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[GIF] Back Away (Alternated cubic honeycomb)

Posted 1 year ago
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Alternated cubic honeycomb

Back Away

These are the vertices of the alternated cubic honeycomb, a tiling of 3-space by tetrahedra and octahedra. The vertices are all moving away from the camera, but they also fade in or out as they enter or leave the bounding box.

Here's the code, which is too slow for a useful Manipulate, so I just give the code for building the table of frames and exporting the GIF:

dots = Module[
   {n = 12, o = 0.5, points, edges, fadeinpoints, fadeoutpoints,
    cols = RGBColor /@ {"#122D42", "#CBF9DA"}},
   points = 
    Select[Flatten[
      Table[{i, j, k}, {i, -n, n - 2}, {j, -n, n}, {k, -n, n}], 2], 
     EvenQ[Total[#]] &];
   fadeinpoints = 
    Select[Flatten[
      Table[{i, j, k}, {i, -n - 2, -n - 1}, {j, -n, n}, {k, -n, n}], 2], 
      EvenQ[Total[#]] &];
   fadeoutpoints = 
    Select[Flatten[
      Table[{i, j, k}, {i, n - 1, n}, {j, -n, n}, {k, -n, n}], 2], 
     EvenQ[Total[#]] &];
   ParallelTable[
      Graphics3D[{PointSize[.012], Opacity[o], cols[[1]], 
        Point[{d, 0, 0} + #] & /@ points, Opacity[o*d/2], 
        Point[{d, 0, 0} + #] & /@ fadeinpoints, Opacity[o (1 - d/2)], 
        Point[{d, 0, 0} + #] & /@ fadeoutpoints},
       Boxed -> False, ViewPoint -> {-2, 0, 0}, 
       ViewVertical -> {0, 0, 1}, ViewAngle -> π/7, 
       PlotRange -> n + 2, ImageSize -> 540, SphericalRegion -> True, 
       Background -> Lighter[cols[[-1]], .7]],
      {d, 0., 2 - #, #}] &[2/10]
   ];

Export[NotebookDirectory[] <> "dots.gif", dots, "DisplayDurations" -> {1/24}]

enter image description here - another post of yours has been selected for the Staff Picks group, congratulations! We are happy to see you at the top of the "Featured Contributor" board. Thank you for your wonderful contributions, and please keep them coming!

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