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Fractal Dimension of Color Fractal Images
IEEE Transactions on Image Processing, 2011Fractal dimension is a very useful metric for the analysis of the images with self-similar content, such as textures. For its computation there exist several approaches, the probabilistic algorithm being accepted as the most elegant approach. However, all the existing methods are defined for 1-D signals or binary images, with extension to grayscale ...
Mihai Ivanovici, Noël Richard
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Physical Review Letters, 1986
At a critical point the golden-mean Kolmogorov-Arnol'd-Moser trajectory of Chirikov's standard map breaks up into a fractal orbit called a cantorus. The transition describes a pinning of the incommensurate phase of the Frenkel-Kontorowa model. We find that the fractal dimension of the cantorus is D-italic = 0 and that the transition from the Kolmogorov-
, Li, , Bak
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At a critical point the golden-mean Kolmogorov-Arnol'd-Moser trajectory of Chirikov's standard map breaks up into a fractal orbit called a cantorus. The transition describes a pinning of the incommensurate phase of the Frenkel-Kontorowa model. We find that the fractal dimension of the cantorus is D-italic = 0 and that the transition from the Kolmogorov-
, Li, , Bak
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APPROXIMATION WITH FRACTAL FUNCTIONS BY FRACTAL DIMENSION
Fractals, 2022On the basis of previous studies, we explore the approximation of continuous functions with fractal structure. We first give the calculation of fractal dimension of the linear combination of continuous functions with different Hausdorff dimension. Fractal dimension estimation of the linear combination of continuous functions with the same Hausdorff ...
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Fractal Dimensions in Dynamics
2006This is an invited article for the Encyclopedia of Mathematical Physics, published by Elsevier in Oxford in 2006. We describe some basic methods of fractal analysis in dynamics. A special emphasis is on the computation of Hausdorff and box dimensions.
Županović, Vesna, Žubrinić, Darko
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Fractal dimensions and homeomorphic conjugacies
Journal of Statistical Physics, 1988no ...
Arneodo, A., Holschneider, M.
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Mathematical Logic Quarterly, 2004
AbstractClassical fractal dimensions (Hausdorff dimension and packing dimension) have recently been effectivized by (i) characterizing them in terms of real‐valued functions called gales, and (ii) imposing computability and complexity constraints on these gales.
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AbstractClassical fractal dimensions (Hausdorff dimension and packing dimension) have recently been effectivized by (i) characterizing them in terms of real‐valued functions called gales, and (ii) imposing computability and complexity constraints on these gales.
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INFORMATION VOLUME FRACTAL DIMENSION
Fractals, 2021There has been immense interest in uncertainty measurement because most real-world problems are accompanied by uncertain events. Therefore, Deng entropy has been proposed to measure the uncertainty in the probability theory and evidence theory. In this paper, we show that the uncertainty of the basic probability assignment (BPA) separated through the ...
QIUYA GAO, TAO WEN, YONG DENG
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Self-Affine Fractals and Fractal Dimension
Physica Scripta, 1985Evaluating a fractal curve's approximate length by walking a compass defines a compass exponent. Long ago, I showed that for a self-similar curve (e.g., a model of coastline), the compass exponent coincides with all the other forms of the fractal dimension, e.g., the similarity, box or mass dimensions. Now walk a compass along a self-affine curve, such
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A Unified Approach to Fractal Dimensions
International Journal of Cognitive Informatics and Natural Intelligence, 2005Many scientific chapters treat the diversity of fractal dimensions as mere variations on either the same theme or a single definition. There is a need for a unified approach to fractal dimensions for there are fundamental differences between their definitions.
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2022
Abstract We generalize integral to fractal dimensions: in mathematics, structures are studied which lead to dimensions between the integral values observed in conventional geometry. A standard example is the coastline of Britain, whose length increases with the use of ever finer scales.
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Abstract We generalize integral to fractal dimensions: in mathematics, structures are studied which lead to dimensions between the integral values observed in conventional geometry. A standard example is the coastline of Britain, whose length increases with the use of ever finer scales.
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