Chaos game: Difference between revisions
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=={{header|Logo}}== |
=={{header|Logo}}== |
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<lang logo>to chaosgame : |
<lang logo>to chaosgame :sidelength :iterations |
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make "width :sidelength |
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make "height (:sidelength/2 * sqrt 3) |
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make "x (random :width) |
make "x (random :width) |
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make "y (random :height) |
make "y (random :height) |
Revision as of 09:44, 21 August 2016
You are encouraged to solve this task according to the task description, using any language you may know.
The Chaos Game is a method of generating the attractor of an iterated function system (IFS). One of the best-known and simplest examples creates a fractal, using a polygon and an initial point selected at random.
- Task
Play the Chaos Game using the corners of an equilateral triangle as the reference points. Add a starting point at random (preferably inside the triangle). Then add the next point halfway between the starting point and one of the reference points. This reference point is chosen at random.
After a sufficient number of iterations, the image of a Sierpinski Triangle should emerge.
- See also
BASIC
This should require minimal adaptation to work with any of the older Microsoft-style BASICs (IBM PC, AppleSoft, Commodore, etc.). Users of other dialects will need to replace lines 10 and 150 with the appropriate statements to select a graphics output mode (if necessary) and to plot a pixel at x,y in colour v; they should also add LET throughout and 170 END if their dialects require those things. <lang basic>10 SCREEN 1 20 X = INT(RND(0) * 200) 30 Y = INT(RND(0) * 200) 40 FOR I=1 TO 20000 50 V = INT(RND(0) * 3) + 1 60 ON V GOTO 70,100,130 70 X = X/2 80 Y = Y/2 90 GOTO 150 100 X = 100 + (100-X)/2 110 Y = 200 - (200-Y)/2 120 GOTO 150 130 X = 200 - (200-X)/2 140 Y = Y/2 150 PSET X,Y,V 160 NEXT I</lang>
C++
This program will generate the Sierpinski Triangle and save it to your hard drive. <lang cpp>
- include <windows.h>
- include <ctime>
- include <string>
- include <iostream>
const int BMP_SIZE = 600;
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 chaos { public:
void start() { POINT org; fillPts(); initialPoint( org ); initColors(); int cnt = 0, i; bmp.create( BMP_SIZE, BMP_SIZE ); bmp.clear( 255 );
while( cnt++ < 1000000 ) { switch( rand() % 6 ) { case 0: case 3: i = 0; break; case 1: case 5: i = 1; break; case 2: case 4: i = 2; } setPoint( org, myPoints[i], i ); } // --- edit this path --- // bmp.saveBitmap( "F:/st.bmp" ); }
private:
void setPoint( POINT &o, POINT v, int i ) { POINT z; o.x = ( o.x + v.x ) >> 1; o.y = ( o.y + v.y ) >> 1; SetPixel( bmp.getDC(), o.x, o.y, colors[i] ); } void fillPts() { int a = BMP_SIZE - 1; myPoints[0].x = BMP_SIZE >> 1; myPoints[0].y = 0; myPoints[1].x = 0; myPoints[1].y = myPoints[2].x = myPoints[2].y = a; } void initialPoint( POINT& p ) { p.x = ( BMP_SIZE >> 1 ) + rand() % 2 ? rand() % 30 + 10 : -( rand() % 30 + 10 ); p.y = ( BMP_SIZE >> 1 ) + rand() % 2 ? rand() % 30 + 10 : -( rand() % 30 + 10 ); } void initColors() { colors[0] = RGB( 255, 0, 0 ); colors[1] = RGB( 0, 255, 0 ); colors[2] = RGB( 0, 0, 255 ); } myBitmap bmp; POINT myPoints[3]; COLORREF colors[3];
}; int main( int argc, char* argv[] ) {
srand( ( unsigned )time( 0 ) ); chaos c; c.start(); return 0;
} </lang>
J
<lang j> Note 'plan, Working in complex plane'
Make an equilateral triangle. Make a list of N targets Starting with a random point near the triangle, iteratively generate new points. plot the new points.
j has a particularly rich notation for numbers.
1ad_90 specifies a complex number with radius 1 at an angle of negative 90 degrees.
2p1 is 2 times (pi raised to the first power).
