2007/12/21 by Natalie Priebe Frank, Frank, Natalie Priebe, Sean Hart +1
Mathematics · Physics and Astronomy · #37E99 #52C20 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DS #math.MP #msc:37E99 #msc:52C20
paper · pdf · doi:10.48550/arxiv.0712.3736
13 pages, 8 figures
arxiv created 2007/12/21 · arxiv updated 2009/12/01
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.