Abstract: The main goal of this chapter is to generalize the classical boxDimensionbox(-counting) dimensionDimension in the broader context of fractal structuresFractal structure. We state that whether the so-called natural fractal structure Fractal structure natural fractal structure as a Euclidean set Fractal structure (which any Euclidean subset can be always endowed with) is selected, then the boxDimensionbox(-counting) dimensionDimension remains as a particular case of the generalized fractal dimensionDimension models. That idea allows to consider a wider range of fractal structuresFractal structure to calculate the fractal dimensionDimension of a given subset. Interestingly, unlike how it happens with classical boxDimensionbox(-counting) dimensionDimension, the new models we provide in this chapter can be further extended to non-Euclidean contexts, where the classical definitions of fractal dimensionDimension may lack sense or cannot be calculated. In this chapter, we illustrate this fact in the context of the domain of words. Another advantage of these models of fractal dimensionDimension for fractal structuresFractal structure lies in the possibility of their effective calculationDimensioncalculation of or estimationDimensionestimation of for any space admitting a fractal structureFractal structure. To calculate these dimensions, we can proceed as easy as to estimate the boxDimensionbox(-counting) dimensionDimension in Euclidean applications.
Publication Year: 2019
Publication Date: 2019-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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