# Two-Dimensional Generalized Arnold Cat Map

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The Arnold cat map has the interesting property that, after some large but finite number of iterations, a state arbitrarily close to the initial state appears. According to the Poincaré recurrence lemma, a map has such a "recurrence property" if and only if it is a measure-preserving map. Thus Arnold's cat map could be generalized to a family of measure-preserving maps of some space to itself.

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Contributed by: Yikai Teng (June 2020)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

This Demonstration provides three pictures as examples: a stack of apples, a flower and a house. You can upload pictures to the initialization section to see the cat map working on other pictures. You can select resolutions from 32 to 256 dots per inch. Powers of 2 are used to minimize the number of iterations required to return to the initial state.

## Permanent Citation