On the Nature of Electronic Wave Functions in One-Dimensional Self-Similar and Quasiperiodic Systems

Figure 1

In 1992 the notion of crystal was widened beyond mere periodicity. This conceptual diagram presents the position of aperiodic crystals, no longer based on the notion of periodic translation symmetry, among the different orderings of matter. The diverse aperiodic crystal families are arranged according to the dimension 𝐷 (see (2)) of their embedding hyperspaces (numerical labels).