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 *
*
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----