In 1704, Sebastien Truchet considered all possible patterns formed by tilings of right triangles oriented at the four corners of a square (Wolfram 2002, p. 875).
Truchet's tiles produce beautiful patterns when laid out on a grid, as illustrated by the 
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 (Pickover 1989). 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" (Berlekamp et al. 1982, pp. 682-684).
The illustration above shows a 
Truchet tiling. For random orientations, the fraction
of closed circles is approximately 0.054 and the fraction of dumbbell shapes is approximately
0.0125 (Pickover 1989).
Artlandia, Inc. "Graphica 2 and Beyond:
Creating Artistic Images with Artlandia."