Barnsley fern
A Barnsley fern is a fractal named after British mathematician Michael Barnsley and can be created using an iterated function system (IFS).
You are encouraged to solve this task according to the task description, using any language you may know.
The 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>
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>
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>
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>
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>
tcl
See Tcl-Wiki [_ttp://wiki.tcl.tk/10492 Fern Fractal]
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>