An Almost Totally Universal Tile Set

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.