Since it was recognized that they could be used for encoding a large class of digitized color images, fractals have become the "golden child" of the computer graphics industry. The original encoding method is based on the identification of an image with the unique stationary distribution of an ergodic Markov chain. The probability structure of the chain is given in terms of an Iterated Function System (IFS) with probabilities, i.e., a finite collection of contractions on the plane and associated weights.

Peruggia takes this method one step further, analyzing a modified version of the widely used probabilistic algorithm generating IFS-encoding images. The modification employs a discrete approximation of the chain, and this book examines the theoretical and practical consequences brought about by the discretization procedure. In particular, Peruggia explores the connections and disparities of continuous and discrete IFSs and illustrates some rather surprising implications of his discretization method. The book also includes a discussion on how IFS techniques can be applied to produce animated motion pictures.