Tilings from tops of overlapping iterated function systems

Michael F. Barnsley; Corey de Wit

doi:10.4171/jfg/192

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Tilings from tops of overlapping iterated function systems

Michael F. Barnsley
Australian National University, Canberra, Australia
Corey de Wit
Australian National University, Canberra, Australia
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Abstract

The top of the attractor of a hyperbolic iterated function system

{f_{i} : R^{n} \to R^{n} ∣ i = 1, 2, \dots, M}

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.

Cite this article

Michael F. Barnsley, Corey de Wit, Tilings from tops of overlapping iterated function systems. J. Fractal Geom. (2026), published online first

DOI 10.4171/JFG/192