Three perfectly deterministic equations, zero randomness — yet the path swirls forever around two wings and never repeats. This is chaos: predictability with a built-in expiry date, the seed of the butterfly effect.
Lorenz simplified a weather model to three equations: dx/dt = σ(y−x), dy/dt = x(ρ−z)−y, dz/dt = xy−βz, with σ=10, ρ=28, β=8/3. There's no randomness anywhere, yet starting points an atom's width apart diverge exponentially — in two weeks of simulated time the forecast is meaningless. That's why "a butterfly's wing can change the weather": tiny causes, enormous, unpredictable effects.