Motifs in self-organising cells
In complex systems, groups of interacting objects may form prevalent and persistent spatiotemporal patterns, which we refer to as motifs. These motifs can exhibit features that reveal how individual objects interact with one another. Simultaneously, the motifs can also interact, causing new coarse-grained properties to emerge in the system. In this paper, we found motifs in a simulated system of Dynamically Self-Organising cells. We also found that quantifying these motifs with a set of physically interpretable structural and dynamic features efficiently captures the interaction dynamics of the motifs' underlying cells. Using these motif features, we revealed packing strain and defects in large compact aggregates, semi-periodicity in motif ensembles, and phase space classes with unsupervised machine learning. Additionally, we trained neural networks to infer the critical hidden microscopic interaction parameters within each motif from coarse-grained motif features extracted from snapshots of the system. Furthermore, we uncovered emergent features that can predict the movement of cell collectives by hierarchically coarse-graining smaller motifs into larger ones (e.g. motif clusters). We speculate that this concept of motif hierarchies may be applied broadly to many-body interacting systems that are otherwise too complex to understand.