Arnold's Cat MapShear a picture sideways, shear it upwards, and wrap whatever falls off the edge back around. Repeat. The image smears into total static within a few steps — yet keep going and it suddenly snaps back to the original, perfectly, then scrambles again forever.Vladimir Arnold demonstrated this in the 1960s with a cat. On a grid of N×N pixels the shear is a shuffle of finitely many tiles, so it must eventually return home — a hands-on version of the Poincaré recurrence theorem.