Algorithm to estimate the Hurst exponent of high-dimensional fractals

TL;DR

This paper introduces a new algorithm for estimating the Hurst exponent in high-dimensional fractals, utilizing a generalized variance approach around a moving average filter, with demonstrated efficiency and accuracy.

Contribution

The paper presents a novel high-dimensional variance-based algorithm for Hurst exponent estimation, applicable to complex fractal surfaces generated by different methods.

Findings

Effective estimation of Hurst exponents from 0.1 to 0.9.

Algorithm demonstrates good accuracy across various surface sizes.

Computational efficiency is suitable for high-dimensional data.

Abstract

We propose an algorithm to estimate the Hurst exponent of high-dimensional fractals, based on a generalized high-dimensional variance around a moving average low-pass filter. As working examples, we consider rough surfaces generated by the Random Midpoint Displacement and by the Cholesky-Levinson Factorization algorithms. The surrogate surfaces have Hurst exponents ranging from 0.1 to 0.9 with step 0.1, and different sizes. The computational efficiency and the accuracy of the algorithm are also discussed.