"How long is the Chaos Game?"

Abstract

In the 1988 textbook Fractals Everywhere, Barnsley introduced an algorithm for generating fractals through a random procedure which he called the chaos game. Using ideas from the classical theory of covering times of Markov chains, we prove an asymptotic formula for the expected time taken by this procedure to generate a 𝛿 -dense subset of a given self-similar fractal satisfying the open set condition.