Fractal tree

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

• Pythagoras Tree

11l

Translation of: Nim

-V
   Width = 1000
   Height = 1000
   TrunkLength = 400
   ScaleFactor = 0.6
   StartingAngle = 1.5 * math:pi
   DeltaAngle = 0.2 * math:pi

F drawTree(outfile, Float x, y; len, theta) -> Void
   I len >= 1
      V x2 = x + len * cos(theta)
      V y2 = y + len * sin(theta)
      outfile.write("<line x1='#.6' y1='#.6' x2='#.6' y2='#.6' style='stroke:white;stroke-width:1'/>\n".format(x, y, x2, y2))
      drawTree(outfile, x2, y2, len * ScaleFactor, theta + DeltaAngle)
      drawTree(outfile, x2, y2, len * ScaleFactor, theta - DeltaAngle)

V outsvg = File(‘tree.svg’, WRITE)
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'>
               <rect width="100%" height="100%" fill="black"/>
               ’)
drawTree(outsvg, 0.5 * Width, Height, TrunkLength, StartingAngle)
outsvg.write("</svg>\n")

Action!

Action! language does not support recursion. Therefore an iterative approach with a stack has been proposed.

DEFINE MAXSIZE="12"

INT ARRAY SinTab=[
  0 4 9 13 18 22 27 31 36 40 44 49 53 58 62 66 71 75 79 83
  88 92 96 100 104 108 112 116 120 124 128 132 136 139 143
  147 150 154 158 161 165 168 171 175 178 181 184 187 190
  193 196 199 202 204 207 210 212 215 217 219 222 224 226
  228 230 232 234 236 237 239 241 242 243 245 246 247 248
  249 250 251 252 253 254 254 255 255 255 256 256 256 256]

INT ARRAY xStack(MAXSIZE),yStack(MAXSIZE),angleStack(MAXSIZE)
BYTE ARRAY lenStack(MAXSIZE),dirStack(MAXSIZE)
BYTE stacksize=[0]

INT FUNC Sin(INT a)
  WHILE a<0 DO a==+360 OD
  WHILE a>360 DO a==-360 OD
  IF a<=90 THEN
    RETURN (SinTab(a))
  ELSEIF a<=180 THEN
    RETURN (SinTab(180-a))
  ELSEIF a<=270 THEN
    RETURN (-SinTab(a-180))
  ELSE
    RETURN (-SinTab(360-a))
  FI
RETURN (0)

INT FUNC Cos(INT a)
RETURN (Sin(a-90))

BYTE FUNC IsEmpty()
  IF stacksize=0 THEN
    RETURN (1)
  FI
RETURN (0)

BYTE FUNC IsFull()
  IF stacksize=MAXSIZE THEN
    RETURN (1)
  FI
RETURN (0)

PROC Push(INT x,y,angle BYTE len,dir)
  IF IsFull() THEN Break() FI
  xStack(stacksize)=x yStack(stacksize)=y
  angleStack(stacksize)=angle lenStack(stacksize)=len
  dirStack(stacksize)=dir
  stacksize==+1
RETURN

PROC Pop(INT POINTER x,y,angle BYTE POINTER len,dir)
  IF IsEmpty() THEN Break() FI
  stacksize==-1
  x^=xStack(stacksize) y^=yStack(stacksize)
  angle^=angleStack(stacksize) len^=lenStack(stacksize)
  dir^=dirStack(stacksize)
RETURN

PROC DrawTree(INT x,y,len,angle,leftAngle,rightAngle)
  BYTE depth,dir

  Plot(x,y)
  x==+Cos(angle)*len/256
  y==-Sin(angle)*len/256
  DrawTo(x,y)

  Push(x,y,angle,len,0)

  WHILE IsEmpty()=0
  DO
    Pop(@x,@y,@angle,@len,@dir)
    IF dir<2 THEN
      Push(x,y,angle,len,dir+1)
      IF dir=0 THEN
        angle==-leftAngle
      ELSE
        angle==+rightAngle
      FI
      
      len=13*len/16
      Plot(x,y)
      x==+Cos(angle)*len/256
      y==-Sin(angle)*len/256
      DrawTo(x,y)

