The development of multimedia has often showcased its achievements, in resolution and computing power, by displaying fractal pictures. These pictures of strange attractors and Julia sets have been emblematic of the beauty and depth of mathematics. This mini-symposium will demonstrate, however, that fractals are more than pretty pictures; the underlying mathematics leads to a broad collection of useful mathematical tools, common themes, new ways of looking at and thinking about existing algorithms, and practical applications. The focus will be on the main ideas of fractal mathematics as applied to multimedia, and science, and how they may develop in the future.
Fractal mathematics 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. This mathematics consists of some basic tools and theorems, such as IFS theory and Hutchinson's theorem; it is centered in real analysis, geometry, measure theory, dynamical systems, and stochastic 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.
Topics addressed at the mini-symposium will include multimedia video algorithms, lossless fractal compression, resolution enhancement, fractal transform image compression, fractal image recognition, segmentation, space-filling curves, fractal graphics, and fractals in education. The meeting will involve mathematicians, computer scientists, engineers and industrial researchers who are interested in the application of fractal methods. The philosophical basis for the symposium is the set of those intuitions and insights that a fractal perspective brings, and the mathematics that sustains those realizations. It is intended that the various speakers will say what their intuitions are, how they look mathematically, and how they are applied in his or her topic. The conference would try to identify areas where the fractal viewpoint has potential to increase understanding and lead to new algorithms.