Mandelbrot.java

/**
 * Mandelbrot set implementation. Will draw every pixel so takes some time to compute.
 */
public class Mandelbrot {
    private static final int WIDTH = 960;
    private static final int HEIGHT = 540;

    // Max iterations per pixel
    private static final int MAX_ITER = 500;

    // Bounds in the complex plane
    private static final double X_MIN = -2.5;
    private static final double X_MAX = 1.0;
    private static final double Y_MIN = -1.0;
    private static final double Y_MAX = 1.0;

    /** Map a pixel coordinate to the real axis */
    private static double mapX(int px) {
        return X_MIN + px * (X_MAX - X_MIN) / WIDTH;
    }

    /** Map a pixel coordinate to the imaginary axis */
    private static double mapY(int py) {
        return Y_MIN + py * (Y_MAX - Y_MIN) / HEIGHT;
    }

    /** Compute the Mandelbrot iteration count for c = (cr, ci) */
    private static int mandelbrotIterations(double cr, double ci) {
        double zr = 0;
        double zi = 0;

        int count = 0;

        while (count < MAX_ITER) {
            // z^2 = (zr + i zi)^2 = zr^2 - zi^2 + 2 zr zi i
            double zr2 = zr * zr - zi * zi;
            double zi2 = 2 * zr * zi;

            zr = zr2 + cr;
            zi = zi2 + ci;

            // If magnitude escapes
            if (zr * zr + zi * zi > 4.0)
                break;

            count++;
        }

        return count;
    }

    /** Simple coloring: black if inside, gradient if outside */
    private static void setColor(int iter) {
        if (iter == MAX_ITER) {
            StdDraw.setPenColor(0, 0, 0);  // black (inside)
        } else {
            // Smooth gradient (blue-ish)
            int val = 255 * iter / MAX_ITER;
            StdDraw.setPenColor(0, val, 255 - val);
        }
    }

    public static void main(String[] args) {
        StdDraw.setTitle("Mandelbrot Set");
        StdDraw.setCanvasSize(WIDTH, HEIGHT);
        StdDraw.setXscale(0, WIDTH);
        StdDraw.setYscale(0, HEIGHT);

        // Draw each pixel
        for (int px = 0; px < WIDTH; px++) {
            for (int py = 0; py < HEIGHT; py++) {
                double cr = mapX(px);
                double ci = mapY(py);

                int iter = mandelbrotIterations(cr, ci);
                setColor(iter);

                StdDraw.point(px, py);
            }
        }
    }
}