Warren,
You wrote:
--re your helix idea, seems simpler but think still works, to use straight rods in straight holes, but tilted at angles so they do not hit each other? Not that it really makes a difference, but screws with my mind less. (Literally.)
Correct, that works.
--I've actually had a lot of these thoughts for many years, but your lego-ism stimulated me.
Very well.
--It is more than CAs. See, with CAs, there is a unique successor given the neighborhood state is known. With tiles we could permit non-unique successors (i.e several allowed) or could permit none (i.e. tiling fails if that local configuration occurs).
Agreed.
The tiles which correspond to CAs are interesting and could be searched for by an easy add-on to my program I sent you (the "interesting tile" condition is a uniqueness criterion) but the fact 24 is not a perfect power seems a bit of an obstacle... 24=3*8 and 8 is a power, though, so given 3-way identification you could do a 3-neighborhood 2-alphabet.
--I'm confused about reversible CAs.
Reversible cellular automata are more amenable to implementation in the Margolus neighbourhood, which is precisely the type of neighbourhood directly implemented by truncated octahedra where only the hexagonal faces are coloured. There's a LBA-complete two-state cellular automaton of this type, by Ed Fredkin and Tommaso Toffoli: https://en.wikipedia.org/wiki/Billiard-ball_computer Sincerely, Adam P. Goucher http://cp4space.wordpress.com