A and B tiles arranged by substitution rule — quasiperiodic order with 5-fold diffraction
Fibonacci substitution: A → AB, B → A. After n iterations the sequence has F(n+2) tiles. The ratio #A/#B → φ (golden ratio) as n→∞. Despite having no translational period, the diffraction pattern has sharp Bragg peaks at positions τ⁻ⁿ (quasiperiodic long-range order). When φ = golden ratio the peaks cluster at Fibonacci-spaced frequencies — exactly 5-fold self-similar. Discovered experimentally by Shechtman 1982 (Nobel 2011).