Unexpected Beauty Hidden in Radin-Conway's Pinwheel Tiling

Douglas G. Burkholder
Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)
Pages 383–386 Short Papers


In 1994, John Conway and Charles Radin created a non-periodic Pinwheel Tiling of the plane using only 1 by 2 right triangles. By selectively painting either every fifth triangle or two out of every five triangles, based only upon their location in the next larger triangle, one can discern 15 unexpected and distinctive patterns. Each of these patterns retains the non-periodic nature of the original tiling.