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Published in:
2009 | OriginalPaper | Chapter
An Almost Totally Universal Tile Set
Authors : Grégory Lafitte, Michael Weiss
Published in: Theory and Applications of Models of Computation
Publisher: Springer Berlin Heidelberg
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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.