Pond hydraulics. Level-pool routing: dV/dt = Q_in - Q_out - evaporation, with V(h) from the terrain stage-storage table. Outflow = broad-crested weir flow Q = C_w W (h - z_crest)^3/2 over the notch and crest + Dupuit seepage through the dam, reduced by the mud seal. Check: the steady level equals z_notch + (Q / (C_w W_n))^2/3.

Weather. Stream inflow = base flow + a gamma-like storm pulse (peak about 4 h after the rain starts) [illustrative numbers]. Air temperature: seasonal sine + daily sine. Water temperature relaxes toward air temperature; ice grows by Stefan's law h = sqrt(2 k ΔT t / (ρ L)).

Beavers. Energy use = Kleiber basal rate 70 M^0.75 kcal/day times an activity factor and a cold multiplier; they eat from the berry patches and the food cache. Trees regrow logistically; planted saplings use a faster illustrative rate (0.12 per day).

Fish and marsh. Trout count follows a water-quality index built from depth, temperature, dissolved oxygen (Elmore-Hayes saturation polynomial), marsh vegetation and tree cover. Marsh vegetation grows logistically with the flooded area.

Honest simplifications. A compressed 120-day year; one pond table; 1x speed is 0.4 simulated hours per second (a day in 60 s). The valley, dam shape and all rates are illustrative and not a model of a real site; spot-check typical values before quoting them.

3D models, terrain and textures were baked in Blender (shared with the beaver colony simulator); Three.js r160 runs the world. Not affiliated with any game.