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

PeerJ

article

Igor Smolyar¹  Tim Bromage²  Martin Wikelski³ 

[1] National Centers for Environmental Information, National Oceanic and Atmospheric Administration;Department of Biomaterials & Biomimetics and Basic Science & Craniofacial Biology, College of Dentistry, New York University;Max-Planck Institute for Ornithology and Department of Biology, Konstanz University

关键词: Anisotropy of layered systems;    Boolean functions;    Structural anomaly;    0-gravity;    N-partite graph;    World ocean;    Disorder of structure;    Anisotropic growth;   

DOI  :  10.7717/peerj.7813

学科分类：社会科学、人文和艺术（综合）

来源: Inra

【 摘 要 】

Various natural patterns—such as terrestrial sand dune ripples, lamellae in vertebrate bones, growth increments in fish scales and corals, aortas and lamellar corpuscles in humans and animals—comprise layers of different thicknesses and lengths. Microstructures in manmade materials—such as alloys, perlite steels, polymers, ceramics, and ripples induced by laser on the surface of graphen—also exhibit layered structures. These layered patterns form a record of internal and external factors regulating pattern formation in their various systems, making it potentially possible to recognize and identify in their incremental sequences trends, periodicities, and events in the formation history of these systems. The morphology of layered systems plays a vital role in developing new materials and in biomimetic research. The structures and sizes of these two-dimensional (2D) patterns are characteristically anisotropic: That is, the number of layers and their absolute thicknesses vary significantly in different directions. The present work develops a method to quantify the morphological characteristics of 2D layered patterns that accounts for anisotropy in the object of study. To reach this goal, we use Boolean functions and an N-partite graph to formalize layer structure and thickness across a 2D plane and to construct charts of (1) “layer thickness vs. layer number” and (2) “layer area vs. layer number.” We present a parameter disorder of layer structure (DStr) to describe the deviation of a study object’s anisotropic structure from an isotropic analog and illustrate that charts and DStr could be used as local and global morphological characteristics describing various layered systems such as images of, for example, geological, atmospheric, medical, materials, forensic, plants, and animals. Suggested future experiments could lead to new insights into layered pattern formation.

【 授权许可】

CC BY