  We describe a way to obtain a two-dimensional quasiperiodic tiling with
eight-fold symmetry using cold atoms. A series of such optical tilings, related
by scale transformations, is obtained for a series of specific values of the
chemical potential of the atoms. A theoretical model for the optical system is
described and compared with that of the well-known cut-and-project method for
the Ammann-Beenker tiling. This type of cold atom structure should allow the
simulation of several important lattice models for interacting quantum
particles and spins in quasicrystals.
