Examples gallery

Each entry is a canonical system with a short description, the exact lawsynth discover command that recovers it, and the law system a clean run produces. Every result is a portable .lsworld bundle you can explain, forecast, and report on.

• Lorenz system — A three-variable convection model and the textbook example of deterministic chaos and a strange attractor.

• Lotka–Volterra — Predator–prey dynamics recovered from the classic Hudson's Bay lynx–hare pelt record: coupled populations that cycle out of phase.

• Damped oscillator — A mass on a spring bleeding energy to friction — the simplest system where a recovered parameter (ζ) maps directly to a physical regime.

• Van der Pol oscillator — A nonlinear oscillator with a self-sustaining limit cycle — the amplitude-dependent damping term is where symbolic search earns its keep.

• SIR epidemic — The compartmental susceptible–infected–recovered model recovered from a synthetic outbreak curve, including the mass-action infection term.