English

A dynamical system using the Voronoi tessellation

Dynamical Systems 2007-12-24 v1 Mathematical Physics math.MP

Abstract

We introduce a dynamical system based on the vertices of Voronoi tessellations. This dynamical system acts on finite or discrete point sets in the plane, taking a point set to the vertex set of its Voronoi tessellation. We explore the behavior of this system for small point sets, then prove a general result quantifying the growth of the sizes of the point sets under iteration. We conclude by giving the most interesting open problems.

Keywords

Cite

@article{arxiv.0712.3736,
  title  = {A dynamical system using the Voronoi tessellation},
  author = {Natalie Priebe Frank and Sean Hart},
  journal= {arXiv preprint arXiv:0712.3736},
  year   = {2007}
}

Comments

13 pages, 8 figures

R2 v1 2026-06-21T09:56:52.501Z