Local Rules for Computable Planar Tilings
Formal Languages and Automata Theory
2012-09-04 v1 Computational Complexity
Discrete Mathematics
Combinatorics
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.
Cite
@article{arxiv.1208.2759,
title = {Local Rules for Computable Planar Tilings},
author = {Thomas Fernique and Mathieu Sablik},
journal= {arXiv preprint arXiv:1208.2759},
year = {2012}
}
Comments
In Proceedings AUTOMATA&JAC 2012, arXiv:1208.2498