Computer Graphics and Geometric Ornamental Design
Author(s): Craig S. Kaplan.
PhD Thesis: University of Washington,
2002.
[BibTeX] 
Abstract:
Throughout history, geometric patterns have formed an important part of art and ornamental design.
Today we have unprecedented ability to understand ornamental styles of the past, to recreate traditional
designs, and to innovate with new interpretations of old styles and with new styles altogether.
The power to further the study and practice of ornament stems from three sources. We have new
mathematical tools: a modern conception of geometry that enables us to describe with precision
what designers of the past could only hint at. We have new algorithmic tools: computers and the
abstract mathematical processing they enable allow us to perform calculations that were intractable
in previous generations. Finally, we have technological tools: manufacturing devices that can turn a
synthetic description provided by a computer into a real-world artifact. Taken together, these three
sets of tools provide new opportunities for the application of computers to the analysis and creation
of ornament.
In this dissertation, I present my research in the area of computer-generated geometric art and
ornament. I focus on two projects in particular. First I develop a collection of tools and methods
for producing traditional Islamic star patterns. Then I examine the tesselations of M. C. Escher,
developing an “Escherization” algorithm that can derive novel Escher-like tesselations of the plane
from arbitrary user-supplied shapes. Throughout, I show how modern mathematics, algorithms, and
technology can be applied to the study of these ornamental styles.