Quasicrystals as a hierarchy of clusters

Diffraction approaches suggest that some quasicrystal structures can be described as hierarchical packing of atomic clusters. When treated as spherical potentials, these clusters may contain ``magic numbers'' of electrons which allow exact filling of the electronic shells of the hierarchy of wells. Physical propeties such as high resistivity and diamagnetism are consistent with the model. Formation of quasicrystals at very critical composition is also explained.