When species respond to each other's gradients — richer pattern formation than Turing
System
Diffusion Matrix
Kinetics
About
Standard Turing patterns arise from a diagonal diffusion matrix. Cross-diffusion adds off-diagonal terms D_uv and D_vu — species respond to each other's gradients.
This enables patterns impossible with simple Turing (e.g., traveling waves, rotating spirals, super-labyrinthine structures).
The Gray-Scott kinetics: u reacts with v² → 2v; v decays at rate k.