Medieval Islamic designs: Tiled pattern-making

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.

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 (Feb. 23), 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, meaning they look the same if they are rotated 72 or 36 degrees. These symmetries are "forbidden" in repeating patterns. For example, it's impossible to fit pentagonal tiles side-by-side on a floor; there will always be gaps in between.

Before the Science study, Lu, a PhD candidate in physics, had collaborated with Steinhardt, himself a cosmologist, to look for quasicrystals in nature.

Traveling in Uzbekistan, Lu found himself looking at a medieval Islamic building and saw decagonal motifs, prompting him to wonder if there were any quasicrystalline Islamic tilings. A new research project was born.

Upon returning to Harvard, he began analyzing photos of artwork, buildings, and architectural scrolls from Iran, Iraq, Turkey, Afghanistan, and other countries in the Islamic world. He discovered that architects had drawn the outlines of the five girih tiles in scrolls that were essentially training manuals for other architects, including a 15th-century Timurid-Turkmen scroll now held by the Topkapi Palace Museum in Istanbul.

"The fact that we can explain so many sets of tilings, from such a wide range of archictectural structures throughout the Islamic world, with the same set of tiles makes this an incredibly interesting universal picture," Lu said.

In their study, the researchers further show how, in 1453, Islamic architects had created overlapping patterns with girih tiles at two different sizes to produce nearly perfect quasicrystalline patterns, reflecting mathematical procedures not understood in the West for another 500 years.