Wood-ant mounds (genus Formica) are not random heaps: many are built asymmetrically, extended and gently sloped on the sun-facing side, which increases the surface area intercepting low-angle sunlight and lets the colony use solar gain instead of metabolic heat alone to warm the brood chambers.
Each thatch patch on the dome absorbs solar power by the cosine (Lambert) law, using the local outward surface normal n̂ and the sun-direction unit vector ŝ:
Irradiance on patch = S₀ · max(0, n̂ · ŝ)
Sun direction from elevation θ and azimuth φ (0 = solar noon, due south):
ŝ = (sinφ·cosθ, sinθ, cosφ·cosθ)
The nest core temperature T follows Newton's law of cooling with a solar source term and an extra ventilation loss term that switches on once vents are open:
dT/dt = a·Q_solar(t) − b·(T − T_amb) − v(t)·c·(T − T_amb)
Q_solar = mean absorbed irradiance over the whole dome (0 at night)
v(t) = fraction of vents currently open (bang-bang control)
- Peak sun elevation — the sun's maximum altitude at solar noon (stands in for season/latitude); the sun traces a sine arc from sunrise to sunset each simulated day.
- South-slope elongation — how much the dome's footprint is stretched toward the sun; 0 is a symmetric hemisphere, higher values mimic the real elongated, low-angle Formica profile and visibly raise the daily peak temperature.
- Vent-opening threshold — each of the 8 surface vents has its own threshold (jittered around this value, matching how individual workers react at slightly different set-points) and opens with hysteresis once the core exceeds it, closing again a couple of degrees below it — the same bang-bang strategy real colonies use, adding worker-carried soil to plug holes or removing it to vent.
- Heat map toggles the dome's coloring between "natural thatch" and a live red↔blue map of absorbed solar flux per patch; Vents toggles their visibility.