How long is the Chaos Game?
Abstract
In the 1988 textbook "Fractals Everywhere" M. 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 $\delta$dense subset of a given selfsimilar fractal satisfying the open set condition.
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2007.11517
 Bibcode:
 2020arXiv200711517J
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Metric Geometry