INTRODUCTION TO IMA FRACTAL PROCEEDINGS MICHAEL F. BARNSLEY* This volume describes the status of fractal imaging research and looks to future directions. It is to be useful to researchers in the areas of fractal image compression, analysis, and synthesis, iterated function systems, and fractals in education. In particular it includes a vision for the future of these areas. It is intended to provide an efficient means by which researchers can look back over the last decade at what has been achieved, and look forward towards second-generation fractal imaging. The articles in themselves are not supposed to be detailed reviews or expositions, but to serve as signposts to the state-of-the art in their areas. What is important is what they mention and what tools and ideas are seen now to be relevant to the future. The contributors, a number of whom have been involved since the start, are active in fractal imaging, and provide a well-informed viewpoint on both the status and the future. Most were invited participants at a meeting on Fractals in Multimedia held at the IMA in January 2001. Some goals of the mini-symposium, shared with this volume, were to demonstrate that the fractal viewpoint leads to a broad collection of useful mathemat- ical tools, common themes, new ways of looking at and thinking about existing algorithms and applications in multimedia; and to consider future developments. The fractal viewpoint has developed out of the observation that in the real world and in the scientific measurement of it, there can occur patterns that repeat at different scales. It upholds the intuition that the mathe- matical world of geometry and the infinitely divisible Euclidean plane are relevant to the understanding of the physical world; and in particular that geometrical entities such as lines, ferns, and other fractal attractors are related to actual pictures. This viewpoint is captured in fractal mathe- matics, which consists of some basic tools and theorems, such as iterated function systems (IFS) theory and Hutchinson's theorem, and is centered in real analysis, geometry, measure theory, dynamical systems, and stochas- tic processes. Its application to multimedia lies principally in the attempt to bridge the divide between the discrete world of digital representation and the natural continuum world in which we seem to live. It has served as inspiration for algorithms that try to recreate sounds, pictures, motion video and textures, and to organize databases in computer environments. In the papers in this volume we outline ways in which this bridge, between intuition and reality, has been built, mainly in the area of imaging. We *Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3052, Australia. Currently at 335 Pennbrooke Trace, Duluth, GA 30097 (Mbarnsley@aol. com). 1 M. F. Barnsley et al. (eds.), Fractals in Multimedia © Springer-Verlag New York, Inc. 2002