Multi-scale causality in active matter

Deciphering how local interactions drive self-assembly and multi-scale organization is essential for understanding active matter systems, such as self-organizing bacterial colonies. This study combines topological data analysis with causal discovery to capture the complex, hierarchical causality within these dynamic systems. By leveraging the Euler characteristic as a topological descriptor, we reduce high-dimensional, multi-scale data into essential structural representations, enabling efficient, meaningful analysis. Through causal discovery methods applied to the topology of these dynamic, multi-scale structures, we reveal how localized bacterial interactions propagate, guiding global organization in systems with both homogeneous and heterogeneous ordering. The findings indicate that, while ordering patterns may differ, the mechanisms underlying multi-scale self-assembly remain consistent, with information flowing primarily from local, highly-ordered structures. This framework enhances understanding of self-organization principles and supports applications requiring scalable causal analysis in complex data environments across natural and synthetic active matter.