Map Attractors in Mathematica

*Subject*: [mg3041] Map Attractors in Mathematica*From*: bobjon at gatewest.net (Jonathan Lee)*Date*: 25 Jan 1996 05:17:17 -0600*Approved*: usenet@wri.com*Distribution*: local*Newsgroups*: wri.mathgroup*Organization*: Gate West Communications, Winnipeg, Manitoba, Canada*Sender*: mj at wri.com

I am looking for a method to display chaotic map attractors in Mathematica. The idea is to take some rectangular area (usually a unit square) with some shape in it and continually deform the rectangle. Some examples are Henon's attractor, the Baker's transformation, and Arnol'd's cat map. In each case, each point (x_n, y_n) is moved to a new point by the relation (x_n+1, y_n+1)=(f(x_n, y_n), g(x_n, y_n)). For example with the Arnol'd's cat map the transformation goes along these lines: 1)start with a unit square with some shape in it (traditionally a cat's face) then 2)stretch the unit square to twice it's original width and three times it's original height, finally 3)cut up the 2*3 rectangle into 6 unit squares and mash them together (layer them one on top of another). This process is continually done to produce more complex maps. In short the transformation is this x_n+1=x_n+y_n mod 1 y_n+1=x_n+2 y_n mod 1 Does anyone have any suggestions of how I can apply this transformation to each point in the square. Any help is appreciated. Thanks in advance. --Jonathan Lee