A framework for the construction of self-replicating tilings
type: Item
instance of: scholarly article
title: A framework for the construction of self-replicating tilings
zbMATH Open document ID: 1186.28007
author: María del Carmen Moure
published in: Discrete \& Computational Geometry
publication date: 2009-12-14T00:00:00Z
review text: A lattice tiling of \({\mathbb R}^2\) is a self-replicating tiling if all tiles are translates of each other by elements of the lattice and there is an expanding linear map of the plane that maps each tile to a union of other tiles. \textit{F. M. Dekking} [J. Comb. Theory, Ser. A 32, 315--320 (1982; Zbl 0492.05019)] gave a method to compute the boundaries of self-replicating tilings as a `recurrent set' on a free group of a finite alphabet. The author generalizes Dekking's construction to deal with multi-tiles and generations by both translations and rotations. He presents examples including self-replicating tiles for crystallographic tilings and aperiodic tilings.
reviewed by: Takahisa Miyata
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 52C23
zbMATH DE Number: 5646271
zbMATH Keywords: self-replicating tile
zbMATH Keywords: multi-tile
zbMATH Keywords: recurrent set
zbMATH Keywords: alphabet
zbMATH Keywords: rotation
MaRDI profile type: Publication
full work available at URL: s00454-009-9219-6
OpenAlex ID: W2121599681
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DOI: 10.1007/S00454-009-9219-6
description: scientific article; zbMATH DE number 5646271