GG = (Sqrt[5] + 1)/2

standardhosoi = {1/2 + Sqrt[GG^2 - (1/2)^2] I , 0, 1}

standardfutoi = {GG/2 + Sqrt[1 - (GG/2)^2] I, 0, GG}

secthosoi[n_, t_] := 
      If[n > 0, 
        Join[secthosoi[
            n - 2, {t[[2]], t[[3]], 
              (GG*t[[3]] + t[[1]])/(GG + 1)}], 
          sectfutoi[
            n - 1, {(GG*t[[3]] + t[[1]])/(GG + 1), 
              t[[1]], t[[2]]}]], {hosoi@@N[t]}]

sectfutoi[n_, t_] := 
      If[n > 0, 
        Join[sectfutoi[
            n - 2, {(GG*t[[2]] + t[[3]])/(GoldenRatio + 1), 
              t[[1]], t[[2]]}], 
          secthosoi[
            n - 1, {t[[3]], 
              (GG*t[[2]] + t[[3]])/(GG + 1), t[[1]]}]], {
          futoi@@N[t]}]

addtofutoi[n_, t_, d_] := 
      If[d == 0, {}, 
        Join[{waku@@t}, 
          If[EvenQ[d], 
            Join[addtofutoi[
                n + 2, {t[[2]], t[[3]], 
                  ((GG + 1)*t[[1]] - GG*t[[3]])}, d/2], 
              secthosoi[
                n + 1, {((GG + 1)*t[[1]] - GG*t[[3]]), 
                  t[[1]], t[[2]]}]], 
            Join[addtohosoi[
                n + 1, {t[[2]], t[[3]], 
                  ((GG + 1)*t[[1]] - t[[2]])/GG}, 
                (d - 1)/2], 
              secthosoi[
                n - 1, {t[[3]], 
                  ((GG + 1)*t[[1]] - t[[2]])/GG, 
                  t[[1]]}]]]]]

addtohosoi[n_, t_, d_] := 
      If[d == 0, {}, 
        Join[{waku@@t}, 
          If[EvenQ[d], 
            Join[addtohosoi[
                n + 2, {((GG + 1)*t[[3]] - GG*t[[2]]), 
                  t[[1]], t[[2]]}, d/2], 
              sectfutoi[
                n + 1, {t[[3]], 
                  ((GG + 1)*t[[3]] - GG*t[[2]]), 
                  t[[1]]}]], 
            Join[addtofutoi[
                n + 1, {t[[3]], 
                  ((GG + 1)*t[[2]] - t[[1]])/GG, t[[1]]}, 
                (d - 1)/2], 
              sectfutoi[
                n - 1, {t[[2]], t[[3]], 
                  ((GG + 1)*t[[2]] - t[[1]])/GG}]]]]]

triangle[a_, b_, c_] := 
      Graphics[Line[{Re[#], Im[#]}&/@{a, b, c, a}]]hosoi := trianglefutoi := triangle

waku[a_, b_, c_] := 
      Graphics[{Thickness[0.005], Line[{Re[#], Im[#]}&/@{a, b, c, a}]}]

Append[addtohosoi[0, standardhosoi, 123], triangle@@standardhosoi]

Show[%, AspectRatio -> Automatic]