Aperiodic tilings generated by substitution rules — each tile is replaced by smaller copies of the same tile types. These self-similar structures tile the plane without ever repeating. Drag to pan, scroll to zoom.
Penrose tilings (Roger Penrose, 1974) use two rhombus types with matching rules enforcing aperiodicity. They have 5-fold quasicrystalline symmetry — no translation period, yet the diffraction pattern has sharp peaks. The ratio of fat-to-thin rhombi is always the golden ratio φ=(1+√5)/2. Dan Shechtman's quasicrystal discovery (1984, Nobel Prize 2011) was explained by Penrose-like order.