Hyperbolic Truchet Tilings

Douglas Dunham
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 311–318 Regular Papers


About 300 years ago Sébastien Truchet systematically studied patterns that could be formed from square tiles that were divided by a diagonal into a white triangle and a black triangle. Other pattern creators have been inspired by him to make Truchet-like tilings composed of circular arcs and other motifs. These tilings are all based on Euclidean tessellations, usually the tiling by squares. In this paper we extend the concept of a Truchet tiling to the hyperbolic plane and show some sample patterns.