Inverse Iteration Algorithms for Julia Sets

by Mark McClure  

Inverse iteration algorithms are extremely fast methods to generate images of Julia sets.  While they are fairly simple to understand and implement, a little thought can improve their performance dramatically.  In this article, we discuss several variations of the basic inverse iteration scheme.










Introduction

The Theory of Fatou and Julia

A Simple Deterministic Inverse Iteration Algorithm

Improving The Simple Deterministic Algorithm

The Mandelbrot Set

Generalizing the Deterministic Algorithm

A Stochastic Algorithm

References

About the Author


Mark McClure
Department of Mathematics
University of North Carolina at Asheville
Asheville, North Carolina 28804
mcmcclur@bulldog.unca.edu
http://www.unca.edu/~mcmcclur/


Converted by Mathematica      November 12, 1999