polygons to ellipses

n = 12;
ngen = 100;
gen0 = RandomReal[{-1, 1}, {n, 2}];
nextgen[gen_] := (gen + RotateLeft[gen])/2;
gens = NestList[nextgen, gen0, ngen];
frame[m_] := Graphics[{
    If[m - Floor@m == 0,
     {
      FaceForm[None],
      EdgeForm[Directive[Thick, Black]],
      Polygon[gens[[Floor@m]]],
      PointSize[0.025], Black,
      Point[gens[[Floor@m]]]
      },
     If[m - Floor@m == 0.25,
      {
       FaceForm[None],
       EdgeForm[Directive[Thick, Black]],
       Polygon[gens[[Floor@m]]],
       PointSize[0.025], Black,
       Point[gens[[Floor@m]]],
       Red,
       Point[gens[[Floor@m + 1]]]
       }
      ,
      If[m - Floor@m == 0.5,
       {
        FaceForm[None],
        EdgeForm[Directive[Thick, Black]],
        Polygon[gens[[Floor@m]]],
        PointSize[0.025], Black,
        Point[gens[[Floor@m]]],
        Red,
        Point[gens[[Floor@m + 1]]],
        EdgeForm[Directive[Thickness[0.0025], Red]],
        Polygon[gens[[Floor@m + 1]]]
        }
       ,
       If[m - Floor@m == 0.75,
        {
         FaceForm[None],
         EdgeForm[Directive[Thick, Red]],
         Polygon[gens[[Floor@m + 1]]],
         PointSize[0.025], Red,
         Point[gens[[Floor@m + 1]]]
         }
        ,
        {}
        ]
       ]
      ]
     ]

    }
   , PlotRange -> 1, ImageSize -> 300];
Manipulate[
 frame[m]
 , {m, 1, ngen - 1, 0.25}]