      IF IsFull()=0 THEN
        Push(x,y,angle,len,0)
      FI
    FI
  OD
  
RETURN

PROC Main()
  BYTE CH=$02FC,COLOR1=$02C5,COLOR2=$02C6

  Graphics(8+16)
  Color=1
  COLOR1=$BA
  COLOR2=$B2

  DrawTree(140,191,40,110,35,15)

  DO UNTIL CH#$FF OD
  CH=$FF
RETURN

Output:

Screenshot from Atari 8-bit computer

Ada

Library: SDLAda

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;

Amazing Hopper

Translation of: BBCBasic

"Una suma que no quería salir, pero ya salió" :D

Caption

/*
   Execute with:

   $ hopper jm/tree.jambo -x -o bin/tree
   $ rxvt -g 280x250 -fn "xft:FantasqueSansMono-Regular:pixelsize=1" -e ./bin/tree

*/

#include <jambo.h>

Main
   Set '25, 0.76, 160, 100, 10' Init 'Spread, Scale, SizeX, SizeY, Depth'
   Color back '22', Cls
   Color back '15'
   Set '{SizeX} Mul by (2), -30, Div(SizeY,2), 90, Depth' Gosub 'Branch'
   Pause
End

Subrutines

Define 'Branch, x1, y1, size, angle, depth'
   x2=0, y2=0
   Let ( x2 := #(x1 + size * cos(d2r(angle))) )
   Let ( y2 := #(y1 + size * sin(d2r(angle))) )
   Draw a line ( #(180-y1), #(180-x1), #(180-y2), #(180-x2))
   If ( #( depth > 0) )
       Set (x2, y2, {size} Mul by 'Scale', {angle} Minus 'Spread',\
            Minus one(depth)) Gosub 'Branch'
       Set (x2, y2, {size} Mul by 'Scale', {angle} Plus 'Spread',\
            Minus one(depth)) Gosub 'Branch'
   End If
Return

Arturo

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

Output:

Fractal Tree output in Arturo

AutoHotkey

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

Library: GDIP

#SingleInstance, Force
#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

BASIC

BASIC256

Asymmetric fractal tree image created by the BASIC-256 script

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

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"
#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

BBC BASIC

Output:

Works with: BBC BASIC for Windows

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

      
      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

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

C

Library: SDL

Library: SGE

or

Library: cairo

#include <SDL/SDL.h>
#ifdef WITH_CAIRO
#include <cairo.h>
#else
#include <SDL/sge.h>
#endif
#include <cairo.h>
#include <stdlib.h>
#include <time.h>
#include <math.h>

#ifndef M_PI
#define M_PI           3.14159265358979323846
#endif

#define SIZE           800   // determines size of window
#define SCALE          5     // determines how quickly branches shrink (higher value means faster shrinking)
#define BRANCHES       14    // number of branches
#define ROTATION_SCALE 0.75  // determines how slowly the angle between branches shrinks (higher value means slower shrinking)
#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) {
#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);
#else
  sge_AALine(surface,
      (int)offsetx, (int)offsety,
      (int)(offsetx + directionx * size), (int)(offsety + directiony * size),
      SDL_MapRGB(surface->format, 0, 0, 0));
#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,
      M_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;
}

C++

#include <windows.h>
#include <string>
#include <math.h>

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

//--------------------------------------------------------------------------------------------------
#ifndef M_PI
#define M_PI           3.14159265358979323846
#endif

//--------------------------------------------------------------------------------------------------
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 * ( M_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;
}
//--------------------------------------------------------------------------------------------------

Ceylon

Translation of: Java

Library: Swing

Library: AWT

Be sure to import java.desktop and ceylon.numeric in your module.ceylon file.

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;
}

Clojure

Translation of: Java

Library: Swing

Library: AWT

(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)

Common Lisp

Library: lispbuilder-sdl

Translation of: Clojure

;; (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)

D

SVG Version

Translation of: Raku

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;
}

Turtle Version

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

Translation of: Logo

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");
}

Alternative version

Translation of: Java

Using DFL.

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;
}

EasyLang

Run it

# Fractal tree
# 
color 555
proc tree x y deg n . .
   if n > 0
      linewidth n * 0.4
      move x y
      x += cos deg * n * 1.3 * (randomf + 0.5)
      y += sin deg * n * 1.3 * (randomf + 0.5)
      line x y
      tree x y deg - 20 n - 1
      tree x y deg + 20 n - 1
   .
.
timer 0
on timer
   clear
   tree 50 10 90 10
   timer 2
.

