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
>
> alternative email: rlbtftn at netscape.net
>
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

```

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