Swift-Hohenberg Pattern Formation

The Swift-Hohenberg equation ∂u/∂t = εu − (∇²+k₀²)²u − u³ generates spontaneous stripe and spot patterns via a wavelength-selecting instability. Near onset (ε>0) the system amplifies modes at the critical wavenumber k₀, producing spatially periodic structures reminiscent of convection rolls, animal coats, and chemical waves.

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