Function Repository Resource:

CatMap

Source Notebook

Apply a cat map to 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 (3) 

Apply a single step CatMap on an image:

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

Apply multiple steps of CatMap to an image:

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]=

With a color image, the mapping is performed to each color channel:

In[3]:=
(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/28e30690-a104-4c8d-ad27-091356754c11"]
Out[3]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Version History

  • 2.0.0 – 30 July 2020
  • 1.0.0 – 11 March 2019

Related Resources

License Information