Chiral non-totalistic rules

[Hdjensofjfnen]

Recently, there's been some discussion in the Conwaylife Lounge Discord server and in the Other Cellular Automata forum about chiral (rotate4) non-totalistic rules, so I created this thread to discuss them. These rules maintain four-way rotational symmetry but not necessarily reflection symmetry, so they're a superset of INT rules but a subset of MAP rules.

Docsy on the Conwaylife Lounge Discord server recently created a notation for chiral non-totalistic rules that's consistent with Hensel notation for isotropic non-totalistic rules. The proposed notation uses < and > characters to denote only the "left" and "right" versions of chiral transitions. These can be combined with the - character from INT to subtract transitions from the full set of transitions. Thus, the rulestring B2e>k3/S2-ci<k3 is valid, and is equivalent to B2e>k3/S2aen>k3.*

This leaves the difficulty of assigning the arbitrary labels of "left" and "right" to particular orientations of chiral transitions. I've decided to assign "right" to the lowest MAP transition indices for the transitions B2k (12), B2a (3), B3n (13), B3q (70), B3j (14), B3r (41), B4k (99), B4a (15), B4n (71), B4y (101), B4j (106), B4r (43), and B4z (108). "Left" is assigned to the mirror images of those transitions. B5 and B6 chiral transitions are consistent with their B3 and B2 counterparts, and survival transitions are consistent with birth transitions.

I've written two short Python scripts to convert Docsy's notation to MAP rule notation. The first one (main.py) is intended for command-line use, while the second one (rotate4.py) is intended to be run within Golly and automatically sets the rule for convenience. B(...)/S(...) format is expected. There are some basic tests for improperly formatted rulestrings, but don't expect the scripts to catch everything.

I checked for completeness and correctness of transitions by generating the MAP rule for Day & Night (B3678/S34678) and verifying that the spaceship file on the wiki runs correctly in all eight orientations. Any additional testing is welcome!

*To demonstrate some nuances with chiral non-totalistic rules, note that B2e>k3/S2-ci<k3 is not explosive while B2e>k3/S2-ci>k3 (equivalent to B2e>k3/S2aen<k3) is.