Fractal Wallpaper Patterns

Douglas Dunham and John Shier
Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)
Pages 183–190 Regular Papers


In the past we presented an algorithm that can fill a region with an infinite sequence of randomly placed and progressively smaller shapes, producing a fractal pattern. In this paper we extend that algorithm to fill rectangles and triangles that tile the plane, which yields wallpaper patterns that are locally fractal in nature. This produces artistic patterns which have a pleasing combination of global symmetry and local randomness. We show several sample patterns.