Detail publikace
Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension
MARTIŠEK, D.
Anglický název
Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension
Typ
článek v časopise ve Scopus, Jsc
Jazyk
en
Originální abstrakt
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.
Anglický abstrakt
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.
Klíčová slova anglicky
Distance; Higuchi’s fractal dimension; Higuchi’s method; Metric space
Vydáno
20.12.2022
Nakladatel
Brno University of Technology
Místo
Brno, Czech Republic
ISSN
1803-3814
Ročník
28
Číslo
2
Strany od–do
93–96
Počet stran
4
BIBTEX
@article{BUT182736,
author="Dalibor {Martišek},
title="Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension",
year="2022",
volume="28",
number="2",
month="December",
pages="93--96",
publisher="Brno University of Technology",
address="Brno, Czech Republic",
issn="1803-3814"
}