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
This implementation requires the WinBGIm library. Iteration starts from (0,0) as required by the task however before plotting the point is translated and scaled as negative co-ordinates are not supported by the graphics window, scaling is necessary as otherwise the fern is tiny even for large iterations ( > 1000000). <lang C> /*Abhishek Ghosh, 23rd September 2017*/
- include<graphics.h>
- include<stdlib.h>
- include<stdio.h>
- include<time.h>
void barnsleyFern(int windowWidth, unsigned long iter){
double x0=0,y0=0,x1,y1; int diceThrow; time_t t; srand((unsigned)time(&t));
while(iter>0){ diceThrow = rand()%100;
if(diceThrow==0){ x1 = 0; y1 = 0.16*y0; }
else if(diceThrow>=1 && diceThrow<=7){ x1 = -0.15*x0 + 0.28*y0; y1 = 0.26*x0 + 0.24*y0 + 0.44; }
else if(diceThrow>=8 && diceThrow<=15){ x1 = 0.2*x0 - 0.26*y0; y1 = 0.23*x0 + 0.22*y0 + 1.6; }
else{ x1 = 0.85*x0 + 0.04*y0; y1 = -0.04*x0 + 0.85*y0 + 1.6; }
putpixel(30*x1 + windowWidth/2.0,30*y1,GREEN);
x0 = x1; y0 = y1;
iter--; }
}
int main() { unsigned long num;
printf("Enter number of iterations : "); scanf("%ld",&num);
initwindow(500,500,"Barnsley Fern");
barnsleyFern(500,num);
getch();
closegraph();
return 0; } </lang>
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>
C#
<lang csharp>using System; using System.Diagnostics; using System.Drawing;
namespace RosettaBarnsleyFern {
class Program
{
static void Main(string[] args)
{
const int w = 600;
const int h = 600;
var bm = new Bitmap(w, h);
var r = new Random();
double x = 0;
double y = 0;
for (int count = 0; count < 100000; count++)
{
bm.SetPixel((int)(300 + 58 * x), (int)(58 * y), Color.ForestGreen);
int roll = r.Next(100);
double xp = x;
if (roll < 1)
{
x = 0;
y = 0.16 * y;
} else if (roll < 86)
{
x = 0.85 * x + 0.04 * y;
y = -0.04 * xp + 0.85 * y + 1.6;
} else if (roll < 93)
{
x = 0.2 * x - 0.26 * y;
y = 0.23 * xp + 0.22 * y + 1.6;
} else
{
x = -0.15 * x + 0.28 * y;
y = 0.26 * xp + 0.24 * y + 0.44;
}
}
const string filename = "Fern.png";
bm.Save(filename);
Process.Start(filename);
}
}
}</lang>
Common Lisp
This code uses the opticl package for generating an image and saving it as a PNG file.
<lang lisp>(defpackage #:barnsley-fern
(:use #:cl
#:opticl))
(in-package #:barnsley-fern)
(defparameter *width* 800) (defparameter *height* 800) (defparameter *factor* (/ *height* 13)) (defparameter *x-offset* (/ *width* 2)) (defparameter *y-offset* (/ *height* 10))
(defun f1 (x y)
(declare (ignore x)) (values 0 (* 0.16 y)))
(defun f2 (x y)
(values (+ (* 0.85 x) (* 0.04 y))
(+ (* -0.04 x) (* 0.85 y) 1.6)))
(defun f3 (x y)
(values (+ (* 0.2 x) (* -0.26 y))
(+ (* 0.23 x) (* 0.22 y) 1.6)))
(defun f4 (x y)
(values (+ (* -0.15 x) (* 0.28 y))
(+ (* 0.26 x) (* 0.24 y) 0.44)))
(defun choose-transform ()
(let ((r (random 1.0)))
(cond ((< r 0.01) #'f1)
((< r 0.86) #'f2)
((< r 0.93) #'f3)
(t #'f4))))
