arXiv subjects
Publications and source records attributed to Corey de Wit.
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.
The top of the attractor $A$ of a hyperbolic iterated function system $\left\{ f_{i}:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}|i=1,2,\dots,M\right\} $ is defined and used to extend self-similar tilings to overlapping systems. The theory provides sequences of approximate supertiles that converge to tilings. Individual tiles in a tiling are limits of nested decreasing sequences of approximate tiles. Examples include systems of finite type, tilings related to aperiodic monotiles, and ones where there are infinitely many distinct but related prototiles.