The Art of Iterated Function Systems with Expanding Functions

Philip Van Loocke
Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture (2009)
Pages 55–62 Regular Papers


Iterated function systems with contracting functions have been widely applied in contexts relating art and science. This paper explores iterated function systems which consist of expanding linear functions. An area in the plane is divided in parts which are defined implicitly by an inverse function technique. With each part, an expanding function is associated. A coloring technique is proposed which yields textures suggestive of sophisticated patterns of depth and light. It is briefly described how a rendering technique for recurrent origami can be obtained as a special case of this method.