谢宾斯基三角上的随机游走

一段关于谢宾斯基三角上的随机游走的代码，记录一下。

n = 5;
steps = 1000;
dir = {{0, 0}, {1, 0}, {0, 1}};

start = FromDigits[#, 2] & /@Transpose@Append[RandomChoice[dir, n - 1], RandomInteger[1, 2]];

move[pt_] :=
    With[{c =  RandomChoice@Pick[-dir, BitAnd @@ (# + pt) & /@ -dir, 0]},
         pt + c + RandomChoice@DeleteCases[dir, -c]];
move[{2^n, 0}] := {2^n - 1, RandomInteger@1};
move[{0, 2^n}] := {RandomInteger@1, 2^n - 1};
move[{0, 0}] := RandomChoice@Rest@dir;
ListLinePlot[{#1 + #2/2, #2*Sqrt@3/2} & @@@
      NestList[move, start, steps],
   PlotRange -> {{0, 2^n}, {0, 2^n*Sqrt[3]/2}},
   AspectRatio -> Sqrt[3]/2]

运行上面的代码可以得到下面的图形：