Re: Map Attractors in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg3110] Re: Map Attractors in Mathematica
• From: Pasquale Nardone <pnardon at ulb.ac.be>
• Date: Fri, 2 Feb 1996 03:35:52 -0500
• Organization: Université Libre de Bruxelles
• Sender: owner-wri-mathgroup at wri.com

```let's define the first image in 2 dimension:

image[x_,y_]:=any function which define the image,
for example:

image[x_,y_]:=If[(x>0.5)&&(y>0.5),1,0]

define the upper right square as the starting image. Then
define the recursive image:

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

That's all

you get the image by doing (for example the 3 iteration)

DensityPlot[g[{x,y},3],{x,0,1},{y,0,1},
PlotPoints->20];

The difficult point is to choose image[x,y] to get a Cat.
for example a small face could be:
image[x_,y_]=If[((x-0.5)^2+(y-0.5)^2<0.1),1,0]
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Pasquale Nardone                          *
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```

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