IFS links sierpinski to ferns

f[p_, \[Theta]_] :=
  If[RandomReal[] > 0.5, (p + {1, 1})/2, RotationMatrix[\[Theta]].p];
Picture[\[Theta]_, n_] :=
 Graphics[{PointSize[Small],
   Point[NestList[f[#, \[Theta]] &, {0.2, 0.2}, n][[10 ;;]],
    VertexColors ->
     ColorData["AvocadoColors"] /@
      RandomReal[{0.5, 0.7}, n][[10 ;;]]]},
  PlotRange -> {{-2, 2}, {-2, 2}}, Background -> Black,
  ImageSize -> {300, 300}];
Manipulate[
 Picture[\[Theta], n],
 {{\[Theta], 2 Pi/3, "Angle"}, 0, 2 Pi},
 {{n, 100, "Number of Points"}, 100, 10000, 1}
 ]