Voronoi-Diagram Approach to Escher-Like Tiling

This paper presents an interactive system for generating tiling patterns composed of a single type of complex tile. M. C. Escher, a Dutch artist, created many interesting tiling artworks of this class using animal-shaped tiles such as lizards, fishes, and birds. Our system is intended to help human users create such Escher-like tiling patterns. The basic idea is to place points according to some subgroup of a congruent transformation group on the plane, and to consider a collection of Voronoi regions as tiles. In this system, users supply an initial set of points. The system generates copies via a subgroup of the congruent transformation group, and constructs the Voronoi diagram for these points. The Voronoi regions belonging to the copied set of points are merged and the resulting region is considered as a tile. This results in a tiling pattern that covers the plane with a single tile shape. Users can generate their own tile shapes by editing the initial set of points. The performance of the system is demonstrated by example.