Re: Martin Map (a.k.a. hopalong).
- To: mathgroup at smc.vnet.net
- Subject: [mg52300] Re: Martin Map (a.k.a. hopalong).
- From: Peter Pein <petsie at arcor.de>
- Date: Sun, 21 Nov 2004 07:23:42 -0500 (EST)
- References: <cnn1gn$8to$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Roger Bagula wrote: > I only found one concrete link to this map on the web: > http://www.flex.com/~dimai/hopmarti.html > > Clear[x,y,a,b,s,g,a0] > (* Martin map*) > b0=Cos[Pi/4]/(1.+Sqrt[3]/10 ); > c0=Cos[Pi/4]/(1.+Sqrt[3]/10 );s=-1; > digits=10000; > x[n_]:=x[n]=y[n-1]+s*Sign[x[n-1]]*Sqrt[Abs[b0*x[n-1]+c0]] > y[n_]:=y[n]=1-x[n-1] > x[0]=.6135;y[0]=.6135; > 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 > Mr Baluga, you can save a lot of time by using NestList when calculating these iterations: Clear[a, s, a0, b0, c0] (*Martin map*) b0 = c0 = Cos[Pi/4]/(1. + Sqrt[3]/10); s = -1; iterations = 10000; f[{x_, y_}] := {y + s*Sign[x]*Sqrt[Abs[b0*x + c0]], 1 - x}; a = NestList[f, {.6135, .6135}, iterations]; ListPlot[a, PlotRange -> All] Sincerly, Peter Pein -- Peter Pein 10245 Berlin