Reaction-Diffusion Patterns: How Spots And Stripes Emerge

Reaction-diffusion systems are one of the cleanest ways to see complexity emerge from local rules. Two abstract chemicals spread, consume each other and replenish at different rates. With the right parameters, a plain grid turns into spots, stripes, coral-like fronts or labyrinths.

The Reaction-Diffusion Morphogenesis Lab turns that idea into a working browser artifact. It shows the Gray-Scott equations, exposes feed and kill controls, renders an SVG field map and reports pattern metrics so the output is more than decoration.

The Gray-Scott Equations

The model tracks two concentrations, U and V. U is replenished by feed. V is removed by kill. The two chemicals diffuse across a grid and react through the u*v^2 term. That single nonlinear term is enough to create rich structure.

The lab uses u_t = Du*lap(u) - u*v^2 + F*(1-u) and v_t = Dv*lap(v) + u*v^2 - (F+k)*v. The grid wraps around the edges, which keeps the visual artifact stable and repeatable in the browser.

Why Feed And Kill Matter

Feed and kill are small numbers, but they steer the whole pattern family. A lower kill value can preserve V long enough for spots to split. A higher kill value can make coral-like fronts. A higher feed can wash out detail or make the system too active. That is why the lab pairs the final pattern with a small local parameter sweep.

The sweep is not a full phase diagram. It is a practical editor's check: if a tiny feed or kill change flips the classification, the current setup is sensitive and should be described carefully.

What The Metrics Mean

Pattern score combines variance, edge density and active area into a compact signal. Entropy estimates how much concentration variety exists in the field. Active area counts how much of the grid has meaningful V concentration. Edge density tells whether the pattern has boundaries or is mostly flat.

Those metrics do not replace visual judgment. They make the visual honest. A field that looks dramatic but has poor score or low entropy may be a transient artifact, not a stable pattern family.

How To Use The Lab

1. Open the Reaction-Diffusion Morphogenesis Lab.
2. Run the coral sample first.
3. Switch to fingerprint, mitosis or labyrinth preset.
4. Change only feed or kill by a small amount.
5. Compare SVG output, pattern score, entropy trace and sweep CSV.

What This Does Not Prove

This is an educational numerical Gray-Scott model. It is not biological proof, medical advice, tissue simulation, manufacturing specification or safety-critical physics. Its value is that it turns a famous pattern-formation idea into an inspectable artifact with formulas, outputs and limits in one place.