Fractal Images -- Mathematics With Silverlight Again

Hi all,
When I first seen fractal images I was really impressed and wanted a bit try for making one myself. I have made a simple application that will generate some kool images based on fractal algorithms. This program is not for describing fractals, this is just to make some pretty images totally by complex mathematics.

here is one image that uses (Z * Z * Z + C) / (Z * Z * Z - C) formula and C=0.45 here. (C and Z are complex numbers)



You can make lots of images using different equation and different values of C.


How the Images are created.....

The image is actually a collection of 1 x 1 pixel ellipse different color. These ellipses are placed in a 500 x 600 Canvas. fractal algorithm determines how to color the ellipses and that is the only magic.

Algorithm.....

int iteration = 0;
do
{
R = (Z * Z * Z + C) / (Z * Z * Z - C);
Z = R;
iteration++;
} while (iteration < 100 && (R.Real * R.Real + R.Imaginary * R.Imaginary) < 4);

For coloring the ellipse

Random r = new Random(iteration);
byte red = (byte)r.Next(255);
byte green = (byte)r.Next(255);
byte blue = (byte)r.Next(255);
Plot(x, y, Color.FromArgb(255, red, green, blue));

Though it is using random number for same iteration value the color will be same as iteration is been used as seed for the random number. This is the beauty of pseudo numbers.

Here you can download the complete source code.

You can see the application running here.

One caution:- The code involve too many computation and placing 300000 ellipses. So it takes about 20 seconds to complete and might hang your browser during this time.

Here and here you can see details about fractals and algorithms.

I have updated some of my applications and posts in last few days. I will complete it as soon as I can.