Elsevier

Applied Mathematics Letters

Volume 25, Issue 2, February 2012, Pages 206-208
Applied Mathematics Letters

The chaos game revisited: Yet another, but a trivial proof of the algorithm’s correctness

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Abstract

The aim of this work is to explain why the most popular algorithm for approximating IFS fractals, the chaos game, works. Although there are a few proofs of the algorithm’s correctness in the relevant literature, the majority of them utilize notions and theorems of measure and ergodic theories. As a result, paradoxically, although the rules of the chaos game are very simple, the logic underlying the algorithm seems to be hard to comprehend for non-mathematicians. In contrast, the proof presented in this work uses only fundamentals of probability and can be understood by anyone interested in fractals.

Keywords

Fractal
Iterated function system
IFS attractor
Chaos game

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