Publication detail
Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension
MARTIŠEK, D.
English title
Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension
Type
journal article in Scopus
Language
en
Original abstract
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.
English abstract
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.
Keywords in English
Distance; Higuchi’s fractal dimension; Higuchi’s method; Metric space
Released
20.12.2022
Publisher
Brno University of Technology
Location
Brno, Czech Republic
ISSN
1803-3814
Volume
28
Number
2
Pages from–to
93–96
Pages count
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"
}