(* should work with old Mathematica versions, too *)

norm = Sqrt[#.#] &
rot[vec_, a_] := {{Cos[a], Sin[a]}, {-Sin[a], Cos[a]}}.vec

aba[mid_, vec_, n_] := 
  {Disk[mid, norm[vec]], 
    {GrayLevel[1 - n/5], 
      Table[
        With[{v = rot[vec, 0.3 + k 2 Pi/num]}, 
          aba[mid + 1.5 v, .5 v, n - 1]], 
        {k, num}]}}
aba[mid_, vec_, 0] := Disk[mid, norm[vec]]

num := 5;
Graphics[aba[{0, 0}, {0, 1}, 5], AspectRatio -> Automatic] // Show