(defun set-pixel (image x y)
(let ((%x (round (+ (* *factor* x) *x-offset*)))
(%y (round (- *height* (* *factor* y) *y-offset*))))
(setf (pixel image %y %x) (values 0 255 0))))
(defun fern (filespec &optional (iterations 10000000))
(let ((image (make-8-bit-rgb-image *height* *width* :initial-element 0))
(x 0)
(y 0))
(dotimes (i iterations)
(set-pixel image x y)
(multiple-value-setq (x y) (funcall (choose-transform) x y)))
(write-png-file filespec image)))</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>
Fortran
<lang fortran> !Generates an output file "plot.dat" that contains the x and y coordinates !for a scatter plot that can be visualized with say, GNUPlot program BarnsleyFern implicit none
double precision :: p(4), a(4), b(4), c(4), d(4), e(4), f(4), trx, try, prob integer :: itermax, i
!The probabilites and coefficients can be modified to generate other !fractal ferns, e.g. http://www.home.aone.net.au/~byzantium/ferns/fractal.html !probabilities p(1) = 0.01; p(2) = 0.85; p(3) = 0.07; p(4) = 0.07
!coefficients a(1) = 0.00; a(2) = 0.85; a(3) = 0.20; a(4) = -0.15 b(1) = 0.00; b(2) = 0.04; b(3) = -0.26; b(4) = 0.28 c(1) = 0.00; c(2) = -0.04; c(3) = 0.23; c(4) = 0.26 d(1) = 0.16; d(2) = 0.85; d(3) = 0.22; d(4) = 0.24 e(1) = 0.00; e(2) = 0.00; e(3) = 0.00; e(4) = 0.00 f(1) = 0.00; f(2) = 1.60; f(3) = 1.60; f(4) = 0.44
itermax = 100000
trx = 0.0D0 try = 0.0D0
open(1, file="plot.dat") write(1,*) "#X #Y" write(1,'(2F10.5)') trx, try
do i = 1, itermax
call random_number(prob) if (prob < p(1)) then trx = a(1) * trx + b(1) * try + e(1) try = c(1) * trx + d(1) * try + f(1) else if(prob < (p(1) + p(2))) then trx = a(2) * trx + b(2) * try + e(2) try = c(2) * trx + d(2) * try + f(2) else if ( prob < (p(1) + p(2) + p(3))) then trx = a(3) * trx + b(3) * try + e(3) try = c(3) * trx + d(3) * try + f(3) else trx = a(4) * trx + b(4) * try + e(4) try = c(4) * trx + d(4) * try + f(4) end if write(1,'(2F10.5)') trx, try
end do close(1) end program BarnsleyFern </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>
gnuplot
<lang gnuplot>
- Barnsley fern fractal 2/17/17 aev
reset fn="BarnsleyFernGnu"; clr='"green"'; ttl="Barnsley fern fractal" dfn=fn.".dat"; ofn=fn.".png"; set terminal png font arial 12 size 640,640 set print dfn append set output ofn unset border; unset xtics; unset ytics; unset key; set size square set title ttl font "Arial:Bold,12" n=100000; max=100; x=y=xw=yw=p=0; randgp(top) = floor(rand(0)*top) do for [i=1:n] {
p=randgp(max);
if (p==1) {xw=0;yw=0.16*y;}
if (1<p&&p<=8) {xw=0.2*x-0.26*y;yw=0.23*x+0.22*y+1.6;}
if (8<p&&p<=15) {xw=-0.15*x+0.28*y;yw=0.26*x+0.24*y+0.44;}
if (p>15) {xw=0.85*x+0.04*y;yw=-0.04*x+0.85*y+1.6;}
x=xw;y=yw; print x," ",y;
} plot dfn using 1:2 with points pt 7 ps 0.5 lc @clr set output unset print </lang>
- Output:
File: BarnsleyFernGnu.png (also BarnsleyFernGnu.dat)
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
Julia
