φ = (1+√5)/2 ≈ 1.61803...
Cut-and-project method:
1. Take 2D square lattice
2. Define a strip (window) at angle θ
3. Project lattice points inside the
strip onto the cut line
4. Result: quasiperiodic sequence
Fibonacci chain:
θ = arctan(1/φ) gives the
Fibonacci tiling: LSLLSLSL...
Only two tile lengths L,S with
ratio φ. Never periodic, yet
has 5-fold diffraction spots!
Projection counts: 0