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Fractal Dimension for Fractal Structures
ISBN-13:
9783030166458
Veröffentl:
2019
Seiten:
204
Autor:
Manuel Fernández-Martínez
Serie:
19, SEMA SIMAI Springer Series
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts.
1 Mathematical background.- 2 Box dimension type models.- 3 A middle definition between Hausdorff and box dimensions.- 4 Hausdorff dimension type models for fractal structures.
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