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:
“But parents can be understanding and accept the more difficult stages as necessary times of growth for the child. Parents can appreciate the fact that these phases are not easy for the child to live through either; rapid growth times are hard on a child. Perhaps it’s a small comfort to know that the harder-to-live-with stages do alternate with the calmer times,so parents can count on getting periodic breaks.”
—Saf Lerman (20th century)