Barnsley fern
You are encouraged to solve this task according to the task description, using any language you may know.
A Barnsley fern is a fractal named after British mathematician Michael Barnsley and can be created using an iterated function system (IFS).
- Task
Create this fractal fern, using the following transformations:
- ƒ1 (chosen 1% of the time)
xn + 1 = 0 yn + 1 = 0.16 yn
- ƒ2 (chosen 85% of the time)
xn + 1 = 0.85 xn + 0.04 yn yn + 1 = −0.04 xn + 0.85 yn + 1.6
- ƒ3 (chosen 7% of the time)
xn + 1 = 0.2 xn − 0.26 yn yn + 1 = 0.23 xn + 0.22 yn + 1.6
- ƒ4 (chosen 7% of the time)
xn + 1 = −0.15 xn + 0.28 yn yn + 1 = 0.26 xn + 0.24 yn + 0.44.
Starting position: x = 0, y = 0
C++
<lang cpp>
- include <windows.h>
- include <ctime>
- include <string>
const int BMP_SIZE = 600, ITERATIONS = static_cast<int>( 15e5 );
class myBitmap { public:
myBitmap() : pen( NULL ), brush( NULL ), clr( 0 ), wid( 1 ) {} ~myBitmap() { DeleteObject( pen ); DeleteObject( brush ); DeleteDC( hdc ); DeleteObject( bmp ); } bool create( int w, int h ) { BITMAPINFO bi; 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 clear( BYTE clr = 0 ) { memset( pBits, clr, width * height * sizeof( DWORD ) ); } void setBrushColor( DWORD bClr ) { if( brush ) DeleteObject( brush ); brush = CreateSolidBrush( bClr ); SelectObject( hdc, brush ); } void setPenColor( DWORD c ) { clr = c; createPen(); } void setPenWidth( int w ) { wid = w; createPen(); } void saveBitmap( std::string path ) { BITMAPFILEHEADER fileheader; BITMAPINFO infoheader; BITMAP bitmap; DWORD wb; GetObject( bmp, sizeof( bitmap ), &bitmap ); DWORD* 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 ); HANDLE 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() const { return hdc; } int getWidth() const { return width; } int getHeight() const { return height; }
private:
void createPen() { if( pen ) DeleteObject( pen ); pen = CreatePen( PS_SOLID, wid, clr ); SelectObject( hdc, pen ); } HBITMAP bmp; HDC hdc; HPEN pen; HBRUSH brush; void *pBits; int width, height, wid; DWORD clr;
}; class fern { public:
void draw() { bmp.create( BMP_SIZE, BMP_SIZE ); float x = 0, y = 0; HDC dc = bmp.getDC(); int hs = BMP_SIZE >> 1; for( int f = 0; f < ITERATIONS; f++ ) { SetPixel( dc, hs + static_cast<int>( x * 55.f ), BMP_SIZE - 15 - static_cast<int>( y * 55.f ), RGB( static_cast<int>( rnd() * 80.f ) + 20, static_cast<int>( rnd() * 128.f ) + 128, static_cast<int>( rnd() * 80.f ) + 30 ) ); getXY( x, y ); } bmp.saveBitmap( "./bf.bmp" ); }
private:
void getXY( float& x, float& y ) { float g, xl, yl; g = rnd(); if( g < .01f ) { xl = 0; yl = .16f * y; } else if( g < .07f ) { xl = .2f * x - .26f * y; yl = .23f * x + .22f * y + 1.6f; } else if( g < .14f ) { xl = -.15f * x + .28f * y; yl = .26f * x + .24f * y + .44f; } else { xl = .85f * x + .04f * y; yl = -.04f * x + .85f * y + 1.6f; } x = xl; y = yl; } float rnd() { return static_cast<float>( rand() ) / static_cast<float>( RAND_MAX ); } myBitmap bmp;
}; int main( int argc, char* argv[]) {
srand( static_cast<unsigned>( time( 0 ) ) ); fern f; f.draw(); return 0;
} </lang>
Delphi
Hint: After putting a TPaintBox on the main form align it to alClient. Client width / heigth of the main form should be no less than 640 x 480. <lang delphi>unit Unit1;
