Penrose tiling: two tiles (thick and thin rhombi) tile the plane aperiodically via inflation rules — each tile subdivides into smaller copies of both tiles, scaled by φ = (1+√5)/2 (the golden ratio). The resulting pattern has 10-fold rotational symmetry in diffraction but no translational periodicity. Quasicrystals (Shechtman 1984, Nobel 2011) are the 3D crystallographic realization — forbidden by classical crystallography, yet real.