How long is the chaos game?. Issue 6 (20th September 2021)

• Record Type: Journal Article
• Authors: Morris, Ian D.; Jurga, Natalia
• Is Part Of: Bulletin of the London Mathematical Society. Volume 53:Issue 6(2021)
• Page Start: 1749
• Page End: 1765
• Publication Date: 2021-09-20
• Subjects: 28A80 (primary) -- 00A08 -- 60J10 (secondary); Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12539
• Languages: English
• ISSNs: 0024-6093

Abstract

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.