How long is the chaos game?. Issue 6 (20th September 2021) - Morris, Ian D.; Jurga, Natalia
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.