Abstract
In this chapter, we explore a new model to calculate the fractal dimension of a subset with respect to a fractal structure. The new definition we provide presents better analytical properties than box dimension and can be calculated with easiness. It is worth mentioning that such a fractal dimension will be formulated as a discretization of Hausdorff dimension. Interestingly, we shall prove that it equals box dimension for Euclidean subsets endowed with their natural fractal structures. Therefore, it becomes a middle definition of fractal dimension which inherits some of the advantages of classical Hausdorff dimension and can be also calculated in empirical applications.
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Fernández-Martínez, M., García Guirao, J.L., Sánchez-Granero, M.Á., Trinidad Segovia, J.E. (2019). A Middle Definition Between Hausdorff and Box Dimensions. In: Fractal Dimension for Fractal Structures. SEMA SIMAI Springer Series, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-030-16645-8_3
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DOI: https://doi.org/10.1007/978-3-030-16645-8_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-16644-1
Online ISBN: 978-3-030-16645-8
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