Lorenz attractor

Can three simple deterministic equations be unpredictable — and how do we measure that?

How the lab tests it

Integrate the Lorenz system (σ=10, ρ=28, β=8/3) with RK4 alongside a near-identical Benettin twin started δ₀=1e-9 away; track the phase-space separation, renormalise it, and average its log-growth into the largest Lyapunov exponent λ.

What it checks

the textbook λ ≈ 0.9056 > 0 (exponential divergence ⇒ deterministic chaos), on the famous two-lobed butterfly attractor whose dissipative flow contracts phase volume at ∇·f = −(σ+1+β) = −13.667