A small aperiodic set of Wang tiles
type: Item
instance of: scholarly article
title: A small aperiodic set of Wang tiles
zbMATH Open document ID: 0861.05017
DOI: 10.1016/0012-365X(95)00120-L
author: Jarkko Kari
published in: Discrete Mathematics
publication date: 1997-05-04T00:00:00Z
review text: A Wang tile is a unit square tile with colored edges. Consider tilings of the Euclidean plane by arbitrarily many copies from a given finite tile set \(T\) of Wang tiles translated to integer lattice points and such that contiguous edges have the same color. Such a tiling, determined by a function \(f:Z^2\to T\), is periodic if there exists \((a,b)\in Z^2\backslash\{(0,0)\}\) such that \(f(x,y)= f(x+a,y+b)\) for every \((x,y)\in Z^2\). A tile set \(T\) is called aperiodic if there exists a tiling, but there does not exist any periodic tiling. In 1966 \textit{R. Berger} [Mem. Am. Math. Soc. 66 (1966; Zbl 0199.30802)] constructed an aperiodic tile set consisting of over 20,000 Wang tiles. The number has since been reduced, including a set consisting of 16 Wang tiles due to R. Amman. In the paper under review, the number is further reduced to 14 Wang tiles.
reviewed by: Andrew Vince
Mathematics Subject Classification ID: 05B45
Mathematics Subject Classification ID: 52C20
zbMATH DE Number: 955162
zbMATH Keywords: Wang tile
zbMATH Keywords: integer lattice points
zbMATH Keywords: periodic tiling
zbMATH Keywords: aperiodic tile set
Wikidata QID: Q62045972
MaRDI profile type: Publication
cites work: The undecidability of the domino problem
cites work: Q3735714
DBLP publication ID: journals/dm/Kari96
description: scientific article; zbMATH DE number 955162