A cat portrait scrambled and magically restored by a chaotic torus automorphism
The Arnold cat map acts on the unit torus T² = [0,1)²:
(x,y) → (x+y, x+2y) mod 1
General form: [[1,a],[b,ab+1]] with determinant 1 (area-preserving). The map is Anosov — uniformly hyperbolic with Lyapunov exponent
λ = ln((3+√5)/2) ≈ 0.962
Although chaotic, it is periodic on rational grids: an N×N grid returns to its original state after at most O(N log N) iterations. Watch the cat image get scrambled... then return!
Eigenvectors point along the stable (contracting) and unstable (stretching) manifolds at the golden ratio angle.