Fuzzy recursive map
- To: mathgroup at smc.vnet.net
- Subject: [mg52299] Fuzzy recursive map
- From: Roger Bagula <tftn at earthlink.net>
- Date: Sun, 21 Nov 2004 07:23:41 -0500 (EST)
- Reply-to: tftn at earthlink.net
- Sender: owner-wri-mathgroup at wolfram.com
I did this experiment in the early 90's and it was published in TFTN at
that time.
It gives a relatively triangular cycle. It is based on a
differential equation like: ( on Kosco fuzzy logic)
dx/dt=fuzX(x,y)-x/2
dy/dt=fuzY(x,y)-y/2
It was just a dumb experiment that give a nice picture
and doesn't even have a good rationalization.
The x and y values in the cycle trajectory of the map exceed one.
Clear[x,y,a,b,s,g,a0]
(* fuzzy recursion map*)
(* FUZZY RECURSION OF SECOND TYPE *)
(* by R.L.Bagula 2 May 1994 in TFTN*)
digits=10000;
x[n_]:=x[n]=x[n-1]+(2*(1-Abs[x[n-1]-y[n-1]])-x[n-1])/2
y[n_]:=y[n]=y[n-1]+(2*(1-Abs[x[n-1]+y[n-1]-1])-y[n-1])/2
x[0]=.2;y[0]=.1;
a=Table[{x[n],y[n]},{n,0, digits}];
ListPlot[a, PlotRange->All]
Respectfully, Roger L. Bagula
tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn at netscape.net
URL : http://home.earthlink.net/~tftn