Discrete map · 2D · dim 2
Arnold cat map
Toral automorphism with eigenvalues (3 ± √5)/2. Exponential stretching along the unstable eigendirection, then folding by mod 1. Mixes phase space exponentially; popular in image scrambling.
Equations
(x, y) ↦ ((2x + y) mod 1, (x + y) mod 1)At a glance
| Parameters | (no free parameter) |
|---|---|
| Chaotic for | always |
| Lyapunov exponent | λ = ln((3 + √5)/2) ≈ 0.962 |
| History | Vladimir Arnold's 1960s illustration of hyperbolic mixing. |
Try it
Open the interactive playground at /tools/arnold-cat.