Halfway between two Life-like cellular automata

[confocaloid]

Pick two Life-like cellular automata that are "only one neighbour-counting condition away from each other". Unpack the differing condition into isotropic subconditions. Choose an isotropic CA that is "midway between" the two Life-like CA, in the sense that the set of living conditions should include half of the differing subconditions and exclude the other half.

Example
As an example, one can pick B3/S23 and B37/S23 as the two Life-like cellular automata. The difference in their rulesets is that the former ruleset includes the rule A7 ("if a cell is currently dead and has precisely seven alive neighbours, then the cell remains dead in the next generation"), while the latter ruleset includes the rule B7 ("if a cell is currently dead and has precisely seven alive neighbours, then the cell becomes alive in the next generation").
The differing neighbour-counting condition is "the cell is currently dead and has precisely seven alive neighbours"; this condition can be "unpacked" into two isotropic subconditions depending on whether the currently-dead neighbour is orthogonal or diagonal. In this case, "midway between B3/S23 and B37/S23" would mean that one of those two subconditions should be included in the birth conditions, while the other one should be excluded from the birth conditions. In other words, here "midway between B3/S23 and B37/S23" means either B37c/S23 or B37e/S23.

B(3)4/S23
Endemic diagonal 13c/84 spaceship halfway between B4/S23 and B34/S23:

Code: Select all

x = 21, y = 23, rule = B3aciky4/S23
5bo2bo$9bo$5b2o2bo$5bob3o$bo$4o$b2o5$18b2o$16bo2b2o$17b3o$16bo2$12b2o$12b3o$
13bo3$2o$2o!
#C [[ ZOOM 10 TRACKLOOP 84 13/84 13/84 ]]

B3(6)/S23
Midway between B3/S23 and B36/S23:

Orthogonal 6c/58 spaceship:

Code: Select all

x = 4, y = 4, rule = B36aci/S23
bo$3o$o2bo$b3o!
#C [[ ZOOM 14 TRACKLOOP 58 6/58 0/58 ]]

Orthogonal 4c/42 spaceship:

Code: Select all

x = 3, y = 5, rule = B36cek/S23
bo$obo$obo$b2o$b2o!
#C [[ ZOOM 14 TRACKLOOP 42 4/42 0/42 ]]

B3(5)/S23
Midway between B3/S23 and B35/S23:

6c/370 orthogonal, c/8 diagonal and p88 oscillator:

Code: Select all

x = 27, y = 34, rule = B35acjny/S23
6b3o3b3o3b3o9$24bo$bobo18bo2bo$3b2o17bo3bo$25bo$23bo2$bo21bo$3o19bobo$
b2o20b2o14$10bo5bo5bo$10bo5bo5bo$10bo5bo5bo!
#C [[ ZOOM 10 TRACKLOOP 370 6/370 0/370 ]]

Code: Select all

x = 39, y = 9, rule = B35acjny/S23
b3o26bo6bo$o3b2o23b2o6b2o$bob3o24bo6bo$2b2o$4b2o2$30bo6bo$29b2o6b2o$30bo6bo!
#C [[ ZOOM 8 ]]

[confocaloid]

B(3)4/S23
Endemic diagonal 13c/84 spaceship halfway between B4/S23 and B34/S23:

Code: Select all

x = 21, y = 23, rule = B3aciky4/S23
5bo2bo$9bo$5b2o2bo$5bob3o$bo$4o$b2o5$18b2o$16bo2b2o$17b3o$16bo2$12b2o$12b3o$
13bo3$2o$2o!
#C [[ ZOOM 10 TRACKLOOP 84 13/84 13/84 ]]

The same CA

Code: Select all

x = 26, y = 16, rule = B3aciky4/S23
19b3o2$18bo2b2o$18bobo2b2o$18b2o3bobo$24bo2$12b3o7b2o$12b3o6b4o$11bo$
11bo2bo$11bo2b2o$2o11b4ob2o$2o12bo3b2o$18b2o$15b3o!
#C [[ THEME Fire ZOOM 4 ]]

