✔ Apfelmänchen wird nur verzerrt gezeichnet.

import java.awt.Color;
import java.awt.Graphics2D;

public class MandelbrotPainter {
    
    private int width = 100;
    private int height = 100;
    
    private double left   = -2;
    private double right  = 1;
    private double top    = 1.5;
    private double bottom = -1.5;
    
    private int iterations = 100;
    
    private double getRealFromPixel(final int pixelX) {
        return this.getLeft() + ((double)pixelX / (double)this.getWidth()) * (this.getRight() - this.getLeft());
    }
    
    private double getImaginaryFromPixel(final int pixelY) {
        return -(this.getTop() + ((double)pixelY / (double)this.getHeight()) * (this.getBottom() - this.getTop()));
    }
    
    private double getMagnitude(final double real, final double imag) {
        return Math.sqrt(real * real + imag * imag);
    }
    
    private int calculateSequence(final double real, final double imag) {
        double zReal = 0.0d;
        double zImag = 0.0d;
        
        for(int n = 0; n <= this.getIterations(); n++) {
            if(this.getMagnitude(zReal, zImag) > 2) {
                return n;
            }
            else {
                zReal = zReal * zReal - zImag * zImag + real;
                zImag = 2 * zReal * zImag + imag;
            }
        }
        
        return 0;
    }
    
    private Color generateColor(int n) {
//        return new Color(
//                (float)(n * n) / (float)(this.getIterations() * this.getIterations()),
//                (float)n / (float)this.getIterations(),
//                (float)(n*n*n) / (float)(this.getIterations() * this.getIterations() * this.getIterations()));
        return new Color(
                (float)n / (float)this.getIterations(),
                (float)n / (float)this.getIterations(),
                (float)n / (float)this.getIterations());
    }
    
    public void render(Graphics2D g2) {
        for(int y = 0; y < this.getHeight(); y++) {
            for(int x = 0; x < this.getWidth(); x++) {
                final int n = this.calculateSequence(
                        this.getRealFromPixel(x), 
                        this.getImaginaryFromPixel(y));
                
                g2.setColor(this.generateColor(n));
                g2.drawLine(x, y, x, y);
            }
        }
    }
    
    public int getWidth() {
        return this.width;
    }
    
    public void setWidth(int width) {
        this.width = width;
    }
    
    public int getHeight() {
        return this.height;
    }
    
    public void setHeight(int height) {
        this.height = height;
    }
    
    public double getLeft() {
        return this.left;
    }
    
    public void setLeft(double left) {
        this.left = left;
    }
    
    public double getRight() {
        return this.right;
    }
    
    public void setRight(double right) {
        this.right = right;
    }
    
    public double getTop() {
        return this.top;
    }
    
    public void setTop(double top) {
        this.top = top;
    }
    
    public double getBottom() {
        return this.bottom;
    }
    
    public void setBottom(double bottom) {
        this.bottom = bottom;
    }
    
    public int getIterations() {
        return this.iterations;
    }
    
    public void setIterations(int iterations) {
        this.iterations = iterations;
    }
}

import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.image.BufferedImage;

import javax.swing.JFrame;
import javax.swing.JPanel;

public class MandelbrotPanel extends JPanel {
    
    private static final long serialVersionUID = -138220849693387138L;
    
    private final MandelbrotPainter painter = new MandelbrotPainter();
    
    private BufferedImage image = new BufferedImage(600, 600, BufferedImage.TYPE_INT_RGB);
    
    public MandelbrotPanel() {
        this.painter.setIterations(30);
        this.painter.setHeight(this.image.getHeight());
        this.painter.setWidth(this.image.getWidth());
        this.painter.render(this.image.createGraphics());
    }
    
    public static void main(String[] args) {
        
        MandelbrotPanel panel = new MandelbrotPanel();
        
        JFrame frame = new JFrame("Mandelbrot");
        
        frame.add(panel);
        frame.pack();
        
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        frame.setVisible(true);
    }
    
    @Override
    public Dimension getMinimumSize() {
        return new Dimension(this.image.getWidth(), this.image.getHeight());
    }
    
    @Override
    public Dimension getPreferredSize() {
        return this.getMinimumSize();
    }
    
    @Override
    protected void paintComponent(Graphics g) {
        super.paintComponent(g);
        
        g.drawImage(this.image, 0, 0, this);
    }
    
}

double zRealNew = zReal * zReal - zImag * zImag + real;
zImag = 2 * zReal * zImag + imag;
zReal = zRealNew;