Theme: SIGGRAPH Core
The rise and spread of Islamic culture from the seventh century onward has provided us with one of history's great artistic and decorative traditions. Across Europe, Africa, and Asia, we find artistic treasures of unrivaled beauty in calligraphy, stylized floral designs, architecture, and abstract geometric star patterns. Except for a few scattered remnants of this technical knowledge, the design of Islamic star patterns is a mystery. As a guide, we have only the end product: hundreds of beguiling geometric designs found all over the world. One thing known with certainty is that star patterns are deeply mathematical in nature.
In the past 100 years or so, many mathematicians and hobbyists have studied the construction of Islamic star patterns. The result is a small set of practical techniques that can be used to generate traditional and novel star patterns, techniques that may or may not resemble those practiced historically.
Kaplan's work provides an opportunity to extend the range and scope of Islamic star patterns beyond the boundaries of the historical canon. Non-Euclidean geometry would have been inconceivable hundreds of years ago; Kaplan has shown how star patterns can be adapted to the hyperbolic plane and the sphere. His "Islamic parquet deformations" exhibit a slow geometric evolution in space. The mathematical technique is straightforward, but it would have been impractical to produce these designs without computers because of the lack of strict repetition. Kaplan's designs can be passed to any number of computer-controlled manufacturing devices, and he has experimented with sculptural, architectural and decorative forms in a variety of media.
Craig S. Kaplan
University of Waterloo