University of Washington / Department of Computer Science and Engineering / GRAIL / Projects

Tilings and Geometric Ornament


The goal of this project is to explore the relationship between computer graphics, geometry, and ornamental design. Each of these three subjects has been studied extensively on its own. Even the pairwise intersections have been fairly well-traveled. But there is lots of room for exploration in the intersection of all three.

We view this research as an attempt to apply principles of computer graphics to the creation of geometric ornament, as a continuation of the tradition of ornamental design using modern tools and algorithms.

It's exciting to know that people out there are reading this page and finding it interesting. But it's also a serious wake-up call! Exposure makes me think about how much more information I'd love to put up here if I had the time. In the meantime, if you have questions, or even requests for what else I should publish here, please get in touch.


Craig S. Kaplan   David H. Salesin



M.C. Escher was amazingly good at creating tesselations of the plane out of recognizable or lifelike shapes. Can we do automatically what he did with great effort? That is, given an arbitrary shape in the plane, can we come up with a tiling that resembles that shape? We call this the Escherization problem.

Islamic Star Patterns

A thousand years ago, Islamic artisans developed a system of architectural decoration that remains unparalleled to this day. Since that time, many techniques have been proposed for recreating some of their designs. Strangely, all these techniques are successful in some ways, making it harder to determine how these designs were really constructed. We have successfully applied one such technique to the creation of novel Islamic ornament.

Parquet Deformations

In Metamagical Themas, Douglas Hofstadter presents parquet deformations, the work of William Huff at SUNY Buffalo. Huff got his architecture students to create strips of geometric ornament where the shapes involved deform in one direction of space, in a kind of frozen, spatial animation. We have developed an initial system for creating parquet deformations out of tilings, and have examined several extensions to Huff's idea.

Symmetrohedra (with George Hart)

Symmetrohedra are a new infinite class of polyhedra. Each has the symmetries of one of the five Platonic solids, but they allow a wide range of regular polygons as faces.

Voronoi Diagrams

Voronoi diagrams are a well known and powerful tool in mathematics and the sciences. Despite their historical connections to symmetry via crystallography, the use of Voronoi diagrams in the construction of ornamental designs has not been well-explored. We have carried out a preliminary inquiry into art from Voronoi diagrams.

Last modified: by Craig S. Kaplan