Mathematical Incorrectness of So-Called Higuchi‘s Fractal Dimension
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Date
2022-12-20
Authors
Martišek, Dalibor
ORCID
Advisor
Referee
Mark
Journal Title
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Volume Title
Publisher
Institute of Automation and Computer Science, Brno University of Technology
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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.
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Citation
Mendel. 2022 vol. 28, č. 2, s. 93-96. ISSN 1803-3814
https://mendel-journal.org/index.php/mendel/article/view/178
https://mendel-journal.org/index.php/mendel/article/view/178
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Peer-reviewed
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Language of document
en
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Defence
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Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International license
http://creativecommons.org/licenses/by-nc-sa/4.0
http://creativecommons.org/licenses/by-nc-sa/4.0