Problems with animation

Question

I am trying to make a random walk simulation with Animate, but somehow it doesn't produce the animation I want.

SingleRandomWalk[k_] := Module[
  {pts = {{0, 0}}},
  Do[AppendTo[
    pts, {0, 
     pts[[i, 2]] + RandomVariate[NormalDistribution[0, 1/k]]}], {i, 1,
     k}];
  Print[pts];
  Animate[
   Graphics[{PointSize[0.03], Point[pts[[i]]]}, Axes -> True, 
    AspectRatio -> 2, PlotRange -> {{-1, 1}, {-2, 2}}], {i, 1, k+1}, 
   DefaultDuration -> 1]]
SingleRandomWalk[5]

Where is the problem?

Answer 1

Try

SingleRandomWalk[k_] := 
 Module[{pts = {{0, 0}}}, 
  Do[AppendTo[
    pts, {0, 
     pts[[i, 2]] + RandomVariate[NormalDistribution[0, 1/k]]}], {i, 1,
     k}];
  Print[pts];
  Animate[
   Graphics[{PointSize[0.03], Point[pts[[i]]]}, Axes -> True, 
    AspectRatio -> 2, PlotRange -> {{-1, 1}, {-2, 2}}], {i, 1, 
    Length@pts, 1}, DefaultDuration -> 1]]
SingleRandomWalk[5]

You need {i, 1, Length@pts, 1} and not {i, 1, Length@pts} otherwise Animate does not know it is discrete ! It will otherwise try to use continuous increments which does not work for Part

Answer 2

In your code, the step of the variable of the animation is wrong. In the document, it says

Animate[expr,{u,Subscript[u, min],Subscript[u, max]}]generates an animation of expr in which u varies continuously from Subscript[u, min] to Subscript[u, max].

which means that the variable of your code i in Animate[...pts[[i]], {i, 1, k+1}] is wrong as it can be decimal. You need to add a step such as {i, 1, k+1, 1}.