<lang julia>function barnsleyfern(n::Integer)
funs = (
(x, y) -> (0, 0.16y),
(x, y) -> (0.85x + 0.04y, -0.04x + 0.85y + 1.6),
(x, y) -> (0.2x - 0.26y, 0.23x + 0.22y + 1.6),
(x, y) -> (-0.15x + 0,28y, 0.26x + 0.24y + 0.44))
rst = Matrix{Float64}(n, 2)
rst[1, :] = 0.0
for row in 2:n
r = rand(0:99)
if r < 1; f = 1;
elseif r < 86; f = 2;
elseif r < 93; f = 3;
else f = 4; end
rst[row, 1], rst[row, 2] = funs[f](rst[row-1, 1], rst[row-1, 2])
end
return rst
end</lang>
Kotlin
<lang scala>// version 1.1.0
import java.awt.* import java.awt.image.BufferedImage import javax.swing.*
class BarnsleyFern(private val dim: Int) : JPanel() {
private val img: BufferedImage
init {
preferredSize = Dimension(dim, dim)
background = Color.black
img = BufferedImage(dim, dim, BufferedImage.TYPE_INT_ARGB)
createFern(dim, dim)
}
private fun createFern(w: Int, h: Int) {
var x = 0.0
var y = 0.0
for (i in 0 until 200_000) {
var tmpx: Double
var tmpy: Double
val r = Math.random()
if (r <= 0.01) {
tmpx = 0.0
tmpy = 0.16 * y
}
else if (r <= 0.86) {
tmpx = 0.85 * x + 0.04 * y
tmpy = -0.04 * x + 0.85 * y + 1.6
}
else if (r <= 0.93) {
tmpx = 0.2 * x - 0.26 * y
tmpy = 0.23 * x + 0.22 * y + 1.6
}
else {
tmpx = -0.15 * x + 0.28 * y
tmpy = 0.26 * x + 0.24 * y + 0.44
}
x = tmpx
y = tmpy
img.setRGB(Math.round(w / 2.0 + x * w / 11.0).toInt(),
Math.round(h - y * h / 11.0).toInt(), 0xFF32CD32.toInt())
}
}
override protected fun paintComponent(gg: Graphics) {
super.paintComponent(gg)
val g = gg as Graphics2D
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
g.drawImage(img, 0, 0, null)
}
}
fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE
f.title = "Barnsley Fern"
f.setResizable(false)
f.add(BarnsleyFern(640), BorderLayout.CENTER)
f.pack()
f.setLocationRelativeTo(null)
f.setVisible(true)
}
}</lang>
Lua
Needs LÖVE 2D Engine <lang Lua> g = love.graphics wid, hei = g.getWidth(), g.getHeight()
function choose( i, j )
local r = math.random() if r < .01 then return 0, .16 * j elseif r < .07 then return .2 * i - .26 * j, .23 * i + .22 * j + 1.6 elseif r < .14 then return -.15 * i + .28 * j, .26 * i + .24 * j + .44 else return .85 * i + .04 * j, -.04 * i + .85 * j + 1.6 end
end function createFern( iterations )
local hw, x, y, scale = wid / 2, 0, 0, 45
local pts = {}
for k = 1, iterations do
pts[1] = { hw + x * scale, hei - 15 - y * scale,
20 + math.random( 80 ),
128 + math.random( 128 ),
20 + math.random( 80 ), 150 }
g.points( pts )
x, y = choose( x, y )
end
end function love.load()
math.randomseed( os.time() ) canvas = g.newCanvas( wid, hei ) g.setCanvas( canvas ) createFern( 15e4 ) g.setCanvas()
end function love.draw()
g.draw( canvas )
end </lang>
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>
Oberon-2
<lang oberon2> MODULE BarnsleyFern; (** Oxford Oberon-2
- )
IMPORT Random, XYplane;
VAR a1, b1, c1, d1, e1, f1, p1: REAL; a2, b2, c2, d2, e2, f2, p2: REAL; a3, b3, c3, d3, e3, f3, p3: REAL; a4, b4, c4, d4, e4, f4, p4: REAL; X, Y: REAL; x0, y0, e: INTEGER;
