I'm creating a game world that consists of a 16 x 16 x 16 rubix cube (pictured), where the individual cubes are floating in space. The cubes continuously move along a single set path that links up with itself at the end. It might be helpful to think of them as traversing a 3D maze. Are there any algorithms or solutions that could help me generate this path?
As I mentioned in a comment, one possible way to solve this is to weave a path back & forth across a face using 2 pencils. One pencil draws the beginning of the path, and the other draws the end.
Here's an example for one face:
+----------------+
|abcdefghijklmnop|
|ZYXWVUTSRQPONMLq|
|****ABCDEFGHIJKr|
|*###3210zyxwvuts|
|*###############|
|***************#|
|***************#|
|*###############|
|*###############|
|***************#|
|***************#|
|*###############|
|*###############|
|***************#|
|***************#|
|*###############|
+----------------+
One pencil starts in the top row, left column, "abcd..."
The other pencil starts in the 2nd row, left column, "ZYXWV..."
As you can see, both paths end in the left column, bottom 2 rows. At that point you move to the next face & repeat the process.
When you've finished you have to "parallel" paths. Just tie the ends together & you have your loop that visits each node.
a limitation
This only works because the number of rows (or columns) is a multiple of 2. If your grid was 15x15x15, you'd have a problem.
