The geometric formulas of the Lewis’s law and Aboav-Weaire’s law in two dimensions based on ellipse packing
Fisheries College, Jimei University, Xiamen, China
- Published
- Accepted
- Subject Areas
- Computational Biology, Mathematical Biology, Computational Science
- Keywords
- Voronoi diagram, Lewis’s law, Aboav-Weaire’s law, ellipse packing, von Neumann-Mullins’s law, 2D topology
- 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. The geometric formulas of the Lewis’s law and Aboav-Weaire’s law in two dimensions based on ellipse packing. PeerJ Preprints 7:e27797v1 https://doi.org/10.7287/peerj.preprints.27797v1
Abstract
The two-dimensional (2D) Lewis’s law and Aboav-Weaire’s law are two simple formulas derived from empirical observations. Numerous attempts have been made to improve the empirical formulas. In this study, we simulated a series of Voronoi diagrams and analyzed the cell topology based on ellipse packing and then given the improved formulas. Specifically, we found that the upper limit of the second moment of edge number is 3. In addition, we derived the geometric formula of the von Neumann-Mullins’s law based on the improved formula of Aboav-Weaire’s law.
Author Comment
This is a preprint submission to PeerJ Preprints.