Capped guns (p420, p588, p756)

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x = 356, y = 159, rule = B3aciky4/S23
4b2o98b2o98b2o$4b2o98b2o98b2o18$2o98b2o98b2o$2o33bo64b2o33bo64b2o33bo$
34b2o98b2o98b2o$33b2o98b2o98b2o$33b3o97b3o97b3o$31bobo3b2o92bobo3b2o
92bobo3b2o$30b3o4bo92b3o4bo92b3o4bo$33bo3bo95bo3bo95bo3bo$29bo6bo92bo
6bo92bo6bo$28bo6bo92bo6bo92bo6bo$27bo6bo92bo6bo92bo6bo$27bo4bo12bo81bo
4bo12bo81bo4bo12bo$27bo3bo13b2o80bo3bo13b2o80bo3bo13b2o$28b3o13bo2bo
80b3o13bo2bo80b3o13bo2bo$45b2o98b2o98b2o$45bo99bo99bo6$22b2o18b2o78b2o
18b2o78b2o18b2o$22b2o18b2o78b2o18b2o78b2o18b2o$42b2o98b2o98b2o$24b2o
16b2o80b2o16b2o80b2o16b2o$24b2o16b2o80b2o16b2o80b2o16b2o8$67b2o$67b2o
12$180b2o$180b2o12$293b2o$293b2o59$154b2o98b2o98b2o$154b2o98b2o98b2o
18$150b2o98b2o98b2o$150b2o98b2o98b2o!
#C [[ THEME Golly ]]

Other CA midway between B4/S23 and B34/S23:

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#C endemic oblique (13,9)c/82 spaceship
x = 26, y = 22, rule = B3aiqry4/S23
6bo$4bo$4b2o2$7bo$2o$2o$8b3o$8bo$8b3o$10b2o$11bo$10bo$9bo$8bo2bo$11bo
11bobo$9b3o9b2o2bo$21bo2bo$21bo2bo$19b2o$19bo3bo$20b3o!
#C [[ THEME MCell ZOOM 8 TRACKLOOP 82 13/82 9/82 ]]

Code: Select all

#C orthogonal 10c/140 spaceship
x = 9, y = 9, rule = B3aciqy4/S23
5b3o$5bo2bo$5bo2bo$5bobo$5b2o$bo$o2bo$o2bo$b2o!
#C [[ THEME MCell ZOOM 8 TRACKLOOP 140 10/140 0/140 ]]

Code: Select all

#C orthogonal 33c/243 puffer
x = 114, y = 40, rule = B3aiknr4/S23
69b3o$65bo$65bo21bo21bo$65bo20b3o19b3o$83bo3bo21bo3bo4$2o31b2o$2o31b2o
$83bo3bo21bo3bo$65bo20b3o19b3o$65bo21bo21bo$65bo$69b3o2$79bo$79bo$79bo
3$79bo$79bo$79bo2$69b3o$65bo$65bo21bo21bo$65bo20b3o19b3o$83bo3bo21bo3b
o$2o31b2o$2o31b2o4$83bo3bo21bo3bo$65bo20b3o19b3o$65bo21bo21bo$65bo$69b
3o!
#C [[ THEME MCell ZOOM 4 TRACKLOOP 243 33/243 0/243 ]]

Code: Select all

#C 4c/12o, 2c/10o, p36, (7,3)c/33 puffer
x = 44, y = 38, rule = B3aikqr4/S23
b3o$o3bo$o3bo33b3o$5o13b3o20bo$19b2o20bo$20b2o16bo2bo$20b2o15b4o$bobo
16b2o14b3o$2bo34bo14$24bo$23b3o9bo$23bo10bobo$24b3o8b2o$25b2o15bo$41bo
bo$42b2o5$32b2o$32b2o2$39b2o$39b2o!
#C [[ THEME MCell ]]

[confocaloid]

B3/S0(2)3
Some objects halfway between B3/S03 and B3/S023:

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#C orthogonal c/4 spaceship
x = 6, y = 5, rule = B3/S02ace3
2bo$b3obo$o$b3obo$2bo!

