This pattern, called a Penrose tiling, is a classic example of an aperiodic pattern that exhibits long-range order.

Crazy Quasicrystals

To understand the maddeningly paradoxical state of quasicrystals, first consider kitchen floor tiles. Tiles can be arranged in patterns of squares, hexagons, or octagons without leaving gaps. But cover the floor with pentagons or decagons and you'll see a patchwork of empty space. These gaps mean the pattern doesn't possess periodicity, meaning the tiles can't theoretically stretch to infinity in a regularly repeating pattern. In periodic patterns, if one tile is surrounded by six neighbors, then every tile is surrounded by six neighbors.

But in aperiodic structures, this regular pattern breaks down. Until the early 1980s, scientists believed all crystals were composed of atoms arranged periodically much like four or six-sided tiles. They believed this because light diffracted from crystals produces sharp, crisp patterns indicative of periodicity. Then along came quasicrystals with five or tenfold symmetry. These structures aren't periodic, yet they produce sharp diffraction patterns. Something was wrong with the definition of crystals. This discovery, in fact, spurred an international union of crystallographers to redefine crystals as anything with a sharp diffraction pattern.

Further analysis revealed that like conventional crystals, quasicrystals exhibit perfect long-range structural order, meaning once the location of a single atom is known, the precise location of all other atoms can be calculated. This newfound combination of aperiodic structure and long-range order captured the imagination of many physicists.

"I think they're beautiful, and that's the main reason why I'm studying them," Rotenberg says.

More about the theory of quasicrystals.