In Paterson's worms, a triangular lattice is used. A worm can move in 6 directions. As each node is hit, the worm follows an internal rule for which edge it will eat next based on the edges already eaten. If it reaches the starting node with all exits eaten, it dies.
For a 3D lattice, a worm would need to store 2 directional states to orient it in 3D space.
I expect most 3D worms to travel off in some direction for most lattices. What are the exceptions?
Have other 2D lattices be explored, such as Knight-move based lattices?