Turing's insight
In 1952 Alan Turing proposed that two chemicals — an activator and an inhibitor — diffusing at different rates could spontaneously form stable patterns. It was decades ahead of the biology that confirmed it.
The Gray–Scott model
Gray–Scott is a two-species reaction–diffusion system whose feed and kill rates select between spots, stripes, and self-replicating mazes. Small parameter changes produce dramatically different patterns.
Running it live
PolySim's dynamics studio integrates Gray–Scott with an explicit finite-difference Laplacian on a periodic grid, so you can drag the feed and kill sliders and watch the pattern regime shift in real time.