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Self checkerboard dual (SCBD) rules

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Self checkerboard dual (SCBD) rules

Posted: January 23rd, 2026, 9:15 pm
by speedydelete
There's been some growing interest in these, so I decided to make a thread.
I also wrote a program to find checkerboard duals, available at https://speedydelete.com/cbdual.

Here are the transition pairs:

Code: Select all

0, 4e / 4e, 0
4c, 8 / 8, 4c

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

1c, 5c / 5c, 1c
3c, 7c / 7c, 3c

1e, 3e / 3e, 1e
5e, 7e / 7e, 3e

2a, 4j / 4j, 2a
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
Notably, rules cannot have both of B2c/S2c, B2n/S2n, and so on for 2c, 2n, 3n, 3q, 5n, 5q, 6c, and 6n. This rules out the glider.

Also, the rulespace for no B012a is B/S3c4cy5e to B2-a3-e4-ej5-c678/S012345678.

Re: Self checkerboard dual (SCBD) rules

Posted: January 23rd, 2026, 9:55 pm
by R2INT
I have some SCBD rules for you.
The first one (and my most explored one so far) is Checkerboard, Day & Night, which has a reasonably common c/2 spaceship and has some intermediate technology:

Code: Select all

x = 90, y = 46, rule = B2en3cin4aciknqt5eny6ikn78/S2ace3-eny4cjnqyz5-cin6-en78
52b3o$52bobo$52b2obo$15bo34bob2o$13bobo35bo2bo$15bo38bo$51b2o$8bo28bo
13b2o2b2o$2bo40bo9bo$ob2o2b5obo20bob5o2b2obo6b2o$3bobo5bo22bo5bobo9b3o
bo$bob3obobo2b4o14b4o2bobob3obo7b3obo$2b3o6bobobo14bobobo6b3o9bobo$12b
ob2o14b2obo20bo$14bo16bo4$33bo16bo$33b3o14b3o$33bo16bo3$88b2o$87bo$33b
o16bo37b2o$33b3o14b3o$33bo16bo4$14bo16bo$12bob2o14b2obo20bo$2b3o6bobo
bo14bobobo6b3o9bobo$bob3obobo2b4o14b4o2bobob3obo7b3obo$3bobo5bo22bo5b
obo9b3obo$ob2o2b5obo20bob5o2b2obo6b2o$2bo40bo9bo$8bo28bo13b2o2b2o$51b
2o$15bo38bo$13bobo35bo2bo$15bo34bob2o$52b2obo$52bobo$52b3o!
The main limitation preventing me from making further progress is the lack of stable circuitry (that could be fixed by running a catalyst search program, but currently I do not know how to configure ntcatforce to B2en3cin4aciknqt5eny6ikn78/S2ace3-eny4cjnqyz5-cin6-en78 or run transparent object searches.) We could also try advancing our c/2 technology; there are some natural linear growth patterns travelling at this speed and we could use those to build advanced patterns.

Next up, I have some less explored but still interesting ones. This one, which I call CheckerboardDiagonal, has 3 naturally occurring spaceship speeds:

Code: Select all

x = 20, y = 4, rule = B2cen3y4-ejqrz5aijk6-ei8/S12ei3-aijk4cnwyz5-y6aik78
b2o7bo7b2o$o10bo5bo$o9b3o$o!
Thirdly, we have Checkerboard-V, which also has a c/2o spaceship and block looks promising for stable circuitry:
R2INT wrote: May 19th, 2025, 9:43 am Adding a new checkerboard-complementary rule: Checkerboard-V:

