Sierpinski triangle/Graphical: Difference between revisions

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 Show[Graphics[{Opacity[1], Black, Map[Polygon, Sierpinski[8], 1]}, AspectRatio -> 1]]</lang>
+Another faster version
+<lang Mathematica>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;
-<lang Mathematica>sierpinski[v_, 0] := Polygon@v;
+pts=Flatten[Nest[cf,N@{{{0,0},{1,0},{1/2,√3/2}}},n],n];
-sierpinski[v_, n_] := sierpinski[#, n - 1] & /@ (Mean /@ # & /@ v~Tuples~2~Partition~3);
-Graphics@sierpinski[N@{{0, 0}, {1, 0}, {.5, .8}}, 3]</lang>
+Graphics[Polygon/@pts]</lang>
-<lang Mathematica>sierpinski = Map[Mean, Partition[Tuples[#, 2], 3], {2}] &;
-p = Nest[Join @@ sierpinski /@ # &, {{{0, 0}, {1, 0}, {.5, .8}}}, 3];
-Graphics[Polygon@p]</lang>
 [[File:MmaSierpinski.png]]