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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