Beautiful Math, Part 2: Aesthetic Patterns Based on Fractal Tilings

A fractal tiling (f-tiling) is a tiling whose boundary is fractal. This article presents two families of rare, infinitely many f-tilings. Each f-tiling is constructed by reducing tiles by a fixed scaling factor, using a single prototile, which is a segment of a regular polygon. The authors designed invariant mappings to automatically produce appealing seamless, colored patterns from such tilings.