An Almost Totally Universal Tile Set

Authors:
Grégory Lafitte;Michael Weiss
Affiliations:
Laboratoire d'Informatique Fondamentale de Marseille (LIF), CNRS --- Aix-Marseille Université, Marseille Cedex 13, France F-13453;Bicocca Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano, Milano, Italy 20126
Venue:
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Year:
2009

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Abstract

Wang tiles are unit size squares with colored edges. In this paper, we approach one aspect of the study of tilings computability: the quest for a universal tile set. Using a complex construction, based on Robinson's classical construction and its different modifications, we build a tile set μ (pronounced ayin ) which almost always simulates any tile set. By way of Banach-Mazur games on tilings topological spaces, we prove that the set of μ -tilings which do not satisfy the universality condition is meager in the set of μ -tilings.