SWIFT-HOHENBERG EQUATION
∂u/∂t = εu − (1+∇²)²u − u³ — pattern formation near bifurcation
PARAMETERS
t = 0 | step = 0
ε (bifurcation parameter):
0.10
Noise amplitude:
0.05
Color map:
Green (default)
Plasma
Blue-gold
Reset (noise)
Pause
Swift-Hohenberg (1977)
is the canonical pattern-formation PDE. The operator (1+∇²)² selects a critical wavenumber q_c=1.
ε < 0:
uniform state stable
ε = 0:
onset of patterns (stripes, hexagons)
ε > 0:
saturated patterns; cubic nonlinearity −u³ limits amplitude
Different ε values select different pattern morphologies.