Turing’s 1952 insight — that reacting and diffusing chemicals can pattern a tissue — is foundational to morphogenesis. In Cognimed it returns with a precise division of labour.
The head is the reaction. Each head’s MLP is the local per-cell gene-kinetics rule — the reaction term. It is not an alternative to a differential equation; it is the reaction function of one, learned from and traceable to the genome.
The field is the diffusion. Gap junctions and ligand diffusion couple the per-cell rule across the tissue, and the coupled system becomes a reaction–diffusion PDE integrated by the automaton. The linear, spectral part of the operator supplies the frame; the nonlinear reaction supplies spacing and identity; lateral inhibition discretizes; adhesion binds. Run in order on one domain, these four effectors recover an organ’s axis, its bilaterally symmetric spacing, its unit count and its cohesion.
Generatively: a stable diffusion. Read as a generative process, morphogenesis is a genome-conditioned stable diffusion — the reaction supplies the drive, field relaxation supplies the diffusion that settles the tissue into a stable equilibrium, and the genome is the prompt. The robustness is inherited from the biology: the canonical developmental network holds its topology across orders of magnitude of parameter variation, which is why a handful of genome-read parameters suffice.
See the papers, especially Paper 8, where the reaction-head / diffusion-field split is developed in full.