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#C spaceships: diagonal 2c/22, orthogonal c/5, orthogonal c/12
x = 23, y = 6, rule = B3/S02ack3
10b3o$2o9bo9bo$2o9bo8b3o$2o$bo8b3o$10bo!

Code: Select all

#C oscillators: p16, p8, p7, p6, p4, p4
x = 66, y = 7, rule = B3/S02aei3
14b3o$b2ob2o8b2o11b2ob2o8bo11bo11b2o$o3bo12b2o8b2ob2o7b2o10b2o11b2o$bo
2bo11b2o22b2o11b3o8b2o$2b3o10b2o12b2ob2o6b3o10b3o8b2o$3b3o23b2ob2o7b2o
10b3o8b2o$64b2o!

Code: Select all

#C orthogonal 6c/12 spaceship
x = 5, y = 6, rule = B3/S02aek3
2b2o$bo2bo$bo2bo$2ob2o$obo$o!

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#C diagonal c/4 spaceship
x = 5, y = 5, rule = B3/S02akn3
b2o$3bo$o3bo$4bo$2b3o!

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#C orthogonal 6c/12 dot puffer and two c/3 spaceships
x = 22, y = 18, rule = B3/S02cek3
11bo$10bobo6bo$11b2o6b2o$12bo8bo$11bo7b2o$8bo2bo7bo$9b2o6$8b2o$o6bo2bo
$7bo2b2o$3bo2bo2b2o$9bo$8bo!

Code: Select all

#C orthogonal c/6 spaceship
x = 5, y = 3, rule = B3/S02cen3
b3o$bo2bo$4o!

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#C diagonal c/6 spaceship
x = 5, y = 5, rule = B3/S02cik3
b3o$o3bo$bo2bo$2b2o$3bo!

Code: Select all

#C orthogonal 6c/12 spaceship
x = 9, y = 5, rule = B3/S02eik3
3bo2b2o$o3b2ob2o$4b4o$bo2b3o$3bo!

[confocaloid]

p680 reflectorless rotating oscillator in an isotropic CA that is "midway between" Life-like CA B3/S23 and B35/S23

Code: Select all

x = 55, y = 19, rule = B35acejk/S23
bobo47bobo$3b2o48b2o$o2bo46bo2bo$b2o48b2o4$o49bo$o49bo$o35bo13bo$36bo$
36bo4$34b2o$33bo2bo$32b2o$33bobo!

6c/370 orthogonal, c/8 diagonal and p88 oscillator:

Code: Select all

x = 27, y = 34, rule = B35acjny/S23
6b3o3b3o3b3o9$24bo$bobo18bo2bo$3b2o17bo3bo$25bo$23bo2$bo21bo$3o19bobo$
b2o20b2o14$10bo5bo5bo$10bo5bo5bo$10bo5bo5bo!
#C [[ ZOOM 10 TRACKLOOP 370 6/370 0/370 ]]

Code: Select all

x = 39, y = 9, rule = B35acjny/S23
b3o26bo6bo$o3b2o23b2o6b2o$bob3o24bo6bo$2b2o$4b2o2$30bo6bo$29b2o6b2o$30bo6bo!
#C [[ ZOOM 8 ]]

There are 252 rulesets "midway between" B3/S23 and B35/S23. (Every such ruleset includes exactly five out of ten Hensel conditions from the set {B5c, B5e, B5k, B5a, B5i, B5n, B5y, B5q, B5j, B5r}. Those without B5n support the xq4_153 glider.)

One such CA has a sparky diagonal 3c/34 spaceship which can be used to construct glider rakes, a p220 oscillator which can be used to construct a glider gun, and p38 and p30 oscillators. Is there a stable glider eater?