Code: Select all

x = 564, y = 236, rule = B2ei3in4aciktwy5eny6a7e8/S1c2-a3-eny4cnrwyz5-in6-ei78
20bo$17b5o18bo$17bob3o15b5o$16b7o14bob3o$17b7obo10b7o$19b6o12b7obo$19b
5o2bo12b8o$20b4o15b6o$22b2o17b4obo$21bob2obo15b4o70bo11bo10bo29b2o11b
2o12b2o11b2o$42b5o67bo2bo8bo2bo7bob3o12bo14b2o11b2o12b2o11b2o$44b2o21b
4o9bo32b6o6b6o9b4o8b3obo10bo4bo7bo4bo8bo4bo7bo4bo$44b4o31bobo5bo4bo5b
o6b2o5bob7o3bob7o4b2ob2obo6b4o13bo4bo7bo4bo8bo4bo7bo4bo$46b2o3b2o13b6o
7bo6bobo2bobo3bobo3b6o7b3ob2o6b3ob2o3b4obo7bob2ob2o9b8o5b8o6b8o5b8o$46b
5ob3o11b6o6bobo22bo4bo4b2ob3obo4b2ob3obo4b2obob2o7bob4o10b2o2b2o7b2o2b
2o8b2o2b2o7b2o2b2o$48b4o2bo10b8o6bo13bo2bo7bo2bo9b2ob2o7bo2b2o3bobo10b
2obob2o12b2o11b2o12b2o11b2o$2b3ob2o40bo2bo13b2o4b2o24bo19bo11bobo6b3o
13bobo9b3o2b3o5b3o2b3o6b3o2b3o5b3o2b3o$2b3ob2o46bo11bo4bo25bo38b3o14b
3o11bo4bo7bo4bo8bo4bo7bo4bo$2bob2obo44b4o10bo4bo26bo32bo5b3o15b3o8bo6b
o5bo6bo247bo20bo21bo20bo21bo20bo$obobobob2o43b4o10bo2bo25bo42b4o11b3o
11b4o9b4o9b2o2b2o7b2o2b2o220bo20bo21bo20bo21bo20bo$2b2obob4o45bo9b2o2b
2o67b4o9b4ob2o9bo2bo9bo2bo9bo4bo7bo4bo221bo20bo21bo20bo21bo20bo$3b2o5b
2o54bo4bo67bo3bo8b5obo9bo2bo9bo2bo8bo6bo5bo6bo$3b4o2b3o53bobo2bobo70b
o9b4o11bo2bo9bo2bo9b6o7b6o$5b2o3bob3o49b4o2b4o65b4o10b3o10b8o5b8o5b4o
2b4o3b4o2b4o$6b2o2b2o54b2o2b2o65b5obo8b6o8bo6bo5bo6bo7b6o7b6o215bo19b
o20bo19bo20bo19bo$6b3ob6o48b10o63b2o2bo12b3o10b6o7b6o6b4o2b4o3b4o2b4o
212bobo17bobo18bobo17bobo18bobo17bobo$5bob5o3b2o49bob2obo64b4obo52bob
2obo7bob2obo$8b4o4b3o46bobo2bobo94b6o7b6o8b2o2b2o7b2o2b2o$8b5obo2bo119b
2o29b4o9b4o$9b6obobobo117b3o26b2o2b2o7b2o2b2o7b8o5b8o$9b9ob3o116b3o27b
o2bo9bo2bo9b2o2b2o7b2o2b2o$11b7obob2o114b3o52b4o2b4o3b4o2b4o$11b6obob
o117bo2bo26bo2bo9b4o8b2ob2ob2o5b2ob2ob2o$12b6o4bo117bo26b6o8bo2bo7bo2b
o2bo2bo3bo2bo2bo2bo$13b5o121b2o27b4o8bo4bo7b2ob2ob2o5b2ob2ob2o$15b4ob
o118bo27bo4bo7b2o2b2o6b10o3b10o$15b5o118bo30b2o8b2o4b2o8b4o9b4o$16b4o
174b6o7b6o$17b3o2b3o142b6o6bo6bo7b6o7b6o$18bobob5o139bo2b2o2bo6b2o2b2o
8b6o7b6o$21bo2bo142bob2obo5b4o2b4o7b4o9b4o221b2o19b2o20b2o19b2o20b2o19b
2o20b2o$21b2obo140b2ob4ob2o4bob4obo8b4o9b4o221bo20bo21bo20bo21bo20bo21b
o$167b2o2b2o5b2ob4ob2o6b6o7b6o220b2o19b2o20b2o19b2o20b2o19b2o20b2o$165b
3ob2ob3o18b2o4b2o5b2o4b2o$167b2o2b2o6bo6bo5bob2o2b2obo3bob2o2b2obo$166b
