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

Martin Wikelski,Igor Smolyar,Tim Bromage

doi:10.7717/peerj.7813

Abstract

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.

Highlights

Layered structures can be found in various patterns—including satellite images of the surfaces of Mars, Pluto (Fig. 1A), Titan (Fig. 1B), in lamella bones (Fig. 1C), human aortaKonstanzer Online-Publikations-System (KOPS) URL: http://nbn-resolving.de/urn:nbn:de:bsz:352-2-eolfr7uojdyz3How to cite this article Smolyar I, Bromage T, Wikelski M. 2019
We have proposed an empirical model (EM) of 2D layered patterns, with the aim of providing tools to quantify the morphological features of anisotropic layered objects (Smolyar, Ermolaeva & Chernitsky, 1987; Smolyar & Bromage, 2004; Smolyar, 2014; Smolyar, Bromage & Wikelski, 2016)
Local methods are based on finding a threshold for each individual pixel or local area of an image; global methods attempt to find a single threshold for the entire image

Summary

Introduction

Layered structures can be found in various patterns—including satellite images of the surfaces of Mars, Pluto (Fig. 1A), Titan (Fig. 1B), in lamella bones (Fig. 1C), human aortaKonstanzer Online-Publikations-System (KOPS) URL: http://nbn-resolving.de/urn:nbn:de:bsz:352-2-eolfr7uojdyz3How to cite this article Smolyar I, Bromage T, Wikelski M. 2019. Layered structures can be found in various patterns—including satellite images of the surfaces of Mars, Pluto (Fig. 1A), Titan (Fig. 1B), in lamella bones (Fig. 1C), human aorta. Medicine, and materials: quantifying anisotropic structures and cyclicity. Coral growth increments, leaf structures and flower surface microstructures, alloy (Fig. 2A), fish skin (Fig. 2B), wild turkey wings (Fig. 2C), bird plumage patterns, three-dimensional (3D) images of shells (Fig. 2D), lightning (Fig. 2E), human and animal hairs, and skeletal muscle (Fig. 2F) all exhibit patterns of this type. Natural layered patterns are attractive objects of study for specialists of different disciplines for several reasons. Layer thickness and structure represent the cumulative effect of internal and external factors regulating pattern formation. Layered patterns serve as a record of diverse events occurring in different space–time domains

Objectives

Methods

Results

Discussion

Conclusion