Sierpinski[n_] :=
 Nest[Join @@ Table[With[{a = #[[i, 1]], b = #[[i, 2]],  c = #[[i, 3]]},
   {{a, (a + b)/2, (c + a)/2}, {(a + b)/2, b, (b + c)/2}, {(c + a)/2, (b + c)/2, c}}],
 {i, Length[#]}] &, {{{0, 0}, {1/2, 1}, {1, 0}}}, n]

Graphics[{Black, Polygon /@ Sierpinski[8]}]