interface
uses
Windows, SysUtils, Graphics, Forms, Controls, Classes, ExtCtrls;
type
TForm1 = class(TForm) PaintBox1: TPaintBox; procedure FormPaint(Sender: TObject); private { Private declarations } public { Public declarations } end;
var
Form1: TForm1;
implementation
{$R *.dfm}
procedure CreateFern(const w, h: integer); var r, x, y: double;
tmpx, tmpy: double; i: integer;
begin
x := 0; y := 0; randomize();
for i := 0 to 200000 do begin r := random(100000000) / 99999989; if r <= 0.01 then begin tmpx := 0; tmpy := 0.16 * y; end else if r <= 0.08 then begin tmpx := 0.2 * x - 0.26 * y; tmpy := 0.23 * x + 0.22 * y + 1.6; end else if r <= 0.15 then begin tmpx := -0.15 * x + 0.28 * y; tmpy := 0.26 * x + 0.24 * y + 0.44; end else begin tmpx := 0.85 * x + 0.04 * y; tmpy := -0.04 * x + 0.85 * y + 1.6; end; x := tmpx; y := tmpy;
Form1.PaintBox1.Canvas.Pixels[round(w / 2 + x * w / 11), round(h - y * h / 11)] := clGreen; end;
end;
procedure TForm1.FormPaint(Sender: TObject); begin
CreateFern(Form1.ClientWidth, Form1.ClientHeight);
end;
end.</lang>
FreeBASIC
<lang freebasic>' version 10-10-2016 ' compile with: fbc -s console
Sub barnsley(height As UInteger)
Dim As Double x, y, xn, yn Dim As Double f = height / 10.6 Dim As UInteger offset_x = height \ 4 - height \ 40 Dim As UInteger n, r
ScreenRes height \ 2, height, 32
For n = 1 To height * 50
r = Int(Rnd * 100) ' f from 0 to 99
Select Case As Const r Case 0 To 84 xn = 0.85 * x + 0.04 * y yn = -0.04 * x + 0.85 * y + 1.6 Case 85 To 91 xn = 0.2 * x - 0.26 * y yn = 0.23 * x + 0.22 * y + 1.6 Case 92 To 98 xn = -0.15 * x + 0.28 * y yn = 0.26 * x + 0.24 * y + 0.44 Case Else xn = 0 yn = 0.16 * y End Select
x = xn : y = yn PSet( offset_x + x * f, height - y * f), RGB(0, 255, 0)
Next
' remove comment (') in next line to save window as .bmp file ' BSave "barnsley_fern_" + Str(height) + ".bmp", 0
End Sub
' ------=< MAIN >=------
' adjustable window height ' call the subroutine with the height you want ' it's possible to have a window that's large than your display
barnsley(800)
' empty keyboard buffer
While Inkey <> "" : Wend
Windowtitle "hit any key to end program"
Sleep
End</lang>
G'MIC
<lang c>
- Put this into a new file 'fern.gmic' and invoke it from the command line, like this:
- $ gmic fern.gmic -barnsley_fern
barnsley_fern :
1024,2048 -skip {" f1 = [ 0,0,0,0.16 ]; g1 = [ 0,0 ]; f2 = [ 0.2,-0.26,0.23,0.22 ]; g2 = [ 0,1.6 ]; f3 = [ -0.15,0.28,0.26,0.24 ]; g3 = [ 0,0.44 ]; f4 = [ 0.85,0.04,-0.04,0.85 ]; g4 = [ 0,1.6 ]; xy = [ 0,0 ]; for (n = 0, n<2e6, ++n, r = u(100); xy = r<=1?((f1**xy)+=g1): r<=8?((f2**xy)+=g2): r<=15?((f3**xy)+=g3): ((f4**xy)+=g4); uv = xy*200 + [ 480,0 ]; uv[1] = h - uv[1]; I(uv) = 0.7*I(uv) + 0.3*255; )"} -r 40%,40%,1,1,2
</lang>
Go
<lang go>package main
import (
"image" "image/color" "image/draw" "image/png" "log" "math/rand" "os"
)
// values from WP const (
xMin = -2.1820 xMax = 2.6558 yMin = 0. yMax = 9.9983
)
// parameters var (
width = 200 n = int(1e6) c = color.RGBA{34, 139, 34, 255} // forest green
)
func main() {
