Work

Tilings from tops of overlapping iterated function systems

Year: 2026

Type: article

Abstract: The top of the attractor of a hyperbolic iterated function system \bigl\{f_{i}:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}| i=1,2,\ldots,M \bigr\} 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.

Source: Journal of Fractal Geometry Mathematics of Fractals and Related Topics

DOI: 10.4171/jfg/192

Authors: Michael F. Barnsley, Corey de Wit

Institution: Australian National University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4416541064

FWCI:

Cites:

Cited by:

Related to: