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MathGroup Archive 1996

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Re: Map Attractors in Mathematica

  • Subject: [mg3135] Re: Map Attractors in Mathematica
  • From: pnardon at ulb.ac.be (Pasquale Nardone)
  • Date: 7 Feb 1996 10:40:39 -0600
  • Approved: usenet@wri.com
  • Distribution: local
  • Newsgroups: wri.mathgroup
  • Organization: Université Libre de Bruxelles
  • Sender: daemon at wri.com

suppose that you have a starting function in 2 dimension
f[x_,y_]:=....
you can then define the recursive mapping by:

g[{x_,y_},n_]:=g[Mod[{x+y,x+2*y},1],n-1];
g[{x_,y_},0]:=f[x,y];

and then use the DensityPlot to see what happens:

DensityPlot[g[{x,y},5],{x,0,1},{y,0,1},PlotPoints->30]

(for example this is the 5 iterate)

For the f[x_,y_] you can define it mathematically
i.e.
f[x_,y_]=If[((x-0.5)^2+(y-0.5)^2<0.1),1,0]

or, if you have a bitmap object, for example on my Mac I use
a "icon" (a 32x32 bitmap with a "smile"):

AFile="2G:smile";
data=ReadList[fichier,Byte,1024];
data=Partition[data,32];
Show[DensityGraphics[1-data/255,ColorFunction->(Hue[1-#,1-#,1]&)]];

(* this is the starting image *)

f[x_,y_]:=Transpose[data][[Floor[31*x+1],Floor[-31*y+32]]];

DensityPlot[f[x,y],{x,0,1},{y,0,1},PlotPoints->32];

(*this define a 2 dimension function which correspond to
the bitmap *)


-- 
--------------------------------------------
 Pasquale Nardone                          *
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 CP 231, Sciences-Physique                 *
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        ,,,
       (o o)
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