Truffles (the fruiting body of a mycorrhizal fungus) never break the soil surface, so a bettong can only find one by smell. Each buried truffle is a scent source of strength S that matures with age; the concentration reaching the surface at distance r follows a diffusion-decay profile:
C(r) = S · e^(−r / L) / (r + r0)
— a screened-diffusion form: geometric spreading (1/r) combined with first-order decay of the volatile compound over the range L set by the slider. The bettong senses two points offset left/right of its heading (tropotaxis, like paired nostrils) and steers toward the stronger one; when the local gradient is too weak to detect (scaled by smell sensitivity), it switches to an undirected random search instead — a biased random walk, the same qualitative model used for chemotaxis in animals from insects to mammals.
Digging only succeeds probabilistically, from the concentration actually present at that spot: P(success) = 1 − e^(−k·C), so the animal must get close to a real truffle to have good odds — a wrong dig on a weak whiff usually fails. A successful dig starts a gut-passage timer (gut retention time); when it elapses the bettong defecates spores at its current location, which germinate into a brand-new truffle with probability set by germination chance — the real ecological mutualism: truffles depend on bettongs for spore dispersal since they can't release spores into the wind, and forest trees depend on the fungus for mycorrhizal nutrient exchange.
- Heatmap — the surface scent field, summed over every active truffle.
- Dashed rings — buried truffles (ground truth, for you — the bettong only ever senses the field).
- Green sparks — a spore drop; if germination succeeds a new dashed ring fades in nearby.