About This Tool
Predator Prey is a cyclic cellular automaton — also known as a rock-paper-scissors automaton — where three states chase each other across a grid: empty space is colonised by prey, prey is eaten by predators, and predators eventually die leaving empty space behind. The result is perpetual spiral waves that never settle, driven entirely by three simple neighbourhood rules.
How to Use
Watch the simulation start from a random cluster seed and evolve on its own.
Use the Speed buttons to slow down or speed up the generation rate.
Use the Cell size buttons (S / M / L) to zoom in for more detail or zoom out to see the full wave pattern.
Hit Reset at any time to start a fresh random configuration.
Frequently Asked Questions
Does the simulation ever end?
No. The cyclic rule is mathematically guaranteed to keep all three states in competition on a toroidal grid, so the spiral waves continue indefinitely.
What is a cyclic cellular automaton?
A cyclic CA is a grid where each cell has N states that cycle like rock-paper-scissors. A cell advances to the next state only when enough neighbours are already in that next state, creating propagating wave fronts.
Why does it form spirals?
Spirals emerge naturally from the cyclic rules whenever a small asymmetry exists in the initial conditions. They are a self-organising attractor of the system — no special setup is needed.
Is this related to the Lotka-Volterra predator-prey model?
It captures the same intuition — populations oscillate because prey enables predators which then overshoot and collapse — but the mechanism is a spatial cellular automaton rather than differential equations.