Repeating Fractal Patterns with 4-Fold Symmetry

Douglas Dunham and John Shier
Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture (2016)
Pages 523–524


Previously we described 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 this algorithm to fill a fundamental region for the “wallpaper” group p4, then we tile the plane with copies of that region. This produces artistic patterns which have a pleasing combination of local randomness and global symmetry.