The 1D Replicator Collection

[muzik]

We've had 5s for a while at this point to show the interesting diversity of spaceships that exist in isotropic non-totalistic Life-like rules, yet haven't had any such collection for one-dimensional replicators. This is something I've been planning for a long time, beginning with my earlier attempt at classifying 1D replicators (in which it turns out that the classical types need up to six values to describe), such that we have a way of actually classifying them.

This collection is still in its very early stages at the moment and I'm still figuring out how to tabulate what we have so far (as well as any given replicator that fits within the scope) in an accessible way. The following list currently contains known 1D replicators up to a period of 16, in which both sides replicate at the same period and move at the same (or rather, opposite) velocity:
https://conwaylife.com/wiki/User:AwesoM ... eriods_1-X

Submissions of known 1D replicators are welcome (although I plan on dumping a bunch I've grabbed from earlier forum posts here first, so keep that in mind to avoid duplication). The guidelines are as follows:

- Permitted rulespace is the same as that of 5s - the rule must be 2-state, range-1 Moore, on the 2D square grid, and isotropic.
- Replicators submitted must be one-dimensional, as I haven't started figuring out a classification for higher-order replicators in the same depth as 1D.
- Submitted replicators must also be proven to replicate strongly. For replicators in which both sides are the same period, this should be as easy as going through three replication cycles and then deleting one of the two middle replicators, and then showing it still co tinted to replicate cleanly. (If three doesn't work, try six. If not six, try twelve. If you can't get it to replicate cleanly, then it's probably not a strong replicator.) For example, here's the tHighLife replicator, as well as a proof of strong replication (see generation 88, which demonstrates that this same three-replicator pattern itself replicates):

Code: Select all

x = 5, y = 3, rule = B36/S2-i34q
5o$5o$5o!

Code: Select all

x = 29, y = 3, rule = B36/S2-i34q
5o3b5o11b5o$5o3b5o11b5o$5o3b5o11b5o!

There are some other minor rules I'm still in the process of thinking through, such as the replicators being submitted in a D4-symmetric phase and also in the first possible iteration with no fading junk, but that's for later as I have other things to deal with first.

Anyway, submit away (preferably after I've reposted examples first)!

[muzik]

Here's a collection of some of those oddballs which I'm yet to fully figure out how to incorporate:

- Perpendicular-displacement replicators. These replicate linearly like the rest, but the line across which they replicate is also in motion, effectively sweeping out a path in the process. A small example, alongside a proof of strength:

Code: Select all

x = 2, y = 2, rule = B2a4i5j/S1e3r
bo$2o!
[[ ZOOM 4 ]]

Code: Select all

x = 14, y = 14, rule = B2a4i5j/S1e3r
13bo$12b2o7$5bo$4b2o3$bo$2o!
[[ ZOOM 4 ]]

- Parallel-displacement replicators: While both sides are (technically speaking) of the same period, the replication moves a different amount in each direction. For example, this replicator replicates at 2c/2 to the right and 0c/2 to the left:

Code: Select all

x = 2, y = 3, rule = B1e3r4i/S1e2ae3enr4i
2o$o$2o!
[[ ZOOM 4 ]]

Code: Select all

x = 8, y = 3, rule = B1e3r4i/S1e2ae3enr4i
4o2b2o$obo3bo$4o2b2o!
[[ ZOOM 4 ]]

Differing-period replicators: These are the weirdest of the bunch, as both sides replicate at different periods, yet still do so strongly. Proving them to replicate strongly is a bit more challenging as a result.

Code: Select all

x = 3, y = 3, rule = B3aiy4qt5i/S2a3aeiq4e5iy6c
b2o$3o$b2o!
[[ ZOOM 4 ]]

Code: Select all

x = 55, y = 3, rule = B3aiy4qt5i/S2a3aeiq4e5iy6c
b4o3b2o3b2o34b2o2b2o$2ob2o3b3ob3o33b3ob3o$b4o3b2o3b2o34b2o2b2o!
[[ ZOOM 4 ]]

[muzik]

A quick dump of oddball replicators (without any strength proofs so far - this is something I'll deal with later):

Parallel-displacement:

Code: Select all

x = 2, y = 3, rule = B2e3in4ceit5i6c/S1c2-kn3a
bo$o$bo!

Perpendicular-displacement:

Code: Select all

x = 2, y = 2, rule = B2a4w/S2e3j
o$2o!

Code: Select all

x = 11, y = 41, rule = B2ei3aeij4cjt5ky6ei/S1c2ace3jkn4aeijktw5ekry6in7e
3bo3bo$4b3o$4bobo$4b3o$3bo3bo14$3bo3bo$4b3o$4bobo$4b3o$3bo3bo8$4bobo$
3bobobo$4bobo$bo3bo3bo$obob3obobo$bob2ob2obo$obob3obobo$bo3bo3bo$4bobo
$3bobobo$4bobo!

