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Ingy döt Net 2013-06-05 21:47:54 +00:00
parent 1f1ad49427
commit 6f050a029e
2496 changed files with 37609 additions and 3031 deletions
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8
Task/Sierpinski-triangle-Graphical/Mathematica/sierpinski-triangle-graphical-1.math Normal file
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Sierpinski[n_] :=Nest[Flatten[Table[{{
#[[i, 1]], (#[[i, 1]] + #[[i, 2]])/2, (#[[i, 1]] + #[[i, 3]])/
2}, {(#[[i, 1]] + #[[i, 2]])/2, #[[i,
2]], (#[[i, 2]] + #[[i, 3]])/2}, {(#[[i, 1]] + #[[i, 3]])/
2, (#[[i, 2]] + #[[i, 3]])/2, #[[i, 3]]}}, {i, Length[#]}],
1] &, {{{0, 0}, {1/2, 1}, {1, 0}}}, n]
Show[Graphics[{Opacity[1], Black, Map[Polygon, Sierpinski[8], 1]}, AspectRatio -> 1]]

3
Task/Sierpinski-triangle-Graphical/Mathematica/sierpinski-triangle-graphical-2.math Normal file
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sierpinski[v_, 0] := Polygon@v;
sierpinski[v_, n_] := sierpinski[#, n - 1] & /@ (Mean /@ # & /@ v~Tuples~2~Partition~3);
Graphics@sierpinski[N@{{0, 0}, {1, 0}, {.5, .8}}, 3]

3
Task/Sierpinski-triangle-Graphical/Mathematica/sierpinski-triangle-graphical-3.math Normal file
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sierpinski = Map[Mean, Partition[Tuples[#, 2], 3], {2}] &;
p = Nest[Join @@ sierpinski /@ # &, {{{0, 0}, {1, 0}, {.5, .8}}}, 3];
Graphics[Polygon@p]

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Task/Sierpinski-triangle-Graphical/Racket/sierpinski-triangle-graphical.rkt Normal file
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#lang racket
(require 2htdp/image)
(define (sierpinski n)
(if (zero? n)
(triangle 2 'solid 'red)
(let ([t (sierpinski (- n 1))])
(freeze (above t (beside t t))))))
;; the following will show the graphics if run in DrRacket
(sierpinski 8)
;; or use this to dump the image into a file, shown on the right
(require file/convertible)
(display-to-file (convert (sierpinski 8) 'png-bytes) "sierpinski.png")