cf = Compile[{{A, _Real, 2}},
   With[{a = A[[1]], b = A[[2]], c = A[[3]]},
    With[{ab = (a + b)/2, bc = (b + c)/2, ca = (a + c)/2},
     {{a, ab, ca}, {ab, b, bc}, {ca, bc, c}}]],
       RuntimeAttributes -> {Listable}
   ];

n = 3;
pts = Flatten[Nest[cf, N@{{{0, 0}, {1, 0}, {1/2, √3/2}}}, n], n];
Graphics[Polygon /@ pts]