Take Flight

Taking the butterfly conceit from my last animation even more literally.

Here's the code:

DynamicModule[{t = ?/6., s, cols},
 cols = RGBColor /@ {"#FA5555", "#F7FB76", "#8DED8E", "#2D7D8F"};
 Manipulate[
  Graphics[{FaceForm[None], EdgeForm[Thickness[.005]], 
    Table[s = ?/3. Haversine[2 r]; {EdgeForm[
       Blend[{GrayLevel[.9], If[EvenQ[x], cols[[1]], cols[[2]]]}, 
        3 s/?]], 
      Polygon[FoldList[
        Plus, {Sqrt[3] (x + (-1)^x 2 Haversine[r]), 
         2 Sqrt[3] y + Sqrt[3] HeavisideTheta[(-1)^x]}, 
        Table[{Cos[?], 
          i (3/4 + Cos[2 i r]/4) Sin[?]}, {?, 
          Accumulate[{?/3, ?/2, ?/3, ?/
             2}]}]]]}, {x, -9, 8}, {y, -4, 4}, {i, {-1, 1}}], 
    Table[s = ?/3. Haversine[2 r]; {EdgeForm[
       Blend[{GrayLevel[.9], If[EvenQ[x], cols[[3]], cols[[4]]]}, 
        3 s/?]], 
      Polygon[FoldList[
        Plus, {2 Sqrt[3] y + 
          Sqrt[3] HeavisideTheta[(-1)^x] - (3 Sqrt[3] - 1)/2, 
         Sqrt[3] (x + (-1)^x 2 Haversine[r]) + (Sqrt[3] - 1)/2}, 
        Table[{i (3/4 + Cos[2 i r]/4) Sin[?], 
          Cos[?]}, {?, 
          Accumulate[{?/3, ?/2, ?/3, ?/
             2}]}]]]}, {x, -9, 8}, {y, -4, 4}, {i, {-1, 1}}]}, 
   PlotRange -> {{-9 - Sqrt[3], 10}, {-10, 10}}, ImageSize -> 540, 
   Background -> GrayLevel[.15]], {r, 0., ?}]]