Reaction and diffusion, computed live. One rule for every pattern; two numbers decide which.
Two chemicals soak the sheet. Call them u and v. Wherever v is thick, it converts u into more of itself. Both spread by diffusion, but u spreads twice as fast, so the feed drains away from a growing spot faster than the spot can follow it. Growth up close, starvation at a distance. That pairing, a short-range activator with a long-range inhibitor, is the whole of Turing's 1952 argument, and it is what the film keeps returning to.
u' = Du ∇²u − u v² + f (1 − u) v' = Dv ∇²v + u v² − (f + k) v
This is the Gray-Scott form. Fresh u is fed in at rate f; v is removed at rate f + k. Every disc in the catalogue runs the same two lines with Du 0.16, Dv 0.08, a 96 by 96 grid and unit time step. Only f and k change from disc to disc. The zebra disc cheats once: it lets u and v diffuse four times faster sideways than up and down, which is enough to comb a labyrinth into stripes.
| Regime | f | k | Seed |
|---|
Boris Belousov mixed bromate, malonic acid and a cerium catalyst in 1951 and watched the solution flip colour on a steady beat. Chemists refused to publish it for years because it looked like a perpetual motion machine. It is not; it is a battery running down in oscillations. Spread the mixture thin and each tick triggers the next cell over, so waves travel. Break a wave and its free end curls, and you get the spirals.
The last act runs Barkley's two-variable excitable medium (a 0.75, b 0.02, ε 0.02, dt 0.02) rather than the full Oregonator. It reproduces the wave and spiral behaviour with a fraction of the arithmetic, which is why it can play at full speed in a browser tab.