Code: Select all

x = 5, y = 5, rule = B3-k4k7c/S2-i3-c4i
2bo$3o$o2b2o$o2bo$b3o!

Code: Select all

x = 5, y = 5, rule = B3aeijr4ejz5cr6cin/S2-i3-aky4ceinrtz5cejkr6cin7c
3o$bobo$2bobo$3b2o$4bo!

Code: Select all

x = 6, y = 6, rule = B3-ckry4z5c7c/S2-cn3-aky4it5j
3bo$2b3o$bo2b2o$2o2bo$b4o$2bo!

Code: Select all

x = 3, y = 3, rule = B3-c4q/S236c
3o$obo$obo!

Code: Select all

x = 20, y = 12, rule = B3ai4ekq5cy6n/S2-ci3-ace4inr5eqry
16b2o$b2o13bobo$2obo12bo2bo$b3o13b3o$2bo4$8b3o$8bo2bo$9bobo$10b2o!

Code: Select all

x = 3, y = 2, rule = B2a3ejk4acenrtw5aei6-ce7c8/S1c2c3-jy4aik5ackn6akn7e
bo$3o!

Code: Select all

x = 14, y = 8, rule = B2n3-j4i6n/S2-i3-ay4ciqr5i6c7
$6bo$3b2obob2o$3bo5bo$3b2obob2o$5bobo$6bo!

Code: Select all

x = 2, y = 3, rule = B2cek3aejnr4ejn5acejy6n/S01c2ack3ai4nw5a7c
o$2o$o!

Code: Select all

x = 57, y = 64, rule = B3-jknr4ity5ijk6i8/S23-a4ity6c7c
18$40bo$39b3o$38b2ob2o$38b4o$37bob2o$32bo6bo$31bobob2o$30b2o2bo$29bob
3o2bo$28b3obo$27bo2b2o$28bobo$29bo$28bo$28bobo$26bo$24b2o$23b5o$22b2ob
2o$23b3o$24bo!

Code: Select all

x = 4, y = 3, rule = B2n34yz/S2-i3-a4iqy
$b3o$o2bo!

Mixed periods:

Code: Select all

x = 9, y = 10, rule = B2ei3aeijr4cjrt5aky6ei8/S1c2ace3jkn4aeijktw5ejkry6in7e
3$3b4o$3bo2bo$3bobo$3b2o!

Code: Select all

x = 4, y = 5, rule = B2kn3aijn4acik8/S2n3-cek4aint5-aky67c8
b2o$3o$4o$3o$b2o!

Code: Select all

x = 3, y = 13, rule = B3-nqy4aqz5ckn6n/S2-i3-a4inqz
o2$o$3o$obo$3o2$3o$obo$3o$o2$o!

Code: Select all

x = 3, y = 2, rule = B2-a3ckq4ektwyz5-in6-i7e8/S1c3cijnr4ejrw5eq6ai
bo$obo!

Code: Select all

x = 5, y = 14, rule = B3aikn4ijk5ac6c/S2-ci3-ae4in
2bo$3bo$bob2o$b3o$2bo6$3o$o2bo$o2bo$b3o!

Code: Select all

x = 7, y = 13, rule = B378/S23e458
obobobo$o5bo$o5bo$obobobo6$2bo$2ob2o$2ob2o$2bo!

[muzik]

And another quick dump of more traditional replicators, again for convenience's sake so I don't have to keep digging through forum threads. Again, no strength proofs yet:

(12,0)c/34

Code: Select all

x = 9, y = 3, rule = B34tw5y/S23
3o3b3o$obo3bobo$3o3b3o!

(10,0)c/51

Code: Select all

x = 2, y = 4, rule = move_rep
o$2o$2o$o!

(7,0)c/27 (likely identical)

Code: Select all

x = 3, y = 4, rule = B34k5y/S234n7e
bo$3o2$bo!

Code: Select all

x = 9, y = 3, rule = B2n35jkny/S23
3o3b3o$obo3bobo$3o3b3o!

(4,4)c/26

Code: Select all

x = 3, y = 3, rule = B3-cer4eqt6n/S2-c3-k4eiq5a
2bo$b2o$2o!

(11,11)c/97

Code: Select all

x = 35, y = 36, rule = B3ainqy4jqry5y6-ai8/S2-ci3-a4ceiqt5aeq6kn8
4$20b2o$20bobo$20bo$21b4o$24bo$24bobo$24bo2bo$25b3o6$7b3o$7bo2bo$8bobo
$10bo$10b4o$14bo$12bobo$13b2o!

(6,0)c/31

Code: Select all

x = 10, y = 14, rule = B34cj6c8/S23-e8
6$4b3o$4bobo$4bobo$5bo$4bobo$4bobo$4b3o!

