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 -dense subset of a given self-similar fractal satisfying the open set condition.
Citation
Morris , I D & Jurga , N 2021 , ' How long is the chaos game? ' , Bulletin of the London Mathematical Society , vol. 53 , no. 6 , pp. 1749-1765 . https://doi.org/10.1112/blms.12539
Publication
Bulletin of the London Mathematical Society
Status
Peer reviewed
ISSN
0024-6093Type
Journal article
Description
Funding: Leverhulme Trust (Grant Number(s): RPG-2016-194), Engineering and Physical Sciences Research Council (Grant Number(s): EP/R015104/1).Collections
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