obo2bobo5bo6bo5b10o3b10o$166b2o4b2o6bo4bo7b8o6b6o215bo19bo20bo19bo20b
o19bo20bo$168b4o6bo8bo4bobob2obobo5b6o214bobo17bobo18bobo17bobo18bobo
17bobo18bobo$179bo6bo5b2obo2bob2o$179bobo2bobo7b6o9b2o$168b4o8bo4bo10b
2o$180bo4bo$168b4o8bo4bo$169b2o8bobo2bobo$169b2o9bo4bo$169b2o$168bo2b
o8bo4bo5$81b2o47b3o6bo4bo3bobobo$81b2o10bo2b3o5b3o6bo4bobobobo15b4o5b
obo$86b3o3bo4b2o4b2o6b4o3bo2bo2bo3bobobobo5bo2bo4b2o2bo$91bo6bo4bo7b4o
3bobobobo3bo2bo2bo5bo2bo4bob2o$80bobo20bo8bo15bobobobo5b4o5b2obo$81bo
38b3o16bo4bo$80bobo47b3o2$86bo2b2o2bo2bo3bobobo2bo2b2o2bobobo3bo12bob
2o3bob2o$49bobo4bobo3bo9bo7bo6b2o5b2o5bobo4b2o5bobo5b3o2bob2o3bobo4bo
bo$50bo6bo5b2o3bob2o7b3o4b5o2b4o3bobobo2b5o2b2ob2o3b3o3bobobo3b4o3b4o
299bobo12bobo12bobo12bobo13bobo$49bo2bo3bobo3b3o4b2obo7b3o3bobobo2bob
o4bo3bo3b2obo3bobo7bo3b2obo2b2obo3bob2o301bo14bo14bo14bo15bo$51bo5bo5b
obo2bo12bo6bo6bo6bo4bo2bo3bobobo17bo7bo$50bobo3bobo3$53bo6bobo5bobo8b
o$54b2o5bo7bo2bo7b2o5b2o6bo2bo5bo2bo4bobo6bob2o4bob2o5bobo$53bob2o3bo
bobo3bo2bo7bob2o4b2o2bo4b2obo5b2obo4bo2bo5b2obo4b2obo3b2ob2o$56bo6bo6b
2o8b2o8b2o3bobo2bo3bobo2bo2bob3o4b2o3bo2b2o3bo6b2o304bo13bo13bo13bo14b
o$55bobo4bobo4bo9bo9bo2bo3bob2o5b4o5bo2bo3bo3b2o2bo3b2o2b2o307bobo11b
obo11bobo11bobo12bobo$88b2obo4b2obo5b2obo4b2obo5bob2o4bob2o4b2ob2o$90b
o4bo2bobo6bobo5bo7b2obo4b2o6bobo2$30bobo4bobo5bobo3bobo4bobobo5bo13bo
$31bo6bo2bo4bo5bo2bo3bobo4b2o12b2o$30bobobo2bo2bo4b3o3bo2bo3bobobo3bo
bo11bobo$32b2o5b2o5b3o3bo2bo3bo5bobo2bobo4bobo$32b2o4bo2bo5bo3bobo4bo
bo8bobo6b2o16b2o8bo9bobob2o$70b2o5bo9b2o7b2o9b2obo6bo2b2o$69bo17b2o2b
3o5bo6bob5o3bob2ob2o$92b2o4b2obo4bob2obo5bobo$40bo4bo8bo35b2o4bo2b3o5b
5o5b2obobo$37bob3o2b3o6b3o6bo5bobobo9bo4b2obo6bo2bobo3b2obo8b2obo$38b
3o4b3o6b3o3b2o7bobo6bob2o5b2o7bobob2o5bo12bobo323bobo12bobo12bobo12bo
bo13bobo$38b2o6b3o4b3o4b3obo3bob2o7b2obo363b3o12b3o12b3o12b3o13b3o$40b
o6bo6bo7b2o5b2o7bob2o$62b2o4bo13bo3$27bo8bo9bo9bo3bobo5bobo7bo2bo$20b
o4b2o7b2o8b2o8b2o5bo7bob2o6b2o$16bob2o5bobo6bobo7bobo7bobo3b3obo3bob3o
5b4o$17b2obo3bo8bo9bo9bo7b3o5bo9b2o6bobo357bo13bo13bo13bo14bo$16b2o8b
o4b2obo9bo8bo8bobo3bobo7bo2bo6bobo355bobo11bobo11bobo11bobo12bobo$16b
o6bobo5bo9bobo6bobo35b2obo$15bobo6b2o4bobo9b2o7b2o36b2o$23bo17bo8bo40b
