Truchet pattern | Truchet tile

In 1704, Sebastien Truchet considered all possible patterns formed by tilings of right triangles oriented at the four corners of a square. Truchet's tiles produce beautiful patterns when laid out on a grid, as illustrated by the 20×20 arrangement of random tiles illustrated above. A modification of Truchet's tiles leads to a single tile consisting of two circular arcs of radius equal to half the tile edge length centered at opposed corners. There are two possible orientations of this tile, and tiling the plane using tiles with random orientations gives visually interesting patterns. In fact, these tiles have been used in the construction of various games, including the "black path game" and "meander" .

b-cluster | s-cluster