dx := xMax - xMin dy := yMax - yMin fw := float64(width) fh := fw * dy / dx height := int(fh) r := image.Rect(0, 0, width, height) img := image.NewRGBA(r) draw.Draw(img, r, &image.Uniform{color.White}, image.ZP, draw.Src) var x, y float64 plot := func() { // transform computed float x, y to integer image coordinates ix := int(fw * (x - xMin) / dx) iy := int(fh * (yMax - y) / dy) img.SetRGBA(ix, iy, c) } plot() for i := 0; i < n; i++ { switch s := rand.Intn(100); { case s < 85: x, y = .85*x+.04*y, -.04*x+.85*y+1.6 case s < 85+7: x, y = .2*x-.26*y, .23*x+.22*y+1.6 case s < 85+7+7: x, y = -.15*x+.28*y, .26*x+.24*y+.44 default: x, y = 0, .16*y } plot() } // write img to png file f, err := os.Create("bf.png") if err != nil { log.Fatal(err) } if err := png.Encode(f, img); err != nil { log.Fatal(err) }
}</lang>
Haskell
<lang haskell>import Data.List (scanl') import Diagrams.Backend.Rasterific.CmdLine import Diagrams.Prelude import System.Random
type Pt = (Double, Double)
-- Four affine transformations used to produce a Barnsley fern. f1, f2, f3, f4 :: Pt -> Pt f1 (x, y) = ( 0, 0.16 * y) f2 (x, y) = ( 0.85 * x + 0.04 * y , -0.04 * x + 0.85 * y + 1.60) f3 (x, y) = ( 0.20 * x - 0.26 * y , 0.23 * x + 0.22 * y + 1.60) f4 (x, y) = (-0.15 * x + 0.28 * y , 0.26 * x + 0.24 * y + 0.44)
-- Given a random number in [0, 1) transform an initial point by a randomly -- chosen function. func :: Pt -> Double -> Pt func p r | r < 0.01 = f1 p
| r < 0.86 = f2 p | r < 0.93 = f3 p | otherwise = f4 p
-- Using a sequence of uniformly distributed random numbers in [0, 1) return -- the same number of points in the fern. fern :: [Double] -> [Pt] fern = scanl' func (0, 0)
-- Given a supply of random values and a count, generate a diagram of a fern -- composed of that number of points. drawFern :: [Double] -> Int -> Diagram B drawFern rs n = frame 0.5 . diagramFrom . take n $ fern rs
where diagramFrom = flip atPoints (repeat dot) . map p2 dot = circle 0.005 # lc green
-- To generate a PNG image of a fern, call this program like: -- -- fern -o fern.png -w 640 -h 640 50000 -- -- where the arguments specify the width, height and number of points in the -- image. main :: IO () main = do
rand <- getStdGen mainWith $ drawFern (randomRs (0, 1) rand)</lang>
J
<lang j>require 'plot'
f=: |: 0 ". ];._2 noun define
0 0 0 0.16 0 0 0.01 0.85 -0.04 0.04 0.85 0 1.60 0.85 0.20 0.23 -0.26 0.22 0 1.60 0.07 -0.15 0.26 0.28 0.24 0 0.44 0.07
)
fm=: {&(|: 2 2 $ f) fa=: {&(|: 4 5 { f) prob=: (+/\ 6 { f) I. ?@0:
ifs=: (fa@] + fm@] +/ .* [) prob getPoints=: ifs^:(<200000) plotFern=: 'dot;grids 0 0;tics 0 0;labels 0 0;color green' plot ;/@|:
plotFern getPoints 0 0</lang>
Java
<lang java>import java.awt.*; import java.awt.image.BufferedImage; import javax.swing.*;
public class BarnsleyFern extends JPanel {
BufferedImage img;
public BarnsleyFern() { final int dim = 640; setPreferredSize(new Dimension(dim, dim)); setBackground(Color.white); img = new BufferedImage(dim, dim, BufferedImage.TYPE_INT_ARGB); createFern(dim, dim); }
void createFern(int w, int h) { double x = 0; double y = 0;
for (int i = 0; i < 200_000; i++) { double tmpx, tmpy; double r = Math.random();
