# Fractal Dimension Estimation with Persistent Homology: A Comparative Study

## TL;DR

This paper introduces a new method using persistent homology to estimate fractal dimensions from point samples, demonstrating comparable or superior performance to classical techniques across various datasets.

## Contribution

It presents an algorithm for persistent homology dimension estimation and compares its effectiveness with traditional methods on different fractal and empirical datasets.

## Key findings

- Persistent homology dimension estimation performs comparably to correlation dimension.
- It outperforms box-counting in fractal dimension estimation.
- The method is practical for analyzing self-similar fractals and chaotic attractors.

## Abstract

We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate the persistent homology dimension, and compare its performance to classical methods to compute the correlation and box-counting dimensions in examples of self-similar fractals, chaotic attractors, and an empirical dataset. The performance of the $0$-dimensional persistent homology dimension is comparable to that of the correlation dimension, and better than box-counting.