arXiv subjects

Dmitry Zhabin

Publications and source records attributed to Dmitry Zhabin.

2 recordsLinked to original sources

arXiv2021

On estimation of fractal dimension for 2D time-series based on functional relation between areas of covers

It is shown that fractal dimension can be estimated seeking a solution of functional equation defined for areas of coverages of different scales. The method proposed is compared with widely known way to estimate fractal dimension via linear regression for numbers of ordinary sets, which are used to cover the fractal, and scale size. Due to its simplicity the method described in the article may be useful to get estimation of fractal dimension for 2D time-series.

nlin.CD↗

arXiv2019

On optimal cover and its possible shape for fractals embedded into 2D Euclidian space

In this article a definition of optimal cover for fractal structures is proposed. Expression for Minkowsky dimension is rewritten in terms of functional equation on areas of covers that constructed for different scales.Given the definition, the functional equation is resolved and possible shapes of optimal coverage are defined in correspondence with fractal dimension values.

math.DS↗