Craig S. Kaplan: Islamic Patterns

  • ©2008, Craig S. Kaplan, Islamic Patterns



Islamic Patterns


SIGGRAPH 2008: Design and Computation

Creation Year:




Artist Statement:

The rise and spread of Islamic culture from the 7th 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. Islamic star patterns adorn buildings, particularly mosques and tombs, throughout the Islamic world.

Design methods for construction of Islamic patterns were the private domain of the artisans who practiced them. The knowledge was passed down from master to apprentice over generations and ultimately was lost as the practice declined during the 15th century. 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. The artisans were well versed in geometry; in their pursuit of mathematical knowledge, early Islamic scholars translated Euclid’s Elements into Arabic. And so even though we cannot peer back through time to understand their design techniques, we can at least be confident that their constructions were firmly rooted in geometry.

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.

Craig Kaplan develops software for design and rendering of Islamic geometric patterns. His work is inspired both by historical examples and by contemporary research into the mathematical structure of these patterns. Kaplan’s software marries algorithms from computer graphics with the modern mathematical machinery of symmetry theory and tiling theory.

His work breaks the process of pattern construction into two steps. First, the designer chooses a tiling of the plane. Then the software places small geometric motifs in every tile, a process governed by a small set of parameters under the designer’s control. The motifs link together to form a finished design. The computer handles the tedium of precise, repetitive drawing, thus freeing the human designer to explore the space of star patterns quickly and enjoyably.

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.

The connection between computer graphics and computer-controlled manufacturing offers the exciting possibility of realizing computergenerated art as physical artifacts. Kaplan has experimented with sculptural, architectural, and decorative forms using a variety of manufacturing technologies and media.