PROCEDURE Draw; VAR x, y: REAL; xi, eta: INTEGER; rn: REAL; BEGIN REPEAT rn := Random.Uniform(); IF rn < p1 THEN x := a1 * X + b1 * Y + e1; y := c1 * X + d1 * Y + f1 ELSIF rn < (p1 + p2) THEN x := a2 *X + b2 * Y + e2; y := c2 * X + d2 * Y + f2 ELSIF rn < (p1 + p2 + p3) THEN x := a3 * X + b3 * Y + e3; y := c3 * X + d3 * Y + f3 ELSE x := a4 * X + b4 * Y + e4; y := c4 * X + d4 * Y + f4 END; X := x; xi := x0 + SHORT(ENTIER(X * e)); Y := y; eta := y0 + SHORT(ENTIER(Y * e)); XYplane.Dot(xi, eta, XYplane.draw) UNTIL "s" = XYplane.Key() END Draw;
PROCEDURE Init; BEGIN X := 0; Y := 0; x0 := 120; y0 := 0; e := 25;
a1 := 0.00; a2 := 0.85; a3 := 0.20; a4 := -0.15; b1 := 0.00; b2 := 0.04; b3 := -0.26; b4 := 0.28; c1 := 0.00; c2 := -0.04; c3 := 0.23; c4 := 0.26; d1 := 0.16; d2 := 0.85; d3 := 0.22; d4 := 0.24; e1 := 0.00; e2 := 0.00; e3 := 0.00; e4 := 0.00; f1 := 0.00; f2 := 1.60; f3 := 1.60; f4 := 0.44; p1 := 0.01; p2 := 0.85; p3 := 0.07; p4 := 0.07; XYplane.Open; END Init;
BEGIN Init;Draw END BarnsleyFern. </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
<lang Phix>-- -- demo\rosetta\BarnsleyFern.exw -- include 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()
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>
PureBasic
<lang PureBasic>EnableExplicit DisableDebugger
DataSection
R84: : Data.d 0.85,0.04,-0.04,0.85,1.6 R91: : Data.d 0.2,-0.26,0.23,0.22,1.6 R98: : Data.d -0.15,0.28,0.26,0.24,0.44 R100: : Data.d 0.0,0.0,0.0,0.16,0.0
EndDataSection
Procedure Barnsley(height.i)
Define x.d, y.d, xn.d, yn.d, v1.d, v2.d, v3.d, v4.d, v5.d,
f.d=height/10.6,
offset.i=Int(height/4-height/40),
n.i, r.i
For n=1 To height*50
r=Random(99,0)
Select r
Case 0 To 84 : Restore R84
Case 85 To 91 : Restore R91
Case 92 To 98 : Restore R98
Default : Restore R100
EndSelect
Read.d v1 : Read.d v2 : Read.d v3 : Read.d v4 : Read.d v5
xn=v1*x+v2*y : yn=v3*x+v4*y+v5
x=xn : y=yn
Plot(offset+x*f,height-y*f,RGB(0,255,0))
Next
EndProcedure
Define w1.i=400,
h1.i=800
If OpenWindow(0,#PB_Ignore,#PB_Ignore,w1,h1,"Barnsley fern")
If CreateImage(0,w1,h1,24,0) And StartDrawing(ImageOutput(0)) Barnsley(h1) StopDrawing() EndIf ImageGadget(0,0,0,0,0,ImageID(0)) Repeat : Until WaitWindowEvent(50)=#PB_Event_CloseWindow
EndIf End</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
Racket
File:Racket-barnsley-fern.png : file uploading broken :-( <lang racket>#lang racket
(require racket/draw)
(define fern-green (make-color #x32 #xCD #x32 0.66))
(define (fern dc n-iterations w h)
(for/fold ((x #i0) (y #i0))
((i n-iterations))
(define-values (x′ y′)
(let ((r (random)))
(cond
[(<= r 0.01) (values 0
(* y 16/100))]
[(<= r 0.08) (values (+ (* x 20/100) (* y -26/100))
(+ (* x 23/100) (* y 22/100) 16/10))]
[(<= r 0.15) (values (+ (* x -15/100) (* y 28/100))
(+ (* x 26/100) (* y 24/100) 44/100))]
[else (values (+ (* x 85/100) (* y 4/100))
