Fractal Dimension for Fractal Structures: A Hausdorff Approach
Chaotic Dynamics
2010-07-23 v1
Abstract
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.
Cite
@article{arxiv.1007.3960,
title = {Fractal Dimension for Fractal Structures: A Hausdorff Approach},
author = {M. A. Sánchez-Granero and Manuel Fernández-Martínez},
journal= {arXiv preprint arXiv:1007.3960},
year = {2010}
}