分形算法与程序设计——Java实现

import java.applet.*; import java.awt.*; // The main Mandelbrot/Julia applet public class Juliet extends Applet implements Runnable { // Inner class for manipulating a complex number (real + imag*i) public class ComplexPoint { // Default constructor public ComplexPoint() { set(0,0); }; // Constructor with args public ComplexPoint(double set_real, double set_imag) { set(set_real, set_imag); }; // Set to new values public void set(double set_real, double set_imag) { real = set_real; imag = set_imag; }; // Set to equal another ComplexPoint public void set(ComplexPoint p) { real = p.real; imag = p.imag; }; // Add another ComplexPoint public void add(ComplexPoint p) { real += p.real; imag += p.imag; }; // Subtract another ComplexPoint public void subtract(ComplexPoint p) { real -= p.real; imag -= p.imag; }; // Mirror this ComplexPoint in the origo public void negate() { real = -real; imag = -imag; }; // Return the square of the distance from origo to this ComplexPoint // (|p|^2 == (sqrt(p.r^2 + p.i^2))^2 == p.r^2 + p.i ^2) // This is useful for comparing against a value, since the expression // (p.r^2 + p.i ^2 > x^2) is faster than (sqrt(p.r^2 + p.i ^2) > x). public double distance_squared() { return real*real + imag*imag; }; // Replace this ComplexPoint with its square // (a+bi)^2 = (a+bi)(a+bi) = a^2 + 2abi + (bi)^2 = (a^2 - b^2) + (2ab)i public void square() { double new_real = real*real - imag*imag; double new_imag = 2*real*imag; real = new_real; imag = new_imag; }; // Replace this ComplexPoint with its square root public void square_root() { // Square root calculation is easiest done in the polar plane toPolar(); radius = Math.sqrt(radius); angle /= 2; // Convert back to normal (real,imag) plane toCartesian(); }; // The actual real part and imaginary part values public double real, imag; // Convert (internally) to polar representation (radius, angle) private void toPolar() { radius = Math.sqrt(real*real + imag*imag); if (real > 0) angle = Math.atan(imag/real); else if (real < 0) angle = Math.PI + Math.atan(imag/real); else angle = Math.PI; }; // Convert (internally) back to cartesian representation (r,i) private void toCartesian() { real = radius * Math.cos(angle); imag = radius * Math.sin(angle); }; // Internal variables for storing polar representation private double radius, angle; }; // Max iterations for each pixel in Mandelbrot and Julia sets: final int MAX_ITERATIONS = 200; // This many of the first iterations are discarded in the fast and // sketchy Julia set plotting: final int JULIASKETCH_DISCARD = 10; // After this many iterations, the fast and sketchy Julia set plotting // is replaced by the slower, complete and more colorful algorithm: final int JULIASKETCH_REFINE = 10000; // Portion of Mandelbrot set to be displayed: final double REAL_LO = -0.50, REAL_HI = 2.00; final double IMAG_LO = -1.25, IMAG_HI = 1.25; // Max size (in complex coords) of Julia set final double JULIASIZE = 4.0; final int CROSSHAIR_SIZE = 10; // Size of crosshairs int SIZE = 150; // Default value for canvas size ComplexPoint step = new ComplexPoint(); // Variables used in the iteration formulae ComplexPoint z = new ComplexPoint(); ComplexPoint c = new ComplexPoint(); ComplexPoint p = new ComplexPoint(); ComplexPoint u = new ComplexPoint(); Point crosshair = new Point(); // cross hair position boolean restart_julia; Color palette[] = new Color[MAX_ITERATIONS]; Image mandel; // Offscreen bitmap for Mandelbrot Image julia; // Offscreen bitmap for Julia Graphics gm; Graphics gj; Graphics screen; Thread juliathread = null; public String getAppletInfo() { return "Name: Juliet\r\nAuthor: G�ran Wallgren"; } public void init() // Applet initialization { // Read canvas size from applet parameters String param = getParameter("size"); if (param != null) { SIZE = Integer.parseInt(param); } // Calculate the size of one pixel in the Mandelbrot image, // mapped to our portion of the complex number plane step.real = (REAL_HI - REAL_LO)/SIZE; step.imag = (IMAG_HI - IMAG_LO)/SIZE; // Position crosshairs at origo crosshair.setLocation((int)(-REAL_LO / step.real), (int)(-IMAG_LO / step.imag)); // Setup applet drawing area setBackground(Color.black); resize(2*SIZE, SIZE); // Create offscreen bitmaps for drawing the Mandelbrot and Julia sets mandel = createImage(SIZE, SIZE); julia = createImage(SIZE, SIZE); // Setup handles to offscreen bitmaps and screen drawing area gm = mandel.getGraphics(); initBitmap(gm); gj = julia.getGraphics(); initBitmap(gj); screen = getGraphics(); // Create a smooth color palette with MAX_ITERATIONS entries double colfactor = 255.0 / Math.log((double)(MAX_ITERATIONS + 1)); int level; for (int n = 0; n < MAX_ITERATIONS; n++) { level = (int)(colfactor * Math.log(n + 1)); palette[n] = new Color(level, level, 255-level); } } public void start() // Enter thread { if (juliathread == null) { juliathread = new Thread(this); juliathread.start(); } } public void stop() // Exit thread { if (juliathread != null) { juliathread.stop(); juliathread = null; } } public void run() // Thread entry point, from interface Runnable { // Build and draw the Mandelbrot set image drawColoredMandel(); // Enter the Julia set drawing loop drawJuliaInteractively(); } // Called whenever a portion of the applet needs to be redrawn. // Override the default since we don't need to erase... public void update(Graphics g) { paint(g); } // Called from update()... public void paint(Graphics g) { // Paste the saved images onto screen, and apply the crosshairs g.drawImage(julia, SIZE, 0, this); g.drawImage(mandel, 0, 0, this); drawCrosshairs(g); } // Helper function void drawPixel(Graphics g, int xx, int yy) { g.drawLine(xx, yy, xx, yy); } // Helper function void initBitmap(Graphics g) { // Initialize offscreen bitmaps with black background and white border g.setColor(Color.black); g.fillRect(1,1, SIZE-2,SIZE-2); g.setColor(Color.white); g.drawRect(0,0, SIZE-1,SIZE-1); repaint(); // Update screen } // Draw an image of the Mandelbrot set in memory and on screen void drawJuliaInteractively() { final double JULIASCALE = (double)SIZE / JULIASIZE; final int CENTRE_X = SIZE + SIZE/2; final int CENTRE_Y = SIZE/2; int iter = 0; // Counter for iterations // Make sure parameters will be initialized when we enter the eternal loop restart_julia = true; // Loop forever, drawing the selected Julia set using a fast and sketchy // plotting at first, then replacing it with the complete algorithm... while (true) { // The restart_julia flag is set when the crosshairs are moved if (restart_julia) { initBitmap(gj); // Update value of c with new crosshair position c.set(REAL_LO + step.real * crosshair.x, IMAG_LO + step.imag * crosshair.y); // Reset starting point for Julia iterations iter = 0; z.set(1,1); // Reset flag restart_julia = false; } // Perform one iteration step of the "sketchy" Julia set formula. // Here, the "z := z^2 - c" formula is traced "backwards" using // its inverse "z := sqrt(z + c)". The calculation is separated // into two steps: "z := z + c" followed by z := sqrt(z). z.add(c); z.square_root(); // However,