How long is the chaos game?
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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 -dense subset of a given self-similar fractal satisfying the open set condition.
Morris , I D & Jurga , N 2021 , ' How long is the chaos game? ' , Bulletin of the London Mathematical Society , vol. Early View . https://doi.org/10.1112/blms.12539
Bulletin of the London Mathematical Society
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DescriptionFunding: Leverhulme Trust (Grant Number(s): RPG-2016-194), Engineering and Physical Sciences Research Council (Grant Number(s): EP/R015104/1).
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