if (r <= 0.01) { tmpx = 0; tmpy = 0.16 * y; } else if (r <= 0.08) { tmpx = 0.2 * x - 0.26 * y; tmpy = 0.23 * x + 0.22 * y + 1.6; } else if (r <= 0.15) { tmpx = -0.15 * x + 0.28 * y; tmpy = 0.26 * x + 0.24 * y + 0.44; } else { tmpx = 0.85 * x + 0.04 * y; tmpy = -0.04 * x + 0.85 * y + 1.6; } x = tmpx; y = tmpy;
img.setRGB((int) Math.round(w / 2 + x * w / 11), (int) Math.round(h - y * h / 11), 0xFF32CD32); } }
@Override public void paintComponent(Graphics gg) { super.paintComponent(gg); Graphics2D g = (Graphics2D) gg; g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
g.drawImage(img, 0, 0, null); }
public static void main(String[] args) { SwingUtilities.invokeLater(() -> { JFrame f = new JFrame(); f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); f.setTitle("Barnsley Fern"); f.setResizable(false); f.add(new BarnsleyFern(), BorderLayout.CENTER); f.pack(); f.setLocationRelativeTo(null); f.setVisible(true); }); }
}</lang>
JavaScript
<lang javascript> // Barnsley fern fractal //6/17/16 aev function pBarnsleyFern(canvasId,lim) {
// DCLs var canvas = document.getElementById(canvasId); var ctx = canvas.getContext("2d"); var w = canvas.width; var h = canvas.height; var x=0.,y=0.,xw=0.,yw=0.,r; // Like in PARI/GP: return random number 0..max-1 function randgp(max) {return Math.floor(Math.random()*max)} // Clean canvas ctx.fillStyle="white"; ctx.fillRect(0,0,w,h); // MAIN LOOP for(var i=0; i<lim; i++) { r=randgp(100); if (r<=1) {xw=0;yw=0.16*y;} else if (r<=8) {xw=0.2*x-0.26*y;yw=0.23*x+0.22*y+1.6;} else if (r<=15) {xw=-0.15*x+0.28*y;yw=0.26*x+0.24*y+0.44;} else {xw=0.85*x+0.04*y;yw=-0.04*x+0.85*y+1.6;} x=xw;y=yw; ctx.fillStyle="green"; ctx.fillRect(x*50+260,-y*50+540,1,1); }//fend i
} </lang> Executing: <lang html> <html>
<head><script src="BarnsleyFern.js"></script></head> <body onload="pBarnsleyFern('canvas', 100000)">
Barnsley fern fractal
<canvas id="canvas" width="540" height="540" style="border: 2px inset;"></canvas> </body>
</html> </lang>
- Output:
Page with BarnsleyFernjs.png
Nim
<lang Nim> import nimPNG, random
randomize()
const
width = 640 height = 640 minX = -2.1815 maxX = 2.6556 minY = 0.0 maxY = 9.9982 iterations = 1_000_000
var img: array[width * height * 3, char]
proc floatToPixel(x,y:float): tuple[a:int,b:int] =
var px = abs(x - minX) / abs(maxX - minX) var py = abs(y - minY) / abs(maxY - minY)
var a:int = (int)(width * px) var b:int = (int)(height * py)
a = a.clamp(0, width-1) b = b.clamp(0, height-1) # flip the y axis (a:a,b:height-b-1)
proc pixelToOffset(a,b: int): int =
b * width * 3 + a * 3
proc toString(a: openArray[char]): string =
result = newStringOfCap(a.len)
for ch in items(a): result.add(ch)
proc drawPixel(x,y:float) =
var (a,b) = floatToPixel(x,y) var offset = pixelToOffset(a,b)
#img[offset] = 0 # red channel img[offset+1] = char(250) # green channel #img[offset+2] = 0 # blue channel
- main
var x, y: float = 0.0
for i in 1..iterations:
var r = random(101) var nx, ny: float if r <= 85: nx = 0.85 * x + 0.04 * y ny = -0.04 * x + 0.85 * y + 1.6 elif r <= 85 + 7: nx = 0.2 * x - 0.26 * y ny = 0.23 * x + 0.22 * y + 1.6 elif r <= 85 + 7 + 7: nx = -0.15 * x + 0.28 * y ny = 0.26 * x + 0.24 * y + 0.44 else: nx = 0 ny = 0.16 * y
x = nx y = ny
drawPixel(x,y)
discard savePNG24("fern.png",img.toString, width, height) </lang>
