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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >An improved method to estimate the fractal dimension of physical fractals based on the Hausdorff definition
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An improved method to estimate the fractal dimension of physical fractals based on the Hausdorff definition

机译：一种基于Hausdorff定义的估计物理分形的分形维数的改进方法

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摘要

In this paper we present an algorithm to estimate the Hausdorff fractal dimension. The algorithm uses a recursive formula with a fast enough convergence. The accuracy of results is independent on the size, i.e., degree of definition of the fractal set. This fact is particularly useful when studying real physical fractals with a low definition, such as colloidal aggregates of small size. The different tests reveal no dependence of the results on the irregularities of the fractal. Thus, self-similarity or statistical similarity of the fractal set does not affect results. The proposed algorithm gives correct values for all the fractal dimension of the tested sets. Finally, the algorithm was used to evaluate the Henon attractor fractal dimension and was applied to an experimental system obtained from a two-dimensional aggregation of latex colloidal particles. (C) 2001 Elsevier Science B.V. All rights reserved. [References: 19]
机译：在本文中，我们提出了一种估计Hausdorff分形维数的算法。该算法使用具有足够快收敛性的递归公式。结果的准确性与大小即分形集的定义度无关。当研究低清晰度的真实物理分形（例如小尺寸的胶体聚集体）时，此事实特别有用。不同的测试表明，结果不依赖于分形的不规则性。因此，分形集的自相似性或统计相似性不会影响结果。所提出的算法为测试集的所有分形维数提供了正确的值。最后，将该算法用于评估Henon吸引子的分形维数，并将其应用于由胶乳胶体颗粒的二维聚集得到的实验系统。 （C）2001 Elsevier Science B.V.保留所有权利。 [参考：19]

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