Re: random walk visualization

*To*: mathgroup at smc.vnet.net*Subject*: [mg105259] Re: random walk visualization*From*: Albert Retey <awnl at gmx-topmail.de>*Date*: Wed, 25 Nov 2009 06:21:32 -0500 (EST)*References*: <heimn8$5mc$1@smc.vnet.net>

Alexei Boulbitch schrieb: > 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? the reason is that Animate has no clue that it should only use integer values for i, so tab[[1;;i]] will give errors. You should use tab[[1;;Round[i]]] or, even better, the iterator {i,2,1000,1} instead, which will increase i in steps of 1. there are some other things you might want to change, the following should do what you want: n = 1000; points = NestList[# + RandomInteger[{-1, 1}, 2] &, {0, 0}, n]; Animate[Graphics[{ Blue, Dynamic[Line[points[[1 ;; i]]]], Red, Thick, Arrowheads[0.03], Arrow[points[[{1, i}]]] }, PlotRange -> Max[Norm /@ points]], {i, 2, n, 1}, AnimationRepetitions -> 1 ] hth, albert