Fractal dimension for fractal structures: A Hausdorff approach

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• 作者：M. Ferná ; ndez-Martí ; nez ; ¹ ; ^{fmm124@ual.es} ; M.A. Sá ; nchez-Granero² ; ^{misanche@ual.es}
• 关键词：primary ; 28A80 ; secondary ; 37F35 ; 54E35
• 刊名：Topology and its Applications
• 出版年：2012
• 期刊代码：60_01668641
• 类别：mt
• 出版时间：15 April, 2012
• 卷：159
• 期：7
• 页码：1825-1837
• 文件大小：249 K

摘要

This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a suitable discretization of the Hausdorff theory of fractal dimension. We also find some connections between our definition and the classical ones and also with fractal dimensions I & II (see M.A. S谩nchez-Granero and M. Fern谩ndez-Mart铆nez (2010) ). Therefore, we generalize them and obtain an easy method in order to calculate the fractal dimension of strict self-similar sets which are not required to verify the open set condition.