw([0,size,size]); }

{\\ Executing: FractalTree(9,500); \\FracTree1.png FractalTree(12,1100); \\FracTree2.png FractalTree(15,1500); \\FracTree3.png } </lang>

Output:

 *** Fractal Tree, depth 9, size 500
 ***   last result computed in 140 ms.

 *** Fractal Tree, depth 12, size 1100
 ***   last result computed in 236 ms. 

 *** Fractal Tree, depth 15, size 1500
 ***   last result computed in 1,095 ms

Perl

using the GD::Simple module. <lang perl>use GD::Simple;

my ($width, $height) = (1000,1000); # image dimension my $scale = 6/10; # branch scale relative to trunk my $length = 400; # trunk size

my $img = GD::Simple->new($width,$height); $img->fgcolor('black'); $img->penSize(1,1);

tree($width/2, $height, $length, 270);

print $img->png;


sub tree { 

       my ($x, $y, $len, $angle) = @_;

       return if $len < 1;

       $img->moveTo($x,$y);
       $img->angle($angle);
       $img->line($len);

       ($x, $y) = $img->curPos();

       tree($x, $y, $len*$scale, $angle+35);
       tree($x, $y, $len*$scale, $angle-35);

}</lang>

Phix

Translation of: XPL0
Library: Phix/pGUI

<lang Phix>-- demo\rosetta\FractalTree.exw include pGUI.e

Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas

procedure drawTree(integer level, atom angle, atom len, integer x, integer y) integer xn = x + floor(len*cos(angle)) integer yn = y + floor(len*sin(angle)) integer red = 255-level*8 integer grn = level*12+100 

   cdCanvasSetForeground(cddbuffer, red*#10000 + grn*#100)
   cdCanvasLineWidth(cddbuffer,floor(5-level/3))
   cdCanvasLine(cddbuffer, x, 480-y, xn, 480-yn)
   if level<12 then
       drawTree(level+1, angle-0.4, len*0.8, xn, yn)   --left
       drawTree(level+1, angle+0.1, len*0.8, xn, yn)   --right
   end if

end procedure

function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/) 

   cdCanvasActivate(cddbuffer)
   cdCanvasClear(cddbuffer)
   drawTree(0, -PI/2.0, 80.0, 360, 460)
   cdCanvasFlush(cddbuffer)
   return IUP_DEFAULT

end function

function map_cb(Ihandle ih) 

   cdcanvas = cdCreateCanvas(CD_IUP, ih)
   cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
   cdCanvasSetBackground(cddbuffer, CD_PARCHMENT)
   return IUP_DEFAULT

end function

procedure main() 

   IupOpen()

   canvas = IupCanvas(NULL)
   IupSetAttribute(canvas, "RASTERSIZE", "640x480")
   IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
   IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))

   dlg = IupDialog(canvas,"RESIZE=NO")
   IupSetAttribute(dlg, "TITLE", "Fractal Tree")

   IupShow(dlg)
   IupMainLoop()
   IupClose()

end procedure

main()</lang>

PHP

Image is created with GD module. Code adapted from the JavaScript version. <lang php> <?php header("Content-type: image/png");

$width = 512; $height = 512; $img = imagecreatetruecolor($width,$height); $bg = imagecolorallocate($img,255,255,255); imagefilledrectangle($img, 0, 0, $width, $width, $bg);

$depth = 8; function drawTree($x1, $y1, $angle, $depth){ 

   global $img;
   
   if ($depth != 0){
       $x2 = $x1 + (int)(cos(deg2rad($angle)) * $depth * 10.0);
       $y2 = $y1 + (int)(sin(deg2rad($angle)) * $depth * 10.0);
       
       imageline($img, $x1, $y1, $x2, $y2, imagecolorallocate($img,0,0,0));
       
       drawTree($x2, $y2, $angle - 20, $depth - 1);
       drawTree($x2, $y2, $angle + 20, $depth - 1);
   }

}

drawTree($width/2, $height, -90, $depth);

imagepng($img); imagedestroy($img); ?> </lang>

PicoLisp

This uses the 'brez' line drawing function from Bitmap/Bresenham's line algorithm#PicoLisp. <lang PicoLisp>(load "@lib/math.l")

(de fractalTree (Img X Y A D) 

  (unless (=0 D)
     (let (R (*/ A pi 180.0)  DX (*/ (cos R) D 0.2)  DY (*/ (sin R) D 0.2))
        (brez Img X Y DX DY)
        (fractalTree Img (+ X DX) (+ Y DY) (+ A 30.0) (dec D))
        (fractalTree Img (+ X DX) (+ Y DY) (- A 30.0) (dec D)) ) ) )

(let Img (make (do 300 (link (need 400 0)))) # Create image 400 x 300 

  (fractalTree Img 200 300 -90.0 10)              # Draw tree
  (out "img.pbm"                                  # Write to bitmap file
     (prinl "P1")
     (prinl 400 " " 300)
     (mapc prinl Img) ) )</lang>

Plain English

<lang plainenglish>To run: Start up. Clear the screen to the lightest blue color. Pick a brownish color. Put the screen's bottom minus 1/2 inch into the context's spot's y coord. Draw a tree given 3 inches. Refresh the screen. Wait for the escape key. Shut down.

To draw a tree given a size: If the size is less than 1/32 inch, exit. Put the size divided by 1/4 inch into the pen size. If the size is less than 1/4 inch, pick a greenish color. Remember where we are. Stroke the size. Turn left 1/16 of the way. Draw another tree given the size times 2/3. Turn right 1/16 of the way. Turn right 1/16 of the way. Draw a third tree given the size times 2/3. Turn left 1/16 of the way. Go back to where we were.</lang>

Output:

[1]

PostScript

<lang postscript>%!PS %%BoundingBox: 0 0 300 300 %%EndComments /origstate save def /ld {load def} bind def /m /moveto ld /g /setgray ld /t /translate ld /r /rotate ld /l /lineto ld /rl /rlineto ld /s /scale ld %%EndProlog /PerturbateAngle {} def /PerturbateLength {} def % ** To add perturbations, define properly PerturbateAngle and PerturbateLength, e.g. % /PerturbateAngle {realtime 20 mod realtime 2 mod 1 eq {add} {sub} ifelse} def % /PerturbateLength {realtime 10 mod 100 div realtime 2 mod 1 eq {add} {sub} ifelse} def /fractree { % [INITLENGTH, SPLIT, SFACTOR, BRANCHES] 

 dup 3 get 0 gt
 {
   0 0 m dup 0 get 0 exch l
   gsave
     dup 0 get 0 exch t
     dup 1 get PerturbateAngle r
     dup 2 get dup PerturbateLength s
     dup aload pop 1 sub 4 array astore fractree stroke
   grestore
   gsave
     dup 0 get 0 exch t
     dup 1 get neg PerturbateAngle r
     dup 2 get dup PerturbateLength s
     dup aload pop 1 sub 4 array astore fractree stroke
   grestore
 } if pop

