How to color code Lattice sites using 3d matrix of size (4,4,16) in Mathematica?

Question

cell = LatticeData["SimpleCubic", "Image"];
Graphics3D[Translate[cell[[1]], 2 Tuples[Range[3], 3]],   Boxed -> False]

I know this creates 4x4x4 lattice; how can I make it to graph 4x4x16 lattice? I have created a simple cubic lattice using graphics. Now, I wanna color code these points using (4,4,16) matrix containing 1's and 0's. So, my question is how can I do this?

Answer 1

Generate a $4 \times 4\times 16$ binary matrix using RandomInteger and replace 0s with Red and 1s with Green:

SeedRandom[1]
matrix = RandomInteger[1, {4, 4, 16}] /. {0 -> Red, 1 -> Green};

Use MapIndexed with level specification {3} to combine colors in matrix with spheres and cuboids placed in coordinates given by the index:

spheres = MapIndexed[{#, Sphere[#2, .15]} &, matrix, {3}];

cuboids =  MapIndexed[Cuboid @ #2 &, matrix[[;; -2, ;; -2, ;; -2]], {3}];

Graphics3D[{spheres, FaceForm[{Opacity[.1], Blue}], cuboids}, Boxed -> False]

Alternatively, generate coordinates using Outer and combine the coordinates with the colors from matrix using MapThread:

coords = Outer[List, Range[4], Range[4], Range[16]];

spheres = MapThread[{#, Sphere[#2, .15]} &, {matrix, coords}, 3];

cuboids = Map[Cuboid, coords[[;;-2, ;;-2, ;;-2]], {-2}];

Graphics3D[{spheres, FaceForm[{Opacity[.1], Blue}], cuboids}, Boxed -> False]

Note: You can use RandomChoice to get the 3D array of colors directly:

SeedRandom[1];
matrix2 = RandomChoice[{Red, Green}, {4, 4, 16}];

matrix2 == matrix

True