What is known about which orbit sizes are possible? What is known about which orbit sizes are impossible? How many bits of state are required for an orbit of size N ? (non-trivial max ?, non-trivial min ?) The video talks about parallelizing; is there any kind of "speedup" -- e.g., repeated squaring of matrices or some such? Suppose that a Minsky orbit of size N is known; how hard is it to map the integers 1..N to the elements of the orbit, and how hard is it to map back? Or is a table lookup the fastest method in both directions? More generally, can I use Minsky orbits for addition mod N ? Are there any Minsky orbits which "decompose" into direct products of Minsky orbits? (I'm not entirely certain how such a direct product would work, but perhaps the peculiarities of particular numbers might allow the separation of a "high order" part and a "low order" part that happen not to interfere with one another.) Does Minsky/Trinsky work on any other algebraic objects other than standard integers -- e.g., polynomials over Q in a single variable ? Perhaps I didn't understand the video well enough, but are there elegant cellular automata that perform the Minsky/Trinsky computation?