} def % /BRANCHES 14 def /INITLENGTH 50 def /SPLIT 35 def /SFACTOR .75 def % % BB check %0 0 m 300 0 rl 0 300 rl -300 0 rl closepath stroke % 0 g 150 0 t [INITLENGTH SPLIT SFACTOR BRANCHES] fractree stroke % showpage origstate restore %%EOF</lang>

Shorter version:<lang postscript>%!PS-Adobe-3.0 %%BoundingBox: 0 0 300 300 /!0 { dup 1 sub dup 0 gt } def /trunk { 0 0 moveto 0 60 translate 0 0 lineto stroke } def

/branch { gsave scale rotate dup d exch sub d div setgray tree grestore } def /L { 30 .8 .8 branch } def /M {-10 .7 .7 branch } def /R {-35 .7 .7 branch } def /tree { trunk !0 { L M R } if pop } def

/d 10 def 5 setlinewidth 1 setlinecap 170 20 translate d tree pop %%EOF</lang>

POV-Ray

<lang povray>#include "colors.inc"

  1. include "transforms.inc"
  1. declare CamLoc = <0, 5, 0>;
  2. declare CamLook = <0,0,0>;

camera { 

 location CamLoc
 look_at CamLook
 rotate y*90

}

light_source { 

 CamLoc
 color White

}

  1. declare Init_Height = 10;
  2. declare Spread_Ang = 35;
  3. declare Branches = 14;
  4. declare Scaling_Factor = 0.75;
  1. macro Stick(P0, P1)
 cylinder { 
   P0, P1, 0.02
   texture { pigment { Green } }
 }
  1. end
  1. macro FractalTree(O, D, S, R, B)
 #if (B > 0)
   Stick(O, O+D*S)
   FractalTree(O+D*S, vtransform(D, transform{rotate y*R}),
     S*Scaling_Factor, R, B-1)
   FractalTree(O+D*S, vtransform(D, transform{rotate -y*R}),
     S*Scaling_Factor, R, B-1)
 #end
  1. end

union { 

 FractalTree(<-2,0,0>, <1,0,0>, 1, Spread_Ang, Branches)

}</lang>

Prolog

SWI-Prolog has a graphic interface : XPCE. <lang Prolog>fractal :- new(D, window('Fractal')), send(D, size, size(800, 600)), drawTree(D, 400, 500, -90, 9), send(D, open).


drawTree(_D, _X, _Y, _Angle, 0).

drawTree(D, X1, Y1, Angle, Depth) :- 

       X2 is X1 + cos(Angle * pi / 180.0) * Depth * 10.0,
       Y2 is Y1 + sin(Angle * pi / 180.0) * Depth * 10.0,

new(Line, line(X1, Y1, X2, Y2, none)), send(D, display, Line), A1 is Angle - 30, A2 is Angle + 30, De is Depth - 1, 

       drawTree(D, X2, Y2, A1, De),
       drawTree(D, X2, Y2, A2, De).

</lang>

PureBasic

<lang PureBasic>#Spread_Ang = 35

  1. Scaling_Factor = 0.75
  2. Deg_to_Rad = #PI / 180
  3. SizeH = 500
  4. SizeV = 375
  5. Init_Size = 100

Procedure drawTree(x1, y1, Size, theta, depth) 

 Protected x2 = x1 + Cos(theta * #Deg_to_Rad) * Size, y2 = y1 + Sin(theta * #Deg_to_Rad) * Size
 LineXY(x1, y1, x2, y2, RGB(255, 255, 255))
 If depth <= 0
   ProcedureReturn
 EndIf
 ;draw left branch
 drawTree(x2, y2, Size * #Scaling_Factor, theta - #Spread_Ang, depth - 1)
 ;draw right branch
 drawTree(x2, y2, Size * #Scaling_Factor, theta + #Spread_Ang, depth - 1)

EndProcedure


OpenWindow(0, 0, 0, #SizeH, #SizeV, "Fractal Tree", #PB_Window_SystemMenu) Define fractal = CreateImage(#PB_Any, #SizeH, #SizeV, 32) ImageGadget(0, 0, 0, 0, 0, ImageID(fractal))

If StartDrawing(ImageOutput(fractal)) 

   drawTree(#SizeH / 2, #SizeV, #Init_Size, -90, 9)
 StopDrawing()
 SetGadgetState(0, ImageID(fractal))

EndIf

Repeat: Until WaitWindowEvent(10) = #PB_Event_CloseWindow</lang>

Processing

Using rotation

<lang java>void setup() { 

 size(600, 600);
 background(0);
 stroke(255);
 drawTree(300, 550, 9);

}

void drawTree(float x, float y, int depth) { 

 float forkAngle = radians(20);
 float baseLen = 10.0;
 if (depth > 0) {
   pushMatrix();
   translate(x, y - baseLen * depth);
   line(0, baseLen * depth, 0, 0);  
   rotate(forkAngle);
   drawTree(0, 0, depth - 1);  
   rotate(2 * -forkAngle);
   drawTree(0, 0, depth - 1); 
   popMatrix();
 }

}</lang>

Calculating coordinates

Translation of: Python

<lang java>void setup() { 

 size(600, 600);
 background(0);
 stroke(255);
 drawTree(300, 550, -90, 9);

}

void drawTree(float x1, float y1, float angle, int depth) { 

 float forkAngle = 20;
 float baseLen = 10.0;
 if (depth > 0) {
   float x2 = x1 + cos(radians(angle)) * depth * baseLen;
   float y2 = y1 + sin(radians(angle)) * depth * baseLen;
   line(x1, y1, x2, y2);
   drawTree(x2, y2, angle - forkAngle, depth - 1);
   drawTree(x2, y2, angle + forkAngle, depth - 1);
 }

