Arnold's Cat Map

Paradigm of Anosov (hyperbolic) diffeomorphism on the torus T². The map is area-preserving, uniformly hyperbolic, ergodic, mixing, and Bernoulli. Images are scrambled then exactly recovered (periodic orbit).

(x,y) → (x+y, x+2y) mod 1

det = 1 (area-preserving)

eigenvalues: φ² ≈ 2.618, 1/φ² ≈ 0.382

Steps: 0 Resolution: Show:

Step 0 of period p (period depends on grid size)