Exponentation

import java.awt.Color;
import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.Image;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;

import javax.imageio.ImageIO;
import javax.swing.JFrame;
import javax.swing.JPanel;


public class Chart extends JFrame implements Runnable
{
    public static final int AREA_RANGE = 400;
    public static final double COLOR_RANGE = 5.0;
    public static final double MAX_AXIS = 10.0;

    private static final long serialVersionUID = -2607877189532852723L;

    public static void main(String[] args)
    {
        try{
         (new Chart()).run();
        } catch (Exception e) {e.printStackTrace();}
    }

    PaintCanvas c;

    public Chart()
    {
        this.setSize(2*AREA_RANGE + 1, 2*AREA_RANGE + 1);
        this.setVisible(true);
        c = new PaintCanvas(this);
        c.setPreferredSize(new Dimension(2*AREA_RANGE + 1, 2*AREA_RANGE + 1));
        this.add(c);
        this.pack();
    }

    @Override
    public void run()
    {
        while (true)
        {
            try {
                Thread.sleep(16);
            } catch (InterruptedException e) {}
            c.repaint();
        }
    }
}

class PaintCanvas extends JPanel
{
    private static final long serialVersionUID = 4255091824970101848L;
    Chart chart;
    private BufferedImage display;

    public PaintCanvas(Chart c)
    {
        chart = c;
        display = (BufferedImage) chart.createImage(2*Chart.AREA_RANGE + 1, 2*Chart.AREA_RANGE + 1);
        init();
    }

    public void init()
    {
        int AREA_RANGE = Chart.AREA_RANGE;
        double COLOR_RANGE = Chart.COLOR_RANGE;
        double DIV_VALUE  = Chart.AREA_RANGE / Chart.MAX_AXIS;

        Graphics g = display.getGraphics();
        for (int x = -AREA_RANGE; x <= AREA_RANGE; x += 1)
        {
            for (int y = -AREA_RANGE; y <= AREA_RANGE; y += 1)
            {
                double a = Math.pow(x/DIV_VALUE, y/DIV_VALUE);
                double b = Math.pow(y/DIV_VALUE, x/DIV_VALUE);
                double diff = a - b;
                diff = Clamp(-COLOR_RANGE, diff, COLOR_RANGE) * (127.0/COLOR_RANGE); //Math.copySign(1, diff) * Math.log(Math.abs(diff)+10)
                if (diff < 0.0) g.setColor(new Color(127, 127, (int)-(diff-127)));
                else if (diff > 0.0) g.setColor(new Color((int) diff+127, 127, 127));
                else g.setColor(new Color(127, 127, 127));
                if (Double.isNaN(a) || Double.isNaN(b)) g.setColor(new Color(63, 63, 63));
                g.fillRect(x+AREA_RANGE, AREA_RANGE-y, 1, 1);
            }
        }

        File outputfile = new File("/home/brandon/Exp.png");
        try {
            ImageIO.write(display, "png", outputfile);
        } catch (IOException e) {e.printStackTrace();}
    }

    @Override
    public void paintComponent(Graphics rg)
    {
        rg.drawImage(display, 0, 0, chart);
    }

    public double Clamp(double min, double val, double max)
    {
        if (val < min) return min;
        if (val > max) return max;
        return val;
    }
    /*
    public int Clamp(int min, int val, int max)
    {
        if (val < min) return min;
        if (val > max) return max;
        return val;
    }*/
}