Fish Schooling — 3-Zone Model

Couzin et al. (2002): repulsion, alignment, attraction zones drive collective behavior

Polarization:
Angular momentum:
Phase:
Three-zone model (Couzin et al. 2002): each fish has zones of repulsion (avoid collision), orientation (align direction), and attraction (move toward neighbors). Varying zone radii produces phase transitions: swarm (high noise/small orient) → torus/milling (intermediate) → polarized school (large orient). Blind angle behind each fish reduces rear awareness.