The inverse problem for fractal curves solved with the dynamical approach method

TL;DR

This paper introduces a dynamical approach method to solve the inverse problem of determining the fractal dimension of plane curves, incorporating physical properties to enhance biological and material characterization.

Contribution

It presents a novel dynamical approach that extends fractal analysis by including physical properties like density and elasticity, improving material and biological object characterization.

Findings

The method successfully determines fractal dimensions of plane curves.

Incorporates physical properties into fractal analysis.

Enhances biological and material object characterization.

Abstract

The purpose of the present paper is to present the main applications of a new method for the determination of the fractal structure of plane curves. It is focused on the inverse problem, that is, given a curve in the plane, find its fractal dimension. It is shown that the dynamical approach extends the characterization of a curve as a fractal object introducing the effects of mass density, elastic properties, and transverse geometry. The dynamical dimension characterizes material objects and suggests that biological characterization can be much more complete with the methodology presented here.