| | # Dr Dan Rust
### ~ Random Substitutions, Entropy and Fractals ~
### Dan Rust is one of a small group of mathematicians who have very successfully defined and developed the idea of a random substitution over the last few years. As Dan explains, “Random substitutions give rise to tilings that possess long-range order but local disorder, and these two properties 'fight' with each other at all levels of the hierarchy of the tiling”. He made a commendable effort to start with the basics and systematically build by firmly founding the discussion in the concrete example of the Tribonacci and Twisted Tribonacci substitutions. With the word 'Fractals' in the talk title, some interesting visuals were expected and Dan did not disappoint; there was a marvellous series of images demonstrating how the Tribonacci substitution morphed into the Twisted Tribonacci substitution as the probability within the random substitution moved from 1 to 0. Aspects of the talk are to be found in Dan's 2024 paper with co-authors Philipp Gohlke, Andrew Mitchell and Tony Samuel; Rauzy Fractals of Random Substitutions.
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