Turing Pattern Playground

Explore how simple reaction–diffusion rules can spontaneously generate spots, stripes, and spirals. This simulator uses the Gray–Scott model as a concrete example of Turing instability.

Simulation

Gray–Scott reaction–diffusion

Dark regions represent low concentration, bright regions high concentration. Use the controls to the right to change diffusion and reaction parameters.

Playback Running
Display What you see
Initial condition Used on reset

Tip: click on the canvas at any time to "add" a patch of v and watch new structures emerge.

Model parameters

Gray–Scott equations

The Gray–Scott model tracks two chemicals, an activator u and an inhibitor v: 

∂u/∂t = Du·∇²u − u·v² + F·(1 − u)
∂v/∂t = Dv·∇²v + u·v² − (F + k)·v

Diffusion

Turing patterns typically require the inhibitor to diffuse faster than the activator: Dv > Du.

Reaction / feed

For explicit Euler updates, stability typically requires dt ≤ 1 / (4·max(Du, Dv)) (with grid step = 1).

Pattern presets

Gray–Scott classics

Each preset sets F and k. Diffusion coefficients are left as-is so you can experiment with the ratio Dv / Du.

After choosing a preset, hit Reset to restart from a fresh initial condition. Then perturb the pattern by clicking in different regions.

What to look for

  • Start from an almost uniform state; small random fluctuations are enough to break symmetry.
  • Increase Dv while keeping Du fixed. Patterns sharpen as inhibition becomes longer-ranged.
  • Vary F (feed) and k (kill). Small changes can switch between isolated spots, labyrinthine stripes, and chaotic turbulence.
  • Notice how diffusion, which usually smooths things out, here creates structure when coupled to nonlinear reactions.