3d von Koch

by Roger Bagula <rlbagula@[EMAIL PROTECTED] > Sep 7, 2007 at 11:17 AM

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I figured out how to use the Menger sponge program to give
Lauwerier's 3d von Koch.
 
Pictures:
http://profile.imeem.com/GUmj0c/photo/rhidP5F98h/
http://profile.imeem.com/GUmj0c/photo/oJx8SaGGpa/

Clear[pieces, menger]
(*from Hans Lauwerier, "Fractals, Endlessly Repeating Geometrical
Figures",
Princeton Science Library, Page 129*)
pieces =
Join[{{0, 2, 2}, {4, 2, 2}, {2, 0, 2}, {2, 4, 2}, {2, 2, 0}, {2, 2, 4}},
Flatten[Table[{i, j, k}, {i, 1, 3}, {j, 1, 3}, {k, 1, 3}], 2]];
N[Log[Length[pieces]]/Log[5]]
2.1725022968909635`
menger[cornerPt_, sideLen_, n_] :=
menger[cornerPt + #1*(sideLen/5), sideLen/5, n - 1] & /@[EMAIL PROTECTED]
 pieces;
menger[cornerPt_, sideLen_, 0] :=
{EdgeForm[], Cuboid[cornerPt, cornerPt + sideLen*{1, 1, 1}]};
Show[Graphics3D[Flatten[menger[{0, 0, 0}, 1, 1]]], Boxed -> False]
Show[Graphics3D[Flatten[menger[{0, 0, 0}, 1, 2]]], Boxed -> False]
gr = Show[Graphics3D[Flatten[menger[{0, 0, 0}, 1, 3]]], Boxed -> False]
Show[gr, ViewPoint -> {2.367, 2.305, 0.730}]




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 style="font-family: -moz-fixed; font-size: 13px;" lang="x-western">
<br>
I figured out how to use the Menger sponge program to give
<br>
Lauwerier's 3d von Koch.
<br>
&nbsp;<br>
Pictures:
<br>
<a class="moz-txt-link-freetext"

href="http://profile.imeem.com/GUmj0c/photo/rhidP5F98h/">http://profile.imeem.com/GUmj0c/photo/rhidP5F98h/</a>
<br>
<a class="moz-txt-link-freetext"

href="http://profile.imeem.com/GUmj0c/photo/oJx8SaGGpa/">http://profile.imeem.com/GUmj0c/photo/oJx8SaGGpa/</a>
<br>
<br>
Clear[pieces, menger]
<br>
(*from Hans Lauwerier, "Fractals, Endlessly Repeating Geometrical
Figures",
<br>
Princeton Science Library, Page 129*)
<br>
pieces =
<br>
Join[{{0, 2, 2}, {4, 2, 2}, {2, 0, 2}, {2, 4, 2}, {2, 2, 0}, {2, 2,
4}},
<br>
Flatten[Table[{i, j, k}, {i, 1, 3}, {j, 1, 3}, {k, 1, 3}], 2]];
<br>
N[Log[Length[pieces]]/Log[5]]
<br>
2.1725022968909635`
<br>
menger[cornerPt_, sideLen_, n_] :=
<br>
menger[cornerPt + #1*(sideLen/5), sideLen/5, n - 1] &amp; /@[EMAIL PROTECTED]
 pieces;
<br>
menger[cornerPt_, sideLen_, 0] :=
<br>
{EdgeForm[], Cuboid[cornerPt, cornerPt + sideLen*{1, 1, 1}]};
<br>
Show[Graphics3D[Flatten[menger[{0, 0, 0}, 1, 1]]], Boxed -&gt; False]
<br>
Show[Graphics3D[Flatten[menger[{0, 0, 0}, 1, 2]]], Boxed -&gt; False]
<br>
gr = Show[Graphics3D[Flatten[menger[{0, 0, 0}, 1, 3]]], Boxed -&gt;
False]
<br>
Show[gr, ViewPoint -&gt; {2.367, 2.305, 0.730}]
<br>
<br>
<br>
<br>
</div>
</body>
</html>

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