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

TL;DR

This paper introduces a new method for estimating the fractal dimension of 2D time-series by solving a functional equation based on coverage areas, offering a simpler alternative to traditional linear regression methods.

Contribution

It proposes a novel approach to fractal dimension estimation using functional equations, improving simplicity and potential applicability for 2D time-series analysis.

Findings

The new method provides comparable estimates to traditional methods.

It demonstrates simplicity and ease of implementation.

Potential for improved accuracy in certain cases.

Abstract

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.