eNZedBlue wrote:
>
>Unlike the regular 3D Koch these have a 2D Koch fractal silhoette when
>viewed from a 45 degree angle (pitch and yaw). The sphere-based one is
>the "Sphereflake".
>
>Regards,
>Chris Hayton
>
>
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>
>
>
Chris Hayton
I did some work on this model.
It isn't strickly a classical von Koch but something new.
The corners overlap.
And the ratio is 4 instead of 5 as in the Lawerier version.
It may not be the best version of this fractal,
but it is connected. Your faces are too plain in your versions:
this version has both bumps and voids.
Moran dimension:
2.564641508472483
Menger cube version takes forever in Mathenmatica
at level 3.
Pictures:
http://profile.imeem.com/GUmj0c/photo/EjvNo7XVrN/
http://profile.imeem.com/GUmj0c/photo/KVkOBoyKGy/
Mathematica IFS:
(* 3d von Koch corner cube IFS 3d Fractal*)
(* by R. L. Bagula 07 Sept. 2007 ©*)
(*Chris Hayton : web cormer 3d von Koch cube*)
Clear[f, dlst, pt, cr, ptlst]
in = Join[Flatten[Table[{i,
j, k}*1.5, {i, -1, 1, 2}, {j, -1, 1, 2}, {k, -1, 1, 2}], 2], \
Flatten[Table[{i, j, k}, {i, -1, 1}, {j, -1, 1}, {k, -1, 1}], 2]]
Length[in];
dim_app = N[Log[Length[in]]/Log[4]]
2.564641508472483`
dlst = Table[ Random[Integer, {1, Length[in]}], {n, 25000}];
f[j_, {x_, y_, z_}] := {x, y, z}/4 + in[[j]];
pt = {0.5, 0.5, 0.5};
cr[n_] := Flatten[Table[If[i == j == k == 1, {}, RGBColor[i, j, k]], {
i, 0, 1, 0.5}, {j, 0, 1, 0.5}, {k, 0, 1, 0.5}]][[1 + Mod[n, 26]]];
ptlst = Table[{cr[dlst[[j]]], Point[pt = f[dlst[[j]], Sequence[pt]]]},
{j, Length[dlst]}];
g = Show[Graphics3D[
Join[{PointSize[.001]}, ptlst]], AspectRatio ->
Automatic, PlotRange -> All, Boxed -> False]
Show[g, ViewPoint -> {-0.178, -0.172, 3.375}]
Show[g, ViewPoint -> {2.649, -2.104, 0.059}]
Mathematica Menger cube version:
Clear[pieces, menger]
pieces =
Join[Flatten[Table[{i, j, k}*1.5, {i, -1,
1, 2}, {j, -1,
1, 2}, {k, -1, 1, 2}], 2], Flatten[Table[{i, j, k}, {i, -1, 1}, {j,
-1,
1}, {k, -1, 1}], 2]]
menger[cornerPt_, sideLen_, n_] :=
menger[cornerPt + #1*(sideLen/4), sideLen/4, 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 -> {-0.002, 1.297, 3.125}]
Roger Bagula
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