2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144763We 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.13 pages, 8 figuresDynamical SystemsMathematical Physics37E99;52C20text