This paper finds aperiodic hat tiling in an iterated function system, suggesting innovative modeling techniques.
This paper describes the celebrated aperiodic hat tiling by Smith et al. [Comb. Theory 8 (2024), 6] as generated by an overlapping iterated function system. We briefly introduce and study infinite sequences of iterated function systems that converge uniformly in each component, and use this theory to model the hat tiling's associated imperfect substitution system.
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Corey de Wit (2025) studied this question.
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