Code: Select all

x = 104, y = 83, rule = B35aceiy/S23
82b2o$56b3o23b2o$57b2o23b2o$57b2o3b2o$57b2o3b2o13b2o$57b2o18b2o$56b3o
18b2o14$79b2o$42b2ob2o31bo2bo$39b6o35b2o$12bo26b2o5b2o$11b2o26b4o3b2o
35b2o$9b3o31b3o33bo$9b2o67bobo3b2o$8bo2bo67bo$9bobob2o$11b3o16bo$4bo7b
o16b2o53bob2o$2b2obo22bo12bo27b2o12bo4bo$2b2o25b2ob2o6bo28bobo11bo3b2o
$b2ob3o23b4o6b3o26bo13bo$2o4b2o24bo54bo$5b2o77b3o$5bo2$29bo$28bo2bo$
29bobo70bo$30bo68b2o2bo$56b2o4bo35b3o$17bobo15bo19bo3bobobo34b6o$18b2o
15bobo17bo3bo2bo$18bo16b2o22bo$56b3o$92b2o3b3o$70bo20b2obo2bo2bo$68bo
2bo21bo4bo$65bobo2$65bo$67b3o$29bo$30b2o$29b3obo6b2o$31b2o4bob3o$31b2o
bobobobo$32b2o5bo$37bobo$35bo12b3o$35b2o11b3o$47b2o3bo$33bo12bo3bobo$
32bo14b2o2b2o$31bo12bo2b2o$31b3o5b2o2bo$34bo4b2o$34b3o7b2o11$38bo$37bo
$37b3o!

[Period1GliderGun]

One such rule has a sparky diagonal 3c/34 spaceship which can be used to construct glider rakes, a p220 oscillator which can be used to construct a glider gun, and p38 and p30 oscillators. Is there a stable glider eater?

No stable eater yet, but I found a rephasing G-to-TL and a p36 right off the bat:

Code: Select all

x = 42, y = 25, rule = B35aceiy/S23
21b2o15b2o$19bo2bo15bo2bo3$19b2obo15bob2o$21bobo2b2o5b2o2bobo$22bo4bo
5bo4bo$23bo13bo$23bo2bo7bo2bo$31bo$31b3o$8bo$7bo$7b3o$29b2o$29b2o9$3o
!

EDIT: p20:

Code: Select all

x = 16, y = 8, rule = B35aceiy/S23
14b2o$8b3o3b2o$8b3o3$5b3o$2o3b3o$2o!

p11:

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x = 22, y = 22, rule = B35aceiy/S23
10b2o$10b2o$10b2o2$5b3o6b3o$4bob2o6b2obo$4b2o10b2o$4b2o10b2o3$3o16b3o
$3o16b3o3$4b2o10b2o$4b2o10b2o$4bob2o6b2obo$5b3o6b3o2$10b2o$10b2o$10b2o
!

EDIT2: Different rule; p26 glider gun and p38, more coming:

Code: Select all

x = 25, y = 28, rule = B35aciqy/S23
10b2o$9bobo10b2o$9b2o11b2o2$21b4o$7bo$6bobo12b4o$6bobo12bo2bo$7bo14b2o
3$2o$obo$b2o19b2o$22b2o5$3b3o3$3b3o3$b2o$obo$2o!

[snowman]

Is "betweening" B4 or S4 off the table, since they have an odd number of transitions? (13)

EDIT: I'm making this post constructive. Spaces involving B3/S345 seem interesting. A rule between B3/S(3)4578 has a (16, 5)c/82 and p34:

Code: Select all

x = 4, y = 5, rule = B3/S3aeijn4578
bo$3o$obo$ob2o$2b2o!

Code: Select all

x = 8, y = 8, rule = B3/S3aeijn4578
3o2b3o$2o4b2o$o2b2o2bo$2b4o$2b4o$o2b2o2bo$2o4b2o$3o2b3o!

[confocaloid]

I'm not sure how to handle the B4/S4 cases best (13 is not divisible by 2). One possibility is indeed to exclude them as "offtopic". Another way is to include as many subconditions as possible, while still avoiding minuses in the canonical rulestring. That means including =7 out of 13 subconditions, with 1716 CA in the set.
Here are some such CA, which are "almost halfway between" B3/S23 and B34/S23:

Code: Select all

x = 13, y = 9, rule = B34ceqtwyz/S23
bo$2bo$3o5$11b2o$11b2o!
#C [[ ZOOM 6 THEME LifeHistory ]]

Code: Select all

x = 3, y = 3, rule = B34cikqtyz/S23
o$3o$bo!
#C [[ ZOOM 6 THEME LifeHistory ]]

Spaces involving B3/S345 seem interesting. A rule between B3/S(3)4578 has a (16, 5)c/82 and p34:

Code: Select all

x = 4, y = 5, rule = B3/S3aeijn4578
bo$3o$obo$ob2o$2b2o!

