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Showing 1 to 10 of 10 for “"iterated function systems"”.
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Examples and Applications of Infinite Iterated Function Systems
… of this work is the study of infinite conformal iterated function systems. More specifically, we investigate some properties of a limit set J associated to such system, its Hausdorff and packing measure and Hausdorff dimension. We provide necessary and sufficient conditions for such systems to be …
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Dimensions of Self-Similar Fractals
… fractals that are the invariant sets of iterated function systems. We start with the Contraction Mapping Theorem, which will give us a constructive method in which to find fractals using iterated function systems. We then define the Hausdorff metric in order to use the Contraction Mapping …
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Completely Invariant Julia Sets of Rational Semigroups
We also develop some of the theory of Iterated Function Systems that seems to have particular importance to the study of rational semigroups.
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One-Dimensional Fractal Wave Equations
… are defined by fractal measures generated by iterated function systems with overlaps, such as the well-known infinite Bernoulli convolution associated with golden ratio and the 3-fold convolution of the Cantor measure. The iterated function systems defining these measures do not satisfy the …
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A genetic algorithm applied to the fractal inverse problem
The theory of iterated function systems (IFS) allows one to construct a fractal which depends on a finite number of parameters. The associated inverse problem, finding a set of parameters which reconstructs a given fractal, is much more difficult. This paper explores the possibility of solving the …
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The noncommutative geometry of ultrametric cantor sets
… are then presented: attractors of self-similar iterated function systems, attractors of cookie cutter systems, and the transversal of an aperiodic, repetitive Delone set of finite type. In particular, the example of the transversal of the Fibonacci tiling is studied.
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Quantization Dimension for Probability Definitions
… in certain cases the quantization dimension function D(r)=Dr is a transform of the temperature function b(q), which is already known to be the Legendre transform of the multifractal spectrum f(a). Hence, these ideas are all closely related and it would be expected that progress in one area …
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Dynamics of Iterated Functions Systems: Hausdorff Dimension and Related Topics
… Hausdorff dimension of fractal sets generated by iterated function systems (IFS). Hutchinson studied IFS and obtained a useful formula to compute the Hausdorff dimension of fractals generated by a finite family of disjoint similar IFS, where by disjoint we mean the IFS satisfies the open set …
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Applications of fractals to image data compression
… the lookup process in vector quantisation. Iterated function systems are compared with vector quantisers and the computational complexity or iterated function system encoding is also reduced by using the efficient matching algcnithms identified for vector quantisers.
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Self Similar Optical Fiber
… obtained by following the formula for generating iterated function systems (IFS) in Fractal Theory. The resulted SSF can be viewed as a true fractal object in optical fibers. In addition, the method of fabricating SSF makes it possible to generate desired structures exponentially in numbers, …