On the practice of estimating fractal dimension |
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Authors: | James R Carr and William B Benzer |
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Institution: | (1) Department of Geological Sciences, University of Nevada, Mail Stop 168, 89557-0138 Reno, Nevada;(2) 1400 140th Avenue, NE, 98005 Bellevue, Washington |
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Abstract: | Coastlines epitomize deterministic fractals and fractal (Hausdorff-Besicovitch) dimensions; a divider compass] method can be used to calculate fractal dimensions for these features. Noise models are used to develop another notion of fractals, a stochastic one. Spectral and variogram methods are used to estimate fractal dimensions for stochastic fractals. When estimating fractal dimension, the objective of the analysis must be consistent with the method chosen for fractal dimension calculation. Spectal and variogram methods yield fractal dimensions which indicate the similarity of the feature under study to noise (e.g., Brownian noise). A divider measurement method yields a fractal dimension which is a measure of complexity of shape. |
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Keywords: | fractals fractal dimension Hausdorff-Besicovitch dimension power spectra divider method variograms |
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