o3$32bo9bo3bo5bobo5bobobo3bobobo7bo$31b3o6b2o3b3obo3bob2o4bobo5bobo6b
2o7b2ob2o5bo2bo$30b5o5bobo3b3o3bob3o3bobobo3b4o6bobo6b2o2b2o5bo2bo$31b
3o5bo5b3obo3b2o6bobo5b2o6bob3o8bobo7bobo$32bo5b3o5bo6b2o5bobobo3bo2bo
8b3o4bob3o5bobo$37b3o41bo5b2ob2o6bo2bo$38bo49b2o9bo2bo3$446bobo12bobo
12bobo12bobo13bobo$25bobo3bobo12bo6bo7bo11bo6bo366bo14bo14bo14bo15bo$
24b5o3b3o7bob2o3bob2o6b2o10b2o6b3o$25b3o3bob3o2bob2ob2obo3b2obo5bobo9b
obo5bobo$24b3o5b3o4b2obo7b2obo3b4o7bobo7bo3bo5bo$25bo5bobo4bo10bob2o4b
ob2o8bobo6bo3bo4bobo$53bo2bobo7bobo10bobo7b2o$67b2o10b3o5b2o2bo$66bo13b
o7bobo356bo13bo13bo13bo14bo$446bobo11bobo11bobo11bobo12bobo2$79bo$77b
2o$77bobo$76bob3o$79b3obo4b2o$80bobo4bob2o$81b2o5bobo$80bo8bo4$53bobo
7bo7bo7b2o$52b5o2bob2o4bob2o8b2o$53b3o4b2obo4b2obo5b3obo$52b5o3b3o4b2o
bo6b2obo2bo$53bobo3bob2o5b2obo7bo2bo$60b2obo3bob2o10b2o$59bo11bo8bo6$
71bo10bo$69b2o9b2o$69bobo8bobo$68bo10bo$67b3o8b3o$66b3o8b3o$67bo7b2ob
o$64bobo8bo$65b2o7bobo$64bo2$79bo$75bob2o$76b2obo363bobo13bobo11bobo13b
obo$75bo3bo364bo15bo13bo15bo$79b3obo$82bo$81b2o364b2o13b2o11b2o13b2o$
81bo365b2o13b2o11b2o13b2o$80bobo6$53bo9bo6bo12bo$49bob2o6bob2o5b2o11b
2o$47b2ob2obo3b2ob2obo4bobo10bobo$47b4o6bob2o5b6o6bobo$46bobo7bob2o6b
ob3o6b4o$47b2o8b2o6bob3o8b2o$46b2o8b2o10bo8b2o$46bo9bo18b2o354bobo11b
obo11bobo11bobo11bobo11bobo11bobo11bobo14bobo$45bobo7bobo17bo356bo13b
o13bo13bo13bo13bo13bo13bo16bo$74bobo3$437bo12bo12bo12bo12bo12bo12bo12b
o15bo$76bo359bo12bo12bo12bo12bo12bo12bo12bo15bo$74b2o359bo12bo12bo12b
o12bo12bo12bo12bo15bo$74bobo$72b3obo$72bo3b3obo$71bob3o3bo$75bob3o$75b
obo$76b2o$75bo2$80bo$76bob2o$74b2ob2obo$74bob2obo351bobo11bobo11bobo11b
obo11bobo11bobo11bobo11bobo14bobo$73bob2ob2o351b3o11b3o11b3o11b3o11b3o
11b3o11b3o11b3o14b3o$74b2obo$73b2obo$73bob2o$72bobo362bo12bo12bo12bo12b
o12bo12bo12bo15bo$436bo12bo12bo12bo12bo12bo12bo12bo15bo$435bo12bo12bo
12bo12bo12bo12bo12bo15bo$79bo$77b2o$77bobo$75b6o$75b5o$73b6o$73bob3o$
72bob3o$75bo4$76bo$74b2o$74bobo$72b6o$72b2ob4o$74b4ob2o$75b6o$76bobo$
77b2o$76bo!
The term I used for SCBD previously was Checkerboard-complementary, in reference to the termSelf-complementary. These rule behave the same in 4 universes: standard, inverted, checkerboard, and inverted checkerboard.

