Emergent behavior in collective dynamics
A fascinating aspect of collective dynamics is the self-organization of small scales into large-scale structures --- clusters, flocks, tissues, parties, etc.
A variety of patterns can be system-specific, yet the emerging equilibria can be derived from a few fundamental principles.
We discuss the large-time, large-crowd dynamics driven by different “rules of interactions”, which balance the competition between anticipation to align local parts of the crowd, and different external forces that keep the crowd together. We address the question how short-range interactions lead, over time, to the emergence of long-range patterns, comparing geometric vs. topological interactions.