Fibonacci Rotation

f[i_] := ColorData["DarkRainbow"][i];
Manipulate[
 If[\[Phi], \[Theta] = Pi (Sqrt[5] - 1)/4];
 Graphics[
  Reverse@Table[
    {f[1 - i/n],
     Rotate[Scale[Rectangle[{-1, -1}, {1, 1}], (i/n)^2],
      i \[Theta], {0, 0}]}
    , {i, n}]
  , PlotRange -> 1.5, Background -> f[0]],
 {{n, 50}, 1, 100, 1},
 {\[Theta], 0, Pi/2},
 {\[Phi], {False, True}}
 ]