How much faster must U diffuse than V before the seed spreads instead of freezing? The dark red seed square (V = 1) thins into a green ring (V around 0.4), which sprouts narrow stripes that grow outward in every direction.
Try this While the stripes are spreading, lower diffuse-u from 0.3 to 0.16 (it takes effect live). Growth stops: active-patches holds where it was and the stripes freeze in place. The Frozen ring preset starts from that setting.
About this model Where it ends up
Alan Turing's 1952 paper on morphogenesis showed that two chemicals that react and diffuse at different rates can form stable spatial patterns from a nearly uniform start. This model uses the Gray–Scott reaction (Gray and Scott, 1983–84), whose spots, stripes and labyrinths John Pearson classified in 1993.
Each patch of a 129 × 129 grid holds U and V. Setup sets U = 1 and V = 0 everywhere, then U = 0 and V = 1 in a square of half-width seed-radius (default 9) at the center, plus a few random specks nearby. Each tick is one explicit Euler step (dt = 1) computed from the previous tick: U changes by diffuse-u·∇²U − UV² + feed·(1 − U), V by diffuse-v·∇²V + UV² − (kill-rate + feed)·V, and both are clamped to [0, 1]. ∇² is a 3 × 3 stencil (0.2 for side neighbors, 0.05 for corners, −1 for the center), and the edges are closed. Color shows V on the turbo scale.
The uniform state U = 1, V = 0 is stable, so nothing grows without the seed: patterns here start from a finite disturbance, not from the small-noise instability Turing analyzed. Whether the seed spreads depends on how much faster U diffuses than V: with diffuse-v at 0.08, stripes spread once diffuse-u is above about 0.2 (the default is 0.3), and below that the seed settles into a stationary ring. The Spots preset (diffuse-v 0.15, feed 0.037, kill-rate 0.065) grows round spots that split in two. The four rates are read every tick; seed-radius applies at Reset.
