(Image Eric Heller)
(Image J. W. Evans)
(Image Mark Grundland)
(Image Eric Weeks)
This week Dan Shechtman won the Nobel Prize for the discovery of quasicrystals, ordered but not periodic crystal mineral structures that lack traditional symmetry. Many people have since noted that Islamic tiles exhibit similar ordering. I took the last pic above at the Alhambra, built in the 14th century.
Here's a funny quote from Shechtman's wikipedia page. "(he) experienced several years of hostility toward his non-periodic interpretation (no less a figure than Linus Pauling said he was "talking nonsense" and "There is no such thing as quasicrystals, only quasi-scientists.")"