Fractal Dimension of the Kronecker Product Based Fractals

TL;DR

This paper introduces a straightforward method and an R script for calculating the Hausdorff-Besicovitch dimension of Kronecker Product based fractals, demonstrating reliability and consistency with known fractal dimensions.

Contribution

It presents a new formula for fractal dimension calculation using Kronecker products, applicable to a wide range of fractals, with an accompanying R implementation.

Findings

Method produces dimensions matching known fractals

The formula is based on self-similarity and scale factors

The approach is reliable and easy to implement

Abstract

A simple method of calculating the Hausdorff-Besicovitch dimension of the Kronecker Product based fractals is presented together with a compact R script realizing it. The proposed new formula is based on traditionally used values of the number of self-similar objects and the scale factor that are now calculated using appropriate values of both the initial fractal matrix and the second order resultant matrix. This method is reliable and producing dimensions equal to many already determined values of well-known fractals.