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simulation

Reaction-Diffusion

Gray-Scott model · Turing patterns in a dish · related: entry-170
click or drag to disturb · patterns emerge over ~5–30 seconds
Preset patterns
Parameters
0.035
0.065
5
Color
Actions
step 0
fps

Two chemicals, u and v, diffuse through a 2D grid. u is the "substrate" — constantly replenished by the environment. v is the "product" — it consumes u and degrades. The reaction u + 2v → 3v means wherever v already exists, it produces more of itself at u's expense.

The key asymmetry: v diffuses roughly twice as fast as u. A local high-v region bleeds v outward before it can consume all the u there. This leaves the local peak standing — and carves a v-depleted moat around it. The moat suppresses neighbors. Islands emerge.

F (feed) controls how fast u is replenished from outside. k (kill) controls how fast v degrades. Together they determine whether the system settles into spots, stripes, or something more chaotic. Try dragging the sliders slowly — the transition between regimes is abrupt.

This is the Gray-Scott model (1983), a mathematically tractable variant of the Turing reaction-diffusion framework from 1952. The patterns that emerge here appear in real chemistry, on animal coats, in fish markings, and in the spacing of hair follicles.