2012
DOI: 10.1016/j.topol.2011.04.023
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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 [7]). Therefore, we generalize them and obtain an easy method in order to calculate the fr… Show more

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Cited by 25 publications
(57 citation statements)
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“…It is an application of fractal dimension III defined in [32], and is based both in the box-counting and Hausdorff dimensions (see [31], end of Sect. 3.1 for the relation between both classical dimensions, which is also the motivation for this definition).…”
Section: The Fractal Dimension Of a Curvementioning
confidence: 99%
“…It is an application of fractal dimension III defined in [32], and is based both in the box-counting and Hausdorff dimensions (see [31], end of Sect. 3.1 for the relation between both classical dimensions, which is also the motivation for this definition).…”
Section: The Fractal Dimension Of a Curvementioning
confidence: 99%
“…It is worth pointing out that such a dimension leads to fruitful applications and results for those interested in the calculation the self-similarity exponent. The main references this work is based on are [1][2][3][4][5]. Next, we brie y describe how the present article is organized.…”
Section: Introductionmentioning
confidence: 99%
“…In the present work, we apply the fractal dimension definition for a curve introduced in [23] (based on a fractal dimension model contributed previously in [7]) to provide an algorithm which allows its estimation.…”
Section: Introductionmentioning
confidence: 99%
“…In this way, some definitions of fractal dimension for a fractal structure have been already studied in [7][8][9]11] and applied in [10,23], to quote some of them.…”
Section: Introductionmentioning
confidence: 99%
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