A survey on fractal dimension for fractal structures

Área de investigación: Applied Mathematics Año: 2016
Tipo de publicación: Artículo Palabras clave: Fractals; fractal structures; fractal dimension; Hausdorff dimension; box-counting dimension; fractal geometry; fractal stochastic processes; Hurst exponent; applications of fractal dimension
Autores: Fernández Martínez, Manuel
Journal: Applied Mathematics and Nonlinear Sciences Volumen: 1
Número: 2 Páginas: 437-472
Mes: October
ISSN: 2444-8656
Along the years, the foundations of Fractal Geometry have received contributions starting from mathematicians like Cantor, Peano, Hilbert, Hausdorff, Carathéodory, Sierpinski, and Besicovitch, to quote some of them. They were some of the pioneers exploring objects having self-similar patterns or showing anomalous properties with respect to standard analytic attributes. Among the new tools developed to deal with this kind of objects, fractal dimension has become one of the most applied since it constitutes a single quantity which throws useful information concerning fractal patterns on sets. Several years later, fractal structures were introduced from Asymmetric Topology to characterize self-similar symbolic spaces. Our aim in this survey is to collect several results involving distinct definitions of fractal dimension we proved jointly with Prof.M.A. Sánchez-Granero in the context of fractal structures.
Texto completo: Paper 3.pdf