  We propose a means to realize two-dimensional quasiperiodic structures by
trapping atoms in an optical potential. The structures have eight-fold symmetry
and are closely related to the well-known quasiperiodic octagonal
(Ammann-Beenker) tiling. We describe the geometrical properties of the
structures obtained by tuning parameters of the system. We discuss some
features of the corresponding tight-binding models, and experiments to probe
quantum properties of this optical quasicrystal.
