famous feather map

*To*: mathgroup at smc.vnet.net*Subject*: [mg52296] famous feather map*From*: Roger Bagula <tftn at earthlink.net>*Date*: Sun, 21 Nov 2004 07:23:35 -0500 (EST)*Reply-to*: tftn at earthlink.net*Sender*: owner-wri-mathgroup at wolfram.com

Dr Pickover published a program for this in Algorthm in the early 90's as well. Gumowski and Mira made up this model as a physics experiment. Clear[x,y,a,b,s,g,a0] (* Mira map: from Fractals ( Endlessly Repeated Geometrical Figures) page136 by Hans Lauwerier,1991*) (* famous feather map*) f[x_]:=a0*x+2*(1-a0)*x^2/(1+x^2) a0=-.48;b0=0.93; digits=10000; x[n_]:=x[n]=N[b0*y[n-1]+f[x[n-1]],100] y[n_]:=y[n]=N[-x[n-1]+f[x[n]],100] x[0]=15;y[0]=0; 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