}</lang>

Processing Python mode

Using rotation

Translation of: Processing

<lang python>def setup(): 

   size(600, 600)
   background(0)
   stroke(255)
   drawTree(300, 550, 9)

def drawTree(x, y, depth): 

   fork_ang = radians(20)
   base_len = 10
   if depth > 0:
       pushMatrix()
       translate(x, y - baseLen * depth)
       line(0, baseLen * depth, 0, 0)  
       rotate(fork_ang)
       drawTree(0, 0, depth - 1)  
       rotate(2 * -fork_ang)
       drawTree(0, 0, depth - 1) 
       popMatrix()</lang>

Calculating coordinates

Translation of: Python

<lang python>def setup(): 

   size(600, 600)
   background(0)
   stroke(255)
   drawTree(300, 550, -90, 9)

def drawTree(x1, y1, angle, depth): 

   fork_angle = 20
   base_len = 10.0
   if depth > 0:
       x2 = x1 + cos(radians(angle)) * depth * base_len
       y2 = y1 + sin(radians(angle)) * depth * base_len
       line(x1, y1, x2, y2)
       drawTree(x2, y2, angle - fork_angle, depth - 1)
       drawTree(x2, y2, angle + fork_angle, depth - 1)</lang>

Python

File:Fractal-tree-python.png
Library: pygame

<lang python>import pygame, math

pygame.init() window = pygame.display.set_mode((600, 600)) pygame.display.set_caption("Fractal Tree") screen = pygame.display.get_surface()

def drawTree(x1, y1, angle, depth): 

   fork_angle = 20
   base_len = 10.0
   if depth > 0:
       x2 = x1 + int(math.cos(math.radians(angle)) * depth * base_len)
       y2 = y1 + int(math.sin(math.radians(angle)) * depth * base_len)
       pygame.draw.line(screen, (255,255,255), (x1, y1), (x2, y2), 2)
       drawTree(x2, y2, angle - fork_angle, depth - 1)
       drawTree(x2, y2, angle + fork_angle, depth - 1)

def input(event): 

   if event.type == pygame.QUIT:
       exit(0)

drawTree(300, 550, -90, 9) pygame.display.flip() while True: 

   input(pygame.event.wait())</lang>

QB64

<lang qb64>_Title "Fractal Tree" Const sw% = 640 Const sh% = 480

Screen _NewImage(sw, sh, 8) Cls , 15: Color 2

Call tree(sw \ 2, sh - 10, _Pi * 1.5, _Pi / 180 * 29, 112, 15)

Sleep System

Sub tree (x As Integer, y As Integer, initAngle As Double, theta As Double, length As Double, depth As Integer) 

   Dim As Integer iL, newX, newY, iX, iY, iD
   iL = length: iX = x: iY = y: iD = depth
   newX = Cos(initAngle) * length + iX
   newY = Sin(initAngle) * length + iY
   Line (iX, iY)-(newX, newY)
   iL = length * .78
   iD = iD - 1
   If iD > 0 Then
       Call tree(newX, newY, initAngle - theta, theta, iL, iD)
       Call tree(newX, newY, initAngle + theta, theta, iL, iD)
   End If

End Sub</lang>

Quackery

<lang Quackery>[ $ "turtleduck.qky" loadfile ] now!

[ [ 1 1 

   30 times 
      [ tuck + ] 
  swap join ] constant 
  do ]                  is phi  (       --> n/d )

[ 2dup 5 1 v< iff 

   2drop done
 2dup 5 1 v/ 
 proper 2drop wide
 2dup walk
 1 5 turn
 2dup phi v/
 2dup recurse
 -2 5 turn
 recurse
 1 5 turn
 -v fly ]               is tree ( n/d -->     )

turtle -1 4 turn -450 1 fly 500 1 tree</lang>

Output:

https://imgur.com/x0TdhS5

R

Translation of: PARI/GP
Works with: R version 3.3.3 and above
File:FRTR9.png
Output FRTR9.png
File:FRTR12.png
Output FRTR12.png
File:FRTR15.png
Output FRTR15.png

<lang r>

    1. Recursive FT plotting

plotftree <- function(x, y, a, d, c) { x2=y2=0; d2r=pi/180.0; a1 <- a*d2r; d1=0; if(d<=0) {return()} if(d>0) 

 { d1=d*10.0;
   x2=x+cos(a1)*d1;
   y2=y+sin(a1)*d1;
   segments(x*c, y*c, x2*c, y2*c, col='darkgreen');
   plotftree(x2,y2,a-20,d-1,c);
   plotftree(x2,y2,a+20,d-1,c);
   #return(2);
 }

}

    1. Plotting Fractal Tree. aev 3/27/17
    2. ord - order/depth, c - scale, xsh - x-shift, fn - file name,
    3. ttl - plot title.

pFractalTree <- function(ord, c=1, xsh=0, fn="", ttl="") { 

 cat(" *** START FRT:", date(), "\n");
 m=640;
 if(fn=="") {pf=paste0("FRTR", ord, ".png")} else {pf=paste0(fn, ".png")};
 if(ttl=="") {ttl=paste0("Fractal tree, order - ", ord)};
 cat(" *** Plot file -", pf, "title:", ttl, "\n");
 ##plot(NA, xlim=c(0,m), ylim=c(-m,0), xlab="", ylab="", main=ttl);
 plot(NA, xlim=c(0,m), ylim=c(0,m), xlab="", ylab="", main=ttl);
 plotftree(m/2+xsh,100,90,ord,c);
 dev.copy(png, filename=pf, width=m, height=m);
 dev.off(); graphics.off();
 cat(" *** END FRT:",date(),"\n");

}

    1. Executing:

pFractalTree(9); pFractalTree(12,0.6,210); pFractalTree(15,0.35,600); </lang>

Output:
> pFractalTree(9);
 *** START FRT: Tue Mar 28 16:49:49 2017 
 *** Plot file - FRTR9.png title: Fractal tree, order - 9 
 *** END FRT: Tue Mar 28 16:49:50 2017 
> pFractalTree(12,0.6,210);
 *** START FRT: Tue Mar 28 17:32:15 2017 
 *** Plot file - FRTR12.png title: Fractal tree, order - 12 
 *** END FRT: Tue Mar 28 17:32:16 2017 
> pFractalTree(15,0.35,600);
 *** START FRT: Tue Mar 28 17:38:34 2017 
 *** Plot file - FRTR15.png title: Fractal tree, order - 15 
 *** END FRT: Tue Mar 28 17:38:41 2017

Racket

<lang racket>

  1. lang racket

(require graphics/turtles)

(define (tree n) 

 (when (> n 1)
   (draw (/ n 2))
   (tprompt (split* (turn 60) (turn -60))
            (tree (/ n 2)))
   (draw (/ n 2))
   (turn 5)
   (tree (- n 1))))

