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Metric Morphological Interpretation of 3D Structures by Gray–Scott Model Simulation Utilising 2D Multifractal Analysis

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  • Akira Takahara

    (Faculty of Design and Data Science, Tokyo City University, 3-3-1 Ushikubonishi Tuzuki-ku, Yokohama, Kanagawa 224-8551, Japan)

  • Yoshihiro Sato

    (Faculty of Design and Data Science, Tokyo City University, 3-3-1 Ushikubonishi Tuzuki-ku, Yokohama, Kanagawa 224-8551, Japan)

Abstract

Various structures that exist worldwide are three-dimensional. Consequently, evaluating only two-dimensional cross-sectional structures is insufficient for analysing all worldwide structures. In this study, we interpreted the generalised fractal-dimensional formula of two-dimensional multifractal analysis and proposed three computational extension methods that consider the structure of three-dimensional slices. The proposed methods were verified using Monte Carlo and Gray–Scott simulations; the pixel-existence probability (PEP)-averaging method, which averages the pixel-existence probability in the slice direction, was confirmed to be the most suitable for analysing three-dimensional structures in two dimensions. This method enables a stable quantitative evaluation, regardless of the direction from which the three-dimensional structure is observed.

Suggested Citation

  • Akira Takahara & Yoshihiro Sato, 2025. "Metric Morphological Interpretation of 3D Structures by Gray–Scott Model Simulation Utilising 2D Multifractal Analysis," Mathematics, MDPI, vol. 13(19), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:19:p:3234-:d:1767292
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