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Estimation of fractal dimension of random fields on the basis of variance analysis of increments |
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| Authors: | S M Prigarin K Hahn G Winkler |
| Institution: | 1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia 2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia 3. Institute of Biomathematics and Biometry, Helmholtz Zentrum Muenchen, Ingolst?dter Landstra?e 1, Neuherberg, 85764, Germany |
| Abstract: | This paper deals with estimation of fractal dimension of realizations of random fields. Numerical methods are based on analysis of variance of increments. It is proposed to study fractal properties with the use of a specific characteristic of randomfields called a “variational dimension.” For a class of Gaussian fields with homogeneous increments the variational dimension converges to the Hausdorff dimension. Several examples are presented to illustrate that the concept of variational dimension can be used to construct effective computational methods. |
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