Recap of Julia Sets

We've been studying the iteration of polynomial functions mapping the complex plane to itself; i.e. f:C→C.

We've focused mostly on functions of the form (z) = + c.

When we iterate this function, the complex plane C breaks up into two regions:
   a stable set, where points are attracted to a periodic orbit or ∞  and
   an unstable set, called the Julia set where the dynamics are very complex.

We have two algorithms to vizualize this:
   The escape time algorithm  and
   The inverse iteration algorithm

The escape time algorithm

The inverse iteration algorithm

Created by Mathematica  (October 25, 2005)