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MathGroup Archive 2001

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Re:chaos-to -order transform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg27372] Re:chaos-to -order transform
  • From: bghiggins at ucdavis.edu (Brian Higgins)
  • Date: Thu, 22 Feb 2001 02:25:17 -0500 (EST)
  • Organization: The Math Forum
  • References: <96t8ss$pqi@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Roberto,

The following Mathematica code will display the sequence of points in
a list of graphic objects which can be then animated using the
"animated selected graphics: under the Cell menu.


myiterator[x0_, y0_] := Module[{T, mylist}, T = {{2 Cos[t], Cos[t] -
Sin[t]},
         {Cos[t] + Sin[t], Cos[t]}} ;
    mylist := NestList[(Mod[T.{#[[1]], #[[2]]}, 1]) &, {x0, y0}, 200];
    Table[
      ListPlot[mylist, Frame -> True, Axes -> False, AspectRatio -> 1,

        Epilog -> {PointSize[0.04], RGBColor[0, 0, 1], Point[{x0,
y0}]}], {t, 
        0, \[Pi]/2, .02}]]

myiterator[.4, .7]

The seed is colored blue.

Hope this helps you get started

Cheers,
Brian



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