Every bird carries its own body-heat state Tb, integrated each frame with Newton's law of cooling toward a moving equilibrium Teq set by how sheltered it currently is:
shelter = blocked fraction of the upwind cone by nearby neighbors (0..1)
T_eq = 36.5°C · shelter + (T_amb − 0.45·wind + 9°C) · (1−shelter)
dT_b/dt = (T_eq − T_b) / τ, τ larger when sheltered (thicker boundary layer)
shiver = extra metabolic heat once T_b < 32°C (bounded thermogenesis)
Shelter is computed geometrically: a neighbor only blocks wind for a bird if it sits within roughly a 120° cone on the upwind side and close enough to interrupt airflow — exactly the mechanism that makes windward-edge birds in a real emperor penguin huddle lose heat far faster than sheltered interior birds.
Behavior: a bird's urge to shuffle scales with how cold it has become. Instead of just heading for the geometric centre, it steers toward the locally warmest nearby neighbors — which, because shelter clusters on the lee side, pulls cold edge birds specifically toward the downwind interior. Combined with body-to-body collision avoidance (excluded volume), that continuous inward flux displaces already-warm interior birds back out toward the edge over time. This individually-driven turnover reproduces the qualitative "huddle wave" reported in emperor penguin field studies (e.g. Zitterbart et al., 2011): the pack never sits still, and its centroid slowly creeps downwind as new arrivals keep packing in on the windward side.
- Colony size — more birds means a deeper, better-insulated core; edge fraction shrinks relative to the group.
- Wind speed — raises the windward-edge chill component of Teq and the pace of shuffling.
- Ambient temperature — sets the baseline Teq everyone relaxes toward when exposed.