(7,7)c/81

Code: Select all

x = 20, y = 21, rule = B35y/S234w
4$9b3o$13bo$12b2o$9b2ob3o$11bo2b2o$4bo2bo3b2o3bo$4bo2bo3bo3bo$4bo3b3o
3bo$6b2obo3bo$5b3o4bo$7b2o2bo$8bobo$9bo!

(12,0)c/45

Code: Select all

x = 4, y = 3, rule = B35y/S23-e
b2o$o2bo$b2o!

(9,0)c/18

Code: Select all

x = 7, y = 3, rule = B3-knqr4aen5ekqr6ei7e/S2ae3ijnq4aiknw5eiq6ace
3ob3o$obobobo$3ob3o!

(16,0)c/32

Code: Select all

x = 9, y = 8, rule = B3/S23-a4a
6bo$7bo$7b2o$3o4b2o$3o4b2o$7b2o$7bo$6bo!

(16,16)c/78

Code: Select all

x = 4, y = 5, rule = B2in3aij4acjkwz5ak/S2-i3-aq4acijqwz6c8
2bo$2b2o$2o$bo$o!

(9,9)c/38

Code: Select all

x = 10, y = 9, rule = B3-cekq4jtz5ijry6e/S23-a4cikry6c
2$2b3o$2bo$2b2o2bo$4bobo$4b3o!

(9,9)c/30

Code: Select all

x = 16, y = 17, rule = B2ei3aeijr4cjrt5-cjnq6e8/S1c2ace3jkn4aeijktw5ejry6ein7e
3$10b3o$10bobo$5b3o2b3o$5bobo$5b3o!

(16,0)c/32

Code: Select all

x = 5, y = 3, rule = B2-a5y8/S2-c34r
b3o$o3bo$b3o!

(10,0)c/32

Code: Select all

x = 15, y = 9, rule = B2ce/S1
2$3b2o2b2o$5b2o$3b2o2b2o!

(11,0)c/25, extensible

Code: Select all

x = 30, y = 96, rule = B3-n4w/S23-r4t
3$15b3o$15bobo$15b3o12$17b3o$17bobo$17b3o12$15b3o$15bobo$15b3o12$13b3o
$13bobo$13b3o12$11b3o$11bobo$11b3o12$11b3o$11bobo$11b3o12$11b3o$11bobo
$11b3o!

(21,0)c/48

Code: Select all

x = 3, y = 15, rule = B3-n4w/S23-r4qt
3o$obo$3o10$3o$obo$3o!

(5,2)c/21

Code: Select all

x = 3, y = 5, rule = B3-y4y6ci/S23-e
2bo$b2o$o$o$bo!

(9,0)c/57

Code: Select all

x = 3, y = 7, rule = B2e3-cjy4aeiq8/S23aciqr4ejq
3o2$obo$obo$obo2$3o!

(4,0)c/18

Code: Select all

x = 14, y = 3, rule = B2e3-cjy4aiq/S23-ejkn4ejq
b2o8b2o$obo8bobo$b2o8b2o!

A bunch of others, displacements I'm yet to determine:

Code: Select all

x = 4, y = 3, rule = B2i3/S23-a4it
bo$3o$ob2o!

Code: Select all

x = 33, y = 19, rule = B3aijq4cetz5er6ei8/S2-i3-aek4citz5a6i
6bobo15bobo$3bobo3bobo9bobo3bobo$2bobob3obobo7bobob3obobo$bobo7bobo5bo
bo7bobo$2o5bo5b2o3b2o5bo5b2o$b4o5b4o5b4o5b4o$6bobo15bobo2$4bo5bo11bo5b
o5$2b2o7b2o7b2o7b2o$3o9b3o3b3o9b3o$ob2o7b2obo3bob2o7b2obo$2obo3bo3bob
2o3b2obo3bo3bob2o$2b3obobob3o7b3obobob3o$3bobobobobo9bobobobobo!

Code: Select all

x = 4, y = 4, rule = B2e3-kr4a8/S2-k3aij4eiw
3o$o2bo$o2bo$b3o!

Code: Select all

x = 1, y = 6, rule = B2e3-kr4a8/S2-k3aij4eiw
o$o$o$o$o$o!

Code: Select all

x = 8, y = 11, rule = B3-cknr4i/S2-ik3-ik4aceir5-enqr6ce
b2o2b2o$2o4b2o$b2o2b2o6$b2o2b2o$2o4b2o$b2o2b2o!

Code: Select all

x = 6, y = 4, rule = B34ar5cq/S23-a5j
3b2o$3ob2o$b4o$2b2o!

Code: Select all

x = 7, y = 13, rule = B35y6n/S23-q
2$2bo$b3o7$b3o$2bo!

Code: Select all

x = 6, y = 4, rule = B34ar5cq/S23-a5j
bo2bo$o4bo$o2bobo$5o!

