Theoretical Computer Science
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Tilings: recursivity and regularity
Theoretical Computer Science
Fixed Point and Aperiodic Tilings
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
An Almost Totally Universal Tile Set
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A topological study of tilings
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
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Wang tiles are unit-size squares with coloured edges. In this paper, we approach one aspect of the study of tiling 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 (pronounced ayin) that almost always simulates any tile set. By way of Banach–Mazur games on tilings topological spaces, we prove that the set of -tilings that do not satisfy the universality condition is meagre in the set of -tilings.