Fractal Dimension for Fractal Structures: A Hausdorff Approach

Details Fractal Dimension for Fractal Structures: A Hausdorff Approach Fractal Dimension for Fractal Structures: A Hausdorff Approach

2010-07-22

arxiv.org/abs/1007.3960v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

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.

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