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I have these functions

Randomwalk1[n_] :=Accumulate[2*RandomInteger[{0, 1}, n] - 1];

Randomwalk2[n_] := NestList[# + 2*RandomInteger[{0, 1}] - 1 &, 0, n]

that are random walks in 1D and I have to modify them to get a random walk in 2D, the walker can move right, left, step back or move forward with same probability 1/4 .. I'm a beginner and really don't know how to do that..

Thanks

I was thinking about an other way to do that without using these functions but I don't know if it can work and don't know how to do that in mathematica, here is the idea

if RandomInteger[{1,2}]=1 the walker moves in x direction

and if RandomInteger[{1,2}]=2 the walker moves in y direction

Then we call 2*RandomInteger[{0, 1}] - 1 to randomly generate -1 or +1 and the walker makes this step in the direction that was first determined

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    $\begingroup$ Have you seen RandomChoice[]? $\endgroup$ – J. M.'s ennui♦ Oct 8 '15 at 4:47
  • $\begingroup$ We didn't see a lot ! But we have the right to use everything in mathematica $\endgroup$ – ferrou Oct 8 '15 at 5:07
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    $\begingroup$ From the help data2d = RandomFunction[RandomWalkProcess[0.5], {0, 10^3}, 2]; Graphics[Line[Transpose@data2d["States"]], AspectRatio -> Automatic] $\endgroup$ – Dr. belisarius Oct 8 '15 at 5:30
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    $\begingroup$ A shorter version for your one-dimensional problem using RandomChoice as suggested by @J.M.: randomwalk[n_] := Accumulate[RandomChoice[{-1, 1}, n]]. The extension to the 2D case that you are asking for would read: randomwalk2d[n_] := Accumulate[RandomChoice[{-1, 1}, {n, 2}]]. $\endgroup$ – user31159 Oct 8 '15 at 5:37
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    $\begingroup$ @blochwave Yes I agree, this would be an unfortunate wording though. $\endgroup$ – user31159 Oct 8 '15 at 15:01
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I am also new. But I think the following works

randomwalk[n_] := 
 NestList[move := 
   RandomChoice[{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}]; # + move &, {0, 
   0}, n]
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    $\begingroup$ You can make your code a little simpler with: Randomwalk[n_] := NestList[# + RandomChoice[{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}] &, {0, 0}, n]. $\endgroup$ – user31159 Oct 8 '15 at 5:46
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Try this:

    Manipulate[
 list = Accumulate[RandomInteger[{-1, 1}, {stepsNumber, 3}]];
 xmin = Min[(Transpose@list)[[1]]];
 xmax = Max[(Transpose@list)[[1]]];
 ymin = Min[(Transpose@list)[[2]]];
 ymax = Max[(Transpose@list)[[2]]];
 zmin = Min[(Transpose@list)[[3]]];
 zmax = Max[(Transpose@list)[[3]]];

 Animate[

  Show[{
    Graphics3D[{Blue, Line[Take[list, i]]}],
    Graphics3D[{Darker@Red, Arrowheads[0.03], Thickness[0.005], 
      Arrow[{First[list], list[[i]]}]}]
    }, PlotRange -> {{xmin, xmax}, {ymin, ymax}, {zmin, zmax}}, 
   ImageSize -> {400, 400}],
  {i, 2, Length[list], 1}, AnimationRepetitions -> 1, 
  AnimationRunning -> False], {{stepsNumber, 2


   }, ControlType -> InputField, FieldSize -> 7}, 
 SaveDefinitions -> False]

Put an integer number (say, 10000) into the input field and press the arrow button. That's what you should get:

enter image description here

Have fun!

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