Investigating dynamics of Neural Cellular Automata applied to image data in diverse complex systems

Neural cellular automata (NCA) provide a powerful computational paradigm for modelling morphogenetic processes through local interactions and self-organization. We apply NCAs to a number of prototypical complex systems ranging from morphogenesis to reaction-diffusion systems. We explore the capacity of NCA to not only replicate complex visual patterns, but also to learn the underlying update rules of dynamic systems from spatiotemporal image sequences. We reproduce the behaviour of a morphogenesis system through various training regimes and demonstrate how training strategies critically influence the ability of the NCA to grow, persist, and regenerate patterns from visual data. We find that NCAs cannot be applied "out of the box" to these diverse problems but must be adapted. We introduce a stratified multi-step training process that can be used to train NCAs to replicate diverse complex systems from image observations. Our approach demonstrates the potential for learning complex system dynamics from purely visual observations, a key capability for imageomics applications. Lastly we find that NCAs use the hidden channels to generalize to novel behaviour. We further analyse the role of hidden channels in encoding spatial memory and guiding complex pattern formation. Our experiments provide new insights into how neural CA can be adapted as general-purpose models for learning, replicating, and possibly innovating system dynamics from image-based observations. Our findings illustrate the versatility of NCA as a self-organising and rule-learning system (albeit with complex training regimes) and suggest broader applications in modelling natural and artificial systems through visual pattern analysis.