Line under a line etc.

Clear[ycoords];
ycoords[0] = Accumulate[RandomReal[NormalDistribution[0, 0.1], 100]];
ycoords[n_] :=
  ycoords[n] =
   ycoords[n - 1] + RandomReal[NormalDistribution[0, 0.05], 100];
Clear[xcoords];
xcoords[0] = Accumulate[RandomReal[NormalDistribution[1, 0.1], 100]];
xcoords[n_] :=
  xcoords[n] =
   Sort[xcoords[n - 1] +
     RandomReal[NormalDistribution[0.08, 0.05], 100]];
k = 100; ListPlot[
 Table[Partition[
   Riffle[MovingAverage[xcoords[i], 2],
    MovingAverage[ycoords[i], 2] - i], 2], {i, 0, k}], Axes -> None,
 Joined -> True, InterpolationOrder -> 2, PlotRange -> {2, -102},
 PlotStyle -> Black, ImageSize -> {500}]