First generation fractal technology, based on Barnsley-Jaquin style algorithms, provided popular software for digital image compression in the early 1990's, for example it was used in Microsoft Encarta, but was overtaken by standardized JPEG with the arrival of the Internet. Current good wavelet-based codecs perform better than fractal codecs: they are faster and provide less image degradation, for images of a few million pixels at compression ratios ranging f rom three-to-one to fifty-to-one. However, aided by the low cost of computation, increasing availability of high quality digital images and imaging tools, continued mathematical developments, and significant levels of ongoing research, it is expected that fractal imaging in general, and fractal image compression in particular, will make substantial advances and lead to significant practical applications over the next decade.

Specific areas of interest include theory of iterated function systems (IFS), IFS with place-dependent probabilities, local IFS, fractal image compression, fractal graphics and synthetic fractal imagery, fractal image recognition, educational concepts arising from fractals, fractal-wavelet hybrids, fractal image zooming and resolution enhancement, lossless fractal compression, fractal image segmentation, and space-filling curves.

Fractal mathematics is 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 imaging 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 serves as inspiration for algorithms that try to create pictures and textures in new ways.

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