Lorenz Attractor (3D)

RK4 integration of ẋ=σ(y-x), ẏ=x(ρ-z)-y, ż=xy-βz. σ=10, ρ=28, β=8/3. Drag to rotate. Two nearby trajectories diverge exponentially: Lyapunov exponent λ₁ ≈ 0.906.

Parameters

σ (sigma)10.0

ρ (rho)28.0

β (beta)2.7

Speed5

Divergence

Separation |δ|—

Log growth—

Steps0

Controls

Drag canvas to rotate
Lorenz (1963): strange attractor
Not periodic, not fixed point
Sensitive dependence on ICs
λ₁ ≈ 0.906 bits/sec
Fractal dim ≈ 2.06 (Kaplan-Yorke)