Evaldraw

Evaldraw version creates a 3D tree with a camera rotating around the tree.

Fractal Tree in 3D

4 branches for each recursive step. A forward Z vector is rotated in x or y axis.

static ratio = .75;
static branchlength = 60;
static max_branches = 4;
struct vec3{x,y,z;};
()
{
  t=klock();
  srand(t * 1);
  zero1 = .5+.5*cos(t);
  maxbranches = int( 1+1 + zero1*5);
  
  
  cls(0); clz(1e32);
  distcam = -70;
  camrot = .5 * t;
  ca=distcam * cos(camrot);
  sa=distcam * sin(camrot);
  setcam(sa,-50,ca,camrot,0);
 
  angle = 2*pi / 8;
  branchlen = 10+50 * zero1;
  tree(maxbranches, 0, branchlen, 0,0,0, pi / 2, 0, angle);
  
  moveto(0,0);
  printf("N=%g, frame=%5.0f, cam:%3.0f", maxbranches, numframes, camrot / pi * 180);
  printf("\n%gx%g",xres,yres);
  sleep(16);
}


tree(mb, n, blen, x,y,z, ang_yx, ang_yz, angle) {
  n++; if( n> mb ) return;
  len = blen / n * ratio;
  c = 64 + 128 * n/7; setcol(100,c,38);
  
  dx=0; dy=0; dz=0;
  double mat[9];
  vec3 axis = {0,0,1};
  ang2mat(ang_yz, ang_yx, mat);
  transformPoint(axis,mat);
  dx=axis.x;
  dy=-axis.y;
  dz=axis.z;
  
  ox = x; oy = y; oz = z;
  x += len * dx;
  y += -len * dy;
  z += len * dz;
  
  rd = 8 / n;
  rd2 = 7 / (n+1);
  drawcone(ox,oy,oz,rd,x,y,z,rd2,DRAWCONE_FLAT + DRAWCONE_NOPHONG);  
  
  nextangle = /*(-.5+1*rnd*pi) * */angle;
  tree(mb, n, blen, x, y, z, ang_yx - angle, ang_yz, nextangle);
  tree(mb, n, blen, x, y, z, ang_yx + angle, ang_yz, nextangle);
  
  tree(mb, n, blen, x, y, z, ang_yx, ang_yz - angle, nextangle);
  tree(mb, n, blen, x, y, z, ang_yx, ang_yz + angle, nextangle);
}

ang2mat(hang,vang,mat[9]) {
   mat[6] = cos(vang)*sin(hang); mat[0] = cos(hang);
   mat[7] = sin(vang);           mat[1] = 0;
   mat[8] = cos(vang)*cos(hang); mat[2] =-sin(hang);
   mat[3] = mat[7]*mat[2] - mat[8]*mat[1];
   mat[4] = mat[8]*mat[0] - mat[6]*mat[2];
   mat[5] = mat[6]*mat[1] - mat[7]*mat[0];
}

transformPoint(vec3 v, thisRot[9]) {
   NewX = v.x * thisRot[0] + v.y * thisRot[1] + v.z * thisRot[2];
   NewY = v.x * thisRot[3] + v.y * thisRot[4] + v.z * thisRot[5];
   NewZ = v.x * thisRot[6] + v.y * thisRot[7] + v.z * thisRot[8];
   v.x=newx; v.y=newy; v.z=newz;
}

Delphi

Works with: Delphi version 6.0

Library: SysUtils,StdCtrls

procedure DrawTree(Image: TImage; X1, Y1: integer; Angle: double; Depth: integer);
var X2,Y2: integer;
begin
if Depth = 0 then exit;
X2:=trunc(X1 + cos(DegToRad(Angle)) * Depth * 5);
Y2:=trunc(Y1 + sin(DegToRad(Angle)) * Depth * 5);
Image.Canvas.Pen.Color:=ColorMap47[MulDiv(High(ColorMap47),Depth,11)];
Image.Canvas.Pen.Width:=MulDiv(Depth,5,10);
Image.Canvas.MoveTo(X1,Y1);
Image.Canvas.LineTo(X2,Y2);
DrawTree(Image, X2, Y2, Angle - 10, Depth - 1);
DrawTree(Image, X2, Y2, Angle + 35, Depth - 1);
end;


procedure ShowFactalTree(Image: TImage);
begin
ClearImage(Image,clBlack);
DrawTree(Image, 250, 350, -90, 11);
Image.Invalidate;
end;

Output:

Elapsed Time: 31.913 ms.

