Two-dimensional quasicrystals and their unit cells (elliptical or Gaussian approximations)

In this paper the average unit cell was constructed by a statistical approach and approximated either by elliptically shaped or Gaussian distributions. These approximations were successfully applied to diffraction analysis of the imperfect structures based on Penrose tiling. In the Gaussian approximation the simple analytical expressions for the structure factor were also derived. Elliptical and Gaussian approximations describe well the diffraction patterns of 2D quasicrystals.