QuasicrystalA pattern with order but no repeat. Add up seven ripple sets aimed evenly around a circle and the result has perfect sevenfold symmetry yet never tiles — slide it any distance and it never quite matches itself again.Roger Penrose built such tilings by hand in 1974 and they were filed as a curiosity. In 1982 Dan Shechtman saw the same “forbidden” symmetry in X-rays scattered off an aluminium alloy; mocked for years, he took the 2011 Nobel. The resolution: a quasicrystal is the shadow of a plain repeating lattice sliced at an irrational angle from higher dimensions.