Complex Ginzburg–Landau ●

A field of coupled limit-cycle oscillators — the spatial Stuart–Landau equation. ∂A/∂t = r·A + D(1+i·c₁)∇²A − s(k₀²+∇²)²A − (1+i·c₂)|A|²A. Colour shows phase (hue) and amplitude (brightness). Cross the Benjamin–Feir line 1 + c₁·c₂ = 0 to go from frozen spirals to defect turbulence. Add the Swift–Hohenberg term (s) for stripes, or a pacemaker (Ω) for target waves. Drag on the field to stir in new defects.

−s(k₀²+∇²)²A (Swift–Hohenberg) selects a stripe wavelength; a central pacemaker Ω emits target waves. s=0, Ω=0 ⇒ pure CGLE. Stripes need low D (~0.3).

Save the current parameters + a screenshot + a note.

Record a WebM clip of the field to share (uses the name field above, if set).

A = u + i·v on a periodic grid. Drop ∇² and it is the Stuart–Landau oscillator; keep it and this same equation describes BZ near onset and liquid-crystal light-valve patterns. The −s(k₀²+∇²)²A term is Swift–Hohenberg: it selects a finite wavelength (λ≈2π/k₀) so the field forms stationary stripes / labyrinths — the Turing side of a light valve, which the pure CGLE (s=0) cannot make. It only wins over the diffusion when D is small (~0.3). The pacemaker Ω is a local frequency offset in a central disk that radiates target waves. Integrated with forward Euler and a 9-point isotropic Laplacian (applied twice for ∇⁴); |A| capped at 3 for stability.