Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F22%3APU147597" target="_blank" >RIV/00216305:26210/22:PU147597 - isvavai.cz</a>

Výsledek na webu

<a href="https://mendel-journal.org/index.php/mendel/article/view/178/192" target="_blank" >https://mendel-journal.org/index.php/mendel/article/view/178/192</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.13164/mendel.2022.2.093" target="_blank" >10.13164/mendel.2022.2.093</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension

Popis výsledku anglicky

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.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mendel Journal series

ISSN

1803-3814

e-ISSN

—

Svazek periodika

28

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

4

Strana od-do

93-96

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85144486149