Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2004
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2004

[Date Index] [Thread Index] [Author Index]

Search the Archive

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>
  • Reply-to: tftn at earthlink.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[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



  • Prev by Date: Re: Martin Map (a.k.a. hopalong).
  • Next by Date: Re: Re: Newly Released Mathematica 5.1 Delivers Unmatched Performance for Handling Data
  • Previous by thread: Re: Martin Map (a.k.a. hopalong).
  • Next by thread: Complex plotting