Quasi-crystals-Random Structures or Twins?

This paper discusses different ways of tiling a plane without defects by using two decorating elements. Four classes of structure with different tiling rules and different relative concentrations of the two elements are compared: Penrose tiling, microcrystalline twins, a random structure and a precipitated structure. The four structures have similar diffraction patterns exhibiting tenfold symmetry, but they differ in many essential details. The similarities and differences are discussed with special emphasis on the possibility of distinguishing between the four types of structure.