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Re: random walk visualization

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105258] Re: random walk visualization
  • From: Norbert Marxer <marxer at mec.li>
  • Date: Wed, 25 Nov 2009 06:21:21 -0500 (EST)
  • References: <heimn8$5mc$1@smc.vnet.net>

On Nov 25, 8:35 am, Alexei Boulbitch <Alexei.Boulbi... at iee.lu> wrote:
> Dear Community,
>
> I am making a demonstration for a lecture on random walk. This should
> show the random walk evolving in 2D. The following works nicely:
>
> x := 0;
> y := 0;
> tab = Table[{x += RandomInteger[{-1, 1}],
>     y += RandomInteger[{-1, 1}]}, {1000}];
> imTab = Table[
>    Show[{Graphics[{Blue, Line[tab[[1 ;; i]]]}],
>      Graphics[{Red, Thick, Arrowheads[0.03],
>        Arrow[{tab[[1]], tab[[i]]}]}]},
>     PlotRange -> {{-40, 40}, {-40, 40}}],   {i, 2, 1000}
>    ];
> ListAnimate[imTab]
>
> It however, takes a lot of memory, and few minutes to generate the
> graphics list. That is too long.
>
> If I could directly Animate the graphics instead of generating initially
> a graphics list, it would be much faster. This intends to do such a
> direct animation:
>
> x := 0;
> y := 0;
> tab = Table[{x += RandomInteger[{-1, 1}],
>     y += RandomInteger[{-1, 1}]}, {1000}];
> Animate[Show[{Graphics[{Blue, Line[tab[[1 ;; i]]]}],
>    Graphics[{Red, Thick, Arrowheads[0.03],
>      Arrow[{tab[[1]], tab[[i]]}]}]},
>   PlotRange -> {{-40, 40}, {-40, 40}}],   {i, 2, 1000}
>  ]
>
> But it does not work. I cannot understand the reason. Any idea?
>
> Regards, Alexei
>
> --
> Alexei Boulbitch, Dr., habil.
> Senior Scientist
>
> IEE S.A.
> ZAE Weiergewan
> 11, rue Edmond Reuter
> L-5326 Contern
> Luxembourg
>
> Phone: +352 2454 2566
> Fax:   +352 2454 3566
>
> Website:www.iee.lu
>
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Hello

All you have to do is to include a step size in Animate: i.e.  {i, 2,
1000, 1}

This works.

x := 0;
y := 0;
tab = Table[{x += RandomInteger[{-1, 1}],
    y += RandomInteger[{-1, 1}]}, {1000}];
Animate[Show[{Graphics[{Blue, Line[tab[[1 ;; i]]]}],
   Graphics[{Red, Thick, Arrowheads[0.03],
     Arrow[{tab[[1]], tab[[i]]}]}]},
  PlotRange -> {{-40, 40}, {-40, 40}}],   {i, 2, 1000,1}
 ]

Best Regards
Norbert Marxer


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