PARI/GP
<lang parigp> \\ Barnsley fern fractal \\ 6/17/16 aev pBarnsleyFern(size,lim)={ my(X=List(),Y=X,x=y=xw=yw=0.0,r); print(" *** Barnsley Fern, size=",size," lim=",lim); plotinit(0); plotcolor(0,6); \\green plotscale(0, -3,3, 0,10); plotmove(0, 0,0); for(i=1, lim,
r=random(100); if(r<=1, xw=0;yw=0.16*y, if(r<=8, xw=0.2*x-0.26*y;yw=0.23*x+0.22*y+1.6, if(r<=15, xw=-0.15*x+0.28*y;yw=0.26*x+0.24*y+0.44, xw=0.85*x+0.04*y;yw=-0.04*x+0.85*y+1.6))); x=xw;y=yw; listput(X,x); listput(Y,y);
);\\fend i plotpoints(0,Vec(X),Vec(Y)); plotdraw([0,-3,-0]); } {\\ Executing: pBarnsleyFern(530,100000); \\ BarnsleyFern.png } </lang>
- Output:
> pBarnsleyFern(530,100000); \\ BarnsleyFern.png *** Barnsley Fern, size=530 lim=100000
Perl
<lang perl>use Imager;
my $w = 640; my $h = 640;
my $img = Imager->new(xsize => $w, ysize => $h, channels => 3); my $green = Imager::Color->new('#00FF00');
my ($x, $y) = (0, 0);
foreach (1 .. 2e5) {
my $r = rand(100); ($x, $y) = do { if ($r <= 1) { ( 0.00 * $x - 0.00 * $y, 0.00 * $x + 0.16 * $y + 0.00) } elsif ($r <= 8) { ( 0.20 * $x - 0.26 * $y, 0.23 * $x + 0.22 * $y + 1.60) } elsif ($r <= 15) { (-0.15 * $x + 0.28 * $y, 0.26 * $x + 0.24 * $y + 0.44) } else { ( 0.85 * $x + 0.04 * $y, -0.04 * $x + 0.85 * $y + 1.60) } }; $img->setpixel(x => $w / 2 + $x * 60, y => $y * 60, color => $green);
}
$img->flip(dir => 'v'); $img->write(file => 'barnsleyFern.png');</lang>
Perl 6
<lang perl6>use Image::PNG::Portable;
my ($w, $h) = (640, 640);
my $png = Image::PNG::Portable.new: :width($w), :height($h);
my ($x, $y) = (0, 0);
for ^2e5 {
my $r = 100.rand; ($x, $y) = do given $r { when $r <= 1 { ( 0, 0.16 * $y ) } when $r <= 8 { ( 0.20 * $x - 0.26 * $y, 0.23 * $x + 0.22 * $y + 1.60) } when $r <= 15 { (-0.15 * $x + 0.28 * $y, 0.26 * $x + 0.24 * $y + 0.44) } default { ( 0.85 * $x + 0.04 * $y, -0.04 * $x + 0.85 * $y + 1.60) } }; $png.set(($w / 2 + $x * 60).Int, $h - ($y * 60).Int, 0, 255, 0);
}
$png.write: 'Barnsley-fern-perl6.png';</lang>
Phix
This file is included in the distro as demo\rosetta\BarnsleyFern.exw
<lang Phix>include ..\pGUI\pGUI.e
Ihandle dlg, canvas cdCanvas cddbuffer, cdcanvas
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/) atom {x,y,r} @= 0 integer {width, height} = IupGetIntInt(canvas, "DRAWSIZE")
cdCanvasActivate(cddbuffer) for i=1 to 20000 do r = rand(100) {x, y} = iff(r<=1? { 0, 0.16*y } : iff(r<=8? { 0.20*x-0.26*y, 0.23*x+0.22*y+1.60} : iff(r<=15?{-0.15*x+0.28*y, 0.26*x+0.24*y+0.44} : { 0.85*x+0.04*y,-0.04*x+0.85*y+1.60}))) cdCanvasPixel(cddbuffer, width/2+x*60, y*60, #00FF00) end for 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_WHITE) cdCanvasSetForeground(cddbuffer, CD_RED) return IUP_DEFAULT
end function
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if return IUP_CONTINUE
end function
procedure main()
IupOpen("..\\pGUI\\")
canvas = IupCanvas(NULL) IupSetAttribute(canvas, "RASTERSIZE", "340x620") -- initial size IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
dlg = IupDialog(canvas) IupSetAttribute(dlg, "TITLE", "Barnsley Fern") IupSetCallback(dlg, "K_ANY", Icallback("esc_close")) IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
