Ring Attractor Dynamics as a Controller for Neural Cellular Automata

Neural Cellular Automata (NCA) have demonstrated robustness to damage by learning local update rules through a small neural network, giving rise to globally coherent morphogenetic structures. However, this coherence and robustness arise from an attractor learned in the hidden space whose underlying mechanism remains uncharacterized; in addition, the learned update rule is opaque. Motivated by the timescale separation observed in biological systems, from fast cell-level dynamics to slower, coordinating processes, we introduce a Hybrid NCA architecture that incorporates a slow-timescale controller governed by the Complex Ginzburg-Landau Equation (CGLE). The controller's state conditions the network's hidden feature space through learned modulation gates using Feature-wise Linear Modulation (FiLM). Phase-portrait analysis shows that the controller's internal state organizes onto a ring geometry. In damage-recovery experiments, the Hybrid model achieves significantly lower reconstruction error than the baseline across all damage conditions, and significantly faster recovery under half and random damage. Moreover, in preliminary experiments, the Hybrid model recovers the target morphology under moderate rotational perturbations (20° and 45°), which the baseline fails to do, although reconstruction degrades at larger angles. These results suggest that the Hybrid model offers more interpretable dynamics and greater robustness than the baseline NCA.