Swift-Hohenberg Pattern Formation
∂u/∂t = (ε − (1+∇²)²)u − u³ — pseudo-spectral 2D simulation
ε (bifurcation):
0.3
Reset
Pause
Pattern:
Stripes
Step:
0
The Swift-Hohenberg equation models spontaneous pattern formation. For ε<0 the uniform state u=0 is stable. For ε>0, patterns emerge: stripes, hexagons, or spots depending on ε. The critical wavenumber q_c=1 selects the spatial scale.