Balancing Centralized Learning and Distributed Self-Organization: A Hybrid Model for Embodied Morphogenesis

We investigate how to couple a learnable brain-like'' controller to a cell-like'' Gray--Scott substrate to steer pattern formation with minimal effort. A compact convolutional policy is embedded in a differentiable PyTorch reaction--diffusion simulator, producing spatially smooth, bounded modulations of the feed and kill parameters (ΔF, ΔK) under a warm--hold--decay gain schedule. Training optimizes Turing-band spectral targets (FFT-based) while penalizing control effort (\ell_1/\ell_2) and instability. We compare three regimes: pure reaction--diffusion, NN-dominant, and a hybrid coupling. The hybrid achieves reliable, fast formation of target textures: 100% strict convergence in \sim 165 steps, matching cell-only spectral selectivity (0.436 vs.\ 0.434) while using \sim 15\times less \ell_1 effort and >200\times less \ell_2 power than NN-dominant control. An amplitude sweep reveals a non-monotonic Goldilocks'' zone (A \approx 0.03--0.045) that yields 100% quasi convergence in 94--96 steps, whereas weaker or stronger gains fail to converge or degrade selectivity. These results quantify morphological computation: the controller seeds then cedes,'' providing brief, sparse nudges that place the system in the correct basin of attraction, after which local physics maintains the pattern. The study offers a practical recipe for building steerable, robust, and energy-efficient embodied systems that exploit an optimal division of labor between centralized learning and distributed self-organization.