Turing Pattern — 3-Component Cross-Diffusion
∂u/∂t = D_u∇²u + f(u,v,w), three morphogen interactions
u (activator)
v (inhibitor)
w (modulator)
Parameters
D_u (activator diff.):
0.10
D_v (inhibitor diff.):
0.45
D_w (modulator diff.):
0.25
Feed rate f:
0.055
Kill rate k:
0.062
w coupling α:
0.20
Reset
Pause
∂u/∂t = D_u∇²u + u²v/(1+αw) − (f+k)u
∂v/∂t = D_v∇²v − u²v + f(1−v)
∂w/∂t = D_w∇²w + β(u−w)
Turing instability: D_v/D_u >> 1
Cross-diffusion w modulates activation
Step:
0
Max u:
—
Pattern:
initializing