University of Washington /
Department of Computer Science and Engineering /
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.
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
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.
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 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.