(*I worked up a pivot/overlap 3d IFS version of this that was a scale \
up
of the working 2d IFS,but I just don't have the computer or skill to \
get a good
looking version of that,so failing there I thought this way to get \
one up
on the next guy who rediscovers one of these.I made a picture
and will post it in as many places as I can with my own distinctive \
name.Since two times now different cubes:first the beta cube and the \
the Cross Menger cube
have been rediscovered and renamed.What has happens twice is pretty \
sure to happen again...
Mathematica and picture:*)
(*Texas Cross \
Menger cube:a single scale simulation of the 3 scale 2 gap Menger \
type cube*)(*a vibrating Menger analog by Roger Bagula 30 June 2014©*)

Clear[pieces, menger]
pieces0 =
Complement[
Flatten[Table[{i, j, k}, {i, 0, 2}, {j, 0, 2}, {k, 0, 2}],
2], {{1, 1, 1}, {0, 1, 1}, {2, 1, 1}, {1, 0, 1}, {1, 2, 1}, {1, 1,
0}, {1, 1, 2}}];
pieces1 = Table[pieces0[[i]] + {6, 0, 0}, {i, 1, Length[pieces0]}];
pieces2 = Table[pieces0[[i]] + {0, 6, 0}, {i, 1, Length[pieces0]}];
pieces3 = Table[pieces0[[i]] + {0, 0, 6}, {i, 1, Length[pieces0]}];
pieces4 = Table[pieces0[[i]] + {6, 6, 0}, {i, 1, Length[pieces0]}];
pieces5 = Table[pieces0[[i]] + {0, 6, 6}, {i, 1, Length[pieces0]}];
pieces6 = Table[pieces0[[i]] + {6, 0, 6}, {i, 1, Length[pieces0]}];
pieces7 = Table[pieces0[[i]] + {6, 6, 6}, {i, 1, Length[pieces0]}];
m1 = Flatten[Table[{i, j, k}, {i, 0, 1}, {j, 0, 1}, {k, 3, 4}], 2];
m2 = Flatten[Table[{i, j, k}, {i, 0, 1}, {j, 3, 4}, {k, 0, 1}], 2];
m3 = Flatten[Table[{i, j, k}, {i, 3, 4}, {j, 0, 1}, {k, 0, 1}], 2];
m4 = Flatten[Table[{i, j, k}, {i, 0, 1}, {j, 7, 8}, {k, 3, 4}], 2];
m5 = Flatten[Table[{i, j, k}, {i, 7, 8}, {j, 3, 4}, {k, 0, 1}], 2];
m6 = Flatten[Table[{i, j, k}, {i, 3, 4}, {j, 0, 1}, {k, 7, 8}], 2];
m7 = Flatten[Table[{i, j, k}, {i, 0, 1}, {j, 3, 4}, {k, 7, 8}], 2];
m8 = Flatten[Table[{i, j, k}, {i, 3, 4}, {j, 7, 8}, {k, 0, 1}], 2];
m9 = Flatten[Table[{i, j, k}, {i, 7, 8}, {j, 0, 1}, {k, 3, 4}], 2];
m10 = Flatten[Table[{i, j, k}, {i, 7, 8}, {j, 7, 8}, {k, 3, 4}], 2];
m11 = Flatten[Table[{i, j, k}, {i, 7, 8}, {j, 3, 4}, {k, 7, 8}], 2];
m12 = Flatten[Table[{i, j, k}, {i, 3, 4}, {j, 7, 8}, {k, 7, 8}], 2];
c1 = {{5, 0, 0}, {0, 5, 0}, {0, 0, 5}};
c2 = {{5, 8, 8}, {8, 5, 8}, {8, 8, 5}};
c3 = {{5, 0, 8}, {0, 5, 8}, {0, 8, 5}};
c4 = {{5, 8, 0}, {8, 5, 0}, {8, 0, 5}};
pieces = Join[pieces0, pieces1, pieces2, pieces3, pieces4, pieces5,
pieces6, pieces7, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11,
m12, c1, c2, c3, c4];
menger[cornerPt_, sideLen_, n_] :=
menger[cornerPt + #1*(sideLen/9), sideLen/9, n - 1] & /@ pieces;
menger[cornerPt_, sideLen_, 0] := {Hue[N[Norm[cornerPt]]],
Specularity[White, 20], EdgeForm[],
Cuboid[cornerPt, cornerPt + sideLen*{1, 1, 1}]};
gg = Show[Graphics3D[Flatten[menger[{0, 0, 0}, 1, 1]]],
Boxed -> False, ImageSize -> 1000, Background -> Black]
ga = Show[Graphics3D[Flatten[menger[{0, 0, 0}, 1, 2]]],
Boxed -> False, ImageSize -> 1000, Background -> Black]

Portfolios: newer fractal

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