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Re: random walk visualization

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105264] Re: random walk visualization
  • From: dh <dh at metrohm.com>
  • Date: Wed, 25 Nov 2009 22:59:52 -0500 (EST)
  • References: <heimn8$5mc$1@smc.vnet.net>


Alexei Boulbitch 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

> 

Hi Alexei,

you need to tell "Animate" taht i should change in steps of 1:

Animate[Show[{Graphics[{Blue, Line[tab[[1 ;; i]]]}],

    Graphics[{Red, Thick, Arrowheads[0.03], Print[i];

      Arrow[{tab[[1]], tab[[i]]}]}]},

   PlotRange -> {{-40, 40}, {-40, 40}}], {i, 2, 1000, 1}]



Daniel




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