oftenpaper.net

axiom = Polygon[{Cos[#], Sin[#]} & /@ (Pi/2 + 2 Pi Range[3]/3)];

next[prev_] := prev /. Polygon[{p1_, p2_, p3_}] :> {
     Polygon[{p1, (p1 + p2)/2, (p1 + p3)/2}],
     Polygon[{p2, (p2 + p3)/2, (p1 + p2)/2}],
     Polygon[{p3, (p1 + p3)/2, (p2 + p3)/2}]};

invert[p_] := p/Norm[p]^2;

draw[n_] := Graphics[{
    EdgeForm[Black], Transparent,
    Nest[next, N@axiom, n]}];

Show[draw[10], draw[12] /. Polygon[pts_] :> Polygon[invert /@ pts],
   Method -> {"ShrinkWrap" -> True}, ImageSize -> 4 750] //
  Rasterize // ImageResize[#, Scaled[1/4]] &