Combinatorial and Computational aspects of Tilings

We introduce a dynamical system based on Voronoi tessellations.
A state is a finite collection P of points in R^2, and our system evolves
by mapping one state to the vertex set v(P) of its Voronoi tessellation.
The number of points in v(P) depends not only on the size of P but also
geometric information about P. We will state and prove a theorem giving an
exact formula for the number of points in v(P). If there is time, we will
discuss some of the dynamical behavior we have seen experimentally.