A primer on substitution tilings of the Euclidean plane

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dc.creatorFrank, Natalie Priebe
dc.date2007-05-08
dc.date.accessioned2026-07-07T08:00:03Z
dc.date.available2026-07-07T08:00:03Z
dc.descriptionThis paper is intended to provide an introduction to the theory of substitution tilings. For our purposes, tiling substitution rules are divided into two broad classes: geometric and combinatorial. Geometric substitution tilings include self-similar tilings such as the well-known Penrose tilings; for this class there is a substantial body of research in the literature. Combinatorial substitutions are just beginning to be examined, and some of what we present here is new. We give numerous examples, mention selected major results, discuss connections between the two classes of substitutions, include current research perspectives and questions, and provide an extensive bibliography. Although the author attempts to fairly represent the as a whole, the paper is not an exhaustive survey, and she apologizes for any important omissions.
dc.description26 pages, 39 figures
dc.identifierhttps://arxiv.org/abs/0705.1142
dc.identifierhttp://arxiv.org/abs/0705.1142
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128590
dc.subjectDynamical Systems
dc.subjectMathematical Physics
dc.subjectHistory and Overview
dc.subjectPrimary 52C23; Secondary 52C20; 37B50
dc.titleA primer on substitution tilings of the Euclidean plane
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