F#

Translation of: Raku

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>"

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
  }
}

FreeBASIC

Translation of: BBC BASIC

' 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

Frege

Works with: Frege version 3.23.888-g4e22ab6

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

Output is here due to Is file uploading blocked forever?

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[]

FutureBasic

_window = 1
_wndWidth = 680

void local fn BuildWindow
  window _window, @"Fractal Tree", ( 0, 0, _wndWidth, 600 )
  WindowSetBackgroundColor( _window, fn ColorBlack )
  WindowSubclassContentView( _window )
end fn

local fn PlotFractalTree( x1 as double, y1 as double, size as long, angle as double, spread as long, depth as long, scale as double )
  double x2, y2
  pen 1.0, fn ColorGreen, NSLineCapStyleSquare
  
  // Convert angle to radians
  x2 = x1 + size * cos(angle * pi / 180)
  y2 = y1 + size * sin(angle * pi / 180)
  
  line x1, y1, x2, y2
  if ( depth > 0 )
    fn PlotFractalTree( x2, y2, size * scale, angle - spread, spread, depth - 1, scale )
    fn PlotFractalTree( x2, y2, size * scale, angle + spread, spread, depth - 1, scale )
  end if
end fn

void local fn DoDialog( ev as long, tag as long )
  select ( tag )
    case _windowContentViewTag
      double spread = ( 80.0 / (_wndWidth / 2 ) ) * 90
      fn PlotFractalTree( _wndWidth / 2, 550, 140, -90, spread, 10, 0.75 )
  end select
  select ( ev )
    case _windowWillClose : end
  end select
end fn

on dialog fn DoDialog

fn BuildWindow

HandleEvents

File:Fractal tree FutureBasic.png

Go

png converted from output ppm

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)
    }
}

Haskell

An elegant yet universal monoidal solution.

Library: Gloss

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)

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.

--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)

Alternative solution

Using the method of the J contribution.

Library: HGL

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

Icon and Unicon

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

Library: Icon Programming Library

WOpen provides graphics I/O

Translation of: Java

J

require'gl2'
coinsert'jgl2'
 
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
 
wd {{)n
 pc P closeok;
 setp wh 480 640;
 cc C isidraw flush;
 pshow;
}}

gllines <.(10 + ,/"2 P-"1<./,/P)

See the talk page for some implementation notes.

Java

Library: Swing

Library: AWT

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);
    }
}

JavaScript

Implementation using HTML5 canvas element to draw tree structure.

<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>

jq

The following generates SVG, which can be viewed by following the link below.

# width and height define the outer dimensions;
# len defines the trunk size;
# 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)

Output:

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

Fractal_tree.svg

Julia

Translation of: F#

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

Kotlin

Translation of: Java

// 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
}

Lambdatalk

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

Liberty BASIC

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

 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
#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

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

Usage:

fractalDepth = 10
initSize = 7.0
spreadAngle = 35*PI/180
scaleFactor = 0.95
img = fractalTree(480, 380, fractalDepth, initSize, spreadAngle, scaleFactor)

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

Lua

Bitmap

Needs LÖVE 2D Engine

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

ASCII

Using the Bitmap class and text renderer from here, then extending...

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]='█'})

Output:

Shown at 25% scale:

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Mathematica / Wolfram Language

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]]

MiniScript

This GUI implementation is for use with Mini Micro.

drawTree = function(x1, y1, angle, depth)
	fork_angle = 20
	base_len = 9
	if depth > 0 then
		radians = angle * pi / 180
		x2 = x1 + cos(radians) * depth * base_len
		y2 = y1 + sin(radians) * depth * base_len
		gfx.line x1, y1, x2, y2, "#008000"
		drawTree x2, y2, angle - fork_angle, depth - 1
		drawTree x2, y2, angle + fork_angle, depth - 1
	end if
end function
clear
gfx.clear "#87CEEB"
drawTree 480, 10, 90, 11
img = gfx.getImage(0, 0, 960, 640)
file.saveImage "/usr/fractalTree.png", img

File:FractalTree-ms.png

NetRexx

Translation of: Java

Library: Swing

Library: AWT

/* 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

Nim

Translation of: Julia

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.