(turtles #t) (move 100) (turn 90) (move -200) (tree 35) (save-turtle-bitmap "tree.png" 'png) </lang>

Raku

(formerly Perl 6) Image is created in SVG format. <lang perl6>my ($width, $height) = (1000,1000); # image dimension my $scale = 6/10; # branch scale relative to trunk my $length = 400; # trunk size

say "<?xml version='1.0' encoding='utf-8' standalone='no'?> <!DOCTYPE svg PUBLIC '-//W3C//DTD SVG 1.1//EN' 'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'> <svg width='100%' height='100%' version='1.1' xmlns='http://www.w3.org/2000/svg'>";

tree($width/2, $height, $length, 3*pi/2);

say "</svg>";

multi tree($, $, $length where { $length < 1}, $) {} multi tree($x, $y, $length, $angle) { my ($x2, $y2) = ( $x + $length * $angle.cos, $y + $length * $angle.sin); say "<line x1='$x' y1='$y' x2='$x2' y2='$y2' style='stroke:rgb(0,0,0);stroke-width:1'/>"; tree($x2, $y2, $length*$scale, $angle + pi/5); tree($x2, $y2, $length*$scale, $angle - pi/5); }</lang>

Red

<lang Red>Red [Needs: 'View]

color: brown width: 9 view/tight/options/flags/no-wait [ ; click image to grow tree img: image 1097x617 draw [ pen brown line-width 9 line 500x600 500x500] [grow] ] [offset: 0x0] [no-border]

ends: reduce [500x500 pi * 3 / 2] ; list of terminal nodes da: pi * 30 / 180 ; angle of branches in radians ea: pi * 5 / 180 ; offset added to angle to break symmetry

l: 200 ; branches initial lenght scale: 0.7 ; branches scale factor grow: does [ ; grows branches l: l * scale color: 2 * color + leaf / 3 width: width - 1 newends: copy [] foreach [p a] ends [ a1: a + da - ea p1: p + as-pair l * cos a1 l * sin a1 a2: a - da - ea p2: p + as-pair l * cos a2 l * sin a2 append img/draw compose/deep [ pen (color) line-width (width) line (p1) (p) (p2)] append newends reduce [p1 a1 p2 a2] ] ends: newends ]</lang>

Output:

fractal tree image

Ring

<lang ring> load "guilib.ring"

new qapp 

       {
       win1 = new qwidget() {
              setwindowtitle("drawing using qpainter")
              setgeometry(100,100,500,500)
              label1 = new qlabel(win1) {
                       setgeometry(10,10,400,400)
                       settext("")
              }
              draw()
              show()
        }
        exec()
        }

func draw 

    p1 = new qpicture()
            color = new qcolor() {
            setrgb(0,0,255,255)
       }
       pen = new qpen() {
             setcolor(color)
             setwidth(1)
       }
       new qpainter() {
           begin(p1)
           setpen(pen)

       sizex = 400
       sizey = 200
       depth = 10

       tree(self, sizex, 0, sizey/2, 90, depth)

       endpaint()
       }
       label1 { setpicture(p1) show() }

       func tree myObj, x1, y1, size, angle, depth
            myObj{
            scale = 0.76
            spread = 25
            x2 = x1 + size * cos(angle)
            y2 = y1 + size * sin(angle)
            drawline(x1, y1, x2, y2)
            if depth > 0 
            tree(self, x2, y2, size * scale, angle - spread, depth - 1)
            tree(self, x2, y2, size * scale, angle + spread, depth - 1) ok}

</lang> Output:

Ruby

Library: Shoes

<lang Ruby>Shoes.app(:title => "Fractal Tree", :width => 600, :height => 600) do 

 background "#fff"
 stroke "#000"
 @deg_to_rad = Math::PI / 180.0
 
 def drawTree(x1, y1, angle, depth)
   if depth != 0
     x2 = x1 + (Math.cos(angle * @deg_to_rad) * depth * 10.0).to_i
     y2 = y1 + (Math.sin(angle * @deg_to_rad) * depth * 10.0).to_i
     
     line x1, y1, x2, y2
     
     drawTree(x2, y2, angle - 20, depth - 1)
     drawTree(x2, y2, angle + 20, depth - 1)      
   end
 end
 
 drawTree(300,550,-90,9)

end</lang>

Rust

Library: Piston

<lang Rust>//Cargo deps : // piston = "0.35.0" // piston2d-graphics = "0.23.0" // piston2d-opengl_graphics = "0.49.0" // pistoncore-glutin_window = "0.42.0"

extern crate piston; extern crate graphics; extern crate opengl_graphics; extern crate glutin_window;

use piston::window::WindowSettings; use piston::event_loop::{Events, EventSettings}; use piston::input::RenderEvent; use glutin_window::GlutinWindow as Window; use opengl_graphics::{GlGraphics, OpenGL}; use graphics::{clear, line, Context};

const ANG: f64 = 20.0; const COLOR: [f32; 4] = [1.0, 0.0, 0.5, 1.0]; const LINE_THICKNESS: f64 = 5.0; const DEPTH: u32 = 11;

fn main() { 

   let mut window: Window = WindowSettings::new("Fractal Tree", [1024, 768])
       .opengl(OpenGL::V3_2)
       .exit_on_esc(true)
       .build()
       .unwrap();
   let mut gl = GlGraphics::new(OpenGL::V3_2);

   let mut events = Events::new(EventSettings::new());
   while let Some(e) = events.next(&mut window) {
       if let Some(args) = e.render_args() {
           gl.draw(args.viewport(), |c, g| {
               clear([1.0, 1.0, 1.0, 1.0], g);
               draw_fractal_tree(512.0, 700.0, 0.0, DEPTH, c, g);
           });
       }
   }

}

fn draw_fractal_tree(x1: f64, y1: f64, angle: f64, depth: u32, c: Context, g: &mut GlGraphics) { 

   let x2 = x1 + angle.to_radians().sin() * depth as f64 * 10.0;
   let y2 = y1 - angle.to_radians().cos() * depth as f64 * 10.0;
   line(
       COLOR,
       LINE_THICKNESS * depth as f64 * 0.2,
       [x1, y1, x2, y2],
       c.transform,
       g,
   );
   if depth > 0 {
       draw_fractal_tree(x2, y2, angle - ANG, depth - 1, c, g);
       draw_fractal_tree(x2, y2, angle + ANG, depth - 1, c, g);
   }

