image credit: Peter J. Lu; image source; larger image

In Medieval Architecture, Signs of Advanced Math

The Muslim design on the left dating from the 1300s may be more than a simple decoration. The tiles on the right show how basic shapes were used to create non-repeating patterns in a process not understood by Western mathematicians until the 1970s.

Read these New York Times and Discover Magazine articles to learn more. See more pictures here. Also, if you click on "Peter J. Lu" above, and then scroll down, you can watch the Flash Video of his Harvard Physics Department colloquium on this work.

[This feature was updated on August 17, 2009.]

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Penrose Tiles

Create your own non-periodic tiling with this Penrose Tiles applet from Grand Valley State University.

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image credit: Ianiv Schweber; image source; larger image

From Quasicrystals to Kleenex

These tiles might appear to follow a simple design, but look closer and you'll see that the pattern never repeats. Read From Quasicrystals to Kleenex to learn the history and rules behind these tiles, as well as how they relate to quasicrystals.

'Impossibly Perfect' Crystals Found in Nature

Quasicrystals were once thought to exist only in laboratories, but now they have been discovered in nature. Read the full story at 'Impossibly Perfect' Crystals Found in Nature.