Craig S. Kaplan.
Voronoi Diagrams and Ornamental Design.
ISAMA '99,
The first annual symposium of the International Society for the Arts,
Mathematics, and Architecture. San Sebastián, Spain, 7-11
June 1999, pages 277-283.
Abstract
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 be used to construct interesting
tilings of tne plane, and their continuity with respect to changes
in the generators, which makes possible smooth, organic animations
of tilings.