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

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 L...

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Bibliographic Details
Published in:arXiv.org 2020-10
Main Authors: Banerjee, Debasmita, Jha, Amit Kumar, Sekar Iyengar, A N, Janaki, M S
Format: Article
Language:English
Subjects:
Data conversion
Fractal analysis
Fractal geometry
Fractals
Image processing
Liapunov exponents
Nonlinear analysis
Spatial data
Time series
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Summary: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.
ISSN:2331-8422