Medieval Islamic artisans developed a pattern-making process for designing ornate tiled surfaces that allowed them to produce sophisticated patterns not seen in the West until centuries later, a new study suggests. The findings appear in the 23 February issue of the journal Science, published by AAAS, the nonprofit science society.

Many walls of medieval Islamic buildings have ornate geometric star-and-polygon, or "girih," patterns, often overlaid with a zig-zagging network of lines. Researchers have generally believed that medieval artisans constructed these patterns using a straightedge and compass.

In their Science paper, Peter J. Lu of Harvard University and Paul J. Steinhardt of Princeton University now show that by the 13th century artisans had begun producing the patterns using a small set of decorated polygonal tiles, which the authors term "girih tiles."

This girih tile method was more efficient and precise than the previous approach, allowing for an important breakthrough in Islamic mathematics and design, the authors say.

By the 15th century the tiled patterns had become extraordinarily complex and a handful of them were what mathematicians today call "quasicrystalline" designs. These were first demonstrated in the West by Roger Penrose, who presented the eponymous Penrose pattern in the early 1970s.

A quasicrystal is made by fitting a set of units together in a predictable way, but, unlike the tiles on a typical floor, the pattern does not regularly repeat.

Quasicrystals have special rotational symmetries, such as pentagonal or decagonal,
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Contact: Natasha Pinol
npinol@aaas.org
202-326-7088
American Association for the Advancement of Science
22-Feb-2007