On the scaling properties of quasicrystalline potentials of eightfold rotational symmetry

We consider a special class of quasi-periodic potentials arising in the physics of photonic systems and possessing rotational symmetry of the 8th order. We are interested in the ``scaling’’ properties of such potentials, namely, the growth rate of their closed level lines near the percolation threshold. Estimates of the corresponding scaling indices allow, in particular, to carry out some comparison of such potentials with various models of random potentials on the plane.