Hunters pursue runners through the passages. Caught creatures return to the habitat.
Density flows only through open passages. Prey grows; feeding sustains predators. No automatic respawns.
The model
At cell i, prey u and predators v follow:
du/dt = Dᵤ Σⱼ(uⱼ − uᵢ) + r uᵢ(1 − uᵢ/K) − F(uᵢ)vᵢ
dv/dt = Dᵥ Σⱼ(vⱼ − vᵢ) + e F(uᵢ)vᵢ − m vᵢ − c vᵢ²
F(u) = a u / (1 + a h u)
Crowding c adds predator competition; c = 0 recovers the original mortality rule. Feeding time h limits how quickly a predator can consume prey. At h = 0, feeding is proportional to prey density. The sum includes open neighboring cells only. Each cell has equal habitat capacity, regardless of its drawn area. Density means expected population per cell. Time and rates use simulation units.
Colors show logarithmic density, saturating at twice the prey capacity. The solver retains fractional populations. Numerical experiments are illustrative, not a validated ecological forecast.
Size, population and pattern apply to the next world. Larger worlds take longer to create.