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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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CALCULATING FRACTAL DIMENSIONS
International Journal of Modern Physics C, 1992An algorithm for calculating fractal dimensions by the box counting method is described. Parallel implementation of the algorithm is presented.
S. GOSHEN, R. THIEBERGER
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Fractal Dimension Segmentation
1997Abstract This paper discusses the use of fractal geometry for segmenting digital images. A method texture segmentation is introduced which uses the Fractal Dimension to measure image texture. Using this approach, variations in texture across an image can be characterised in terms of variations in the fractal dimension.
J M Blackledge, B Foxon, S Mikhailov
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Cell surfaces and fractal dimensions
Journal of Microscopy, 1991SUMMARYThe perimeters of the surface membranes of some different cell types have been digitized from electron micrographs and the data analysed in order to discover whether the perimeter can be described by a fractal dimension, df. Micrographs obtained at various magnifications and subsequently enlarged by different amounts have been used. Values of df
K M, Keough +3 more
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Fractal dimension of semiconducting fractal sensors
2004 14th International Crimean Conference "Microwave and Telecommunication Technology" (IEEE Cat. No.04EX843), 2004Metal oxides are used for analysis of gas in the air in nano-dispersion semiconducting sensors developed in recent years. The fractal dimension of such a semiconductor sufficiently influences the character of the electrical conductivity and hence the sensitivity and operating speed of the sensor.
G. Danik +3 more
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Spectral dimension of fractal trees
Physical Review E, 1995We present in detail a calculation of the spectral dimension for a class of fractal trees called ${\mathrm{NT}}_{\mathit{D}}$ (i.e., ``nice trees of dimension D,'' defined as trees whose branches are splitting in r every time the distance from the origin is doubled, where r is an integer greater than 1) which presents nonanomalous diffusion.
BURIONI, Raffaella, CASSI, Davide
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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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Signal characterization using Fractal Dimension
TENCON 2008 - 2008 IEEE Region 10 Conference, 2008Fractal Dimensions (FD) are one of the popular measures used for characterizing signals. They have been used as complexity measures of signals in various fields including speech and biomedical applications. However, proper interpretation of such analyses has not been thoroughly addressed. In this paper, we study the effect of various signal properties
Raghavendra, BS, Dutt, Narayana D
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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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