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MathGroup Archive 1996

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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]
--------------------------------------------
 Pasquale Nardone                          *
                                           *
 Universiti Libre de Bruxelles             *
 CP 231, Sciences-Physique                 *
 Bld du Triomphe                           *
 1050 Bruxelles, Belgium                   *
 tel: 650,55,15 fax: 650,57,67 (+32,2)     *
        ,,,
       (o o)
----ooO-(_)-Ooo----

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