Balancing centralized learning and distributed self-organization: a hybrid model for embodied morphogenesis

Abstract Background: both embodied intelligence and developmental morphogenesis depend on a division of labour between centralized guidance and distributed material dynamics, but the amount of top-down control needed to steer self-organization remains unclear. Methods: we coupled a compact full-resolution convolutional controller to a differentiable Gray–Scott reaction-diffusion (RD) substrate. The controller observes two fields, U and V, and applies smooth gain-scheduled modulations of the feed and kill parameters (ΔF and ΔK). We compared pure RD, neural network (NN)-dominant and hybrid regimes and evaluated spectral selectivity, convergence and control cost. Results: the hybrid regime achieved 100% strict convergence at approximately 165 steps, whereas pure RD and the NN-dominant baseline did not converge within the same horizon. It matched the substrate's spectral selectivity while using approximately 15× less L1 effort and over 200× less L2 power than the NN-dominant controller. Moderate amplitudes (A ≈ 0.03–0.045) formed a Goldilocks zone with 100% quasi-convergence in 94–96 steps. Conclusions: effective control is best framed as seed then cede: brief, smooth parameter-level nudges place the system in a favourable basin of attraction, after which reaction-diffusion dynamics complete and stabilize the pattern. This provides a quantitative model of morphological computation for controlled self-organization.