Aperiodic tiling with 5-fold symmetry — never repeating, never periodic
Penrose tilings (1974) are aperiodic — they fill the plane without ever repeating. They exhibit 5-fold symmetry (impossible in crystallographic lattices). Generated by inflation/deflation: each triangle substitutes into smaller copies scaled by 1/φ (φ = golden ratio ≈ 1.618). The ratio of fat:thin rhombi (P3) converges to φ:1. Discovered by Roger Penrose; equivalent structures appear in quasicrystals.