} </lang>

Scala

Adapted from the Java version. Screenshot below. <lang scala>import swing._ import java.awt.{RenderingHints, BasicStroke, Color}

object FractalTree extends SimpleSwingApplication { 

 val DEPTH = 9

 def top = new MainFrame {
   contents = new Panel {
     preferredSize = new Dimension(600, 500)

     override def paintComponent(g: Graphics2D) {
       draw(300, 460, -90, DEPTH)

       def draw(x1: Int, y1: Int, angle: Double, depth: Int) {
         if (depth > 0) {
           val x2 = x1 + (math.cos(angle.toRadians) * depth * 10).toInt
           val y2 = y1 + (math.sin(angle.toRadians) * depth * 10).toInt

           g.setColor(Color.getHSBColor(0.25f - depth * 0.125f / DEPTH, 0.9f, 0.6f))
           g.setStroke(new BasicStroke(depth))
           g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
           g.drawLine(x1, y1, x2, y2)

           draw(x2, y2, angle - 20, depth - 1)
           draw(x2, y2, angle + 20, depth - 1)
         }
       }
     }
   }
 }

}</lang>

Scheme

The tree is created as a list of line segments, which can then be drawn on a required device. For this program, the tree is output to an eps file.

<lang scheme> (import (scheme base) 

       (scheme file)
       (scheme inexact)
       (scheme write))

(define *scale* 10) ; controls overall size of tree (define *split* 20) ; controls angle of split (in degrees)

construct lines for tree as list of 5-tuples (x1 y1 x2 y2 depth)
- x1 y1 is start point
- angle of this line, in radians
- depth, depth within tree (controls length of line)

(define (create-tree x1 y1 angle depth) 

 (define (degrees->radians d)
   (let ((pi 3.14159265358979323846264338327950288419716939937510582097))
     (* d pi 1/180)))
 ;
 (if (zero? depth)
   '()
   (let ((x2 (+ x1 (* (cos (degrees->radians angle)) depth *scale*)))
         (y2 (+ y1 (* (sin (degrees->radians angle)) depth *scale*))))
     (append (list (map truncate (list x1 y1 x2 y2 depth)))
             (create-tree x2 y2 (- angle *split*) (- depth 1))
             (create-tree x2 y2 (+ angle *split*) (- depth 1))))))
output the tree to an eps file

(define (output-tree-as-eps filename tree) 

 (when (file-exists? filename) (delete-file filename))
 (with-output-to-file
   filename
   (lambda ()
     (display "%!PS-Adobe-3.0 EPSF-3.0\n%%BoundingBox: 0 0 800 800\n") 

     ;; add each line - sets linewidth based on depth in tree
     (for-each (lambda (line)
                 (display
                   (string-append "newpath\n"
                                  (number->string (list-ref line 0)) " "
                                  (number->string (list-ref line 1)) " "
                                  "moveto\n"
                                  (number->string (list-ref line 2)) " "
                                  (number->string (list-ref line 3)) " "
                                  "lineto\n"
                                  (number->string (truncate (/ (list-ref line 4) 2)))
                                  " setlinewidth\n"
                                  "stroke\n"
                                  )))
               tree)
     (display "\n%%EOF"))))

(output-tree-as-eps "fractal.eps" (create-tree 400 200 90 9)) </lang>

Scilab

L-System approach

This script uses complex numbers to represent (x,y) coordinates: real part as x position, and imaginary part as y position. The tree is generated using an L-system approach, and the lines are then drawn by interpreting the resulting sentence. The output is plotted onto graphic window.

<lang>trunk = 1; //trunk length ratio = 0.8; //size ratio between two consecutive branches depth = 9; //final number of branch levels orign = 0; //origin of the tree (should be complex) angle = 45*%pi/180; //angle between two branches [rad] trunk_angle = 90*%pi/180; //angle between trunk and X-axis [rad]

right_angle = angle/2; //angles to the right or to the left left_angle = 0.8*angle; //can be set independently or 

                           //as function of 'angle'

//L-system definition: //Alphabet: FBD[]+- 

   //F: go forward             B: go backwards
   //[: start new branch       ]: end current branch
   //+: branch to the right    -: branch to the left
   //D: double line (forward then backward)

//Axiom: D //Rule: D -> F[+D-D]B

//L-system sentence generation sentence = 'D' rule = 'F[+D-D]B'; for i=1:depth 

   sentence = strsubst(sentence,'D',rule);

end sentence = strsplit(sentence)';

//Empty tree tree_size = 1.0... 

           + length(find(sentence=='F'|sentence=='B'))...
           + 2 * length(find(sentence=='D'));

tree=zeros(tree_size,1);

//Drawing the tree branch_level = 0; curr_angle = trunk_angle; curr_pos = 1;

for ind = 1:size(sentence,'c') 

   charac = sentence(ind);
   
   select charac
       case 'F' then //Draw line forward
           tree(curr_pos+1) = tree(curr_pos)...
                              + trunk * ratio^branch_level * exp(curr_angle*%i);
           curr_pos = curr_pos + 1;
           
       case 'B' then //Draw line backwards
           tree(curr_pos+1) = tree(curr_pos)...
                              + trunk * ratio^branch_level * exp((%pi+curr_angle)*%i);
           curr_pos = curr_pos + 1;
           
       case '[' then //New branch
           branch_level = branch_level + 1;
           
       case '+' then //Turn right
           curr_angle = curr_angle - right_angle;
           
       case '-' then //Turn left
           curr_angle = curr_angle + right_angle + left_angle;
           
       case ']' then //End of branch
           branch_level = branch_level - 1;
           curr_angle = curr_angle - left_angle;
           
       case 'D' then //Double line
           tree(curr_pos+1) = tree(curr_pos)...
                              + trunk * ratio^branch_level * exp(curr_angle*%i);
           tree(curr_pos+2) = tree(curr_pos+1)...
                              + trunk * ratio^branch_level * exp((%pi+curr_angle)*%i);
           curr_pos = curr_pos + 2;
   end

end

scf(); clf(); xname('Fractal tree: '+string(depth)+' levels') plot2d(real(tree),imag(tree),14); set(gca(),'isoview','on'); set(gca(),'axes_visible',['off','off','off']);</lang>

