An algorithm for computing the centered Hausdorff measure of self-similar sets

TL;DR

This paper introduces an algorithm to compute the centered Hausdorff measure of self-similar sets under the strong separation condition, with proven convergence and practical testing on examples.

Contribution

The paper presents a novel algorithm with convergence proof for calculating the centered Hausdorff measure of specific self-similar sets.

Findings

Algorithm successfully computes the measure for tested sets

Convergence of the algorithm is theoretically established

Practical utility demonstrated through examples

Abstract

We provide an algorithm for computing the centered Hausdorff measure of self-similar sets satisfying the strong separation condition. We prove the convergence of the algorithm and test its utility on some examples.