Reaction–diffusion systems model two chemical species U and V that react and diffuse at different rates. The Gray–Scott model used here produces Turing patterns: spots, stripes, mazes and self-replicating spots — the same mathematics that governs animal coat patterns, sand-dune formation, and embryonic development. Two parameters — feed rate F and kill rate k — control which pattern emerges.
The simulation runs on the GPU as a WebGL fragment shader — it updates thousands of cells per frame in parallel. Click to seed species V at the cursor. Drag the F slider (feed rate) to change pattern type: low F → mazes; medium F → spots; high F → waves. The k slider (kill rate) controls spot replication. Pause, then adjust parameters to watch patterns metamorphose from one type to another.
Alan Turing published "The Chemical Basis of Morphogenesis" in 1952 — two years before his death — proposing that reaction-diffusion could explain biological pattern formation. It was largely ignored for decades. In 2012, biologists confirmed Turing-like patterns directly in mouse embryo digit formation. The mathematics of a 1952 paper shapes every finger you have.