Recursive approach

Translation of: PHP

<lang>width = 512; height = 512; img=scf(); set(img,'figure_size',[width,height]);

function drawTree(x1, y1, angle, depth) 

   if depth ~= 0 then
       x2 = x1 + cos(angle * %pi/180) * depth * 10;
       y2 = y1 + sin(angle * %pi/180) * depth * 10;
       plot2d([x1 x2],[y1 y2],14);
       drawTree(x2, y2, angle - 20, depth - 1);
       drawTree(x2, y2, angle + 20, depth - 1);
   end

endfunction

drawTree(width/2,height,90,10); set(gca(),'isoview','on');</lang>

Seed7

<lang seed7>$ include "seed7_05.s7i"; 

 include "float.s7i";
 include "math.s7i";
 include "draw.s7i";
 include "keybd.s7i";

const float: DEG_TO_RAD is PI / 180.0;

const proc: drawTree (in integer: x1, in integer: y1, in float: angle, in integer: depth) is func 

 local
   var integer: x2 is 0;
   var integer: y2 is 0;
 begin
   if depth <> 0 then
     x2 := x1 + trunc(cos(angle * DEG_TO_RAD) * flt(depth * 10));
     y2 := y1 + trunc(sin(angle * DEG_TO_RAD) * flt(depth * 10));
     lineTo(x1, y1, x2, y2, white);
     drawTree(x2, y2, angle - 20.0, depth - 1);
     drawTree(x2, y2, angle + 20.0, depth - 1);
   end if;
 end func;

const proc: main is func 

 begin
   screen(600, 500);
   clear(curr_win, black);
   KEYBOARD := GRAPH_KEYBOARD;
   drawTree(300, 470, -90.0, 9);
   ignore(getc(KEYBOARD));
 end func;</lang>

Original source: [2]

Sidef

Translation of: Perl

<lang ruby>func tree(img, x, y, scale=6/10, len=400, angle=270) { 

   len < 1 && return()

   img.moveTo(x, y)
   img.angle(angle)
   img.line(len)

   var (x1, y1) = img.curPos
   tree(img, x1, y1, scale, len*scale, angle+35)
   tree(img, x1, y1, scale, len*scale, angle-35)

}

require('GD::Simple')

var (width=1000, height=1000) var img = %s|GD::Simple|.new(width, height) img.fgcolor('black') img.penSize(1, 1)

tree(img, width/2, height)

File('tree.png').write(img.png, :raw)</lang>

Smalltalk

This example is coded for Squeak Smalltalk.

<lang smalltalk> Object subclass: #FractalTree 

   instanceVariableNames: 
   classVariableNames: 
   poolDictionaries: 
   category: 'RosettaCode'

</lang>

Methods for FractalTree class:

<lang smalltalk> tree: aPoint length: aLength angle: anAngle 

   | p a |
       
   (aLength > 10) ifTrue: [
       p := Pen new.
       p up.
       p goto: aPoint.
       p turn: anAngle.
       p down.
       5 timesRepeat: [
           p go: aLength / 5.
           p turn: 5.
       ].
       a := anAngle - 30.
       3 timesRepeat: [
           self tree: p location length: aLength * 0.7 angle: a.
           a := a + 30.
       ]
   ].

draw 

   Display restoreAfter: [
       Display fillWhite.      
       self tree: 700@700 length: 200 angle: 0.
   ]

</lang>

Now open a new Workspace and enter:

<lang smalltalk> FractalTree new draw. </lang>

SVG

In the same style as Dragon curve#SVG. SVG has no parameterized definitions, so the recursion must be unrolled.

<lang xml><?xml version="1.0" standalone="yes"?> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 20010904//EN" 

"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd">

<svg xmlns="http://www.w3.org/2000/svg" 

    xmlns:xlink="http://www.w3.org/1999/xlink"
    width="400" height="320">
 <style type="text/css"><![CDATA[
   line { stroke: black; stroke-width: .05; }
   circle { fill: black; }
 ]]></style>

<defs> 

 <g id="stem"> <line x1="0" y1="0" x2="0" y2="-1"/> </g>

 <g id="l0"><use xlink:href="#stem"/></g>
 <g id="l1"> <use xlink:href="#l0" transform="translate(0, -1) rotate(-35) scale(.7)"/>
             <use xlink:href="#l0" transform="translate(0, -1) rotate(+35) scale(.7)"/>
             <use xlink:href="#stem"/></g>
 <g id="l2"> <use xlink:href="#l1" transform="translate(0, -1) rotate(-35) scale(.7)"/>
             <use xlink:href="#l1" transform="translate(0, -1) rotate(+35) scale(.7)"/>
             <use xlink:href="#stem"/></g>
 <g id="l3"> <use xlink:href="#l2" transform="translate(0, -1) rotate(-35) scale(.7)"/>
             <use xlink:href="#l2" transform="translate(0, -1) rotate(+35) scale(.7)"/>
             <use xlink:href="#stem"/></g>
 <g id="l4"> <use xlink:href="#l3" transform="translate(0, -1) rotate(-35) scale(.7)"/>
             <use xlink:href="#l3" transform="translate(0, -1) rotate(+35) scale(.7)"/>
             <use xlink:href="#stem"/></g>
 <g id="l5"> <use xlink:href="#l4" transform="translate(0, -1) rotate(-35) scale(.7)"/>
             <use xlink:href="#l4" transform="translate(0, -1) rotate(+35) scale(.7)"/>
             <use xlink:href="#stem"/></g>
 <g id="l6"> <use xlink:href="#l5" transform="translate(0, -1) rotate(-35) scale(.7)"/>
             <use xlink:href="#l5" transform="translate(0, -1) rotate(+35) scale(.7)"/>
             <use xlink:href="#stem"/></g>
 <g id="l7"> <use xlink:href="#l6" transform="translate(0, -1) rotate(-35) scale(.7)"/>
             <use xlink:href="#l6" transform="translate(0, -1) rotate(+35) scale(.7)"/>
             <use xlink:href="#stem"/></g>
 <g id="l8"> <use xlink:href="#l7" transform="translate(0, -1) rotate(-35) scale(.7)"/>
             <use xlink:href="#l7" transform="translate(0, -1) rotate(+35) scale(.7)"/>
             <use xlink:href="#stem"/></g>
 <g id="l9"> <use xlink:href="#l8" transform="translate(0, -1) rotate(-35) scale(.7)"/>
             <use xlink:href="#l8" transform="translate(0, -1) rotate(+35) scale(.7)"/>
             <use xlink:href="#stem"/></g>