OCaml

Library: ocaml-cairo

#directory "+cairo"
#load "bigarray.cma"
#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*)

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

\\ 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
}

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.

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);
}

Phix

Translation of: XPL0

Library: Phix/pGUI

Library: Phix/online

You can run this online here.

--
-- demo\rosetta\FractalTree.exw
-- ============================
--
with javascript_semantics
include pGUI.e

Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas

procedure drawTree(integer level, atom angle, len, integer x, y)
    integer xn = x + floor(len*cos(angle)),
            yn = y + floor(len*sin(angle)),
            red = 255-level*8,
            green = level*12+100
    cdCanvasSetForeground(cddbuffer, red*#10000 + green*#100)
    cdCanvasSetLineWidth(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*/, /*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("RASTERSIZE=640x480")
    IupSetCallbacks(canvas, {"MAP_CB", Icallback("map_cb"),
                             "ACTION", Icallback("redraw_cb")})

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

    IupShow(dlg)
    if platform()!=JS then
        IupMainLoop()
        IupClose()
    end if
end procedure

main()

PHP

Image is created with GD module. Code adapted from the JavaScript version.

<?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);
?>

PicoLisp

This uses the 'brez' line drawing function from Bitmap/Bresenham's line algorithm#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) ) )

Plain English

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.

Output:

[1]

PL/pgSQL

Works with: Postgres

This piece of code generates the coordinates of each branch, builds a version in the standardized geometry representation format: WKT.

A temporary table contains the results: coordinates and WKT representation of each branch.

In a query (Postgres + postgis function), we can draw a unique geometry that can be displayed in a tool like QGis or DBeaver database manager for example.

The query exploits the notion of CTE and its recursive form.

Pl/PgSQL fractal tree

drop table if exists my_temp_tree_table;

do $$ 
declare
  _length numeric := 1;
  -- a little random
  _random_length_reduction_max numeric := 0.6;
  _fork_angle numeric := pi()/12;
  -- a little random
  _random_angle numeric := pi()/12;
  _depth numeric := 9 ;

begin
    create temporary table my_temp_tree_table as
        WITH RECURSIVE branch(azimuth, x1, y1, x2, y2, len, n) AS (
            VALUES (pi()/2, 0.0, 0.0, 0.0, _length, _length, _depth)
          UNION all
            select azimuth+a, 
                x2, y2, 
                round((x2+cos(azimuth+a)*len)::numeric, 2), round((y2+sin(azimuth+a)*len)::numeric, 2), 
                (len*(_random_length_reduction_max+(random()*(1-_random_length_reduction_max))))::numeric, 
                n-1
            FROM branch
            cross join (
                select ((-_fork_angle)+(_random_angle)*(random()-0.5)) a 
                union 
                select ((_fork_angle)+(_random_angle)*(random()-0.5)) a2
            ) a
            WHERE n > 0
        )
        select x1, y1, x2, y2, 'LINESTRING('||x1||' '||y1||','||x2||' '||y2||')' as wkt from branch
        ;
end $$
;

-- coordinates and WKT
select * from my_temp_tree_table;

-- binary version (postgis) of each branch
select ST_GeomFromEWKT('SRID=4326;'||wkt) geom from my_temp_tree_table;

-- a unique geometry
select st_union(ST_GeomFromEWKT('SRID=4326;'||wkt)) geom from my_temp_tree_table;

Output:

coordinates and WKT

x1   |y1  |x2   |y2  |wkt                              |
-----+----+-----+----+---------------------------------+
  0.0| 0.0|  0.0|   1|LINESTRING(0.0 0.0,0.0 1)        |
  0.0|   1| 0.15|1.99|LINESTRING(0.0 1,0.15 1.99)      |
  0.0|   1|-0.29|1.96|LINESTRING(0.0 1,-0.29 1.96)     |
 0.15|1.99| 0.36|2.68|LINESTRING(0.15 1.99,0.36 2.68)  |
 0.15|1.99| 0.05|2.70|LINESTRING(0.15 1.99,0.05 2.70)  |
 ...

