oftenpaper.net

axiom = {A};
rules = {A -> {B, R, A, R, B}, B -> {A, L, B, L, A}};
conversions = {A -> forward, B -> forward, L -> left, R -> right};

(* state transformations *)
forward[{z_, a_}] := {z + E^(I a), a};
left[{z_, a_}] := {z, a + 2 Pi/6};
right[{z_, a_}] := {z, a - 2 Pi/6};

draw[n_] := Module[{program, zs},
  program = Flatten[Nest[# /. rules &, axiom, n]] /. conversions;
  zs = First /@ ComposeList[program, N@{0, 0}];
  Graphics[Line[{Re[#], Im[#]} & /@ First /@ Split[zs]]]];