</defs>

<g transform="translate(200, 320) scale(100)"> 

 <use xlink:href="#l9"/>

</g>

</svg></lang>

Swift

Image - Link, since uploads seem to be disabled currently. In a playground: <lang swift>extension CGFloat { 

 func degrees_to_radians() -> CGFloat {
   return CGFloat(M_PI) * self / 180.0
 }

}

extension Double { 

 func degrees_to_radians() -> Double {
   return Double(M_PI) * self / 180.0
 }

}


class Tree: UIView { 


 func drawTree(x1: CGFloat, y1: CGFloat, angle: CGFloat, depth:Int){
   if depth == 0 {
     return
   }
   let ang = angle.degrees_to_radians()
   let x2:CGFloat = x1 + ( cos(ang) as CGFloat) * CGFloat(depth) * (self.frame.width / 60)
   let y2:CGFloat = y1 + ( sin(ang) as CGFloat) * CGFloat(depth) * (self.frame.width / 60)
   
   let line = drawLine(x1, y1: y1, x2: x2, y2: y2)
 
   line.stroke()
   drawTree(x2, y1: y2, angle: angle - 20, depth: depth - 1)
   drawTree(x2, y1: y2, angle: angle + 20, depth: depth - 1)
 }
 
 func drawLine(x1:CGFloat, y1:CGFloat, x2:CGFloat, y2:CGFloat) -> UIBezierPath
 {
   
   let path = UIBezierPath()
   path.moveToPoint(CGPoint(x: x1,y: y1))
   path.addLineToPoint(CGPoint(x: x2,y: y2))
   path.lineWidth = 1
   return path
 }
 
 override func drawRect(rect: CGRect) {
   
   let color = UIColor(red: 1.0, green: 0.0, blue: 0.0, alpha: 1.0)
   color.set()
   drawTree(self.frame.width / 2 , y1: self.frame.height * 0.8, angle: -90 , depth: 9 )
 }

}


let tree = Tree(frame: CGRectMake(0, 0, 300, 300)) tree </lang>

Standard ML

Works with PolyML <lang Standard ML>open XWindows; open Motif;

fun toI {x=x,y=y} = {x=Real.toInt IEEEReal.TO_NEAREST x,y=Real.toInt IEEEReal.TO_NEAREST y}  ;


fun drawOnTop win usegc ht hs {x=l1,y=l2} {x=r1,y=r2} = 

let
 val xy = {x=l1 - ht * (l2-r2) , y = l2 - ht * (r1-l1) }
 val zt = {x=r1 - ht * (l2-r2) , y=  r2 - ht * (r1-l1) }
 val ab = {x= ( (#x xy + #x zt) + hs * (#y zt - #y xy ) )/2.0 ,  y =  ( (#y zt + #y xy) - hs * (#x zt - #x xy )) /2.0 }
in

 if abs (l1 - #x xy ) < 0.9 andalso abs (l2 - #y xy ) < 0.9
  then   XFlush (XtDisplay win)
  else
   (XFillPolygon (XtWindow win) usegc [ (XPoint o toI) {x=l1,y=l2},
                                        (XPoint o toI ) xy ,

(XPoint o toI ) ab , (XPoint o toI ) zt , (XPoint o toI ) {x=r1,y=r2} ] Convex CoordModeOrigin  ; 

 drawOnTop win usegc (0.87*ht) hs xy ab ;
 drawOnTop win usegc (0.93*ht) hs ab zt )

end ;


val demoWindow = fn () => let 

 val shell  =  XtAppInitialise       ""    "tree" "top" []  [ XmNwidth 800, XmNheight 650] ;
 val main   =  XmCreateMainWindow   shell    "main"         [ XmNmappedWhenManaged true ]  ;
 val canvas =  XmCreateDrawingArea  main   "drawarea"       [ XmNwidth 800, XmNheight 650] ;
 val usegc  =  DefaultGC (XtDisplay canvas) ;

in 

 XtSetCallbacks   canvas [ (XmNexposeCallback ,
                              (fn (w,c,t) => ( drawOnTop canvas usegc 8.0 0.85 {x=385.0,y=645.0} {x=415.0,y=645.0} ; t) ) )

] XmNarmCallback ; 

  XtManageChild    canvas ;
  XtManageChild    main   ; 
  XtRealizeWidget  shell

end ;

demoWindow ();</lang>

Tcl

Library: Tk

<lang tcl>package require Tk

set SIZE 800 set SCALE 4.0 set BRANCHES 14 set ROTATION_SCALE 0.85 set INITIAL_LENGTH 50.0

proc draw_tree {w x y dx dy size theta depth} { 

   global SCALE ROTATION_SCALE
   $w create line $x $y [expr {$x + $dx*$size}] [expr {$y + $dy*$size}]
   if {[incr depth -1] >= 0} {

set x [expr {$x + $dx*$size}] set y [expr {$y + $dy*$size}] set ntheta [expr {$theta * $ROTATION_SCALE}]

# Draw left branch draw_tree $w $x $y \ [expr {$dx*cos($theta) + $dy*sin($theta)}] \ [expr {$dy*cos($theta) - $dx*sin($theta)}] \ [expr {$size * (rand() + $SCALE - 1) / $SCALE}] $ntheta $depth # Draw right branch draw_tree $w $x $y \ [expr {$dx*cos(-$theta) + $dy*sin(-$theta)}] \ [expr {$dy*cos(-$theta) - $dx*sin(-$theta)}] \ [expr {$size * (rand() + $SCALE - 1) / $SCALE}] $ntheta $depth 

   }

}

pack [canvas .c -width $SIZE -height $SIZE] draw_tree .c [expr {$SIZE/2}] [expr {$SIZE-10}] 0.0 -1.0 $INITIAL_LENGTH \ 

   [expr {3.1415927 / 8}] $BRANCHES</lang>

TUSCRIPT

Image is created in SVG-format <lang tuscript> $$ MODE TUSCRIPT dest="fracaltree.svg" ERROR/STOP CREATE (dest,fdf-o,-std-) ACCESS d: WRITE/ERASE/RECORDS/UTF8 $dest s,text MODE DATA $$ header=* <?xml version="1.0" standalone="yes"?> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 20010904//EN" 

