Ellipse packing in two-dimensional cell tessellation: a theoretical explanation for Lewis's law and Aboav-Weaire's law.

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 software with the Conicfit package to fit ellipses based on the geometric parameters of polygonal cells of ten different kinds of natural and artificial 2D structures.

Results

Our results indicated that the cells could be classified as an ellipse's inscribed polygon (EIP) and that they tended to form the 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

SUBMITTER: Xu K 

PROVIDER: S-EPMC6525589 | biostudies-literature | 2019

REPOSITORIES: biostudies-literature