 

a simple unparameterized version, without randomness

WITH RECURSIVE noeuds(azimuth, x0, y0, x, y, len, n) AS (
    VALUES (pi()/2, 0::real, 0::real, 0::real, 10::real, 10::real, 9::int)
  UNION all
    select azimuth+a, x, y, (x+cos(azimuth+a)*len)::real, (y+sin(azimuth+a)*len)::real, (len/2)::real, n-1
    FROM noeuds
    cross join (select (-pi()/7)::real a union select (pi()/7)::real a2) a
    WHERE n > 0
)
, branche as (
    select '('||x0||' '||y0||','||x||' '||y||')' b 
    from noeuds
)
select ST_GeomFromEWKT('SRID=4326;MULTILINESTRING('||string_agg(b, ',')||')') tree 
from branche

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

Shorter version:

%!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

POV-Ray

#include "colors.inc"
#include "transforms.inc"

#declare CamLoc = <0, 5, 0>;
#declare CamLook = <0,0,0>;
camera
{
  location CamLoc
  look_at CamLook
  rotate y*90
}

light_source
{
  CamLoc
  color White
}

#declare Init_Height    = 10;
#declare Spread_Ang     = 35;
#declare Branches       = 14;
#declare Scaling_Factor = 0.75;

#macro Stick(P0, P1)
  cylinder { 
    P0, P1, 0.02
    texture { pigment { Green } }
  }
#end

#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
#end

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

Prolog

SWI-Prolog has a graphic interface : XPCE.

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).

PureBasic

#Spread_Ang     = 35
#Scaling_Factor = 0.75
#Deg_to_Rad = #PI / 180
#SizeH = 500
#SizeV = 375
#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

Processing

Using rotation

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();
  }
}

Calculating coordinates

Translation of: Python

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);
  }
}

Processing Python mode

Using rotation

Translation of: Processing

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()

Calculating coordinates

Translation of: 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)

Python

File:Fractal-tree-python.png

Library: pygame

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())

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

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
20 frames
-1 4 turn 
-450 1 fly 
500 1 tree
1 frames

Output:

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

## 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);
  }
}
## Plotting Fractal Tree. aev 3/27/17
## ord - order/depth, c - scale, xsh - x-shift, fn - file name,
##  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");
}
## Executing:
pFractalTree(9);
pFractalTree(12,0.6,210);
pFractalTree(15,0.35,600);

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
(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)

Raku

(formerly Perl 6) Image is created in SVG format.

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);
}

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
]

Output:

fractal tree image

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}

Output:

Ruby

Library: Shoes

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

Rust

Library: Piston

//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);
    }
}

Scala

Adapted from the Java version. Screenshot below.

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)
          }
        }
      }
    }
  }
}

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.

(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))

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.

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']);

Recursive approach

Translation of: PHP

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');

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;

Original source: [2]

Sidef

Translation of: Perl

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)

Smalltalk

This example is coded for Squeak Smalltalk.

Object subclass: #FractalTree
    instanceVariableNames: ''
    classVariableNames: ''
    poolDictionaries: ''
    category: 'RosettaCode'

Methods for FractalTree class:

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.
    ]

Now open a new Workspace and enter:

FractalTree new draw.

SVG

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

<?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>
  <!-- These are identical except for the id and href. -->
  <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>

Swift

Image - Link, since uploads seem to be disabled currently. In a playground:

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

Standard ML

Works with PolyML

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 ();

Tcl

Library: Tk

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

TUSCRIPT

Image is created in SVG-format

$$ MODE TUSCRIPT
dest="fracaltree.svg"
ERROR/STOP CREATE (dest,fdf-o,-std-)
ACCESS d: WRITE/ERASE/RECORDS/UTF8 $dest s,text
MODE DATA
$$ 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

TypeScript

Translation of: 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()

Wren

Translation of: Kotlin

Library: DOME

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)

XPL0

Output

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
]

Yabasic

clear screen
width = 512 : height = 512 : crad = 0.01745329
open window width, height
window origin "cc"

sub drawTree(x, y, deg, n)
    local x2, y2
    
    if n then
        x2 = x + cos(deg * crad) * n * 15 * ran(.5)
        y2 = y + sin(deg * crad) * n * 15 * ran(.5)
        line x, y, x2, y2
        drawTree(x2, y2, deg - 20, n - 1)
        drawTree(x2, y2, deg + 20, n - 1)
     endif
end sub

repeat
    clear window
    drawTree(0, height/3, -90, 10)
until upper$(inkey$(1)) = "Q"

zkl

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

Translation of: BBC BASIC

Translation of: XPL0

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"));
}();

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

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