How long is the chaos game?

Ian D. Morris*, Natalia Jurga*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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.
Original languageEnglish
Pages (from-to)1749-1765
Number of pages17
JournalBulletin of the London Mathematical Society
Volume53
Issue number6
Early online date20 Sept 2021
DOIs
Publication statusPublished - Dec 2021

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