       Re: Fuzzy recursive map

• To: mathgroup at smc.vnet.net
• Subject: [mg52329] Re: Fuzzy recursive map
• From: Roger Bagula <tftn at earthlink.net>
• Date: Tue, 23 Nov 2004 02:12:49 -0500 (EST)
• References: <cnq2m9\$2e8\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```The master fuzzy map programmer is Dr. P. Grim at Stoney Brook:
http://www.sunysb.edu/philosophy/faculty/pgrim/pgrim.htm
His book contains much of his Liar's paradox/ dualistic fuzzy logic work:
The Philosophical Computer, MIT Press/Bradford Books
<http://www.sunysb.edu/philosophy/faculty/pgrim/index.html>
Roger Bagula wrote:

>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=.2;y=.1;
>a=Table[{x[n],y[n]},{n,0, digits}];
>ListPlot[a, PlotRange->All]
>
>Respectfully, Roger L. Bagula
>
>alternative email: rlbtftn at netscape.net
>
>
>

--
Respectfully, Roger L. Bagula