In the beauty and geometric complexity of tile mosaics on walls of medieval Islamic buildings, scientists have recognized patterns suggesting that the designers had made a conceptual breakthrough in mathematics beginning as early as the 13th century.
In their journal report, Mr. Lu and Dr. Steinhardt concluded that by the 15th century, Islamic designers and artisans had developed techniques “to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before discovery in the West.”
Some of the most complex patterns, called “girih” in Persian, consist of sets of contiguous polygons fitted together with little distortion and no gaps. Running through each polygon (a decagon, pentagon, diamond, bowtie or hexagon) is a decorative line. Mr. Lu found that the interlocking tiles were arranged in predictable ways to create a pattern that never repeats — that is, quasi crystals.