Two-color Fractal Tilings

Robert W. Fathauer
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 199–206 Regular papers


A variety of two-color fractal tilings (f-tilings) are described, in which no two adjacent tiles have the same color. Two-colorable examples from f-tilings that have been described previously are identified, and two techniques are used for converting f-tilings that are not two-colorable into new f-tilings that can be so colored. In the first of these, tiles are combined in order to change the valence of vertices to all be even, ensuring two-colorability. This technique is applicable to a limited number of f-tilings and can result in prototiles with an infinite number of edges and corners. In the second technique, tiles are divided into two or more smaller tiles such that all vertices of the new f-tiling have even valence.