Wolfram Research

Function Repository Resource:

CatMap

Source Notebook

Apply cat map on an image

Contributed by: Enrique Zeleny

ResourceFunction["CatMap"][image,n]

gives n steps of the cat map on the points of image.

Details and Options

Arnold's cat map is a simple discrete system that stretches and folds points (x, y) to (x+y, x+2y) 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 positions.

Examples

Basic Examples

Apply CatMap on an image a single step:

In[1]:=
ArrayPlot[ResourceFunction["CatMap"][\!\(\*
GraphicsBox[RasterBox[CompressedData["
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Out[1]=

Apply CatMap different number of steps:

In[2]:=
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"], {{0, 0}, {100, 100}}, {0, 255}]]\), n], Frame -> False, ColorFunction -> GrayLevel], {n, {2, 75, 76, 129, 148, 149}}]} // GraphicsGrid
Out[2]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

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