After notes on self-similarity exponent for fractal structures

Área de investigación: Applied Mathematics Año: 2017
Tipo de publicación: Artículo Palabras clave: Fractal; fractal structure; fractal dimension; Hausdorff dimension; self-similarity index
Autores: Fernández Martínez, Manuel; Caravaca-Garratón, Manuel
Journal: Open Physics (formerly Central European Journal of Physics) Volumen: 15
Número: 1 Páginas: 440-448
Mes: June
ISSN: 2391-5471
Previous works have highlighted the suitability of the concept of fractal structure, which derives from asymmetric topology, to propound generalized definitions of fractal dimension. The aim of the present article is to collect some results and approaches allowing to connect the self-similarity index and the fractal dimension of a broad spectrum of random processes. To tackle with, we shall use the concept of induced fractal structure on the image set of a sample curve. The main result in this paper states that given a sample function of a random process endowed with the induced fractal structure on its image, it holds that the self-similarity index of that function equals the inverse of its fractal dimension.