The Art of Random Fractals

Douglas Dunham and John Shier
Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture (2014)
Pages 79–86 Regular Papers


We describe a mathematically based algorithm that can fill a spatial region with an infinite sequence of randomly placed and progressively smaller shapes, which may be transformed copies of one motif or several motifs. This flexible algorithm can be used to produce a variety of aesthetically pleasing fractal patterns, of which we show a number of examples.