ITERATED FUNCTION SYSTEMS AS NEURAL NETWORKS

Iterated Function Systems (IFSs) provide a framework for encoding and generating a large class of fractals. Barnsley has demonstrated their use for image compression, with compression ratios of up to 10(4):1. The main limitation of such techniques is the large amount of computation that they require. In this paper we consider a relatively unknown class of methods for generating images using IFSs, and show how these can be formulated as neural networks with one neuron per image pixel. Such networks would be able to generate complex images extremely quickly, and are particularly suitable for real-time animation. While not a conventional application of artificial neural networks, this paper does give a very direct illustration of how a complex nonlinear problem can easily be transformed into a simple class of networks.