A survey on fractal dimension for fractal structures

Applied Mathematics and Nonlinear Sciences

Fernández-Martínez M.¹ 

[1] Departamento de Ciencias e Informática, Centro Universitario de la Defensa, Academia General del Aire, 30720Santiago de la Ribera, Murcia, Spain;

关键词: fractals;    fractal structures;    fractal dimension;    hausdorff dimension;    box-counting dimension;    fractal geometry;    fractal stochastic processes;    hurst exponent;    applications of fractal dimension;    37f35;    28a78;    28a80;    11k55;    54e35;    54e99;   

DOI  :  10.21042/AMNS.2016.2.00037

来源: DOAJ

【 摘 要 】

Along the years, the foundations of Fractal Geometry have received contributions starting from mathematicians like Cantor, Peano, Hilbert, Hausdorff, Carathéodory, Sierpiński, 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.

【 授权许可】

Unknown