Pagan

Pagan is an interactive predator-prey ecology laboratory that puts the mathematics of population dynamics in the palm of your hand. Tune prey birth rates, predation coefficients, and carrying capacity, then watch the Lotka-Volterra equations unfold through a high-precision RK4 integrator. Whether populations spiral into steady coexistence, collapse into extinction, or lock into a perpetual limit cycle depends entirely on the parameters you set. The Lab is your primary workspace. Three views illuminate the same simulation from different angles: a Timeline chart traces every population over time, a Phase Portrait maps trajectories through state space with auto-classified fixed points, and the Stability panel reads out equilibria, eigenvalue-derived stability classes, and limit-cycle detection. An optional logistic carrying-capacity term and a third competing species let you push beyond the classic two-species case. Step into Spatial mode to watch population waves ripple across a live reaction-diffusion grid. Paint prey and predator densities cell by cell, adjust diffusion rates, and hit play to see dynamic spatial patterns emerge in real time. Save any run to your personal library, attach a field photo, and reload it into the Lab whenever you like. The built-in Ecology Guide walks you through classic outcomes including stable coexistence, competitive exclusion, limit cycles, and extinction, making Pagan equally useful as a study companion and a sandbox for open-ended exploration. Everything runs on-device with no account required.