Structured Fluctuations and the Information Dynamics of Self-Maintenance in Growing Neural Cellular Automata
Growing Neural Cellular Automata (GNCA) are capable of robust self-maintenance and self-repair, yet the internal dynamical mechanisms that support these capabilities remain poorly understood. Here, we investigate the role of internal fluctuations—temporal micro-variability of hidden channel states—in a trained GNCA model, hypothesizing that they constitute a functional component of the dynamics rather than merely residual stochastic noise. We analyzed the trained model through dynamical-systems analysis (low-dimensional embedding and recurrence analysis of collective state trajectories) and information-theoretic analysis (transfer entropy and partial information decomposition), including its response to localized damage and to suppression of small-magnitude updates. These analyses show that internal fluctuations are spatially structured, dynamically coupled to an attracting collective state, and associated with distributed small-magnitude updates that contribute to damage recovery. Damage induces a global deviation in latent state space followed by gradual re-convergence, and suppressing distributed small-magnitude updates associated with baseline fluctuation dynamics outside a permissive radius that encompasses the majority of the cells significantly impairs recovery. Transfer entropy analysis characterizes a spatially differentiated repair response: corrective inward flow near the damage site coexists with outward perturbation propagation at greater distances. Partial information decomposition further suggests a regime shift from synergy-dominant resting computation to redundancy-increased coordination during recovery. These findings indicate that GNCA self-maintenance and self-repair emerge from high-dimensional nonlinear collective dynamics in which internal fluctuations serve as a functional component supporting information flow, coordination, and return toward an attracting recurrent state.