Islamic "quasicrystals" predate Penrose tiles

Quasicrystals are patterns that fill all the space but lack translational symmetry. Such a structure will produce diffraction patterns when illuminated with light, but without the usual crystalline symmetries. It now seems that the findings of the University of Copenhagen crystallographer Emil Makovicky about the occurance of quasicrystalline patterns in Iran's Islamic architectural decorations and tilings are not just accidental. New findings by Peter J. Lu of Harvard University and Paul Steinhardt of Princeton University (Science 315, 1106)

show that by 1200 C.E. a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons ("girih tiles") decorated with lines. These tiles enabled the creation of increasingly complex periodic girih patterns, and by the 15th century, the tessellation approach was combined with self-similar transformations to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before their discovery in the West.