The chemistry of a leopard, written as two equations.
In his last great paper, The Chemical Basis of Morphogenesis, Turing proposed that the spots, stripes and whorls of living things need no blueprint. They fall out — inevitably — of two substances diffusing and reacting across a sheet of cells. He called them morphogens: shape-makers.
Picture two chemicals soaking through a tissue. One is an activator — where it gathers, it makes more of itself, and more of the second. The second is an inhibitor that spreads faster and shuts the first one down. Local runaway, long-range restraint.
That single tension — promote nearby, suppress at a distance — is enough. A flawlessly even field becomes unstable to its own noise, and out of the flatness a wavelength is chosen. Peaks and troughs lock into place at a spacing set by the rates of diffusion.
This lab runs the Gray–Scott variant of Turing's idea on the GPU. Every pixel holds two numbers, u and v. Each frame they diffuse into their neighbours and react — u feeds the growth of v, and v is quietly removed. Two dials govern everything.
Feed replenishes u everywhere; kill drains v. Nudge them a few thousandths and the whole tissue changes its mind — coral becomes maze becomes drifting spots becomes cells that split and split again. Nothing is drawn. It is all just chemistry finding balance.
∂v/∂t = Dv∇²v + uv² − (f+k)v
A pattern is not painted onto the animal. It is the animal, working out where it is.