Two infinite families of polyominoes that tile the plane by translation in two distinct ways

Blondin Massé, Alexandre; Brlek, Srecko; Garon, Ariane et Labbé, Sébastien (2011). « Two infinite families of polyominoes that tile the plane by translation in two distinct ways ». Theoretical Computer Science, 412(36), pp. 4778-4786.

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Résumé

It has been proved that, among the polyominoes that tile the plane by translation, the so-called squares tile the plane in at most two distinct ways. In this paper, we focus on double squares, that is, the polyominoes that tile the plane in exactly two distinct ways. Our approach is based on solving equations on words, which allows us to exhibit properties about their shape. Moreover, we describe two infinite families of double squares. The first one is directly linked to Christoffel words and may be interpreted as segments of thick straight lines. The second one stems from the Fibonacci sequence and reveals some fractal features.

Type:	Article de revue scientifique
Mots-clés ou Sujets:	Tessellation; Polyomino; Christoffel word; Fibonacci sequence
Unité d'appartenance:	Faculté des sciences > Département d'informatique
Déposé par:	Alexandre Blondin Massé
Date de dépôt:	09 mai 2016 14:32
Dernière modification:	30 mai 2016 14:43
Adresse URL :	http://archipel.uqam.ca/id/eprint/8428

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