Activator-inhibitor Turing pattern — basis for hydra head/foot polarity
Activator u (warm = high)
Inhibitor v (cool = high)
du/dt = Du∇²u + u²/v − μu + ρ | dv/dt = Dv∇²v + u² − νv
Gierer & Meinhardt (1972) explained how hydra can regenerate a head from any fragment.
The key: Du ≪ Dv (inhibitor diffuses much faster). This breaks symmetry and creates stable spots/stripes.