, Volume 9, Issue 2, pp 353-369

Deterministic Aperiodic Tile Sets

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Abstract.

Wang tiles are square tiles with colored edges. We construct an aperiodic set of Wang tiles that is strongly deterministic in the sense that any two adjacent edges of a tile determine the tile uniquely. Consequently, the tiling group of this set is not hyperbolic and it acts discretely and co-compactly on a CAT(0) space.

Submitted: February 1998, revised: October 1998.