Detail publikačního výsledku

Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension

MARTIŠEK, D.

Originální název

Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension

Anglický název

Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension

Druh

Článek Scopus

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

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

Klíčová slova v angličtině

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

Autoři

MARTIŠEK, D.

Rok RIV

2023

Vydáno

20.12.2022

Nakladatel

Brno University of Technology

Místo

Brno, Czech Republic

ISSN

1803-3814

Periodikum

Mendel Journal series

Svazek

28

Číslo

2

Stát

Česká republika

Strany od

93

Strany do

96

Strany počet

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"
}