2D Brusselator Turing Patterns

The Brusselator is a theoretical reaction-diffusion model exhibiting Turing instability. Starting from near-homogeneous initial conditions, the system spontaneously forms spatial patterns — spots or stripes — depending on parameters. The colormap shows the U (activator) concentration field.

Parameter a (source) 1.00

Parameter b (cross-reaction) 3.40

Du (U diffusion) 0.040

Dv (V diffusion) 0.80

Steps per frame 5

Pattern type: Computing...

Colormap: U concentration

lowhigh

Brusselator PDEs:
∂U/∂t = Du·∇²U + a − (b+1)U + U²V
∂V/∂t = Dv·∇²V + bU − U²V

Steady state: U₀ = a, V₀ = b/a
Turing condition: linearizing around (U₀,V₀), instability to wavenumber k occurs when
Dv·f_UU + Du·g_VV > 2√(Du·Dv·det(J))
where f,g are reaction terms. Requires Dv ≫ Du (the inhibitor V must diffuse faster). Spots form at intermediate b; stripes at different a/b combinations.