EDIT: somehow made an extremely large still life:

Code: Select all

x = 57, y = 5, rule = B2cen3y4-ejqrz5aijk6-ei8/S12ei3-aijk4cnwyz5-y6aik78
56bo$56bo$ob2obo2$8b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o3b2o!

Re: Self checkerboard dual (SCBD) rules

Posted: January 23rd, 2026, 10:18 pm
by speedydelete
R2INT wrote: January 23rd, 2026, 9:55 pm I have some SCBD rules for you.
Thank you! I knew you were interested in them, so I suppose it's nice that you found this thread!

I was trying to find self-complementary rules with small stable circuitry earlier. It may be possible with the use of EPE, if it can even be configured to only search these rules. Due to there only being (I think) 2^32 rules, it might not find anything, however.

Re: Self checkerboard dual (SCBD) rules

Posted: January 23rd, 2026, 11:31 pm
by R2INT
If you want to search for an interesting self-complementary rule with stable circuitry, I have made a table of rule counts for you:
Checkerboard-complementary (SCBD): 2^25 = 33.5M
Self-complementary INT: 2^52 = 4.5 quadrillion

Considering most of these rules are hopelessly explosive, we can reduce the count of interesting SCBD rules to 2^21 and the count of self-complementary rules to 2^48.

If this turns out not to be enough rules, there are some alternatives. For example, there are checkerboard and alternating checkerboard rules that aren't self-complementary, but they (sort of) emulate self-complementary rules. If you think about it, inverting the odd parity checkerboard results in an even parity checkerboard. Zebra stripes rules can emulate SCBD rules using the two directions of stripes (but you sacrifice isotropy, meaning it is best to work with diagonal ships). Here is an illustration of how it could work:

Code: Select all

x = 64, y = 17, rule = B/S012345678
9b8o21b8o2bobobobobobobobo$9b8o21b8obobobobo3bobobobo$9b8o21b8o2bobob
obobobobobo$9b8o21b8obobobobo3bobobobo$9b8o21b8o2bobobobobobobobo$9b8o
21b8obobobobo3bobobobo$9b8o21b8o2bobobobobobobobo$9b8o21b8obobobobo3b
obobobo2$bobobobobobobobo14bobobobobobobobo11b8o$obobobo3bobobobo13bo
bobobobobobobo2b8o$bobobobobobobobo14bobobobobobobobo11b8o$obobobo3bo
bobobo13bobobobobobobobo2b8o$bobobobobobobobo14bobobobobobobobo11b8o$
obobobo3bobobobo13bobobobobobobobo2b8o$bobobobobobobobo14bobobobobobo
bobo11b8o$obobobo3bobobobo13bobobobobobobobo2b8o!
# [[ LABEL 0 -2 10 "Checkerboard" LABEL 30 -2 10 "Zebra Stripes" ]]
For the checkerboard and strobing checkerboard combined, we have 2^101 total rules, while for the zebra stripes and strobing zebra stripes we also have 2^101 total rules. In addition, there are plenty of other agars that contain interesting stuff (such as a natural camelship, see below) That should be enough to support lots of interesting and cool stuff, if it weren't for the lack of support for agar rules. Maybe I could add agar support to my R2INT program (though I am still working on the basics for now).

