Spectral characterization of dodecagonal quasicrystals

We propose an analytical method for generating a two-dimensional quasiperiodic pattern with dodocagonal rotational symmetry. The method allows producing the quasiperiodic structure by a finite number of translational steps of a properly designed repeating unit. The quasiperiodic symmetry affects the diffraction pattern and its characteristics are analyzed via theoretical calculation of the Fourier spectrum of the structure. We show that it is possible to express the Fourier spectrum in terms of the spectral distribution of the basic unit.