Beispiel zur Generierung von Fraktalen

[Thomas Darimont]

Hallo,

hier mal ein kleines Beispiel wie man ein Fraktal mit Java erzeugen kann. In diesem Beispiel sehen wir die Visualisierung Mandelbrot-Menge:

Mehr dazu gibts hier:
http://de.wikipedia.org/wiki/Mandelbrot-Menge
http://de.wikipedia.org/wiki/Fraktal
http://de.wikipedia.org/wiki/Komplexe_Zahl

/**
 * 
 */
package de.tutorials;

import java.awt.Color;
import java.awt.Graphics;
import java.awt.image.BufferedImage;
import java.io.File;

import javax.imageio.ImageIO;

/**
 * @author Tom
 * 
 */
public class FractalGeneratorExample {

    /**
     * @param args
     */
    public static void main(String[] args) throws Exception {
        BufferedImage image = new BufferedImage(440, 350, BufferedImage.TYPE_INT_RGB);
        int maxIterations = 30;
        double pixelWidth = 0.00625;
        Graphics g = image.getGraphics();
        
        double imC = -1.1;
        final Complex zero = new Complex(0,0);
        for (int y = 0; y < 350; y++) {
            double reC = -2.1;
            for (int x = 0; x < 440; x++) {
                int iterations = 0;
                Complex c = new Complex(reC,imC);
                
                Complex z = zero;
                
                for (int i = 0; i < maxIterations; i++) {
                    z = z.square().add(c);
                    if (z.dot() > 4.0) {
                        break;
                    }
                    iterations++;
                }

                if (iterations <= 30 && iterations > 25) {
                    g.setColor(Color.RED);
                } else if(iterations <= 25 && iterations > 20){
                    g.setColor(Color.BLUE);
                }else if(iterations <= 20 && iterations > 15){
                    g.setColor(Color.GREEN);
                }else if(iterations <= 15 && iterations > 10){
                    g.setColor(Color.YELLOW);
                }else if(iterations <= 10 && iterations > 5){
                    g.setColor(Color.PINK);
                }else {
                    g.setColor(Color.WHITE);
                }
                g.drawLine(x, y, x, y);

                reC += pixelWidth;
            }
            imC += pixelWidth;
        }

        ImageIO.write(image, "jpeg", new File("c:/temp/fractal.jpg"));

    }

     static class Complex {
        double real;
        double imag;

        public Complex(double imag, double real) {
            super();
            this.imag = imag;
            this.real = real;
        }

        public double getReal() {
            return real;
        }

        public double getImag() {
            return imag;
        }

        public Complex add(Complex other) {
            return new Complex(this.real + other.real, this.imag + other.imag);
        }

        public Complex minus(Complex other) {
            return new Complex(this.real - other.real, this.imag - other.imag);
        }

        public Complex mul(Complex other) {
            return new Complex(this.real * other.real - this.imag * other.imag,
                    this.real * other.imag + this.imag * other.real);
        }

        public Complex square() {
            return new Complex(this.real * this.real - this.imag * this.imag, 2
                    * this.real * this.imag);
        }
        
        /**
         * "self"-dot Product
         * @return
         */
        public double dot(){
            return this.real * this.real + this.imag * this.imag;
        }

        @Override
        public String toString() {
            return this.real + " + " + this.imag + "i";
        }
    }
}

Hier das ganze in einem JFrame:

/**
 * 
 */
package de.tutorials;

import java.awt.BasicStroke;
import java.awt.Color;
import java.awt.Graphics2D;
import java.awt.Point;
import java.awt.Stroke;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;
import java.awt.event.MouseMotionAdapter;
import java.util.concurrent.Executors;
import java.util.concurrent.TimeUnit;

import javax.swing.JFrame;

/**
 * @author Tom
 * 
 */
public class FractalGeneratorExample extends JFrame {

	int currentSelectionStartX;
	int currentSelectionStartY;

	int currentX;
	int currentY;

	Runnable renderLoop = new Runnable() {
		public void run() {

			double zoomFactor = 1.0;
			double dx = 1.0;
			double dy = 1.0;

			Stroke stroke = new BasicStroke(1.0F);
			

			while (true) {
				int windowWidth = getWidth();
				int windowHeight = getHeight();

				Graphics2D g = (Graphics2D) getBufferStrategy().getDrawGraphics();
				g.clearRect(0, 0, windowWidth, windowHeight);

				int maxIterations = 30;
				double pixelWidth = 0.00625 * zoomFactor;

				double imC = -1.1 / dy;

