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

Akira Takahara and Yoshihiro Sato ()
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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

Mathematics, 2025, vol. 13, issue 19, 1-16

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.

Keywords: multifractal; quantitative evaluation; stereology; self-assembly; simulation image; Gray–Scott (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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