Multiple chaotic trajectories forming a luminous ribbon through the butterfly attractor
The Lorenz system (1963): ẋ=σ(y-x), ẏ=x(ρ-z)-y, ż=xy-βz exhibits sensitive dependence on initial conditions — the hallmark of chaos. Multiple nearby trajectories (same initial conditions ± ε) quickly diverge, tracing out the fractal butterfly attractor. The attractor has dimension ≈ 2.06 and is the paradigmatic example of a strange attractor.