Running in Place

Continuing to use essentially the same code as in Reversible, Come Back, and Transition, namely:

DynamicModule[{n = 6, k = 1, j = 3, r, cols, verts},
 cols = RGBColor /@ {"#F9A1BC", "#A9EEE6", "#625772"};
 Manipulate[
  r = Cos[s];
  verts = 
   Table[(1 - r (-1)^(i + 1)) ReIm[
      E^(I (2 ? i/n - ? r/n + ?))], {i, 0, n - 1}];
  Graphics[{Thickness[.004], CapForm["Round"], 
    Opacity[1/3 + 1/6 Haversine[2 s]], 
    Table[{Blend[cols[[;; 2]], t], 
        Line[{t verts[[i]] + (1 - t) RotateRight[verts, j][[i]], 
          t RotateLeft[verts, k][[i]] + (1 - t) RotateLeft[verts, 
              k + 1][[i]]}]}, {i, 1, n - 1, 2}, {t, 0, 1 - #, #}] &[
     1/40]}, PlotRange -> 2.5, ImageSize -> 540, 
   Background -> Last[cols]], {s, 0, ?}]
 ]