Around the Bend

Essentially the same code as Off the End, but without stereographic projection.

Here's the code for a Manipulate version:

With[{max = 12, cols = RGBColor /@ {"#007500", "#007500", "#e6c700"}},
 Manipulate[
  Graphics[
   {FaceForm[Opacity[.1]], 
    EdgeForm[Directive[Thickness[.003], Opacity[.3]]],
    Table[
     {Blend[Reverse@cols[[;; 2]], (n - 3)/(max - 3)], 
      EdgeForm[Blend[Reverse@cols[[;; 2]], (n - 3)/(max - 3)]],
      Polygon[
       Table[
        ReIm[Exp[I (-2 \[Pi] t/n + \[Pi]/2 + 2 \[Pi] i/n)]],
        {i, 1, n}]]},
     {n, 3, max}]},
   Background -> cols[[-1]], PlotRange -> Sqrt[2], ImageSize -> 540],
  {t, 0, 1}]
 ]