Fractals and related mathematical models of chaotic phenomena have become active areas in research and applications in many diverse fields. These include weather forecasting, structural analysis, mapping, entertainment, biology, and many others. Aspects of these fields appear to be a significant part of an emerging inter-disciplinary science of complexity and complex systems in which significant understanding can be attained through the analysis of "simple" nonlinear interactions of large numbers of primitive simple objects. The uses of these models in the rapidly developing field of image computing (i.e., the digital computing aspects of the image sciences: image, analysis, communications, and synthesis) are leading to many innovations. This paper describes a range of activities illustrating significant new developments and a trend toward unification in image computing using these techniques.