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Mathematical Background

In: Fractal Image Compression

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  • Y. Fisher

Abstract

Hutchinson [36] introduced the theory of iterated function systems (a term coined by M. Barnsley) to model collections of contractive transformations in a metric space as dynamical systems. His idea was to use the Contractive Mapping Fixed-Point Theorem to show the existence and uniqueness of fractal sets that arise as fixed points of such systems. It was Barnsley’s observation, however, that led to the idea of using iterated function systems (IFS’s) to encode images. He noted that many fractals that can be very compactly specified by iterated function systems have a “natural” appearance. Given an IFS, it is easy to generate the fractal that it defines, but Barnsley posed the opposite question: given an image, is it possible to find an IFS that defines it?

Suggested Citation

  • Y. Fisher, 1995. "Mathematical Background," Springer Books, in: Yuval Fisher (ed.), Fractal Image Compression, chapter 0, pages 25-53, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2472-3_2
    DOI: 10.1007/978-1-4612-2472-3_2
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