New classes of quasicrystals and marginal critical states.

One-dimensional quasilattices, namely, the geometrical objects that represent quasicrystals, are classified into mutual local-derivability (MLD) classes. Besides the familiar class, there exist an infinite number of new MLD classes, and different MLD classes are distinguished by the inflation rules of their representatives. It has been found that electronic properties of a new MLD class are characterized by the presence of marginal critical states, which are considered to be nearly localized states.