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