Abstract
ABSTRACTThe 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 these formulas. In this study, we simulated a series of Voronoi diagrams by randomly disordering the seed locations of a regular hexagonal 2D Voronoi diagram, and analysed the cell topology based on ellipse packing. We then derived and verified the new formulas for Lewis’s law and Aboav-Weaire’s law. Specifically, we found that the upper limit of the second moment of the edge number is 3. In addition, we derived a new formula for the von Neumann-Mullins law based on the improved Aboav-Weaire’s law. Our results suggest that the cell area, local neighbour relationship, and cell-growth rate are closely linked to each other, and primarily shaped by the effect of deformation from circle to ellipse, and less influenced by the global edge distribution.
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