Quasicrystallic Tilings and Projection Method

Basic notions related to quasiperiodic tilings and Delone sets in Eucledean space are discussed. It is shown how the cut and project method of constructing them is used to calculate their spectra. Special attention is paid to self-similar tilings and the way one can obtain one-dimensional substitutional tilings by the projection scheme. Bibliography: 18 titles.