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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 selfsimilar fractal satisfying the open set condition.
Original language  English 

Pages (fromto)  17491765 
Number of pages  17 
Journal  Bulletin of the London Mathematical Society 
Volume  53 
Issue number  6 
Early online date  20 Sept 2021 
DOIs  
Publication status  Published  Dec 2021 
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Dive into the research topics of 'How long is the chaos game?'. Together they form a unique fingerprint.Projects
 1 Finished

Fourier analytic techniques: Fourier analytic techniques in geometry and analysis
Fraser, J. (PI) & Falconer, K. J. (CoI)
1/02/18 → 11/06/21
Project: Standard