Bridges 2012 Regular Paper
Two-color Fractal Tilings
(Proceedings pages 199–206)
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.