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Re:chaos-to -order transform


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] -
         {Cos[t] + Sin[t], Cos[t]}} ;
    mylist := NestList[(Mod[T.{#[[1]], #[[2]]}, 1]) &, {x0, y0}, 200];
      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


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