Area convergence of Voronoi cells on spiral lattices

TL;DR

This paper proves that the areas of Voronoi cells in spiral lattice patterns converge under certain conditions, specifically when the spiral's angle parameter is badly approximable, contributing to geometric and lattice theory.

Contribution

It introduces a convergence result for Voronoi cell areas on spiral lattices with a focus on the angle parameter's approximation properties.

Findings

Voronoi cell areas converge under scale normalization

Convergence depends on the angle being badly approximable

Results apply to generalized Archimedean spiral lattices

Abstract

It is shown that the area of Voronoi cells for a generalized Archimedean spiral lattice converges under some scale normalization, if the angle parameter is badly approximable.