Gray–Scott · reaction–diffusion

HOW AN ANIMAL GETS ITS MARKINGS

ut = Du2uuv2 + F(1−u) · vt = Dv2v + uv2 − (F+k)v

Two chemicals. u is fed in from outside, v eats u and turns it into more of itself, and both leak away. That is the entire system — and out of it come spots, stripes, splitting cells and travelling waves, none of it drawn or scripted. Turing proposed this in 1952 as the reason an animal has markings at all. Change the feed and kill rates by a thousandth and you get a different animal.