Agent mobility and hotspot adaptability drive group aggregation

We present a model to study how adaptive and static hotspots shape cultural dynamics and group aggregation in spatial populations. Agents and hotspots are represented by cultural vectors, and agents move through a two-dimensional space according to their cultural similarity to nearby hotspots. Our results show that adaptive hotspots, which change their cultural vector to match the modal traits of their occupants, attract larger groups than static hotspots. At moderate and large mobility scales, hotspot occupancies follow heavy-tailed distributions consistent with multiplicative growth, producing lognormal-like patterns observed in firms, cities, and biological systems. This outcome arises from a feedback loop in which adaptive hotspots align neighboring agents who, after moving, are more likely to join them, reinforcing their advantage. Mobility regulates this process: higher mobility facilitates encounters across diverse groups, enhancing integration, while limited mobility constrains agents to suboptimal choices, fostering segregation. Overall, adaptive hotspots emerge as cultural hubs that promote convergence, in line with empirical evidence linking urban mobility to reduced segregation.