"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd">

<svg xmlns="http://www.w3.org/2000/svg" 

xmlns:xlink="http://www.w3.org/1999/xlink"
width="400" height="320">
 <style type="text/css"><![CDATA[
 line { stroke: brown; stroke-width: .05; }
 ]]></style>

$$ WRITE/NEXT d header $$ defsbeg=* <defs> 

 <g id="stem"> <line x1="0" y1="0" x2="0" y2="-1"/> </g>
 <g id="l"><use xlink:href="#stem"/></g>

$$ WRITE/NEXT d defsbeg $$ LOOP n=10,21 $$ id=n+1,lastnr=VALUE(n) $$ g=* 

 <g id="{id}"> <use xlink:href="#{n}" transform="translate(0, -1) rotate(-35) scale(.7)"/>
 <use xlink:href="#{n}" transform="translate(0, -1) rotate(+35) scale(.7)"/> <use xlink:href="#stem"/></g>

$$ WRITE/NEXT d g $$ ENDLOOP $$ defsend = * </defs> <g transform="translate(200, 320) scale(100)"> 

 <use xlink:href="#{lastnr}"/>

</g> $$ MODE TUSCRIPT WRITE/NEXT d defsend WRITE/NEXT d "</svg>" ENDACCESS d </lang>

TypeScript

Translation of: JavaScript

<lang JavaScript>// Set up canvas for drawing var canvas: HTMLCanvasElement = document.createElement('canvas') canvas.width = 600 canvas.height = 500 document.body.appendChild(canvas) var ctx: CanvasRenderingContext2D = canvas.getContext('2d') ctx.fillStyle = '#000' ctx.lineWidth = 1

// constants const degToRad: number = Math.PI / 180.0 const totalDepth: number = 9

/** Helper function that draws a line on the canvas */ function drawLine(x1: number, y1: number, x2: number, y2: number): void { 

   ctx.moveTo(x1, y1)
   ctx.lineTo(x2, y2)

}

/** Draws a branch at the given point and angle and then calls itself twice */ function drawTree(x1: number, y1: number, angle: number, depth: number): void { 

   if (depth !== 0) {
       let x2: number = x1 + (Math.cos(angle * degToRad) * depth * 10.0)
       let y2: number = y1 + (Math.sin(angle * degToRad) * depth * 10.0)
       drawLine(x1, y1, x2, y2)
       drawTree(x2, y2, angle - 20, depth - 1)
       drawTree(x2, y2, angle + 20, depth - 1)
   }

}

// actual drawing of tree ctx.beginPath() drawTree(300, 500, -90, totalDepth) ctx.closePath() ctx.stroke()

</lang>

Wren

Translation of: Kotlin
Library: DOME

<lang ecmascript>import "graphics" for Canvas, Color import "dome" for Window import "math" for Math

var Radians = Fn.new { |d| d * Num.pi / 180 }

class FractalTree { 

   construct new(width, height) {
       Window.title = "Fractal Tree"
       Window.resize(width, height)
       Canvas.resize(width, height)
       _fore = Color.white
   }

   init() {
       drawTree(400, 500, -90, 9)
   }

   drawTree(x1, y1, angle, depth) {
       if (depth == 0) return
       var r = Radians.call(angle)
       var x2 = x1 + (Math.cos(r) * depth * 10).truncate
       var y2 = y1 + (Math.sin(r) * depth * 10).truncate
       Canvas.line(x1, y1, x2, y2, _fore)
       drawTree(x2, y2, angle - 20, depth - 1)
       drawTree(x2, y2, angle + 20, depth - 1)
   }

   update() {}

   draw(alpha) {}

}

var Game = FractalTree.new(800, 600)</lang>

XPL0

Output

<lang XPL0>include c:\cxpl\codes;

proc DrawBranch(Lev, Dir, Len, X, Y); int Lev; real Dir, Len; int X, Y; int Red, Grn; [Move(X, Y); X:= X + fix(Len*Cos(Dir)); Y:= Y + fix(Len*Sin(Dir)); Red:= 255-Lev*8; Grn:= Lev*12+100; Line(X, Y, Red<<16+Grn<<8); if Lev < 12 then \limit level of recursion 

       [DrawBranch(Lev+1, Dir-0.4, Len*0.8, X, Y);     \left
        DrawBranch(Lev+1, Dir+0.1, Len*0.8, X, Y);     \right
       ];

];

[SetVid($112); \set 640x480x24 video graphics mode DrawBranch(0, -3.14159/2.0, 80.0, 360, 460); if ChIn(1) then []; \wait for keystroke SetVid(3); \restore normal text mode ]</lang>

zkl

Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl

Translation of: BBC BASIC
Translation of: XPL0

<lang zkl>fcn fractalTree(){ 

  scale:=0.76;
  sizeX:=400; sizeY:=300;
  bitmap:=PPM(sizeX*2,sizeY*2,0xFF|FF|FF);
  branch:='wrap(x1,y1,size,angle,depth){
     ar:=angle.toRad();
     x2:=x1 - size*ar.cos();
     y2:=y1 + size*ar.sin();
     color:=(0xff-depth*8).shiftLeft(16) + (depth*12+100).shiftLeft(8);
     bitmap.line(x1,y1, x2,y2, color);
     if(depth){
        self.fcn(x2,y2,scale*size,angle - 30,depth - 1,vm.pasteArgs(5));

self.fcn(x2,y2,scale*size,angle + 8, depth - 1,vm.pasteArgs(5)); 

     }
  };
  branch(sizeX,0,sizeY/2,90.0,10);
  bitmap.write(File("foo.ppm","wb"));

}();</lang> The funkyness (pasteArgs) in the recursion (self.fcn) is due to the closure ('wrap): the closed over args are stashed in the arglist, they need to be added to the parameters when recursing.

ZX Spectrum Basic

Translation of: BASIC256

<lang zxbasic>10 LET level=12: LET long=45 20 LET x=127: LET y=0 30 LET rotation=PI/2 40 LET a1=PI/9: LET a2=PI/9 50 LET c1=0.75: LET c2=0.75 60 DIM x(level): DIM y(level) 70 BORDER 0: PAPER 0: INK 4: CLS 80 GO SUB 100 90 STOP 100 REM Tree 110 LET x(level)=x: LET y(level)=y 120 GO SUB 1000 130 IF level=1 THEN GO TO 240 140 LET level=level-1 150 LET long=long*c1 160 LET rotation=rotation-a1 170 GO SUB 100 180 LET long=long/c1*c2 190 LET rotation=rotation+a1+a2 200 GO SUB 100 210 LET rotation=rotation-a2 220 LET long=long/c2 230 LET level=level+1 240 LET x=x(level): LET y=y(level) 250 RETURN 1000 REM Draw 1010 LET yn=-SIN rotation*long+y 1020 LET xn=COS rotation*long+x 1030 PLOT x,y: DRAW xn-x,y-yn 1040 LET x=xn: LET y=yn 1050 RETURN </lang>

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