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Efficient calculation of fractal properties via the Higuchi method
J A Wanliss1, Grace E Wanliss1
1Department of Physics, Presbyterian College, 503 S. Broad St., Clinton, SC 29325 USA.
Nonlinear Dynamics
|June 29, 2022
Summary
Determining fractal dimension using Higuchi's method is efficient but struggles with parameter selection. This study introduces a novel method to optimize the tuning parameter (k_max), ensuring accurate fractal analysis for diverse datasets.
Area of Science:
- Complex Systems Analysis
- Nonlinear Dynamics
- Biophysics
Background:
- Higuchi's method is a widely used technique for estimating fractal dimensions, offering rapid and robust results.
- A significant challenge in applying Higuchi's method is selecting the optimal tuning parameter (k_max), as improper selection can lead to inaccurate fractal dimension estimations.
- Currently, there is no standardized approach for determining the best k_max value, hindering the method's consistent application.
Purpose of the Study:
- To develop a general and a priori method for selecting the optimal tuning parameter (k_max) in Higuchi's fractal dimension analysis.
- To minimize error metrics by analyzing synthetic fractal signals to establish a reliable parameter determination technique.
- To validate the proposed method by applying it to real-world physical data, including magnetohydrodynamic (MHD) turbulence and viral genetic sequences.
Main Methods:
- Analysis of synthetic fractal signals to identify an error metric for optimization.
- Development of a novel methodology for the a priori determination of the optimal tuning parameter (k_max).
- Application and validation of the method on physical datasets, specifically a shell model for MHD turbulence and the SARS-CoV-2 Wuhan-Hu-1 isolate.
Main Results:
- A new, general method for determining the optimal tuning parameter (k_max) for Higuchi's fractal dimension analysis has been established.
- The method allows for accurate and reliable fractal dimension estimations by pre-selecting the best parameter value for a given data length.
- Successful calculation of fractal dimensions for complex physical systems, demonstrating the method's broad applicability.
Conclusions:
- The proposed method addresses a critical limitation in Higuchi's technique, improving the reliability of fractal dimension calculations.
- This approach provides a standardized way to select the tuning parameter, enhancing the robustness and reproducibility of fractal analysis.
- The successful application to MHD turbulence and viral data highlights the method's potential across various scientific disciplines.
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