Code: Select all

x = 8, y = 8, rule = B3/S3aeijn4578
3o2b3o$2o4b2o$o2b2o2bo$2b4o$2b4o$o2b2o2bo$2o4b2o$3o2b3o!

A single block can eat the oblique spaceship:

Code: Select all

x = 28, y = 20, rule = B3/S3aeijn4578
bo$3o$obo$ob2o$2b2o14$26b2o$26b2o!

[b-engine]

B(2)3/S(2)3
Some objects in halfway between B3/S3 and B23/S23:

Code: Select all

x = 58, y = 6, rule = B2ikn3/S2ace3
54bo$3o4b3o4b2o5bo10bo4bo4b2o4bo7bo$13bo7b3o3b2o2bobo2bobo2bobo5bo7bo
$b3o2bo2b2o5bo3b3o4b2o3bo3b2o3b2o4b3o5b3o$14b2o6bo$8bo!

Tubs, boats and ships are extensible, hence infinite still lifes.
There's 2 p2 and 2 p4.
Glider itself do work, and it can pull a dot as "tagalong".
B3(6)/S23(6)
HighLife replicator and bomber does work:

Code: Select all

x = 27, y = 6, rule = B36aen/S236ikn
3o19b3o$o2bo18bo2bo$o3bo17bo3bo$bo2bo18bo2bo$2b3o19b3o$15b3o!

In first glance the rule seems explosive, but soups do stabilize:

