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.
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