Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension
Original language description
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.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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