Compounds in other rulespaces

H. H. P. M. P. Cole · October 19th, 2026, 6:37 am

This is a topic to discuss Hunter's concept of "compounds" in other rulespaces.

In the NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000 rulespace, when one wants to create a nonexplosive nonrelativistic analogue in this rulespace with spaceships, there are a few dos and don'ts:

Use at least one of the conditions B6, B26, B30, B31.

do not use B6 and B30 together as it spawns 2-cell replicators:

Code: Select all

x = 2, y = 1, rule = R3,C2,S,B6,30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2o!

do not use B1, B5 at all

if you are using B25, do not use B25, B26 together:

Code: Select all

x = 1, y = 1, rule = R3,C2,S,B25-26,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o!

do not use B6, B31, S30 together as it spawns a 3-cell replicator:

Code: Select all

x = 3, y = 1, rule = R3,C2,S30,B6,31,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
3o!

(note that B6,31,62/S30,35 has common linear growth)

The only few level-2 spaceships I found without B25 are:

Code: Select all

# AFAICT the rule can only be stabilized by adding S10, S15, B10, B15
x = 24, y = 19, rule = R3,C2,S,B26,50,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o6bo12bo2$o6bo12bo$10bo6bo5bo3$o6$7bo12bo2$7bo12bo$10bo6bo5bo3$7bo12b
o!

Code: Select all

x = 4, y = 2, rule = R3,C2,S1,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
bo$o2bo!

Code: Select all

x = 7, y = 26, rule = R3,C2,S,B30,55,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2b2o$b2o$o3$5b2o$4b2o$o2bo2$2bo3$5b2o$4b2o$o2bo$2bo2$o3$5b2o$4b2o$3bo
$2bo$2bo$o!

I think we should do an analysis of all level-2 rules in this rulespace.