Spots and stripes from two chemicals
How a smooth mixture can make its own pattern.
What you are looking at
The screen starts smooth. Little spots and stripes appear on their own and grow into a pattern.
The idea
Say you have two chemicals mixed evenly. The first one makes more of itself, and it also makes the second one. The second one spreads out faster, and it stops the first one wherever it goes.
Think of a dry forest with fire and firefighters. Fire spreads and makes more fire. But fire also calls firefighters, who run much faster than the fire and put out fires in a ring around it. The result: patches of fire with gaps between them, not one big burn.
Turing, the same man who worked on early computers, showed in 1952 that rules like this can make spots and stripes out of nothing but a smooth start. Nobody has to draw the pattern. It comes from the rules.
Where else you see it
- Scientists think some animal coat and skin patterns, like stripes on fish, form in this way.
- Patterns in some chemical reactions in a dish.
- Sand ripples and other self-made patterns show similar ideas.
Go deeper: the proper names and the math
A reaction–diffusion system is a pair of equations: ∂u/∂t = Du∇²u + f(u,v), ∂v/∂t = Dv∇²v + g(u,v). Turing (1952, The Chemical Basis of Morphogenesis) showed that a uniform state that is stable on its own can become unstable when the two substances diffuse at different rates, usually with the inhibitor diffusing much faster than the activator (Dv ≫ Du).
The pattern has a built-in length scale set by the reaction and diffusion rates. A popular simple version is the Gray–Scott model, which produces spots, stripes, and mazes just by changing two numbers.