  Neural Cellular Automata (NCA) models are trainable variations of traditional
Cellular Automata (CA). Emergent motion in the patterns created by NCA has been
successfully applied to synthesize dynamic textures. However, the conditions
required for an NCA to display dynamic patterns remain unexplored. Here, we
investigate the relationship between the NCA architecture and the emergent
dynamics of the trained models. Specifically, we vary the number of channels in
the cell state and the number of hidden neurons in the MultiLayer Perceptron
(MLP), and draw a relationship between the combination of these two variables
and the motion strength between successive frames. Our analysis reveals that
the disparity and proportionality between these two variables have a strong
correlation with the emergent dynamics in the NCA output. We thus propose a
design principle for creating dynamic NCA.
