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arXiv:2007.11517math.DS

How long is the Chaos Game?

Natalia Jurga, Ian D. Morris

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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 $δ$-dense subset of a given self-similar fractal satisfying the open set condition.

arXiv comments
Journal reference
DOI
doi:10.1112/blms.12539
Subjects
math.DSDynamical Systems math.MGMetric Geometry

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  1. A stochastic method to generate the Sierpinski triangle 1 comment

    • This is fair - there are a decent number of details omitted here. However, a lot of the details are hidden inside the proof that an IFS has a unique fixed point. At least to me, this "proof" is nice because it converts a non-obvious procedure (taking midpoints) into a "standard"…

      arutarView on HNParent context

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