Enumerations of Hyperbolic Truchet Tiles

Sébastien Truchet was a pioneer in applying combinatorics to the study of regular patterns. He enumerated the patterns that could be formed from square tiles that were divided by a diagonal into a black and a white triangle Following Truchet, others have created Truchet-like tilings composed of circular arcs and other motifs. These patterns are all based on Euclidean tessellations, usually the tiling by squares. In this paper we pose corresponding enumeration questions about hyperbolic Truchet tilings and show some sample patterns.