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x = 64, y = 64, rule = B36aen/S236ikn
2obobobob3ob4o3b2o2bob2ob4obo2b3o2b3o2b3obob2o2b2o2bo$bo2b4o2b2ob7o3b
2o2b2obo4bob2obobob3o2bo3bobob2o3bo$ob2o2bo2b2o3b3ob2o3bo4b2obo2b5o3b
ob2o7b5o3b2o$2b2o2bo2b2o2b3o3b2o4bo2b3ob2o4bob4obo2b2o4b2ob5obo$obob2o
b2ob2o5bo2bob2obobobob2obo3bo10b4o4bob2o2bo$2b2obobo4b5o4b4obo3bo4bo2b
2o3bo2b3o3b4ob4obo$o2b2obob3ob2o2bob5o2b2obo4b2o3b2o2bob2o4b3obo4bo2b
o$obob2obo2bo2b3obo2b3o2b4o2b2obobobobob5o2bob2ob2ob2o2bo$2bo2bob2o5b
3obo2bobo2bo3bob4o2bo2b2ob2ob3o2b2o3bobob3o$b4o5bo2bo3b6o2b3ob2obo3b3o
2bob3o2b6ob3obo$bob2obo2b4o3b4o2bobo3b4obob2ob3o2b2ob4o7bob2ob2o$2b3o
bob2ob4obob3o2b2ob4obo2bob3o3b6obobob2ob2o5bo$2obobob3obob2ob3obob5ob
ob3obo3bo2bo4b2ob2obo3b2o3bo$obo3b3o3b4ob2obob10o3bo2bob5obobo2b2o3bo
b3ob2o$o5b2o4bo5b2ob2obo2bo2b3o2b5o2b5obo6bobo2b2o$b4o3bo5bobo2bo2b2o
3bo2b2obo3b2o3bob2obo3b3ob2o2bobo$4o3bo4b3obo4b4ob2o2b2obo2bob2ob4o4b
2o3bo2bob2o$o2b2obo2b2ob2o4b2obob2ob2o2bob5obob5obob5o3bobob3o$2ob8o6b
3o2b2ob2o2b2o2b3o4bo3b2o2b2o10bobo$b2ob2obobobob4obo2bo9bob3obobobobo
3bo3bo2b3o$ob2obob2o2b2obo5b2ob2obo3bo3bo3b4o2bob2obo2b2ob2ob5o$o3b2o
5b2ob2obo2b2obo2b2ob7ob2o2bo4b2ob2ob4o3b2obo$6ob2o3bo2bo2b2ob2obobo3b
o2bobobobob4ob2o2bo6b3o2b2o$2obo2b4o3b6o2b2o2b5obo3b3ob2ob3o3b2o2b2ob
3o2bo$obobob3o7bobob2o2bob2ob3obobob2obo2bobo4bo2b3o2b4o$o2b3obob6o2b
2ob2o5bobob2obo3bob2ob3o6bo4bo3bo$4b4obo4b2o2b5ob5o2bo2bo6bo3b4obo4bo
2b3o2bo$3o6bo5b5o6bo3bo2bo2b5obobo2b3obo7bo$obob2obob2obo2b3obob6o2bo
bo4b2o2b2o5b9o4b2o$2o9b2ob3o2bob3obo2b2ob2obob2o3b5o2b2o6b2o3bo$2bob4o
b2o2bo4b2o2b2obobo5b2o2bobobo2b3o7b3o4bobo$bob7ob3o4bo2b2o2b3obob2ob2o
2bo2b2ob2obo4b3o2bo2bob2o$2obob3o2bo6b3o3bo2bo2b2obo2bobo4b2o4b3obob3o
4bo$2obo4bob2o2bo6bo2bobo3b2obob2o3bo7b2o2bo2b4o3b2o$b2o2b3ob2o2bo3bo
5b2o4bob2ob2o2bobobob3o2bo4bobobob3o$b5o5b3obo2b4o5b2obo4bo7bo3b2obo3b
o2bo4b2o$3obo2b2obob2obob5ob2obob2obob3ob3ob3ob4o3bo9b2o$3bo2bob6obo4b
5o2bobo2bo2bobobob3o5b3ob2o2bo5bo$2obo2bo3bob2ob4o2bo2bob2o2b2o2bo2b2o
bo2b2o6b4obo3bo2bo$2ob2ob2ob2o3bob3obo3b5o4b5o2bo2b2obobob3obo2b3o3bo
$2o2bobo3b5obo2b2obo14bob2ob2o3b2obo2bo2bobob4o$6b2o2bobob3o2b4o2bob2o
2bo2bob2ob2o2b2ob2o4bo2b2o2bo2bo$2o2bobobobo2bob2obobo3b2o2bo2bob2o4b
o3bobob2obobo3b2o3bo$2bobo2bo3bo2b2obobobob9ob2obobo3b3o2bo2b2obo4bo$
bobo5bobo5bobo3b4o4bo3bobobobobo3bo2bob3o2bo3b2o$6o2b2ob5ob5o2b3obo3b
o2bob2obobo2b3o5bo7bo$bo3bo3b3obo3bo4b3ob2ob2o2b7o2bo2b2obo2bob2obobo
4bo$2b2o2bobo4bob3o2b3o4b2o2b2obob2ob2o3bob2obo4b3o5b2o$ob2o2bo2b2ob4o
3b2ob3o2b2o2b3ob2ob2ob2ob2o2b2obo3b2obob2obo$bo2b3o3b3o7b3obob4ob4ob2o
bo2bobobob2o2b4obob5o$b3o2bob2obo2b5o2b6obobob5ob3o2bob2o2b3o2bobo2bo
bo$5o2bob2o3b2o2b6obobob3ob3o4bob3o2b8o2bo4b2o$3obo2bo3b2o2b2obobo2bo
2b5ob6o2bob2o3b7o3b2o2bobo$2b2obo3b2o2bo4b2o2b2ob2o6bob2ob2o2bo2bobo4b
obobo3bo2bo$o5b3obobobobobob5obo6bobob6o4b2obob2o2b3o2bo$b2o3bob6o3bo
2b2ob4ob3o3b2o8b2o3bob3obo4b4o$b2obob3ob2o3bo2bo2bobo3bobo2b2ob2o2bo4b
ob2ob2o3bobo2b2o2bo$bobo3bobobo2bo5b3o2bobo2b2o2bo4bob3ob2obob4o3bo2b
4o$2o4bobo2b3ob3obo3b4ob2obob5o2bo2b2obo2b3o2b4obo$3bob9obob3ob2o3b5o
2bo2b3obob5o3b2o2b5o4bo$ob3o3b4obob4obo2bo3b5ob2ob2ob3ob3obo3bobob5ob
3o$2b3obo4bobobobo4b2o2b4o2bobob2o6b5obo6bobo3bo$bob2o6b3o2b3o3bobo2b
2ob2obob2o3b5ob2ob2obo2b2o3b2obo$o2b3obo2bo3bo2bo9bobob2o2bob3obob3ob
4o2bo3b3o2bo!

