The Mystery of How Quasicrystals Form

New studies of the "platypus of materials" help explain how their atoms arrange themselves into orderly, but nonrepeating, patterns. Since their discovery in 1982, exotic materials known as quasicrystals have bedeviled physicists and chemists. Their atoms arrange themselves into chains of pentagons, decagons, and other shapes to form patterns that never quite repeat. These patterns seem to defy physical laws and intuition. How can atoms possibly "know" how to form elaborate nonrepeating arrangements without an advanced understanding of mathematics?