Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension

Autor:	Dalibor Martišek
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	Higuchi’s method Higuchi’s fractal dimension Distance Metric space Electronic computers. Computer science QA75.5-76.95
Zdroj:	Mendel, Vol 28, Iss 2 (2022)
Druh dokumentu:	article
ISSN:	1803-3814 2571-3701 01984772
DOI:	10.13164/mendel.2022.2.093
Popis:	The so-called Higuchi’s method of fractal dimension estimation is widely used and the term Higuchi’s fractal dimension even occurs in many publications. This paper deals with this method from a mathematical point of view. Terms distance and dimension and its basic properties are explained and Higuchi’s dimension according the original source is defined. The definition of Higuchi’s dimension was compared with the mathematical definition of distance and dimension. It is shown, that the definition of Higuchi’s dimension does not satisfy axioms of distance and dimension. The so-called Higuchi’s method and Higuchi’s dimension are mathematically incorrect. Therefore, all results achieved by this method are scientifically unreliable.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/84ab7eead95b4a019847725f983663d9 Zobrazit plný text záznamu View record in DOAJ