Average unit cell of a square Fibonacci tiling

Abstract

Square Fibonacci tiling is an example of a quasicrystalline structure with classical crystallographic 4-fold symmetry. Using a probabilistic approach, an average unit cell has been constructed in physical space. This allows one to calculate the diffraction patterns in different directions. The projected structure into different directions can be also regarded as decorated Fibonacci chain. The diffraction pattern of the square Fibonacci chain has been fully analyzed in the average unit cell approach.