A homogeneous chemical mixture spontaneously breaks symmetry and starts oscillating between two colors. In 2D, spiral waves nucleate and propagate forever. Boris Belousov discovered it in 1951 — and was rejected by Soviet journals because "the second law forbids chemical oscillations." (It doesn't.) Anatol Zhabotinsky pushed it through in 1964. The same equations describe spiral re-entry in heart fibrillation.
why a beaker should not oscillate (but does)
The Belousov-Zhabotinsky reaction uses bromate, malonic acid, and a ferroin indicator in dilute sulfuric acid. Under steady-state stirring, the solution rhythmically switches between red and blue with a period of ~30 seconds. In an unstirred dish, target waves and spirals appear and propagate outward.
Belousov's struggle: when he submitted his discovery to a Soviet biochemistry journal in 1951, it was rejected for "violating thermodynamics" — common intuition said chemistry approaches equilibrium monotonically. Two errors lurk in that intuition: (1) the second law constrains total entropy, not local concentrations, and (2) a system held far from equilibrium by a constant fuel supply (bromate) can sustain oscillations indefinitely. Belousov gave up; only after Zhabotinsky picked the work up did it gain acceptance.
The Oregonator (Field, Körös, Noyes 1972) is a 3-variable simplification of the BZ chemistry's ~20 elementary reactions:
∂u/∂t = D_u·∇²u + (u − u² − f·v·(u−q)/(u+q))/ε
∂v/∂t = D_v·∇²v + u − v
The simulation here uses Alan Turner's (2009) minimal scheme instead: three species in a cyclic, autocatalytic loop (a converts b, b converts c, c converts a), each step mixed with its 3×3 neighborhood. It isn't the Oregonator, but it captures the same excitable, cyclic chemistry — and the same spirals self-organize out of random noise. Spirals nucleate around topological defects — points where the phase circulates by 2π. Once formed, they persist forever in idealized media; in real fluid, dissipation eventually wins. The same math governs cardiac arrhythmias: spiral waves of electrical depolarization in heart tissue are what doctors mean by "re-entrant arrhythmia" or "ventricular fibrillation."