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

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.