This program maps its drawing area into the region -4 <= x <= 4, -3 <= y <= 3. If you click on a point, the program iterates these equations and plots the points:
Xn+1 = Xn - h * Sin(Yn + Tan(3 * Yn))
Yn+1 = Yn - h * Sin(Xn + Tan(3 * Xn))
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, the program plots the series for every 10th pixel vertically and horizontally.
Experiment with the values in the text boxes to see what difference they make.
For details about how the code works, download the example program and take a look.