(+ (* x -4/100) (* y 85/100) 16/10))])))
(define px (+ (/ w 2) (* x w 1/11))) (define py (- h (* y h 1/11))) (send dc set-pixel (exact-round px) (exact-round py) fern-green) (values x′ y′)))
(define bmp (make-object bitmap% 640 640 #f #t 2))
(fern (new bitmap-dc% [bitmap bmp]) 200000 640 640)
bmp (send bmp save-file "images/racket-barnsley-fern.png" 'png)</lang>
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>
Rust
<lang rust>extern crate rand; extern crate raster;
use rand::Rng;
fn main() {
let max_iterations = 200_000u32; let height = 640i32; let width = 640i32;
let mut rng = rand::thread_rng(); let mut image = raster::Image::blank(width, height); raster::editor::fill(&mut image, raster::Color::white()).unwrap();
let mut x = 0.;
let mut y = 0.;
for _ in 0..max_iterations {
let r = rng.gen::<f32>();
let cx: f64;
let cy: f64;
if r <= 0.01 {
cx = 0f64;
cy = 0.16 * y as f64;
} else if r <= 0.08 {
cx = 0.2 * x as f64 - 0.26 * y as f64;
cy = 0.23 * x as f64 + 0.22 * y as f64 + 1.6;
} else if r <= 0.15 {
cx = -0.15 * x as f64 + 0.28 * y as f64;
cy = 0.26 * x as f64 + 0.26 * y as f64 + 0.44;
} else {
cx = 0.85 * x as f64 + 0.04 * y as f64;
cy = -0.04 * x as f64 + 0.85 * y as f64 + 1.6;
}
x = cx;
y = cy;
let _ = image.set_pixel(
((width as f64) / 2. + x * (width as f64) / 11.).round() as i32,
((height as f64) - y * (height as f64) / 11.).round() as i32,
raster::Color::rgb(50, 205, 50));
}
raster::save(&image, "fractal.png").unwrap();
}</lang>
Scheme
This version creates a list of points, defining the fern, which are then rescaled and output to an eps file.
<lang scheme> (import (scheme base)
(scheme cxr)
(scheme file)
(scheme inexact)
(scheme write)
(srfi 27)) ; for random numbers
(define (create-fern x y num-points)
(define (new-point xn yn)
(let ((r (* 100 (random-real))))
(cond ((< r 1) ; f1
(list 0 (* 0.16 yn)))
((< r 86) ; f2
(list (+ (* 0.85 xn) (* 0.04 yn))
(+ (* -0.04 xn) (* 0.85 yn) 1.6)))
((< r 93) ; f3
(list (- (* 0.2 xn) (* 0.26 yn))
(+ (* 0.23 xn) (* 0.22 yn) 1.6)))
(else ; f4
(list (+ (* -0.15 xn) (* 0.28 yn))
(+ (* 0.26 xn) (* 0.24 yn) 0.44))))))
;
(random-source-randomize! default-random-source)
(do ((i 0 (+ i 1))
(pts (list (list x y)) (cons (new-point (caar pts) (cadar pts)) pts)))
((= i num-points) pts)))
- output the fern to an eps file
(define (output-fern-as-eps filename fern)
(when (file-exists? filename) (delete-file filename))
(with-output-to-file
filename
(lambda ()
(let* ((width 600)
(height 800)
(min-x (apply min (map car fern)))
(max-x (apply max (map car fern)))
(min-y (apply min (map cadr fern)))
(max-y (apply max (map cadr fern)))
(scale-x (/ (- width 50) (- max-x min-x)))
(scale-y (/ (- height 50) (- max-y min-y)))
(scale-points (lambda (point)
(list (truncate (+ 20 (* scale-x (- (car point) min-x))))
(truncate (+ 20 (* scale-y (- (cadr point) min-y))))))))
(display
(string-append "%!PS-Adobe-3.0 EPSF-3.0\n%%BoundingBox: 0 0 "
