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Sierpinski triangle/Graphical: Difference between revisions

Line 1,254:
 
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[NPolygon/@{{0, 0}, {1, 0}, {.5, .8}}, 3pts]</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]]
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