Transient State Reorganization and Cell Differentiation in the Developmental Dynamics of Growing Neural Cellular Automata

Hiroki Sato, Atsushi Masumori, Takashi Ikegami

Growing Neural Cellular Automata (GNCA) develop complex morphologies from a single seed cell through shared local rules, yet the internal dynamics of this process remain poorly understood. To investigate how GNCA grows, the full developmental trajectory of trained GNCA models was traced. The trajectory of cell state development revealed that morphological convergence often proceeds non-monotonically through transient intermediate configurations. In addition, channel-wise analysis showed that the hidden channels self-organize into modular groups in parallel with the visible form. Furthermore, geometric analysis of the cell state space indicated that cell states diversify within a low-dimensional, smooth manifold. To examine cell development in more detail, community detection on an $ε$-neighbour network of cells was conducted. This analysis successfully extracted discrete cell types from this continuous space, and identified transient cell-type communities during early development and stable, finer-grained types corresponding to spatially coherent regions of the mature morphology. The temporal coordination of these phenomena across multiple independent measures indicates that the developmental process of GNCA is a reorganization of transient states rather than incremental refinement.