(number->string width) " " (number->string height) "\n"))
;; add each point in fern as an arc - sets linewidth based on depth in tree
(for-each (lambda (point)
(display
(string-append (number->string (list-ref point 0))
" "
(number->string (list-ref point 1))
" 0.1 0 360 arc\nstroke\n")))
(map scale-points fern))
(display "\n%%EOF")))))
(output-fern-as-eps "barnsley.eps" (create-fern 0 0 50000)) </lang>
Scilab
This version creates a list of points, defining the fern, and shows them on a graphic window which can then be saved to a file via the GUI or the console by the user. <lang> iteractions=1.0d6;
XY=zeros(2,iteractions+1); x=0; y=0;
i=2; while i<iteractions+2
random_numbers=rand();
xp=x;
if random_numbers(1) < 0.01 then
x = 0;
y = 0.16 * y;
elseif random_numbers(1) >= 0.01 & random_numbers(1) < 0.01+0.85 then
x = 0.85 * x + 0.04 * y;
y = -0.04 * xp + 0.85 * y + 1.6;
elseif random_numbers(1) >= 0.86 & random_numbers(1) < 0.86+0.07 then
x = 0.2 * x - 0.26 * y;
y = 0.23 * xp + 0.22 * y + 1.6;
else
x = -0.15 * x + 0.28 * y;
y = 0.26 * xp + 0.24 * y + 0.44;
end
XY(1,i)=x;
XY(2,i)=y;
i=i+1;
end
scf(0); clf(); xname('Barnsley fern'); plot2d(XY(1,:),XY(2,:),-0) axes=gca(); axes.isoview="on"; axes.children.children.mark_foreground=13; </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>
SPL
<lang spl>w,h = #.scrsize() x,y = 0 >
r = #.rnd(100) ? r<85, x,y = f2(x,y) ? r!<85 & r<92, x,y = f3(x,y) ? r!<92 & r<99, x,y = f4(x,y) ? r!<99, x,y = f1(y) #.drawpoint(x/10*w+w/2,h-y/10*h,0,0.5,0,0.1)
< f1(y) <= 0, 0.16*y f2(x,y) <= 0.85*x+0.04*y, -0.04*x+0.85*y+1.6 f3(x,y) <= 0.2*x-0.26*y, 0.23*x+0.22*y+1.6 f4(x,y) <= -0.15*x+0.28*y, 0.26*x+0.24*y+0.44</lang>
Swift
Output is viewable in a playground.
<lang swift>import UIKit import CoreImage import PlaygroundSupport
let imageWH = 300 let context = CGContext(data: nil,
width: imageWH,
height: imageWH,
bitsPerComponent: 8,
bytesPerRow: 0,
space: CGColorSpace(name: CGColorSpace.sRGB)!,
bitmapInfo: CGImageAlphaInfo.premultipliedFirst.rawValue)!
var x0 = 0.0 var x1 = 0.0 var y0 = 0.0 var y1 = 0.0
context.setFillColor(#colorLiteral(red: 0, green: 0, blue: 0, alpha: 1)) context.fill(CGRect(x: 0, y: 0, width: imageWH, height: imageWH)) context.setFillColor(#colorLiteral(red: 0.539716677, green: 1, blue: 0.265400682, alpha: 1))
for _ in 0..<100_000 {
switch Int(arc4random()) % 100 {
case 0:
x1 = 0
y1 = 0.16 * y0
case 1...7:
x1 = -0.15 * x0 + 0.28 * y0
y1 = 0.26 * x0 + 0.24 * y0 + 0.44
case 8...15:
x1 = 0.2 * x0 - 0.26 * y0
y1 = 0.23 * x0 + 0.22 * y0 + 1.6
default:
x1 = 0.85 * x0 + 0.04 * y0
y1 = -0.04 * x0 + 0.85 * y0 + 1.6
}
context.fill(CGRect(x: 30 * x1 + Double(imageWH) / 2.0, y: 30 * y1,
width: 1, height: 1))
(x0, y0) = (x1, y1)
}
let uiImage = UIImage(cgImage: context.makeImage()!)</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.
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