Task
Produce a graphical or ASCII-art representation of a  Sierpinski arrowhead curve  of at least order  3.




ClearAll[DoStep]
DoStep[Line[{x_, y_}]] := Module[{diff, perp, pts},
  diff = y - x;
  perp = Cross[diff] Sqrt[3]/2;
  pts = {x, x + diff/4 + perp/2, x + 3 diff/4 + perp/2, y};
  {Line[pts[[{2, 1}]]], Line[pts[[{2, 3}]]], Line[pts[[{4, 3}]]]}
  ]
lns = {Line[{{0.0, 0.0}, {1.0, 0.0}}]};
lns = Nest[Catenate[DoStep /@ #] &, lns, 5];
Graphics[lns]