Layered patterns in nature, medicine and materials: quantification of anisotropic structures and cyclisity
- Subject Areas
- Bioinformatics, Data Science, Theory and Formal Methods
- Boolean functions, structural anomaly, structural disorder of layered systems, : 0-gravity, world ocean, image processing, biomimetics, anisotropy of layered systems, N-partite graph
- © 2019 Smolyar et al.
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
- Cite this article
- 2019. Layered patterns in nature, medicine and materials: quantification of anisotropic structures and cyclisity. PeerJ Preprints 7:e27451v2 https://doi.org/10.7287/peerj.preprints.27451v2
Various natural patterns—such as terrestrial sand dune ripples, lamellae in vertebrate bones, growth increments in fish scales and corals, aorta and lamellar corpuscle of 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 (2-D) 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 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 2-D plane and to construct charts of 1) “layer thickness vs. layer number” and 2) “layer area vs. layer number.” We present a parameter for structural disorder in a layered pattern (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.
We corrected some grammer and authors information
Raw data for ploting DStr=f(number of transects) and DStr quantification
Raw data used for calculation DStr and DStr=f(number of transects) for Figure XX has been presented on excell sheet Fig_XX. First column represent number of transects in relative inits; second column represent DStr.