Triangle Wave Patterns

x[t_] := {t, TriangleWave[t]};
dt = 0.01;
{tmin, tmax} = {0, 2};
ds = 1/50.0;

pts = Table[x[t], {t, tmin, tmax, dt}];
dists = Round[
   Accumulate[Map[Norm, (pts - RotateRight[pts])[[2 ;;]]]]/ds];
posns = Table[Flatten[Position[dists, i]][[1]], {i, Union[dists]}];
frame[n_] := Module[{imax},
  imax = Length[posns] - n;
  Graphics[{
    Table[
     {ColorData["DarkRainbow"][i/imax],
      Line[{pts[[posns[[i]]]], pts[[posns[[i + n]]]]}]}
     , {i, 1, imax}],
    {Thickness[0.005], RGBColor[0.0, 0.2, 0.4], Line[pts]}
    }, ImageSize -> 400, ImagePadding -> 10]];
Manipulate[frame[n],{n,1,200}]