title: Aperiodic crystals and beyond.
abstract: Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order, encompassing both periodic and aperiodic crystals. The current definition of crystals rests on their essentially point-like diffraction. Considering a number of recently investigated toy systems, with particular emphasis on non-crystalline ordered structures, the limits of the current definition are explored.
authors.affiliation: Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, England.
authors.forename: Uwe
authors.initials: U
authors.lastname: Grimm
keywords: aperiodic crystals; crystalline order; incommensurate structures; mathematical diffraction; pattern theory