Re: Martin Map (a.k.a. hopalong).
- To: mathgroup at smc.vnet.net
- Subject: [mg52328] Re: Martin Map (a.k.a. hopalong).
- From: Roger Bagula <tftn at earthlink.net>
- Date: Tue, 23 Nov 2004 02:12:47 -0500 (EST)
- References: <cnn1gn$8to$1@smc.vnet.net> <cnq2o6$2eb$1@smc.vnet.net>
- Reply-to: tftn at earthlink.net
- Sender: owner-wri-mathgroup at wolfram.com
Here's where you can find the source of the Siegel Disk NestList program: http://alamos.math.arizona.edu/~rychlik/notebooks.html * A visualization of Poincare-Siegel theorem <http://alamos.math.arizona.edu/%7Erychlik/557-dir/Siegel/HTML/Siegel.html> (Mathematica generated HTML) or Siegel.nb.gz <http://alamos.math.arizona.edu/%7Erychlik/557-dir/Siegel.nb.gz> (Mathematica 3.0 notebook) Peter Pein wrote: >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 > > > -- 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