[confocaloid]

B3(6)/S23

A four-engine orthogonal 24c/400 spaceship (simplified speed 3c/50o) where the engines are all in the same phase

Code: Select all

x = 95, y = 217, rule = B36aci/S23
83b2o$86b2o$82b2o8b3o$83bo4bo3bobo$86bobo2bo2bo$87bo3bobo$83bo3bo3b3o$
83bo2bo$83bobo$84b2o4$82b2o$82b2o78$42bo$bo40b2o$b2o38bobo$obo5$43b2o$
2b2o42b2o$5b2o35b2o8b3o$b2o8b3o29bo4bo3bobo$2bo4bo3bobo32bobo2bo2bo$5b
obo2bo2bo33bo3bobo$6bo3bobo30bo3bo3b3o$2bo3bo3b3o30bo2bo$2bo2bo37bobo$
2bobo39b2o$3b2o3$42b2o$b2o39b2o$b2o57$79bobo$38bobo39b2o$39b2o39bo$39b
o19$82bo$82b2o$81bobo6$83b2o$86b2o$82b2o8b3o$83bo4bo3bobo$86bobo2bo2bo
$87bo3bobo$83bo3bo3b3o$83bo2bo$83bobo$84b2o4$82b2o$82b2o!
#C [[ TRACKLOOP 400 24/400 0/400 ]]

Two orthogonal speeds that are very close to each other (one is 6c/58 ~ 18c/174, another is 18c/172)

Code: Select all

#C orthogonal 6c/58 spaceship
x = 4, y = 4, rule = B36aci/S23
bo$3o$o2bo$b3o!
#C [[ ZOOM 6 TRACKLOOP 58 6/58 0/58 ]]

Code: Select all

#C orthogonal 18c/172 puffer
x = 37, y = 20, rule = B36ack/S23
16b2o$10b2o3bo2bo9b2o$9bo2bo2bobo9bo2bo$10b2o4bo11b2o3$31b2o$31b2o5$
31bo4bo$31bo3b2o$31bo4bo2$b2o4bo11b2o$o2bo2bobo9bo2bo$b2o3bo2bo9b2o$7b
2o!
#C [[ ZOOM 6 TRACKLOOP 172 18/172 0/172 ]]

Endemic diagonal 8c/95 spaceship

Code: Select all

x = 6, y = 5, rule = B36cik/S23
2bo$b2o$o3b2o$b2ob2o$4b2o!
#C [[ ZOOM 8 TRACKLOOP 95 8/95 8/95 ]]

B3(5)/S23

Some replicators halfway between B3/S23 and B35/S23:

Code: Select all

x = 4, y = 4, rule = B35aceik/S23
3o$obo$o2bo$b2o!

Code: Select all

#C also B35cjkry/S23
x = 3, y = 3, rule = B35cekry/S23
b2o$obo$bo!

B35acijk/S23, B35acikr/S23, B35aciky/S23 seem to explode.

[rabbit]

Period-60 oscillator found manually in a B3/S23-B35/S23 rule, B35cinry/S23:

Code: Select all

x = 6, y = 9, rule = B35cinry/S23
4b2o$4b2o$4b2o4$2o$2o$2o!