IupMap(dlg) IupSetAttribute(canvas, "RASTERSIZE", NULL) -- release the minimum limitation IupShowXY(dlg,IUP_CENTER,IUP_CENTER) IupMainLoop() IupClose()
end procedure
main()</lang>
Processing
<lang java>void setup() {
size(640, 640); background(0, 0, 0);
}
float x = 0; float y = 0;
void draw() {
for (int i = 0; i < 100000; i++) {
float xt = 0; float yt = 0;
float r = random(100);
if (r <= 1) { xt = 0; yt = 0.16*y; } else if (r <= 8) { xt = 0.20*x - 0.26*y; yt = 0.23*x + 0.22*y + 1.60; } else if (r <= 15) { xt = -0.15*x + 0.28*y; yt = 0.26*x + 0.24*y + 0.44; } else { xt = 0.85*x + 0.04*y; yt = -0.04*x + 0.85*y + 1.60; }
x = xt; y = yt;
int m = round(width/2 + 60*x); int n = height-round(60*y);
set(m, n, #00ff00); } noLoop();
}</lang>
Python
<lang Python>
import random from PIL import Image
class BarnsleyFern(object):
def __init__(self, img_width, img_height, paint_color=(0, 150, 0), bg_color=(255, 255, 255)): self.img_width, self.img_height = img_width, img_height self.paint_color = paint_color self.x, self.y = 0, 0 self.age = 0
self.fern = Image.new('RGB', (img_width, img_height), bg_color) self.pix = self.fern.load() self.pix[self.scale(0, 0)] = paint_color
def scale(self, x, y): h = (x + 2.182)*(self.img_width - 1)/4.8378 k = (9.9983 - y)*(self.img_height - 1)/9.9983 return h, k
def transform(self, x, y): rand = random.uniform(0, 100) if rand < 1: return 0, 0.16*y elif 1 <= rand < 86: return 0.85*x + 0.04*y, -0.04*x + 0.85*y + 1.6 elif 86 <= rand < 93: return 0.2*x - 0.26*y, 0.23*x + 0.22*y + 1.6 else: return -0.15*x + 0.28*y, 0.26*x + 0.24*y + 0.44
def iterate(self, iterations): for _ in range(iterations): self.x, self.y = self.transform(self.x, self.y) self.pix[self.scale(self.x, self.y)] = self.paint_color self.age += iterations
fern = BarnsleyFern(500, 500) fern.iterate(1000000) fern.fern.show()
</lang>
R
<lang r>
- pBarnsleyFern(fn, n, clr, ttl, psz=600): Plot Barnsley fern fractal.
- Where: fn - file name; n - number of dots; clr - color; ttl - plot title;
- psz - picture size.
- 7/27/16 aev
pBarnsleyFern <- function(fn, n, clr, ttl, psz=600) {
cat(" *** START:", date(), "n=", n, "clr=", clr, "psz=", psz, "\n"); cat(" *** File name -", fn, "\n"); pf = paste0(fn,".png"); # pf - plot file name A1 <- matrix(c(0,0,0,0.16,0.85,-0.04,0.04,0.85,0.2,0.23,-0.26,0.22,-0.15,0.26,0.28,0.24), ncol=4, nrow=4, byrow=TRUE); A2 <- matrix(c(0,0,0,1.6,0,1.6,0,0.44), ncol=2, nrow=4, byrow=TRUE); P <- c(.01,.85,.07,.07); # Creating matrices M1 and M2. M1=vector("list", 4); M2 = vector("list", 4); for (i in 1:4) { M1i <- matrix(c(A1[i,1:4]), nrow=2); M2i <- matrix(c(A2[i, 1:2]), nrow=2); } x <- numeric(n); y <- numeric(n); x[1] <- y[1] <- 0; for (i in 1:(n-1)) { k <- sample(1:4, prob=P, size=1); M <- as.matrix(M1k); z <- M%*%c(x[i],y[i]) + M2k; x[i+1] <- z[1]; y[i+1] <- z[2]; } plot(x, y, main=ttl, axes=FALSE, xlab="", ylab="", col=clr, cex=0.1); # Writing png-file dev.copy(png, filename=pf,width=psz,height=psz); # Cleaning dev.off(); graphics.off(); cat(" *** END:",date(),"\n");
}
- Executing:
pBarnsleyFern("BarnsleyFernR", 100000, "dark green", "Barnsley Fern Fractal", psz=600) </lang>
- Output:
