Spiral waves in colonies of the mold Dictyostelium discoideum.
Alan Turing was the first one who proposed reaction-diffusion systems as a theoretical idea to explain biological morphogenesis. It demonstrates how breaking and pattern formation can arise out of a homogeneous, uniform state.
The Belousov-Zhabotinsky reaction is a special non-equilibrium system that works as a chemical oscillator as it cycles through its different states in autocatalytic fashion. If unmixed the diffusing chemicals spread and cause spirals to emerge and grow.