Layered patterns in nature, medicine, and materials: quantifying anisotropic structures and cyclicity

Area of Science:

• Materials Science
• Biomimetics
• Image Analysis

Background:

• Layered structures are prevalent in both natural systems (e.g., bones, scales) and manmade materials (e.g., alloys, polymers).
• The morphology of these layered systems is anisotropic, with layer thickness and number varying across different directions.
• Understanding layered morphology is crucial for materials development and biomimetic research.

Purpose of the Study:

• To develop a quantitative method for characterizing the morphology of 2D layered patterns, specifically addressing anisotropy.
• To provide tools for analyzing trends, periodicities, and formation events recorded in the incremental sequences of layered systems.

Main Methods:

• Formalization of layer structure and thickness using Boolean functions and N-partite graphs.
• Construction of "layer thickness vs. layer number" and "layer area vs. layer number" charts.
• Introduction of a parameter, disorder of layer structure (DStr), to quantify anisotropy.

Main Results:

• The developed method quantifies morphological characteristics of 2D layered patterns while accounting for anisotropy.
• Charts and the DStr parameter serve as effective local and global descriptors for diverse layered systems.
• The approach is applicable to a wide range of image data from geological, medical, and material science domains.

Conclusions:

• The proposed method offers a robust way to quantify anisotropic layered structures.
• The developed charts and DStr parameter can be valuable tools for analyzing and comparing various layered systems.
• Future research could leverage these methods for deeper insights into layered pattern formation mechanisms.