Fractal dimension analysis of spatio-temporal patterns using image processing and nonlinear time-series analysis

TL;DR

This paper introduces a method to estimate the fractal dimension of spatio-temporal patterns generated by the Swift Hohenberg equation by converting images into spatial series and applying nonlinear time-series analysis techniques.

Contribution

It presents a novel approach for estimating fractal dimension from images through spatial series analysis, applicable to experimental data.

Findings

Fractal dimension values ranged between 1 and 2.

Spatial series exhibited long-range correlations.

Patterns were confirmed to be chaotic via Lyapunov exponents.

Abstract

This article deals with the estimation of fractal dimension of spatio-temporal patterns that are generated by numerically solving the Swift Hohenberg (SH) equation. The patterns were converted into a spatial series (analogous to time series) which were shown to be chaotic by evaluating the largest Lyapunov exponent. We have applied several nonlinear time-series analysis techniques like Detrended fluctuation and Rescaled range on these spatial data to obtain Hurst exponent values that reveal spatial series data to be long range correlated. We have estimated fractal dimension from the Hurst and power law exponent and found the value lying between 1 and 2. The novelty of our approach lies in estimating fractal dimension using image to data conversion and spatial series analysis techniques, crucial for experimentally obtained images.