Penrose Tiling
Aperiodic quasicrystal with 5-fold symmetry — never repeating, never random
About: Roger Penrose discovered these aperiodic tilings in 1974. Using only two shapes (here: thick and thin rhombi), the plane can be tiled with perfect 5-fold rotational symmetry — yet the pattern never repeats. This is mathematically impossible for ordinary crystals (crystallographic restriction theorem), yet Dan Shechtman found physical quasicrystals in 1982, winning the 2011 Nobel Prize in Chemistry. The tiling is generated by substitution: each rhombus is inflated and subdivided, with the ratio of thick-to-thin tiles approaching the golden ratio φ = (1+√5)/2 ≈ 1.618.