1D Fibonacci chain: tiling, diffraction peaks, and phason perturbation
Fibonacci sequence: F_{n+1}=F_n∪F_{n-1}, generating L (long) and S (short) tiles with ratio τ=(1+√5)/2. Diffraction: Fourier transform of the density ρ(x). Sharp peaks at q=2π(m+nτ)/a (two incommensurate wavevectors). Phason strain: flips LS→SL locally, broadening some peaks while others remain sharp.