> pBarnsleyFern("BarnsleyFernR", 100000, "dark green", "Barnsley Fern Fractal", psz=600) *** START: Wed Jul 27 13:50:49 2016 n= 1e+05 clr= dark green psz= 600 *** File name - BarnsleyFernR *** END: Wed Jul 27 13:50:56 2016 + BarnsleyFernR.png file
Ring
<lang Ring>
Load "guilib.ring"
/*
+--------------------------------------------------------------------------- + Program Name : Draw Barnsley Fern + Date : 2016.06.12 + Author : Bert Mariani + Purpose : Draw Fern using Quadratic Equation and Random Number +---------------------------------------------------------------------------
- /
- -------------------------------
- DRAW CHART size 400 x 500
- -------------------------------
New qapp {
win1 = new qwidget() {
### Position and Size on Screen
setwindowtitle("Drawing using QPainter")
setgeometry( 10, 25, 400, 500)
### Draw within this Win Box label1 = new qlabel(win1) { ### Label Position and Size setgeometry(10, 10, 400, 500) settext(" ") }
buttonFern = new qpushbutton(win1) { ### Button DrawFern setgeometry(10, 10, 80, 20) settext("Draw Fern") setclickevent("DrawFern()") ### Call DRAW function }
show() } exec() }
- ------------------------
- FUNCTIONS
- ------------------------
Func DrawFern p1 = new qpicture()
colorGreen = new qcolor() { setrgb(0,255,0,255) } penGreen = new qpen() { setcolor(colorGreen) setwidth(1) }
new qpainter() { begin(p1) setpen(penGreen)
###------------------------------------- ### Quadratic equation matrix of arrays
a = [ 0, 0.85, 0.2, -0.15 ] b = [ 0, 0.04, -0.26, 0.28 ] c = [ 0, -0.04, 0.23, 0.26 ] d = [ 0.16, 0.85, 0.22, 0.24 ] e = [ 0, 0, 0, 0 ] f = [ 0, 1.6, 1.6, 0.44 ]
### Initialize x, y points
xf = 0.0 yf = 0.0
### Size of output screen
MaxX = 400 MaxY = 500 MaxIterations = MaxY * 200 Count = 0
###------------------------------------------------
while ( Count <= MaxIterations )
### NOTE *** RING *** starts at Index 1, ### Do NOT use Random K=0 result
k = random() % 100 k = k +1
### if (k = 0) k = 1 ok ### Do NOT use
if ((k > 0) and (k <= 85)) k = 2 ok if ((k > 85) and (k <= 92)) k = 3 ok if (k > 92) k = 4 ok
TempX = ( a[k] * xf ) + ( b[k] * yf ) + e[k] TempY = ( c[k] * xf ) + ( d[k] * yf ) + f[k]
xf = TempX yf = TempY
if( (Count >= MaxIterations) or (Count != 0) ) xPoint = (floor(xf * MaxY / 11) + floor(MaxX / 2)) yPoint = (floor(yf * -MaxY / 11) + MaxY ) drawpoint( xPoint , yPoint ) ok
Count++ end
###----------------------------------------------------
endpaint() }
label1 { setpicture(p1) show() } return
</lang>
Run BASIC
<lang runbasic>maxpoints = 20000 graphic #g, 200, 200
- g fill("blue")
FOR n = 1 TO maxpoints p = RND(0)*100 IF p <= 1 THEN nx = 0 ny = 0.16 * y else if p <= 8 THEN nx = 0.2 * x - 0.26 * y ny = 0.23 * x + 0.22 * y + 1.6 else if p <= 15 THEN nx = -0.15 * x + 0.28 * y ny = 0.26 * x + 0.24 * y + 0.44 else nx = 0.85 * x +0.04 * y ny = -0.04 * x +0.85 * y + 1.6 end if x = nx y = ny
- g "color green ; set "; x * 17 + 100; " "; y * 17
NEXT n render #g
- g "flush"</lang>
SequenceL
Tail-Recursive SequenceL Code:
<lang sequencel>import <Utilities/Math.sl>;
import <Utilities/Random.sl>;
transform(p(1), rand) :=
let x := p[1]; y := p[2]; in [0.0, 0.16*y] when rand <= 0.01 else [0.85*x + 0.04*y, -0.04*x + 0.85*y + 1.6] when rand <= 0.86 else [0.2*x - 0.26*y, 0.23*x + 0.22*y + 1.6] when rand <= 0.93 else [-0.15*x + 0.28*y, 0.26*x + 0.24*y + 0.44];
