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[WSS22] Traversing a 3D cellular automaton

Posted 1 year ago
POSTED BY: Madelyn Mao
3 Replies
POSTED BY: Todd Rowland

Thank you so much, for this project and doing all the things we need to make it doable, it's pretty cool @Madelyn Mao seeing the unseen this is unreal, because a cellular automaton is really just a series of cells that exist, according to a specific rule.

Row[{
  Manipulate[
   Dynamic@Graphics3D[
     {
      Cuboid[#, # + 1] & /@ Position[
        ArrayPad[
         CellularAutomaton[
          {224, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}, {1, 1}},
          RandomInteger[1, {50, 50}],
          {{0, 1}}], 1]
        , 1]
      },
     ViewPoint -> {Infinity, Infinity, Infinity},
     Boxed -> False,
     ViewAngle -> t],
   {{t, 1.8, "View Angle"}, 1.8, 2, .01},
   SaveDefinitions -> True
   ],
  Manipulate[
   Graphics3D[
    {
     RGBColor[
      RandomReal[{0, 1}, 3, WorkingPrecision -> MachinePrecision]^0.1],
     Opacity[0.75],
     Specularity[White, 50],
     EdgeForm[{Thickness[0.001], Blue}],
     Cuboid[#, # + 1] & /@ Position[
       ArrayPad[
        CellularAutomaton[
         {540 + 882, {2, 1}, {1, 1, 1}},
         {{{{1}}}, 0},
         {{{3}}}
         ], 1], 1]
     },
    Boxed -> False,
    ViewPoint -> {15 + x, 15 + y, 15 + z},
    ViewVector -> {{a, b, c}, {15, 15, 15}},
    ViewAngle -> t],
   {{t, 1.3, "View Angle"}, 1.3, 2.5, .01},
   {{x, 0, "X displacement"}, -3, 3, 1},
   {{y, 0, "Y displacement"}, -3, 3, 1},
   {{z, 0, "Z displacement"}, -3, 3, 1},
   {{a, 0, "View vector X"}, -1, 1, .1},
   {{b, 0, "View vector Y"}, -1, 1, .1},
   {{c, 0, "View vector Z"}, -1, 1, .1},
   SaveDefinitions -> True
   ]
  }]

These cellular automatons are mostly cube shaped, it's not like those hexagons and Sierpinski triangles or anything like the fractals, the Game of Life...Conway? Simple rules are creating complicated shapes without intervention, from the initial settings.

Conway's Game of Life & Cellular Automata

I've always been a fan of 3D stuff whether it's on PDF, animated via Wolfram Language, you name it; these transitions are amazing & the cellular automata are so diverse. What makes a cellular automata good? Every cellular automata has had a different life experience and they say, you should do it this way or that but there's no need anymore this is phenomenal.

POSTED BY: Dean Gladish

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