Slopes of Tilings

Emmanuel Jeandel (1) , Pascal Vanier (1)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166

We study here slopes of periodicity of tilings. A tiling is of slope θ if it is periodic along direction θ but has no other direction of periodicity. We characterize in this paper the set of slopes we can achieve with tilings, and prove they coincide with recursively enumerable sets of rationals.

Keywords: tilings; formal languages; foundations of computing

Domains: Other [cs.OH]

Emmanuel Jeandel, Pascal Vanier. Slopes of Tilings. Journées Automates Cellulaires 2010, Dec 2010, Turku, Finland. pp.145-155. ⟨hal-00542000⟩