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Showing 1 to 7 of 7 for “"Iterated function system"”.
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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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3D architecture form synthesizer
… with the theory of Shape Grammar, a rule system that can be used to generate a large number of varied ~nd complex designs using only a small number of simple rules, computers can now have imagination. The problem is addressed here mainly in the domain of architecture. By formulating Shape …
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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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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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Information theory of random trees induced by stochastic grammars.
… described via a continuous non-constant periodic function P#11; → [0,∞), having period one, satisfying the property that H(Tn)/n = P#11;(log#11; n) for every n. The graph of P#11; is seen as a fractal and its fractal properties along with its fractal dimension are investigated. We develop a direct …
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On the Fourier decay and the dimension of self-similar measures
… transform of self-similar measures on $\R$. An iterated function system (IFS) on $\R$ is a collection of maps $f_1, \dots, f_r$ with $f_i(x)=\lambda_i x+\tau_i$, where $|\lambda_i|<1$ and $\lambda_i, \tau_i \in \R$. The self-similar measure $\mu$ associated to an IFS and to probability weights …
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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 …