I couldn't find much else of note in the rule after a soup search.

[confocaloid]

B3(5)/S23

Crossposting a capped p56 orthogonal c/2 glider rake:

The orthogonal c/2 puffer engine from the B35(78)/S23(8) space or thereabouts [1] can be used for some high-period rakes. [...]

p56 glider rake, capped with a p4 spaceship found using qfind

Code: Select all

x = 121, y = 31, rule = B35aikqr/S23
116bo$101b2o12b4o$100bobobo3bob2o3b2ob2o$101bo3b2o2bob3o5b2o$102bobo6b
4o3b2o$112b4o$113b3o$o$3bo$o2bo$4bo3$29bobo$29bo2bo$29bo2bo5b2o$30bobo
3bo2bo24b3o$31b3obo29b2o$30b3o3bobo27bo4b2o8b2o11bo2bo$30b2o5bo32b4o7b
3o6bo4bobob2o$30bo39b2obobo6bo2bo3bobobo6bo$37bo32b3ob3o4bo4bo6bob4obo
$16bo19b5o30bo2b2obo2bo5b2o$17b2o16b3o3bo27bobo4b2o2b2o2bo7bob8o$34b3o
bo31bo9bo2bo3bo3b2o7b2o$39b3o27bobo4b2o2b2o2bo7bob8o$17bobo51bo2b2obo
2bo5b2o$70b3ob3o4bo4bo6bob4obo$70b2obobo6bo2bo3bobobo6bo$70b4o7b3o6bo
4bobob2o$71b2o8b2o11bo2bo!
#C [[ THEME MCell GRID TRACKLOOP 56 28/56 0/56 ]]

[Citation needed]

Code: Select all

x = 31, y = 5, rule = B2ace/S3
b2o3b2o4b2o3b2o4b2o3b2o$o7bo2bo7bo2bo7bo$2bo3bo7bobo2$3bobo!
One cell growth per generation

Code: Select all

x = 3, y = 3, rule = B34jnqrtwz/S23
bo$3o$bo! Failed replicator

Code: Select all

x = 8, y = 6, rule = B34ijnqtwy/S23
6bo$5bo$5b3o2$2o$2o!
Glider + Block = Chaos

Code: Select all

x = 7, y = 6, rule = B35ceiky/S23
3b2o$b2o$2o$2ob2o$2o4bo$3b3o!
Natural p8

[unname4798]

The first pattern also works without changes in B2ace/S:

Code: Select all

#C One cell growth per generation
x = 31, y = 5, rule = B2ace/S
b2o3b2o4b2o3b2o4b2o3b2o$o7bo2bo7bo2bo7bo$2bo3bo7bobo2$3bobo!

[Citation needed]

Code: Select all

x = 31, y = 5, rule = B2ace/S3
b2o3b2o4b2o3b2o4b2o3b2o$o7bo2bo7bo2bo7bo$2bo3bo7bobo2$3bobo!
One cell growth per generation

Code: Select all

x = 3, y = 3, rule = B34jnqrtwz/S23
bo$3o$bo! Failed replicator

Code: Select all

x = 8, y = 6, rule = B34ijnqtwy/S23
6bo$5bo$5b3o2$2o$2o!
Glider + Block = Chaos

Code: Select all

x = 7, y = 6, rule = B35ceiky/S23
3b2o$b2o$2o$2ob2o$2o4bo$3b3o!
Natural p8

I might have made a mistake. There are actually 13 B4 transitions, not 14.

[unname4798]

For 4 neighbors case, you can use either 6 or 7.

[confocaloid]

For 4 neighbors case, you can use either 6 or 7.

I'm not sure how to handle the B4/S4 cases best (13 is not divisible by 2). One possibility is indeed to exclude them as "offtopic". Another way is to include as many subconditions as possible, while still avoiding minuses in the canonical rulestring. That means including =7 out of 13 subconditions, with 1716 CA in the set.
Here are some such CA, which are "almost halfway between" B3/S23 and B34/S23: [...]