Muslim pattern makers were using highly intricate mathematical and geometrical techniques for creating decorative patterns that were not understood in the western world until well into the 20th century, according to new research.

In an article published in the magazine Science, Peter Lu and Paul Steinhardt of Harvard University have suggested that Muslim artisans were using complex mathematics to help design motifs more than 500 years ago.

It has often been suggested that the Koran prohibited the representation of the living world, thus stimulating the development of abstract geometrical arts. But Muslim painters have produced a large body of fine paintings of people and all sorts of animals. Miniatures produced in Iran and India are one such example of the pictures of animate subjects.

Unlike Christianity, Hinduism and Buddhism, Islamic art does not have an image of God. The only visual image of God presented in the Koran is that of Nur, meaning light. Since stars are the source of light from the heavens, it was only natural for the artists to decorate religious buildings with patterns dominated by star shapes.

Stars were also important to Arabs in an additional sense as well, because they were dependent upon the constellations to navigate both in the featureless Arabian deserts and on the seas, as Arabs were consummate seafarers.

Being a nomadic people, the most important piece of furniture available to Arabs was a carpet. Great skills were developed in weaving beautiful motifs and designs for carpets. When the Arabs fanned out of the desert and developed great urban centers in the Middle East, Western Africa, Spain, Iran, Central Asia and India, they extrapolated the patterns on carpets to domes, turrets and walls of the magnificent new style of architecture that they had mastered.

It was previously thought that to create the complex patterns, the medieval Muslim artists had nothing more than a compass and a straightedge at their disposal. Peter Lu and Paul Steinhardt say Islamic designers had mastered techniques "to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before their discovery in the West."

Sir Roger Penrose, a British cosmologist, has explained the mathematics behind non-repeating patterns on a flat surface, called quasicrystal geometry. The most famous example of the pattern is Penrose tiles, which was discovered by Penrose in 1970s.

Peter Lu, made the discovery after a trip to Uzbekistan where he found the breathtakingly beautiful patterns. "It shows us a culture, that we often don't credit enough, was far more advanced than we thought before," he said.

Quasicrystalline patterns comprise a set of interlocking units whose pattern never repeats, even when extended infinitely in all directions. These patterns were used to decorate huge walls of sacred buildings, as in the Darb-I-Imam shrine in Isfahan, Iran, which was built in 1463.

Peter Lu told Voice of America that while traveling in the ancient city of Bukhara, in Uzbekistan, he came across by a large tiling on the wall of the Abdullah Khan madrassa, and was struck by a big geometric star pattern with a bunch of ten-fold stars. That inspired him to look further, which he did upon returning to Harvard.

He found out that those patterns would have been impossible to create with the astonishing accuracy using the basic tools of compass and straightedge.

The artisan made use of special tiles, called "girih tiles," which consist of sets of five contiguous polygons (a decagon, pentagon, diamond, bowtie, and hexagon). These were a blue print on which the artists worked to generate mosaic patterns on large surfaces with astonishing accuracy.

"Individually placing and drafting hundreds of decagons with a straightedge would have been exceedingly cumbersome," Peter Lu says. "It's much more likely these artisans used particular tiles that we've found by decomposing the artwork."

Another feature of Islamic patterns is their ubiquity across the Islamic world. The same patterns were found in as far off places as in Muslim Spain and India.

When VOA asked the Agha Khan professor of Islamic Arts and Architecture Gulru Necipoglu about this issue, she argued that the patterns are so unique and complex, that it's very unlikely they were produced - or 'discovered', as some scholars have written independently. She says that many design manuals were in circulation throughout the Muslim world with instructions on how to create such compositions.

She said one such manuscript "shows that professional mathematicians in the eastern Islamic lands were involved in the earlier stages of inventing a complex geometric star-and-polygon repertoire in collaboration with artisans. The initial steps were likely taken in post-10th-century Baghdad, where scientific/aesthetic innovations were linked with the dissemination of mathematical knowledge to the arts-and-crafts."

Roger Penrose is also impressed with the discovery. "The concept of a quasi-crystal is, in any case, a little vague, but the Islamic patterns do seem to have captured a good measure of the idea, which is indeed remarkable," he said.