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How to transform and filter images using iterated function systems. (English) Zbl 1246.37024

The authors describe the technique of fractal transformations (these being maps between pairs of attractors of iterated function systems (IFSs)) generalizing earlier work on fractal tops were introduced by M. Barnsley in 2005 and further developed by the same author and K. Igudesman. The main idea is this: given an IFS with a coding map and an attractor, a tops mapping can be defined using the “top” addresses of points on the attractor. Given two IFSs each with an attractor, a coding map, and a common code space, a mapping from one attractor to another can be constructed by composing the tops function for the first IFS with the coding map for the second system. In this way one obtains a fractal transformation.
Many of the results concerning fractal transformations in this paper are new. Some general properties and applications of fractal transformations are described.
This is a complex and consistent paper and it contains several important results in the IFS theory.

MSC:

37B10 Symbolic dynamics
28A80 Fractals
54H20 Topological dynamics (MSC2010)
68U10 Computing methodologies for image processing
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