Archeologists and historians have long debated how medieval artists could create patterns of such amazing complexity while providing a balanced work over large areas. Now, using computer technology and other modern tools, the two scientists may have cracked the secret.
Peter Lu, of Harvard University, first became fascinated with Islamic decorative motifs when he visited an old school in Bukhara, Uzbekistan.
Lu was struck by the beauty and technical complexity of a blue wall pattern featuring 10-pointed stars. Being a scientist -- a physics graduate student -- he sought a precise answer as to why this composition appealed to his aesthetic senses.
Mathematicians often talk about the "beauty" or "elegance" of complicated mathematical formulas, meaning their balance and symmetry. That is an idea most people have to accept on trust, as we know too little about higher mathematics to judge for ourselves.
But what if the artists of the Islamic world five centuries or more ago knew the secrets of advanced geometry and used this tool of logic to create designs of such elegance that they lead the spirit to tranquility?
A computer reconstruction of the quasicrystalline patterns of the Darb-i Imam shrine, which was built in 1453 (image courtesy of Peter J. Lu)
Much of the development of traditional Islamic patterns is shrouded in mystery, as the artists of centuries ago rarely revealed their techniques to others. After his experience at the madrasah, however, Lu went out of his way to consult a rare 15th-century scroll that contained example patterns. He began to comprehend the basic puzzle pieces, made up of five geometrical shapes.
Lu eventually found decorations above an archway at the Darb-i Imam shrine at Isfahan, in central Iran, which fitted an advanced mathematical formula based on a crystalline structure. Turning his thoughts to the blue Uzbek pattern that had so impressed him, he was also reminded of a crystal.
Lu tells RFE/RL that his previous studies of crystalline forms predisposed him to be interested in patterns.
"Fortune favors the prepared mind," Lu says. "Mainly it just aroused some interesting suspicions more than anything else about the geometry that might have been used. I guess I would say that I was very much predisposed to thinking about those tilings in that particular way because of my undergraduate work with Professor Steinhardt."
Paul Steinhardt is the eminent physicist who invented the mathematical term "quasicrystal." He is the Albert Einstein Professor of Science at Princeton University. He is noted for his thoughts on big themes, having proposed among other things an alternative to the Big Bang theory on the creation of the universe.
Lu and Steinhardt worked together on the quasicrystalline properties of Islamic design, using computers to identify the elements of design.
Steinhardt tells RFE/RL there is evidence of a connection: "We have shown on the designs that they had discovered the elements needed to construct such designs, and they had a particularly spectacular example -- the one at the Darb-i Imam shrine."
Lu expresses amazement, saying Western mathematicians have only established the principles of quasicrystalline geometry in the last 20 or 30 years.
But both scientists caution that more research is necessary to establish whether the old artists were working intuitively or had a conscious grasp of the mathematical principles involved.
They have written a joint paper on their findings that appeared in the authoritative journal "Science" on February 27.
In part, it says that on the basis of their studies on medieval art and decorations, they "suggest that by 1200 [of the Christian era] there was an important breakthrough in Islamic mathematics and design." That was "the discovery of an entirely new way to conceptualize and construct girih line patterns."
Girih lines are the outlines creating a pattern -- originally limited to relatively simple geometric star and polygon patterns. But the use of tiles and advances in math between the 12th and 15th centuries allowed the creation of increasingly complex girih line patterns, which can continue infinitely without repeating themselves.
"The indications are that they somehow realized that," Steinhardt says. "And once they realized that, there began a series of more and more complex patterns, all based on putting together the same elements, but in more and more complex ways."
A Penrose tiling (image courtesy of Peter J. Lu)
In the course of the research, Lu either visited or studied photographs of buildings in Iran, Afghanistan, Iraq, and Turkey, as well as Uzbekistan. His greatest enthusiasm is reserved for what he saw in Uzbekistan.
"The architecture is fantastic," Lu says. "That was of course the thing that struck me in Bukhara and Samarkand, because Samarkand in particular was the capital of the Timur dynasty; and the types of patterns that I had been working on, it turned out, had their pinnacle in terms of sophistication and complexity around that time and in those places."
The research done by the two scholars is arousing renewed interest in the fascinating world of Islamic pattern art forms.