Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Mathematical Incorrectnes of So Called Higuchi‘S Fractal Dimension

Version 1 : Received: 15 November 2021 / Approved: 16 November 2021 / Online: 16 November 2021 (08:46:26 CET)

How to cite: Martišek, D. Mathematical Incorrectnes of So Called Higuchi‘S Fractal Dimension. Preprints 2021, 2021110276 (doi: 10.20944/preprints202111.0276.v1). Martišek, D. Mathematical Incorrectnes of So Called Higuchi‘S Fractal Dimension. Preprints 2021, 2021110276 (doi: 10.20944/preprints202111.0276.v1).

Abstract

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 mathematical point of view. Terms distance and dimension and its basic properties are explained and Higuchi’s dimension according the original source is defined. Definition of Higuchi’s dimension was comparated with mathematical definition of the distance and dimension. It is showed, that the definition of the Higuchi’s dimension does not satisfy axioms of distance and dimension. So called Higuchi’s method and Higuchi’s dimension are mathematically incorrect. Therefore, all results achieved by this method are scientifically unreliable.

Keywords

Higuchi’s method; Higuchi’s fractal dimension; distance; metric space

Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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