				//final Complex zero = new Complex(0, 0);
				
				double reC = -2.1 / dx;
				
				for (int y = 0; y < windowHeight; y++) {
					reC = -2.1 / dx;
					for (int x = 0; x < windowWidth; x++) {
						
						int iterations = 0;
						
//						Complex c = new Complex(reC, imC);
//						Complex z = zero;
//						for (int i = 0; i < maxIterations; i++) {
//							z = z.square().add(c);
//							if (z.dot() > 4.0) {
//								break;
//							}
//							iterations++;
//						}
						
						double reZ = 0.0;
						double imZ = 0.0;

						for (int i = 0; i < maxIterations; i++) {

							double newReZ = reZ * reZ - imZ * imZ;
							double newImZ = 2.0 * reZ * imZ;

							reZ = newReZ;
							imZ = newImZ;
							
							reZ += reC;
							imZ += imC;

							if (reZ * reZ + imZ * imZ > 4.0) {
								break;
							}
							iterations++;
						}

						if (iterations <= 30 && iterations > 25) {
							g.setColor(Color.RED);
						} else if (iterations <= 25 && iterations > 20) {
							g.setColor(Color.BLUE);
						} else if (iterations <= 20 && iterations > 15) {
							g.setColor(Color.GREEN);
						} else if (iterations <= 15 && iterations > 10) {
							g.setColor(Color.YELLOW);
						} else {
							g.setColor(Color.PINK);

						}
						
						//System.out.printf("reZ: %s imZ: %s\n",reC,imC);
						
						g.drawLine(x, y, x, y);

						reC += pixelWidth;
					}
					imC += pixelWidth;
				}
				
				

				g.setColor(Color.BLACK);
				g.setStroke(stroke);

				double width = currentX - currentSelectionStartX;
				double height = currentY - currentSelectionStartY;

				getBufferStrategy().show();
				g.dispose();

				dx = 2.0 - width / windowWidth / zoomFactor- zoomFactor;
				dy = 2.0 - height / windowHeight / zoomFactor - zoomFactor;

				zoomFactor *= 0.978;

				try {
					TimeUnit.MILLISECONDS.sleep(10);
				} catch (InterruptedException e) {
					e.printStackTrace();
				}
			}
		}
	};

	public FractalGeneratorExample() {
		super("FractalGeneratorExample");
		setLocationRelativeTo(null);

		addMouseMotionListener(new MouseMotionAdapter() {
			@Override
			public void mouseDragged(MouseEvent e) {
				Point p = e.getPoint();
				currentX = p.x;
				currentY = p.y;
			}
		});

		addMouseListener(new MouseAdapter() {
			@Override
			public void mousePressed(MouseEvent e) {
				Point currentPoint = e.getPoint();
				currentSelectionStartX = currentPoint.x;
				currentSelectionStartY = currentPoint.y;

				currentX = currentSelectionStartX;
				currentY = currentSelectionStartY;
			}
		});

		setDefaultCloseOperation(EXIT_ON_CLOSE);
		setSize(512, 384);
		setVisible(true);
		
		createBufferStrategy(2);
		Executors.newSingleThreadExecutor().execute(renderLoop);
	}

	/**
	 * @param args
	 */
	public static void main(String[] args) throws Exception {
		new FractalGeneratorExample();
	}

	static class Complex {
		double real;
		double imag;

		public Complex(double imag, double real) {
			super();
			this.imag = imag;
			this.real = real;
		}

		public double getReal() {
			return real;
		}

		public double getImag() {
			return imag;
		}

		public Complex add(Complex other) {
			return new Complex(this.real + other.real, this.imag + other.imag);
		}

		public Complex minus(Complex other) {
			return new Complex(this.real - other.real, this.imag - other.imag);
		}

		public Complex mul(Complex other) {
			return new Complex(this.real * other.real - this.imag * other.imag, this.real * other.imag + this.imag * other.real);
		}

		public Complex square() {
			return new Complex(this.real * this.real - this.imag * this.imag , 2 * this.real * this.imag);
		}

		/**
		 * "self"-dot Product
		 * 
		 * @return
		 */
		public double dot() {
			return this.real * this.real + this.imag * this.imag;
		}

		@Override
		public String toString() {
			return this.real + " + " + this.imag + "i";
		}
	}
}

Gruß Tom