Poincaré Section — Lorenz Chaos

A Poincaré section slices the Lorenz attractor with a plane (z = z₀), recording each intersection. Chaotic trajectories fill a fractal cantor-like set, while periodic orbits produce isolated points. The section reveals the attractor's hidden structure.

ẋ=σ(y−x), ẏ=x(ρ−z)−y, ż=xy−βz  |  Section: z=z₀ with ż>0  |  Fractal dim≈1.26

Lorenz Parameters

Statistics

Trajectory pts0
Section hits0
Lyapunov λ₁~0.906
Attractor typeStrange
The fractal structure in the Poincaré section (x vs ẋ at z=z₀) reveals Cantor-set-like slices of the strange attractor — infinitely fine detail, never periodic.