🦋 Lorenz Attractor
The Lorenz system (Edward Lorenz, 1963) is a set of three coupled ordinary differential equations originally derived from a simplified atmospheric convection model. For classic parameters (σ=10, ρ=28, β=8/3) trajectories never repeat yet never leave a bounded region — a strange attractor. The iconic butterfly effect: two trajectories starting a distance 10⁻⁵ apart diverge exponentially, yet both trace the same wing-like shape. Drag to rotate. Multi-trajectory mode shows divergence in colour. 🇺🇦 Українська
Parameters
Simulation
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The Lorenz Equations
dx/dt = σ(y − x) dy/dt = x(ρ − z) − y dz/dt
= xy − βz
Integrated with RK4 (dt ≈ 0.005). The two lobes of the
attractor correspond to the two unstable equilibria at (±√(β(ρ−1)),
±√(β(ρ−1)), ρ−1). The Lyapunov exponent λ₁ ≈ 0.91 for classic
parameters — trajectories separate at rate e^(0.91t).