Penguin Huddle: Collective Thermoregulation (2D)

A simplified top-down model of the same real emperor-penguin huddling physics as the 3D version: each bird's exposed circumference fraction — how much of its edge is not shielded by a touching neighbour — sets its individual heat-loss rate, so interior birds barely lose heat while lone edge birds chill fast. Cold birds shuffle toward the centre and warm centre birds cede space outward, reproducing the documented slow traveling-wave rotation that keeps any one penguin from staying on the cold windward edge for long.