speedydelete wrote: January 24th, 2026, 12:12 pm
[...]
Can you figure out a scheme for enumerating every one?
Sure! To begin with, we know that (almost all) of the rules with B1c, B1e, and B2a are not worth exploring, and B0 results in the strobing dual of another checkerboard-complementary rule, so we can rule out B0, B1c, B1e, B2a, and their checkerboard complements, resulting in the forbidden transitions of B012a3e4ej5c/S3c4cy5e6a78. Next, we need to figure out the transitions that need to be flipped. Fortunately, speedydelete has already done this earlier. Here is the full table of pairs that must be swapped with each other with the added restriction that it must not be explosive:
Code: Select all
2e, 2e
2i, 2i
3j, 3j
3r, 3r
4q, 4q
2c, 6c / 6c, 2n
2n, 6n / 6n, 2n
3n, 5n / 5n, 3n
3q, 5q / 5q, 3q
3c, 7c / 7c, 3c
5e, 7e / 7e, 3e
4y, 6a / 6a, 4y
3a, 3k / 3k, 3a
5a, 5k / 5k, 5a
3i, 5y / 5y, 3i
3y, 5i / 5i, 3y
2k, 4r / 4r, 2k
4n, 6k / 6k, 4n
4a, 4k / 4k, 4a
4i, 4t / 4t, 4i
This gives us a space of 2^23 rules (2^22 if you exclude the zebra stripes dual).
Now let's figure out how to enumerate each rule. Here is my algorithm:
1) Start with B/S012345678 (the base checkerboard-complementary rule
2) Randomly flip each transition pair in this string, giving a checkerboard-complementary rule (it is also possible to brute-force possibilities).
3) To make sure that it is apgsearchable, it needs two things:
- It is not explosive, and
-
The rule is sufficiently active such that there are few large blobs of checkerboard or other agars
Here are some example rules that do not match the constraints for interestingness:
Code:
Select all
# Does not satisfy a)
#R B2n3acijy4aikt5iky6n7c/S01e2-n3-iky4-aikt5eknqr6-n78
!
# [[ RANDOMIZE ]]
Code:
Select all
# Does not satisfy b)
#R B2cei3qr4c5r6ci8/S12-ci3-r4-e5-qr6akn78
!
# [[ RANDOMIZE ]]