barnsleyFern(rand, count, result(2)) :=
let nextRand := getRandom(rand); next := transform(result[size(result)], nextRand.value / 2147483647.0); in result when count <= 0 else barnsleyFern(nextRand.generator, count - 1, result ++ [next]);
scale(p(1), width, height) := [round((p[1] + 2.182) * width / 4.8378),
round((9.9983 - p[2]) * height / 9.9983)];
entry(seed, count, width, height) :=
let fern := barnsleyFern(seedRandom(seed), count, 0.0,0.0); in scale(fern, width, height);</lang>
C++ Driver Code:
<lang c>#include "SL_Generated.h"
- include "CImg.h"
using namespace cimg_library;
int main(int argc, char** argv) {
int threads = 0; if(argc > 1) threads = atoi(argv[1]); int width = 300; if(argc > 2) width = atoi(argv[2]); int height = 600; if(argc > 3) height = atoi(argv[3]); int steps = 10000; if(argc > 4) steps = atoi(argv[4]); int seed = 314159; if(argc > 5) seed = atoi(argv[5]); CImg<unsigned char> visu(width, height, 1, 3, 0); Sequence< Sequence<int> > result;
sl_init(threads);
sl_entry(seed, steps, width-1, height-1, threads, result); visu.fill(0); for(int i = 1; i <= result.size(); i++) visu(result[i][1], result[i][2],1) = 255; CImgDisplay draw_disp(visu); draw_disp.set_title("Barnsley Fern in SequenceL"); visu.display(draw_disp); while(!draw_disp.is_closed()) draw_disp.wait();
sl_done();
return 0;
}</lang>
- Output:
Sidef
<lang ruby>require('Imager')
var w = 640 var h = 640
var img = %s<Imager>.new(xsize => w, ysize => h, channels => 3) var green = %s<Imager::Color>.new('#00FF00')
var (x, y) = (0, 0)
for r in (^1e5 -> lazy.map { 100.rand }) {
(x, y) = ( if (r <= 1) { ( 0.00*x - 0.00*y, 0.00*x + 0.16*y + 0.00) } elsif (r <= 8) { ( 0.20*x - 0.26*y, 0.23*x + 0.22*y + 1.60) } elsif (r <= 15) { (-0.15*x + 0.28*y, 0.26*x + 0.24*y + 0.44) } else { ( 0.85*x + 0.04*y, -0.04*x + 0.85*y + 1.60) } ) img.setpixel(x => w/2 + 60*x, y => 60*y, color => green)
}
img.flip(dir => 'v') img.write(file => 'barnsleyFern.png')</lang>
zkl
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl
<lang zkl>fcn barnsleyFern(){
w,h:=640,640; bitmap:=PPM(w+1,h+1,0xFF|FF|FF); // White background
x,y, nx,ny:=0.0, 0.0, 0.0, 0.0; do(0d100_000){ r:=(0).random(100); // [0..100)% if (r<= 1) nx,ny= 0, 0.16*y; else if(r<= 8) nx,ny= 0.2*x - 0.26*y, 0.23*x + 0.22*y + 1.6; else if(r<=15) nx,ny=-0.15*x + 0.28*y, 0.26*x + 0.24*y + 0.44; else nx,ny= 0.85*x + 0.04*y, -0.04*x + 0.85*y + 1.6; x,y=nx,ny; bitmap[w/2 + x*60, y*60] = 0x00|FF|00; // Green dot } bitmap.writeJPGFile("barnsleyFern.jpg");
}();</lang>
ZX Spectrum Basic
<lang zxbasic>10 REM Fractal Fern 20 PAPER 7: BORDER 7: BRIGHT 1: INK 4: CLS 30 LET maxpoints=20000: LET x=0: LET y=0 40 FOR n=1 TO maxpoints 50 LET p=RND*100 60 IF p<=1 THEN LET nx=0: LET ny=0.16*y: GO TO 100 70 IF p<=8 THEN LET nx=0.2*x-0.26*y: LET ny=0.23*x+0.22*y+1.6: GO TO 100 80 IF p<=15 THEN LET nx=-0.15*x+0.28*y: LET ny=0.26*x+0.24*y+0.44: GO TO 100 90 LET nx=0.85*x+0.04*y: LET ny=-0.04*x+0.85*y+1.6 100 LET x=nx: LET y=ny 110 PLOT x*17+127,y*17 120 NEXT n </lang> It is recommended to run on an emulator that supports running at full speed.