I was given an assignment to create a Mandelbrot Fractals Generator at my University – and this is basically what I did.
A short user manual:
- Chose resolution and Color or Black / White and press render to generate the image.
- The field labeled “extra” is the number of iterations. More iterations = more accurate picture (and slowed load of course).
- Press mouse and drag to zoom in. The more you zoom in, the more iterations you’ll need.
- You can save images from the File-menu, the will however be of crappy quality. (Note: I did not design the GUI, it was given to me as part of the assignment).
Example:
import java.awt.Color;
public class Generator {
private int pixelResolution = 1;
private int iterations;
private Color[] colorLevels = new Color[255];;
public Generator() {
for (int i = 0; i < 255; i++) {
colorLevels[i] = new Color(i, 0, i); // From black to pink.
}
}
public void render(MandelbrotGUI mGui) {
switch (mGui.getResolution()) {
case MandelbrotGUI.RESOLUTION_VERY_HIGH:
pixelResolution = 1;
break;
case MandelbrotGUI.RESOLUTION_HIGH:
pixelResolution = 3;
break;
case MandelbrotGUI.RESOLUTION_MEDIUM:
pixelResolution = 5;
break;
case MandelbrotGUI.RESOLUTION_LOW:
pixelResolution = 7;
break;
case MandelbrotGUI.RESOLUTION_VERY_LOW:
pixelResolution = 9;
break;
}
try {
iterations = Integer.parseInt(mGui.getExtraText());
} catch (NumberFormatException e) {
if (mGui.getMode() == MandelbrotGUI.MODE_COLOR) {
iterations = 50;
} else {
iterations = 200;
}
}
Color[][] picture = new Color[mGui.getHeight() / pixelResolution][mGui.getWidth() / pixelResolution];
Complex[][] c = mesh(mGui.getMinimumReal(), mGui.getMaximumReal(), mGui.getMinimumImag(), mGui.getMaximumImag(), mGui.getWidth(), mGui.getHeight());
for (int x = 0; x < mGui.getHeight() / pixelResolution; x++) {
for (int y = 0; y < mGui.getWidth() / pixelResolution; y++) {
int i = 0;
Complex almonds = new Complex(0.0, 0.0);
while (almonds.getAbs2() <= 4 && i < iterations) {
almonds.mul(almonds);
almonds.add(c[x][y]);
i++;
}
if (almonds.getAbs2() <= 4) {
if (mGui.getMode() == MandelbrotGUI.MODE_BW) {
picture[x][y] = Color.BLACK;
} else {
picture[x][y] = new Color(20, 20, 20);
}
} else {
if (mGui.getMode() == MandelbrotGUI.MODE_BW) {
picture[x][y] = Color.WHITE;
} else {
picture[x][y] = colorLevels[(int) Math.ceil((254 / (double) iterations) * i)];
}
}
}
}
mGui.putData(picture, pixelResolution, pixelResolution);
}
private Complex[][] mesh(double minRe, double maxRe, double minIm, double maxIm, int width, int height) {
double positionIm = (maxIm - minIm) / height;
double positionRe = (maxRe - minRe) / width;
Complex[][] c = new Complex[height / pixelResolution][width / pixelResolution];
double alignIm = 0.5 * positionIm * (pixelResolution + 1) - maxIm;
double alignRe = 0.5 * positionRe * (pixelResolution + 1) + minRe;
double posResIm = positionIm * pixelResolution;
double posResRe = positionRe * pixelResolution;
double[] complexX = new double[(width / pixelResolution)];
for (int y = 0; y < width / pixelResolution; y++) {
complexX[y] = posResRe * y + alignRe;
}
for (int a = 0; a < height / pixelResolution; a++) {
double complexY = posResIm * a + alignIm;
for (int b = 0; b < width / pixelResolution; b++) {
c[a][b] = new Complex(complexX[b], complexY);
}
}
return c;
}
}
Note that I did not write the GUI!