# Iterated Function System

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## Iterated Function System

(graphics)
(IFS) A class of fractals that yield natural-looking forms like ferns or snowflakes. Iterated Function Systems use a very easy transformation that is done recursively.
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FORMAL SOLUTION TO THE INVERSE PROBLEM FOR ITERATED FUNCTION SYSTEMS WITH GREYSCALE MAPS
The method of iterated function systems with greyscale maps (IFSM), as formulated by Forte and Vrscay (1995), can be used to approximate a given element u of [L.
where M denotes the number of similitudes in the iterated function system and [?
where M denotes the number of similitudes in iterated function system.
with j = [+ or -] 1, can be seen as the non-linear maps of an Iterated Function System.
We give in this paper an expression for the moment matrix associated to a self-similar measure given by an Iterated Function Systems (IFS).
Hutchinson (1981) and, shortly thereafter, Barnsley and Demko (1985) and Barnsley (1989) showed how systems of contractive maps with associated probabilities, referred to as Iterated Function Systems (IFS), can be used to construct fractal, self-similar sets and measures supported on such sets.
Vrscay, "Solving the inverse problem for function and image approximation using iterated function systems," Dynamic of continuous, discrete and impulsive systems, vol.
In the last two decades Iterated Function Systems (IFS) have been established as intuitive and flexible fractal models in several areas of computer graphics (Turner et al.
Shuman (Grinnell College, Iowa) examine the moments of equilibrium measures for iterated function systems, and draw connections to operator theory.
For instance, in fractal image coding based on Iterated Function Systems (IFS) and their generalization, the self-similar attractor is defined in terms of a compact set and a positive measure supported on it.
Continuity of fixed points for attractors and invariant meaures for iterated function systems.

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