Rep-tiling Euclidean space
type: Item
instance of: scholarly article
title: Rep-tiling Euclidean space
zbMATH Open document ID: 0832.52005
DOI: 10.1007/BF01831118
author: Andrew Vince
published in: Aequationes Mathematicae
publication date: 1995-09-10T00:00:00Z
full work available at URL: https://eudml.org/doc/137625
review text: This is an introduction (for non-specialists) to some aspects of self- replicating (or self-similar) tilings. The author concentrates on the connection between lattice tilings and radix systems (digit sets). In particular, he discusses whether, in a given system, every lattice point has a representation, and whether its representation is unique. But since, moreover, related topics are discussed briefly (with references) the article is also a good survey of recent progress in the subject (in a more general sense). (Remark: There is a slight inconsistency concerning Figure 1. Though all three tilings shown are called reptilings, both in the caption and in the text, only the first meets the definition as given, since the other two contain tiles which are not translates of each other).
Mathematics Subject Classification ID: 52C20
Mathematics Subject Classification ID: 52C22
Mathematics Subject Classification ID: 11A63
Mathematics Subject Classification ID: 52-02
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 794228
zbMATH Keywords: radix systems
zbMATH Keywords: digit expansions
zbMATH Keywords: reptiles
zbMATH Keywords: self-similarity
zbMATH Keywords: self- replicating
zbMATH Keywords: lattice tilings
zbMATH Keywords: survey
MaRDI profile type: Publication
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OpenAlex ID: W4250037278
description: scientific article; zbMATH DE number 794228