From Checkerboard to Cloverfield: Using Wang Tiles in Seamless Non-Periodic Patterns

Tuomas Nurmi
Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture (2016)
Pages 159–166 Regular Papers


This article discusses Wang tiles from an artistic point of view. Mathematically Wang tiles are unit squares with colored edges and a local rule saying that two edges may only be adjacent, if they have the same color. We will present some known methods to use and abuse this concept, ultimately to force aperiodic tilings of arbitrary size, optionally containing irregular tiles and continuity at the tile corners. This paper also introduces a previously unpublished aperiodic set of 30 Wang tiles with colored corners. This is the smallest such set known today.