2010/07/22 by M.A. Sánchez-Granero, Sánchez-Granero, M. A., M. Fernández–Martínez +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #28A80 (Primary) #37F35 (Secondary) #54E35 #Chaotic Dynamics (nlin.CD) #Complex Systems and Time Series Analysis #FOS: Physical sciences #Mathematical Dynamics and Fractals #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1007.3960
openalex publication_date 2010/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 http://arxiv.org/submit/0080421/pdf). 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.