local rules for computable planar tilings

Clicks: 107
ID: 232573
2012
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Abstract
Aperiodic tilings are non-periodic tilings characterized by local constraints. They play a key role in the proof of the undecidability of the domino problem (1964) and naturally model quasicrystals (discovered in 1982). A central question is to characterize, among a class of non-periodic tilings, the aperiodic ones. In this paper, we answer this question for the well-studied class of non-periodic tilings obtained by digitizing irrational vector spaces. Namely, we prove that such tilings are aperiodic if and only if the digitized vector spaces are computable.
Reference Key
fernique2012electroniclocal Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Thomas Fernique;Mathieu Sablik
Journal ama journal of ethics
Year 2012
DOI
10.4204/EPTCS.90.11
URL
http://arxiv.org/pdf/1208.2759v1
Keywords
computer science mathematicselectronic computers

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