Mandelbrot visualisation

f21 = Compile[{{n, _Real}, {x, _Real}, {y, _Real}}, Re[
    With[{f =
       Nest[If[Abs[#] <= 100, (#^2 + x + I y), #] &, 0, Floor[n]],
      t = n - Floor[n]},
     f (1 - t) + (f^2 + x + I y) (t)
     ]

    ], CompilationTarget -> "C"];
f22 = Compile[{{n, _Real}, {x, _Real}, {y, _Real}},
   Im[
    With[{f =
       Nest[If[Abs[#] <= 100, (#^2 + x + I y), #] &, 0, Floor[n]],
      t = n - Floor[n]},
     f (1 - t) + (f^2 + x + I y) (t)
     ]
    ]
   , CompilationTarget -> "C"];

img0 = Rasterize[Graphics[
    Table[
     {ColorData["DarkRainbow"][r], Disk[{0, 0}, 1 - r]}
     , {r, 0, 1, 0.04}]
    , Background -> Black], RasterSize -> 200, ImageSize -> 200];

frame[n_] := ImageTransformation[img0,
   Function[{p}, With[{x = p[[1]], y = p[[2]]},
     {f21[n, x, y], f22[n, x, y]}
     ]
    ]
   , DataRange -> {{-2, 1}, {-1.5, 1.5}}];
frames = Table[frame[n^2], {n, 1, 3.5, 2.5/87}];
Export["mandel.gif", frames]