Pagan

Pagan is an interactive predator–prey ecology laboratory for anyone curious about how populations rise, crash and find their balance ⚖️ over time ⏱️. Set the birth, predation, conversion and starvation rates for two interacting species, press Run, and watch 👀 the mathematics 🧮 come to life. The app 📱 integrates a coupled system of Lotka–Volterra differential equations with a fixed-step RK4 solver and shows the result three ways: • Timeline 🕒 — each population plotted over time ⏱️, so you can see 👀 oscillations, booms and collapses at a glance. • Phase portrait — the trajectory drawn in phase space, with the system's equilibrium points automatically marked and each classified by its Jacobian eigenvalues (stable node, spiral, saddle or centre), plus limit-cycle detection. • Stability — a plain-language 🗣️ read-out of what the model is actually doing. Enable an optional logistic carrying capacity, or add a third competing species, to explore richer and more surprising dynamics. In Spatial mode the same reaction runs across a grid of cells that diffuse to their neighbours — paint prey and predator densities with your finger and watch 👀 the pattern 🔢 spread as a living heatmap 🔥. Everything you build 🔨 can be kept. Save 💾 a run with a name, attach a field photo 📸 to document it, and revisit it later from the Runs library 📚 — reopen it, compare it, or load its parameters straight back into the lab to keep experimenting. The Ecology guide offers a set of ready-made scenarios — classic oscillation, stable coexistence, extinction, limit cycles and competitive exclusion — that each load into the lab with a single tap, so you can start exploring right away. Pagan is built for students, teachers, hobbyists and the simply curious: a real numerical sandbox rather than a one-shot calculator 🧮. Adjust a single rate and the whole story changes — a thriving coexistence can tip 💡 into collapse, or a wild oscillation can settle into a steady cycle. No accounts, no ads — just the model, your parameters, and the curves they produce. Whether you are learning dynamical systems, teaching population ecology, or simply enjoy watching two species chase each other toward equilibrium, Pagan turns abstract equations into something you can see 👀, tune and keep coming back to.