Journal
COMPUTERS & GEOSCIENCES
Volume 31, Issue 10, Pages 1260-1269Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.cageo.2005.03.016
Keywords
fractal dimension estimator; fractal Brownian motion; surface generation algorithms
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Fractal geometry has been actively researched in a variety of disciplines. The essential concept of fractal analysis is fractal dimension. It is easy to compute the fractal dimension of truly self-similar objects. Difficulties arise, however, when we try to compute the fractal dimension of surfaces that are not strictly self-similar. A number of fractal surface dimension estimators have been developed. However, different estimators lead to different results. In this paper, we compared five fractal surface dimension estimators (triangular prism, isarithm, variogram, probability, and variation) using surfaces generated from three surface generation algorithms (shear displacement, Fourier filtering, and midpoint displacement). We found that in terms of the standard deviations and the root mean square errors, the triangular prism and isarithm estimators perform the best among the five methods studied. (C) 2005 Elsevier Ltd. All rights reserved.
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