Impossible Cookware and Other Triumphs of the Penrose Tile - Issue 13: Symmetry - Nautilus: One of the curious aspects of aperiodic division of the plane is that information about positioning is somehow communicated across great distances—a Penrose tile placed in one position prevents the placement of other pieces hundreds (and thousands and millions) of tiles away. “Somehow a local constraint imposes a global constraint,” says Harriss. “You impose that at no scale will these tiles give you something that is periodic..."
It turns out crystals don’t always form atom-by-atom. “In very complex intermetallic compounds, the units are huge. It’s not local,” says Shechtman. When large chunks of crystal form at once, rather than through gradual atom accretion, atoms that are far apart can affect one another’s position, exactly as do Penrose tiles.