Voronoi Diagrams and Ornamental Design

A set of points in the plane induces a Voronoi diagram, a division of the plane based on proximity to points in the set. Voronoi diagrams have been used extensively in engineering and scientific disciplines, but the possibility of using them for creating abstract ornamental designs is largely unexplored. I present some techniques for creating attractive ornamental designs using Voronoi diagrams. I focus on two features of Voronoi diagrams that make them particularly useful artistic tools: their conservation of symmetry, which can be used to construct interesting tilings of the plane, and their continuity with respect to changes in the generators, which makes possible smooth, organic animations of tilings.