Fuzzy recursive map

From: Roger Bagula (tftn_at_earthlink.net)
Date: 11/20/04

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    Date: Sat, 20 Nov 2004 21:26:20 GMT

      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@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
    alternative email: rlbtftn@netscape.net
    URL : http://home.earthlink.net/~tftn

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