)
N=: 3000
require'plot' TAU=: 2p1 NB. tauday.com mean=: +/ % #
NB. equilateral triangle with vertices on unit circle NB. rotated for fun. TRIANGLE=: *(j./2 1 o.(TAU%6)*?0)*1ad_90 1ad150 1ad30
TARGETS=: (N ?@:# 3) { TRIANGLE
NB. start on unit circle START=: j./2 1 o.TAU*?0
NEW_POINTS=: (mean@:(, {.) , ])/ TARGETS , START
'marker'plot NEW_POINTS </lang>
Java
<lang java>import java.awt.*; import java.awt.event.*; import java.util.*; import javax.swing.*; import javax.swing.Timer;
public class ChaosGame extends JPanel {
class ColoredPoint extends Point { int colorIndex;
ColoredPoint(int x, int y, int idx) { super(x, y); colorIndex = idx; } }
Stack<ColoredPoint> stack = new Stack<>(); Point[] points = new Point[3]; Color[] colors = {Color.red, Color.green, Color.blue}; Random r = new Random();
public ChaosGame() { Dimension dim = new Dimension(640, 640); setPreferredSize(dim); setBackground(Color.white);
int margin = 60; int size = dim.width - 2 * margin;
points[0] = new Point(dim.width / 2, margin); points[1] = new Point(margin, size); points[2] = new Point(margin + size, size);
stack.push(new ColoredPoint(-1, -1, 0));
new Timer(10, (ActionEvent e) -> { if (stack.size() < 50_000) { for (int i = 0; i < 1000; i++) addPoint(); repaint(); } }).start(); }
private void addPoint() { try { int colorIndex = r.nextInt(3); Point p1 = stack.peek(); Point p2 = points[colorIndex]; stack.add(halfwayPoint(p1, p2, colorIndex)); } catch (EmptyStackException e) { System.out.println(e); } }
void drawPoints(Graphics2D g) { for (ColoredPoint p : stack) { g.setColor(colors[p.colorIndex]); g.fillOval(p.x, p.y, 1, 1); } }
ColoredPoint halfwayPoint(Point a, Point b, int idx) { return new ColoredPoint((a.x + b.x) / 2, (a.y + b.y) / 2, idx); }
@Override public void paintComponent(Graphics gg) { super.paintComponent(gg); Graphics2D g = (Graphics2D) gg; g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
drawPoints(g); }
public static void main(String[] args) { SwingUtilities.invokeLater(() -> { JFrame f = new JFrame(); f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); f.setTitle("Chaos Game"); f.setResizable(false); f.add(new ChaosGame(), BorderLayout.CENTER); f.pack(); f.setLocationRelativeTo(null); f.setVisible(true); }); }
}</lang>
Logo
<lang logo>to chaosgame :sidelength :iterations
make "width :sidelength make "height (:sidelength/2 * sqrt 3) make "x (random :width) make "y (random :height) repeat :iterations [ make "vertex (random 3) if :vertex = 0 [ make "x (:x / 2) make "y (:y / 2) setpencolor "green ] if :vertex = 1 [ make "x (:width / 2 + ((:width / 2 - :x) / 2)) make "y (:height - ((:height - :y) / 2)) setpencolor "red ] if :vertex = 2 [ make "x (:width - ((:width - :x) / 2)) make "y (:y / 2) setpencolor "blue ] penup setxy (:x - :width / 2) (:y - :height / 2) pendown forward 1 ] hideturtle
end</lang>
Perl 6
<lang perl6>use Image::PNG::Portable;
my ($w, $h) = (640, 640);
my $png = Image::PNG::Portable.new: :width($w), :height($h);
my @vertex = [0, 0], [$w, 0], [$w/2, $h];
my ($x, $y) = (0, 0);
for ^1e5 {
($x, $y) = do given @vertex[3.rand] -> @v { ((($x, $y) »+« @v) »/» 2)».Int }; $png.set: $x, $y, 0, 255, 0;
}
$png.write: 'Chaos-game-perl6.png';</lang>
zkl
This is a half assed animated process - a bunch of pixels are drawn every couple of seconds and the pixmap written [to the file system]. So, if you open the output file ("chaosGame.jpg") it will [auto] update and show the progression of the image.
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl
<lang zkl>w,h:=640,640; bitmap:=PPM(w,h,0xFF|FF|FF); // White background colors:=T(0xFF|00|00,0x00|FF|00,0x00|00|FF); // red,green,blue
margin,size:=60, w - 2*margin; points:=T(T(w/2, margin), T(margin,size), T(margin + size,size) ); N,done:=Atomic.Int(0),Atomic.Bool(False);
Thread.HeartBeat('wrap(hb){ // a thread
var a=List(-1,-1);
if(N.inc()<50){ do(500){
colorIndex:=(0).random(3); // (0..2) b,p:=points[colorIndex], halfwayPoint(a,b); x,y:=p; bitmap[x,y]=colors[colorIndex]; a=p;
} bitmap.writeJPGFile("chaosGame.jpg",True); } else{ hb.cancel(); done.set(); } // stop thread and signal done
},2).go(); // run every 2 seconds, starting now
fcn halfwayPoint([(ax,ay)], [(bx,by)]){ T((ax + bx)/2, (ay + by)/2) }
done.wait(); // don't exit until thread is done println("Done");</lang>