Publication detail

Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension

MARTIŠEK, D.

Original Title

Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension

Type

journal article in Scopus

Language

English

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.

Keywords

Distance; Higuchi’s fractal dimension; Higuchi’s method; Metric space

Authors

MARTIŠEK, D.

Released

20. 12. 2022

Publisher

Brno University of Technology

Location

Brno, Czech Republic

ISBN

1803-3814

Periodical

Mendel Journal series

Year of study

28

Number

2

State

Czech Republic

Pages from

93

Pages to

96

Pages count

4

URL

https://mendel-journal.org/index.php/mendel/article/view/178/192

BibTex

@article{BUT182736,
  author="Dalibor {Martišek}",
  title="Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension",
  journal="Mendel Journal series",
  year="2022",
  volume="28",
  number="2",
  pages="93--96",
  doi="10.13164/mendel.2022.2.093",
  issn="1803-3814",
  url="https://mendel-journal.org/index.php/mendel/article/view/178/192"
}