The Tiling Database. Browse some random patterns. Or narrow down your search here.
Looking for an ornament in the Alhambra? Or a spiral tiling? Or perhaps a Topkapi scroll?
posted by vacapinta on Jan 13, 2009 - 10 comments

This week in mathematical physics, John Baez looks at the amazing tile patterns in the Alhambra in Granada, dividing the patterns into their characteristic Wallpaper Groups based on their symmetries. And if these patterns aren't good enough for you, try drawing your own with the Escher Web Sketch tool. [more inside]
posted by kiltedtaco on Jul 24, 2008 - 20 comments

Nowhere-neat tilings are actually pretty neat. We all know you can't "square the circle", but do you know the story of squaring the square? (And by the way, even if you can't construct π with a ruler and compass, you can come awfully close without too much work.)
posted by Wolfdog on Dec 4, 2007 - 10 comments

"This is a story of how the impossible became possible. How, for centuries, scientists were absolutely sure that solids (as well as decorative patterns like tiling and quilts) could only have certain symmetries - such as square, hexagonal and triangular - and that most symmetries, including five-fold symmetry in the plane and icosahedral symmetry in three dimensions (the symmetry of a soccer ball), were strictly forbidden. Then, about twenty years ago, a new kind of pattern, known as a "quasicrystal," was envisaged that shatters the symmetry restrictions and allows for an infinite number of new patterns and structures that had never been seen before, suggesting a whole new class of materials...."

Physicist Paul J. Steinhardt delivers a fascinating lecture (WMV) on tilings and quasicrystals. However, it turns out science was beaten to the punch: a recent paper (PDF) suggests Islamic architecture developed similar tilings centuries earlier.
posted by parudox on Mar 18, 2007 - 11 comments

Escher Web Sketch [Java]
posted by Gyan on Feb 13, 2005 - 6 comments