Ellipse packing in two-dimensional celltessellation: A theoretical explanation for Lewis’s law and Aboav-Weaire’s law
- Published
- Accepted
- Subject Areas
- Biophysics, Cell Biology, Mathematical Biology
- Keywords
- Ellipse packing, Lewis's law, Aboav-Weaire’s law, 2D structures, tessellation, ellipse’s maximal inscribed polygon
- Copyright
- © 2019 Xu
- Licence
- 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. Ellipse packing in two-dimensional celltessellation: A theoretical explanation for Lewis’s law and Aboav-Weaire’s law. PeerJ Preprints 7:e27421v3 https://doi.org/10.7287/peerj.preprints.27421v3
Abstract
Background: Lewis’s law and Aboav-Weaire’s law are two fundamental laws used to describe the topology of two-dimensional (2D) structures; however, their theoretical bases remain unclear.
Methods: We used R package Conicfit software to fit ellipses based on the geometric parameters of polygonal cells with ten different kinds of natural and artificial 2D structures.
Results: Our results indicated that the cells could be classified as ellipse’s inscribed polygon (EIP) and that they tended to form ellipse’s maximal inscribed polygon (EMIP). This phenomenon was named as ellipse packing. On the basis of the number of cell edges, cell area, and semi-axes of fitted ellipses, we derived and verified new relations of Lewis’s law and Aboav-Weaire’s law .
Conclusions: Ellipse packing is a short-range order that places restrictions on the cell topology and growth pattern. Lewis’s law and Aboav-Weaire’s law mainly reflect the effect of deformation from circle to ellipse on cell area and the edge number of neighboring cells, respectively. The results of this study could be used to simulate the dynamics of cell topology during growth.
Author Comment
We added data of nine different kinds of natural and artificial 2D structures.