Title: Draw a Pickover popcorn fractal in C#

This program maps an iterated function system in its drawing area onto the region -4 <= x <= 4, -3 <= y <= 3. If you click on a point, the program iterates these equations and plots the points:

X_n+1 = X_n - h * Sin(Y_n + Tan(3 * Y_n)) Y_n+1 = Y_n - h * Sin(X_n + Tan(3 * X_n))

Here X₀ and Y₀ are the coordinates of the point you clicked. You can enter values for the constant h and the number of iterations to perform in the text boxes.

If you click the Plot All button, the program plots the series for every dx-th pixel, where dx is taken from the dx text box. For example, if dx = 10 and h = 0.01, the program plots the series for every 10th pixel vertically and horizontally giving this result:

Experiment with the values in the text boxes to see what difference they make. In my next post, I'll add some color to the program.

The details about how the program works are fairly straightforward. Download the example program and take a look for more information.

Download the example to experiment with it and to see additional details.