       Re: Martin Map (a.k.a. hopalong).

• To: mathgroup at smc.vnet.net
• Subject: [mg52324] Re: Martin Map (a.k.a. hopalong).
• From: Roger Bagula <tftn at earthlink.net>
• Date: Tue, 23 Nov 2004 02:12:42 -0500 (EST)
• References: <cnn1gn\$8to\$1@smc.vnet.net> <cnq2o6\$2eb\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Dear Peter Pein,
I developed this type of mechanics not because I didn't have a nestlist
version, but
because these are "plain".
I have a Siegel disk nestlist version and on my machine
I don't remember it being that much faster, but I'm using it for 50000
points not 10000.
That is you can look at them and see what the model is
without the Mathematica nestlist mechanics getting in the way.
In most cases they are fast enough.
It would help to get the point size down though.
The built in point size is too large.

It should be noted that in teaching this kind of
mathematics the method of presentation is important.
Clarity is a factor.
I did this kind of program for an early college or late high school type
of use. Not for Mathematica programmers...
Who is the future user of the software?
What do they need to use it for?
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/10  );
>>c0=Cos[Pi/4]/(1.+Sqrt/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=.6135;y=.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/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