This is a nice visualization. Are there any keyboard keys to just advance one position along the line? I tried the arrow keys but they jumped quite far.

I don't know how this was generated (BFS and flattening?) it seems adjacent indices aren't just one move apart ... but they could be!

There is a Hamiltonian circuit for Rubik's cube: https://bruce.cubing.net/ham333/rubikhamiltonexplanation.htm...

Following the circuit would be like Gray codes instead of binary digits. You only flip one bit at a time when going to the next number.