       Re: Map Attractors in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg3135] Re: Map Attractors in Mathematica
• From: Pasquale Nardone <pnardon at ulb.ac.be>
• Date: Tue, 6 Feb 1996 22:49:28 -0500
• Organization: Université Libre de Bruxelles
• Sender: owner-wri-mathgroup at wolfram.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=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 *)

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```

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