The Fibonacci chain is the canonical 1D quasicrystal, obtained by projecting a 2D square lattice onto a line at the golden angle arctan(1/φ) ≈ 31.7°. Long (L) and Short (S) tiles satisfy L/S=φ. Tiles follow the substitution L→LS, S→L. The diffraction pattern shows sharp Bragg peaks at positions m+nφ (dense, but every peak is sharp — true long-range order). The energy spectrum of the associated Schrödinger operator is a Cantor set of measure zero (Sütő 1989).