I've very busy on some of these 3D fractals
and improving them. I managed to get two levels of an
dodecahedron 3d fractals
and yesterday, a cube octahedron hollow pyramid.
I appended the EdgeForm[] command in Mathematica
so that at level 3 they aren't mostly black with the edges.
These D8 fractals will tile with Diagonal Menger cubes...
First inkling I've had there is a diagonal Menger cube.
I use relative center coordintes x->{0,6},y->{0,6},z->{0,2}
The three level at 40 cubes ber unit is very slow here:
Top layer : 16 cubes in an octagon ( 8 on edges)
Middle layer: 8 cubes at vertices with gaps
Bottom layer : 16 cubes in an octagon ( 8 on edges)
This method gives an uneven octagon with diagonal
edges longer than the flat edges.
Picture of level 3 at:
http://profile.imeem.com/GUmj0c/photo/yLSNmE-k/TgEyoDeAsF/
Mathematica:
Clear[pieces, menger]
p = {{0, 2, 0}, {0, 3,
0}, {0, 4, 0}, {1, 1, 0}, {1, 5, 0}, {2, 0, 0}, {3, 0, 0}, {4, 0, 0}, {2,
6, 0}, {3, 6, 0}, {4, 6, 0}, {5, 1, 0}, {5, 5, 0}, {6, 2, 0}, {6,
3, 0}, {6, 4, 0}};
p1 = {{0, 2, 2}, {0, 3, 2}, {0, 4, 2}, {1, 1, 2}, {1, 5, 2}, {2, 0,
2}, {3, 0, 2}, {4, 0, 2}, {2, 6, 2}, {3, 6, 2}, {4, 6, 2}, {5, 1,
2}, {5, 5, 2}, {6, 2, 2}, {6, 3, 2}, {6, 4, 2}};
p2 = {{0, 2, 1}, {0,
4, 1}, {2, 0, 1}, {4, 0, 1}, {2, 6, 1}, {4, 6, 1}, {6, 2, 1}, {6, 4, 1}};
pieces = Join[p, p1, p2];
Length[pieces]
40
menger[cornerPt_, sideLen_, n_] :=
menger[cornerPt + #1*(sideLen/3), sideLen/3, 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]
Show[Graphics3D[Flatten[menger[{0, 0, 0}, 1, 3]]], Boxed -> False]
Respectfully, Roger L. Bagula
11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814
:http://www.geocities.com/rlbagulatftn/Index.html
alternative email: rlbagula@[EMAIL PROTECTED]
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