Code: Select all

x = 159, y = 41, rule = B2cen3acijk4-einqr5cein6-an/S2cek3ckny4jnqtw5aik6cen78
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobo2$obobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobo$72bo$obobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobob2obo2bobobobo2bo2b
obo2bo2bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bo$73b2o9bobo5bobo$obobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobo2bo2bobobobobobobobo5bobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobo2$obobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobob3obobob3obobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobo2$obobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobo2$obobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobo$90bo$obobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobob2o2bobobo7bobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobo$79b4o7bo$ob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobob2o2bobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobo2$obobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobo2$obobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo2$ob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobo2$obobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobo2$obobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
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Re: Self checkerboard dual (SCBD) rules

Posted: January 24th, 2026, 12:12 pm
by speedydelete
R2INT wrote: January 23rd, 2026, 11:31 pm Considering most of these rules are hopelessly explosive, we can reduce the count of interesting SCBD rules to 2^21 and the count of self-complementary rules to 2^48.
Hmm, 2^21 is low enough that I could potentially check all of them with the program I wrote to search all 2tfl rules. Can you figure out a scheme for enumerating every one?

Re: Self checkerboard dual (SCBD) rules

Posted: January 24th, 2026, 3:05 pm
by R2INT
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:
  1. It is not explosive, and
  2. 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 ]]

Re: Self checkerboard dual (SCBD) rules

Posted: January 24th, 2026, 7:27 pm
by speedydelete
R2INT wrote: January 24th, 2026, 3:05 pm 3) To make sure that it is apgsearchable, it needs two things:
  1. It is not explosive, and
  2. The rule is sufficiently active such that there are few large blobs of checkerboard or other agars
I already have a full script that does this available at https://github.com/speedydelete/lifeweb ... lsearch.ts. It is currently configured to search every hex rule from B2o/SH to B234/S01234H, but can be easily configured for other rule families. I will do that in a few days when I finish some other searches, unless someone else does it first.

Re: Self checkerboard dual (SCBD) rules

Posted: January 25th, 2026, 2:53 pm
by Katrina
Quite a few spaceships (c/2o, c/3o, c/3d, c/4o, 2c/4o, c/4d, c/5o, 2c/5o, c/5d, c/6o, c/6d)

Code: Select all

x = 690, y = 45, rule = B2n3aikqr4acknw5aekqy6kn7e8/S1c2-kn3cijnr4-aekqr5cejny6-n78History
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67.D2.D55.D2.D9.D$.4D3.D7.D2.3D43.4D3.D7.D2.3D52.4D3.D7.D2.4D53.4D3.D
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Re: Self checkerboard dual (SCBD) rules

Posted: February 7th, 2026, 8:43 pm
by R2INT
Variation of Checkerboard, Day & Night with a natural puffer:

Code: Select all

x = 12, y = 9, rule = B2en3cinr4aciknqt5eny6ikn78/S2ace3-eny4cjnqyz5-cinr6-en78
4bo$3b2obo$3b7o$4o2bo2bobo$obobo4bobo$4o2bo2bobo$3b7o$3b2obo$4bo!
EDIT: 3c/16d in another such rule:

Code: Select all

x = 6, y = 5, rule = B2ein3cin4aciknqt5eny6ikn78/S2ace3-eny4cjnqyz5-cin6ack78
bo$ob2o$b2obo$3bobo$4bo!
EDIT2: 2c/10d

Code: Select all

x = 4, y = 4, rule = B2e3cin4aciknqt5eny6ik78/S2-ik3-eny4cjnwyz5-cin6-e78
2b2o$b2o$obo$b2o!
EDIT3: 2c/10d

Code: Select all

x = 6, y = 6, rule = B2en3cinq4aciknqt5enqy6ikn78/S2ace3-enqy4cjnqyz5-cinq6-en78
5bo$4bo$3bo$2bobo$bobo$o!
EDIT4: p880!! :o

Code: Select all

x = 5, y = 5, rule = B2en3cinr4aciknt5eny6ikn78/S2ace3-eny4cjnqwyz5-cinr6-en78
o2bo$5o$b3o$b3o$3b2o!
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