User:DroneBetter/self-complementary outer-totalistic rules
Conjugacy classes of rule are shown by their non-strobing representative.
Presently, there are 47 rules with explicit examples of spaceships known, 198 rules disproven from supporting spaceships and 11 rules unknown.
The disproofs are given by Spaceship#In other rules, the examples are from LaundryPizza03's updated version of David Eppstein's glider.db. (Note that it was last updated on June 1, 2022, new discoveries may have been made since.)
Conditions are iterated over in a Gray code in both axes, but only rows and columns with a nonzero number of nondisproven rules are shown. (Note that this means the bottom row may be removed also, were proofs to be found regarding B348/S123678 and B248/S123578.)
Minimal examples of known spaceships of each period are shown also, those that are endemic (within the outer-totalistic self-complementary rulespace) in the table, polyglots below.
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| Reflection about the upwards-and-rightwards diagonal corresponds with taking a rule's black/white reversal. Along the line of symmetry lie self-complementary rules, which can be reflected about the line's centre to their black/white complements, so only the line's bottom-left half need be considered. This table contains all with spaceships. (See Spaceship#In other rules and file description for more details.) |
Notes
- ↑ Something of a unique case for characterisation, since soups stabilise into strobing mazes and large enough ones develop wickstretchers. Appeared in David Eppstein's "Most Wanted" list.
- ↑ Behaves similarly to its neighbour, B34567/S0678, but without the wickstretchers.
- ↑ Labelled explosive, but this only seems to pertain for sufficiently large soups, it is apgsearchable.
Conclusions: Prospective apgsearchers looking for underexplored self-complementary rules ought to choose B34678/S3678, B3568/S14678, B356/S014678, B3567/S04678 and B367/S034678, which may warrant pages of their own.
Non-complementarily-endemic spaceships
They are denoted by their supported self-complementary rules' birth conditions (from which the survival ones may be uniquely determined), with optional transitions in brackets
- B2(45)67(8): Moon
- B2(456)78: Broken moon
- B2(45)678: Half-broken moon (and p4 tagalong)
- B346(8): (1,1)c/4 thing
- B37(8): Tlife ant
- B346(8): (1,1)c/4 thing
- B367(8): Butterfly (c/3), (1,1)c/4, c/2
- B246(7)8: concave photon
- B256(7)8: beehive photon
- B36(8): skew-glide-symmetric c/2, c/3
- B357(8): glide-symmetric 2c/4, c/2, c/3
- B356(8): c/3
- B2456(7)8: small, large and long photon variants
- B35(8): c/2
- B246(78): c
- B247(8): tree-like c
- B2456(78): chequerboardish greyshippy photon, dual one
- B2457(8): clock-looking photon, photon containing glider, photon containing two gliders, fishy photon
- B256(8): bulbous beehive c, nested
- B24(5)678: 4c/4, dot and line c (dimer)
- B2467(8): 3-cell-tall c
- B24(5)67(8): wide moon following domino
- B257(8): bushel-looking photon
- B24567(8): hivepusher photon, honeycombpusher photon