A little foretaste
As we have seen, for two iterated rotating contractions, arbitrary objects will get drawn towards a limit set. The book Indra's Pearls deals with the generation of limit sets of different transformation groups at great length. This results in a rather computationally intensive procedure which will yield very exact images of high quality. For the interactive material in this tutorial, we have to sacrifice perfect rendering for the sake of "real-time interactivity". Luckily there is a trick which allows a close approximation of the real limit set with little computational effort: randomly generated iterated function systems (abbreviated IFS). While this sounds scary at first, the underlying principle is pretty easy and will be explained in the following. Before that we want to give a little foretaste and have a closer look at the limit set from the previous example. The following applet uses an IFS to calculate this limit set. We'll part with Dr. Stickler for a while -- in the following pictures he'd be so small that you couldn't discern him anyway. Instead we'll start with a single point, and iterate that.Download file:
Contents
An IFS plant
