Optic flow in the visual system determines interaction force and collective motion

Abstract

Collective motion in animal groups relies on visual cues, yet how individual sensory inputs translate into group-level dynamics remains unclear. Traditional models often assume pre-defined ``3A" rules - avoidance, attraction, and alignment - which require agents to directly access the exact positions and velocities of their neighbors. Here, we propose a minimal model based on fundamental visual processing shared across species: detection of image size and optic flow. We show that the collective patterns, such as vortex and polarized school, emerge spontaneously from the competition between image-size-driven avoidance and optic-flow-driven approach. We find that alignment does not require a pre-assumed velocity-matching rule; instead, it arises from the acceleration of an agent toward regions of strong optic flow. The model shows scale-free velocity correlations and topological visual features observed in animal groups. Our results indicate that the phenomenological 3A forces are not irreducible physical rules, but rather emergent outcomes of basic sensorimotor feedback. This framework provides a physical perspective for linking sensory inputs to macroscopic collective behaviors.