Topological vs. Metric distance
Basically all existing models of collective animal behaviour (bird flocks, fish schools, etc) assume that the interaction between different individuals depends on the metric distance, just as in physics. This implies, for example, that two birds 5 meters apart interact more strongly than two birds 10 meters apart.
Models developed by biologists are based on a “behavioural zones” scheme, where each zone is associated to one of the three basic ingredients of all models: short range repulsion, alignment, long range attraction.… Read the rest