Periodic or Aperiodic?
Most uses of girih tiling in Islamic architecture were periodic; they had unit cells that were repeated in the same orientation within a lattice. Some had patterns which could not be extended to a tiling of the entire plane. None of them are known to have had patterns that could be extended to the entire plane only in an aperiodic way.
However, on some buildings, the large girih tiles were decorated with patterns that formed small girih tiles. And on one of these, Darb-i Imam, the subdivision into smaller tiles was done in a way that could have been generalized to an aperiodic tiling of the plane.
Read more about this topic: Girih Tiles
Famous quotes containing the word periodic:
“It can be demonstrated that the child’s contact with the real world is strengthened by his periodic excursions into fantasy. It becomes easier to tolerate the frustrations of the real world and to accede to the demands of reality if one can restore himself at intervals in a world where the deepest wishes can achieve imaginary gratification.”
—Selma H. Fraiberg (20th century)