A dynamical system using the Voronoi tessellation

Details A dynamical system using the Voronoi tessellation A dynamical system using the Voronoi tessellation

2007-12-21

arxiv.org/abs/0712.3736v1

Mathematics

Dynamical Systems

13 pages, 8 figures

Scientific paper

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.

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