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MathGroup Archive 1996

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Map Attractors in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg3048] Map Attractors in Mathematica
  • From: Jonathan Lee <bobjon at gatewest.net>
  • Date: Sun, 28 Jan 1996 03:21:46 -0500
  • Organization: Gate West Communications, Winnipeg, Manitoba, Canada
  • Sender: owner-wri-mathgroup at wri.com

I am looking for a way to generate chaotic maps in Mathematica. The idea is to plot 
the orbits of all points in a rectangular region under a given transformation 
(x,y)->(f(x,y),g(x,y)). For example, the Arnol'd's cat map based on the 
transformation (x,y)->(x+y mod 1,x+2y mod 1) is based on stretching out a unit 
square to twice it's original width and three times it's original height to produce 
6 unit squares which are all mashed together (basically they are layered on top of 
one another). The trick is that the unit square has some sort of shape in it 
(traditionally a cat's face), which is also appropriately distorted.
If anyone has any suggestions on how to generate various iterations of this or any 
other map all and any help is appreciated. Thanks in advance.

--Jonathan Lee

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