Arnold’s Cat Map is an area-preserving linear map on the unit torus. Each step shears the square via the matrix [[1,1],[1,2]] (determinant 1) and wraps coordinates. This visualization uses an exact discrete model (integer arithmetic on a fine 2^32 torus) so the simulated map stays a precise bijection without floating-point orbit collapse. The map stretches and folds phase space so nearby points diverge exponentially while overall density stays uniform — the same stretch-and-fold mechanism that classically scrambles images. Points are colored by their initial height so the shearing and mixing remain visible as iterations proceed.