A Method for Numerical Estimation of Generalized Rényi Dimensions of Affine Recurrent Ifs Invariant Measures

Martyn, Tomasz

doi:10.1142/9789812702746_0006

Cited by 2 publications

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“…Therefore, the entropy of a fractal antenna can be calculated accordingly, in which the input data are essentially the complexity of the shape, as described in this article for the Sierpinski gasket antenna. The numerical estimation of the generalized fractal dimension D α (see [41]) is based both on an integration technique over the fractal measures and a triangulation method. It yields good results for the range α ≥ 0 in an efficient and robust manner.…”

Section: Discussionmentioning

confidence: 99%

“…It is easy to create an algorithm for its computation using Equation (25). This procedure consists of the classical algorithm for numerical estimating D α of affine RIFS-invariant measures; see [41,42]. The Rényi entropy will be computed through Equation (25), considering the logarithm of the cell size (see Figure 9 below).…”

Section: The Entropy Of a Fractal Antennamentioning

confidence: 99%

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Entropy and Fractal Antennas

Guariglia

2016

Entropy

171

103

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Section: Discussionmentioning

confidence: 99%

Section: The Entropy Of a Fractal Antennamentioning

confidence: 99%

Entropy and Fractal Antennas

Guariglia

2016

Entropy

171

103

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The Smallest Enclosing Disc of an Affine Ifs Fractal

Martyn

2009

Fractals

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We present a novel approach to approximate the smallest disc to enclose an affine IFS attractor at any accuracy. The approach is efficient and characterized by very low memory requirements. It is based on a concept of spanning points we introduce to describe the extent of an IFS attractor. We give the formal definition of these points and show how to construct them efficiently in practice. A proof that the smallest disc to enclose the spanning points includes the smallest enclosing disc of the IFS attractor is given. We also show that the former disc approximates the latter with an error depending on parameters relevant to the construction of the points. The main benefit of using the spanning points is that their number is usually small even for high approximation accuracies. Thus, we can apply with success one of the known, smallest enclosing disc algorithms to the spanning points. The enclosed experimental results obtained for popular IFS fractals confirm the theoretical assertions of the paper, by showing that our method performs well in practice.

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A Method for Numerical Estimation of Generalized Rényi Dimensions of Affine Recurrent Ifs Invariant Measures

Cited by 2 publications

References 0 publications

Entropy and Fractal Antennas

Entropy and Fractal Antennas

The Smallest Enclosing Disc of an Affine Ifs Fractal

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