After notes on self-similarity exponent for fractal structures
After notes on self-similarity exponent for fractal structures
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DOI：
10.1515/phys-2017-0049
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发表时间：
2017-06
期刊：
影响因子：
1.9
通讯作者：
M. Fernández-Martínez;Manuel Caravaca Garratón
中科院分区：
文献类型：
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作者：
M. Fernández-Martínez;Manuel Caravaca Garratón
摘要以往的研究都强调了分形结构概念的适用性，该概念来源于不对称拓扑，可用于提出分形维数的广义定义。本文的目的是收集一些结果和方法，允许连接自相似指数和分形维数的广泛的随机过程。为了解决这个问题，我们将在样本曲线的图像集上使用诱导分形结构的概念。本文的主要结果表明，给定一个随机过程的样本函数在其图像上具有诱导分形结构，则该函数的自相似指数等于其分形维数的倒数。
Abstract Previous works have highlighted the suitability of the concept of fractal structure, which derives from asymmetric topology, to propound generalized definitions of fractal dimension. The aim of the present article is to collect some results and approaches allowing to connect the self-similarity index and the fractal dimension of a broad spectrum of random processes. To tackle with, we shall use the concept of induced fractal structure on the image set of a sample curve. The main result in this paper states that given a sample function of a random process endowed with the induced fractal structure on its image, it holds that the self-similarity index of that function equals the inverse of its fractal dimension.