Arnold's Cat Map

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Arnold's cat map is a simple discrete system that stretches and folds points (, ) to (, ) mod 1 in phase space. Typically, any two points that initially are very close together quickly become separated from each other after repeated applications of the map. The picture first shears apart and later looks random, or, in some steps, shows a ghost-like, repeated image of the original. Finally, the points return to their original position after 150 steps. The picture is a portrait of Henri Poincaré, an early pioneer in the study of this kind of recurrent behavior.

Contributed by: Enrique Zeleny (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

detailSectionParagraph


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send