A Mobius transformation is a map from the complex plane to itself (or Riemann sphere if you prefer) of the form f(z) = (az+b)/(cz+d) where a,b,c, and d are nonzero (complex) constants such that ad-bc is nonzero. This applet shows the path of a grid of points as they spiral into or away from the fixed points of the mapping. By clicking in the applet window you can change the values of the constants to see other mappings.

Source code (it is not commented): Mobius Fixed Points. If you do take a look at the source, the two key parameters to play around with are ta and tb. Most of the interesting pictures happen when those values are around 2.

Built with Processing