Tile Color Matching Using Simple Universal Cycles

Anna Virágvölgyi
Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (2010)
Pages 495–496 Short Papers


In a square tiling, one can mark squares using edge-colored matching rules. I describe a set of matching rules based on universal cycles. These arise when one studies arrangements of different letters from a small alphabet into a single sequence in which all possible permutation of a given length can be found. The results are interesting visually. They may have applications in creating parquet or other two dimensional tiling patterns.