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Fractal dimensions and homeomorphic conjugacies
Journal of Statistical Physics, 1988no ...
Arneodo, A., Holschneider, M.
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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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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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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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THE FRACTAL DIMENSION OF TOKYO'S STREETS
Fractals, 2000The following paper presents the results obtained during the analyses of the street structure of Tokyo, focusing on six districts: Shinjuku, Shibuya, Ikebukuro, Ueno, Nakano and Aoto. The length-area relation in the chosen zones shows the presence of the analogue of a fractal dimension.
Rodin, Vladimir, Rodina, Elena
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Fractal dimension and fractal growth of urbanized areas
International Journal of Geographical Information Science, 2002Based on a box-accounting fractal dimension algorithm (BCFD) and a unique procedure of data processing, this paper computes planar fractal dimensions of 20 large US cities along with their surrounding urbanized areas. The results show that the value range of planar urban fractal dimension (D) is 1< D
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1996
Each stage of the generation process for a fractal curve adds more length to the curve. A fractal curve generated through an infinite number of steps will have infinite length. It was demonstrated in Chapter 2 that the length of different fractal curves grows from one generation stage to the next at different rates.
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Each stage of the generation process for a fractal curve adds more length to the curve. A fractal curve generated through an infinite number of steps will have infinite length. It was demonstrated in Chapter 2 that the length of different fractal curves grows from one generation stage to the next at different rates.
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1988
How long is the coast of Norway? Take a look at figure 2.1. On the scale of the map the deep fjords on the western coast show up clearly. The details encountered moving northeast along the coast from the southern tip are more difficult to resolve, but I can assure you that the maps I use when sailing in that area show structures quite similar to those ...
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How long is the coast of Norway? Take a look at figure 2.1. On the scale of the map the deep fjords on the western coast show up clearly. The details encountered moving northeast along the coast from the southern tip are more difficult to resolve, but I can assure you that the maps I use when sailing in that area show structures quite similar to those ...
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