Cross Menger cube ( sponge) in Mathematica
- From: Roger Bagula <rlbagula@xxxxxxxxxxxxx>
- Date: Fri, 03 Aug 2007 19:36:02 GMT
This is not exactly the same as my golden mean cross Menger
but it has the same topology.
It has taken me several years to get a worker graphic for this set.
The IFS for these are pretty inadequate.
Here's a link to my Imeem pictures ( that hopefully will work) :
http://profile.imeem.com/GUmj0c/photo/yLSNmE-k/9zieVrkyzA/
The dimension appears to be:
2.690835916581937
Mathematica:
Clear[pieces, menger]
(*Cross Menger cube by Roger Bagula 3 Aug 2007©*)
(* patterned from Menger cube code by Szabolcs Horvát < szhorvat@xxxxxxxxx >,
University of Bergen in Mathematica newsgroup : Mon, 28 May 2007 09 : 10 :
50*)
Union[Flatten[Table[{{1, 2, i}, {2, 1, i}, {2, 2, i}, {2, 3, i}, {3,
2, i}, {1, i, 2}, {2, i, 1}, {2, i, 2}, {2, i, 3}, {3, i, 2}, {i, 1, 2},
{i, 2, 1}, {i, 2, 2}, {i, 2, 3}, {i, 3, 2}}, {i, 0, 4}], 1]]
Length[%]
N[Log[5^3 - %]/Log[5]]
2.690835916581937`
pieces =
Complement[
Flatten[Table[{i, j, k}, {i, 0, 4}, {j, 0, 4}, {k, 0, 4}],
2], Union[Flatten[Table[{{1, 2, i}, {2, 1, i}, {2, 2, i}, {
2, 3, i}, {3, 2, i}, {1, i, 2}, {2, i, 1}, {2, i, 2}, {2, i, 3}, {
3, i, 2}, {i, 1, 2}, {i, 2, 1}, {i, 2, 2}, {i, 2, 3}, {i, 3, 2}}, {
i, 0, 4}], 1]]]
menger[cornerPt_, sideLen_, n_] :=
menger[cornerPt + #1*(sideLen/5), sideLen/5, n - 1] & /@ pieces
menger[cornerPt_, sideLen_, 0] :=
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]
.
- Prev by Date: Re: very good Menger sponge( cube) posted in the Mathematica newsgroup
- Next by Date: D_3 Prism fractal basic level
- Previous by thread: very good Menger sponge( cube) posted in the Mathematica newsgroup
- Next by thread: boxed set higher level Menger cube/ sponge
- Index(es):