Impossible Crystals

March 18, 2007 8:54 PM

"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 (11 comments total)

This is one of the public lectures of the Perimeter Institute for Theoretical Physics - previously on MeFi.

Full disclosure: I attended that talk and thought it was awesome.
posted by parudox at 8:55 PM on March 18, 2007

And Islam is also much better at "keeping women in their place."
posted by davy at 8:59 PM on March 18, 2007

They not only hate our freedom, they hate our dimension!
posted by maryh at 9:00 PM on March 18, 2007 [1 favorite]

However, it turns out science was beaten to the punch: a recent paper (PDF) suggests Islamic architecture developed similar tilings centuries earlier.

What the hell? The discovery is that these patterns can exist as crystals in nature. They aren't saying they arn't claiming that the patterns have never been thought of before. I mean you give an example of the soccer ball right in the FPP.

The patterns themselves are obvious to any human, what's not obvious is that they would appear in crystals.
posted by delmoi at 9:06 PM on March 18, 2007

Penrose tilings are obvious?
posted by parudox at 9:16 PM on March 18, 2007

They are also fun refrigerator magnets.
posted by D.C. at 9:29 PM on March 18, 2007

NewScientist filter
posted by sisquoc15 at 10:51 PM on March 18, 2007

They are also fun refrigerator magnets.

The fractiles have sevenfold rotational symmetry. Penrose tiles have fivefold rotational symmetry.
http://en.wikipedia.org/wiki/Penrose_tiling

I'm not sure if there have found any sevenfold quasicrystals, but I don't think they're ruled out. Here's a sevenfold aperiodic tiling:
http://local.wasp.uwa.edu.au/~pbourke/texture_colour/nonperiodic/
posted by sebastienbailard at 11:10 PM on March 18, 2007

I will pay good money for magnets of the penrose chicken tiles. My google-fu, however, has failed me or no one has them for sale.
posted by eisbaer at 10:16 AM on March 19, 2007

"For example, the ratio of kits to darts in an infinite tiling is the golden ratio!"

Awesome.
posted by belling at 10:43 AM on March 19, 2007

I will pay good money for magnets of the penrose chicken tiles. My google-fu, however, has failed me or no one has them for sale.

Avery Personal Creations™ Inkjet Magnet Sheets, 8 1/2" x 11"
$11.49 for 5 sheets at Staples

Most local printshops and copyshops can probably do it.
You'd have to cut them yourself, of course.
posted by sebastienbailard at 12:18 PM on March 19, 2007