Updated Pi Random Walk

a = Pi;
vis[a_, b_, n_] :=
  Module[{l = RealDigits[a, b, n][[1]]},
   Line@Accumulate@Map[N@{Sin[2 Pi (#/b) ], Cos[2 Pi (#/b) ]} &, l]];
frame[n_] :=
  Graphics[{{White, Thick, vis[a, 10, n]}}, PlotRange -> All,
   ImageSize -> {300, 300},
   Background -> RGBColor[44/255, 71/255, 98/255]];
Manipulate[frame[n], {n, 1, 1000, 1}]