Fibonacci Quasicrystal & Diffraction

The Fibonacci sequence generates a 1D quasicrystal: substitution L→LS, S→L creates a non-periodic chain with long-range order. Its diffraction pattern shows sharp Bragg peaks at positions indexed by two integers — the signature of quasiperiodicity.

Parameters

Generation N 10 Long/Short ratio τ 1.618 k-space range 30 Peak threshold 0.05

Fibonacci words:
L→LS, S→L
F_n grows as φⁿ
φ=(1+√5)/2≈1.618

Peaks at q = (2πφ/d)·
(m + nφ) for m,n∈ℤ