Code: Select all

x = 5, y = 4, rule = B2n3-ckr5ey/S23-qy4nt
b3o$o3bo$o3bo$b3o!

Code: Select all

x = 5, y = 10, rule = B2n3-kqr5ey/S23-qy4cnt
2bo$bobo$o3bo$o3bo$o3bo$o3bo$o3bo$o3bo$bobo$2bo!

Code: Select all

x = 7, y = 3, rule = B2n3-jn/S1c23-y
3ob3o$obobobo$3ob3o!

Code: Select all

x = 17, y = 6, rule = B37/S2-n3-y4in
14bo$12bobo$4b2o4b2o3b2o$2o3b2o4b2o$2bobo$2bo!

Code: Select all

x = 3, y = 8, rule = B3-er4city/S23-a4city
obo$2o$bo3$bo$2o$obo!

Code: Select all

x = 10, y = 10, rule = B3-nqy4aqz5ckn6n/S2-i3-a4inqz
4bo$6bo$7bo$3bo4bo$o5bo2bo$5b2o2bo$bo2b2o2b2o$2bo$3bo2bo$4b3o!

Code: Select all

x = 1, y = 34, rule = B34e6i/S1e2-k3i
o$o$o29$o$o$o!

Code: Select all

x = 5, y = 3, rule = B3-r4z5y/S238
b3o$o3bo$2ob2o!

Code: Select all

x = 14, y = 3, rule = B3-c4cerwy5a7/S23aiqry
b2o8b2o$3o8b3o$b2o8b2o!

Code: Select all

x = 18, y = 12, rule = B2-ek4i8/S04et
3$7bo$bo5bo5bo$bo5bo5bo3$4bo5bo5bo$4bo5bo5bo$10bo!

Code: Select all

x = 14, y = 10, rule = B2ein3cijn4cnrwy5cnq6e/S1c2-ai3acny4anqy5c6ek8
2$5b5o$5bo3bo4$5bo3bo$5b5o!

Code: Select all

x = 5, y = 14, rule = B3-y8/S2-i3-a4iq5c6e
b2o$2ob2o$bo2bo$bo2bo$2b2o5$2b2o$bo2bo$bo2bo$2ob2o$b2o!

Code: Select all

x = 7, y = 9, rule = B2cei3in4w5n/S14w
2o2b2o$2b2o$2o2b2o4$b2o2b2o$3b2o$b2o2b2o!

Code: Select all

x = 13, y = 5, rule = B2i3ai4cei5c6c7/S2-ae3acein4-t5-aq6cei7c8
2bo7bo$b4obob4o$4obobob4o$b4obob4o$2bo7bo!

Code: Select all

x = 10, y = 14, rule = B3ai4ac7/S3i4a5ai6ac7c8
3b4o$3b4o$3b4o$4b2o3$b8o$b8o$10o$10o$10o$b8o$b8o$3b4o!

Code: Select all

x = 7, y = 8, rule = B2en3ij4a5e7e8/S1c2cek3-a4aiqw5aky
3bo$2b3o$b5o$b5o$2b3o$3bo!

Code: Select all

x = 15, y = 12, rule = B35/S23a4
$5b2ob2o$b3ob2ob2ob3o$b3ob2ob2ob3o$5b2ob2o4$5b2ob2o$b3ob2ob2ob3o$b3ob
2ob2ob3o$5b2ob2o!

Code: Select all

x = 13, y = 17, rule = B2e3eij4ac6ai/S1c2cek3einy4e6i
b3o$obobo2bo$3o3bob2o$obobo4bo$b3o2bo2bo$7b2o3$8b5o3$7b2o$b3o2bo2bo$ob
obo4bo$3o3bob2o$obobo2bo$b3o!

Code: Select all

x = 4, y = 4, rule = B2kn3aijkr4qrz5aejkr6i/S2aek3-acek4ai5ai6i
b3o$o2bo$2obo$o!

Code: Select all

x = 8, y = 4, rule = B2n3-n4e/S23-a4-ikry
2b4o$b6o2$o6bo!

Code: Select all

x = 52, y = 11, rule = B2ei3-jn/S2-i3
3$6bobo3bobobobo3bobobobo3bobobobo3bobo$6bobo3bo5bo3bo5bo3bo5bo3bobo$
5bo4bo9bo9bo9bo4bo$6bobo3bo5bo3bo5bo3bo5bo3bobo$6bobo3bobobobo3bobobob
o3bobobobo3bobo!

Code: Select all

x = 9, y = 3, rule = B34eiw5y/S2-i3-q6ac
b2o3b2o$o2bobo2bo$b2o3b2o!

Code: Select all

x = 18, y = 26, rule = B3aijn4w78/S2-e34eiqtwz5i78
4$9b3o$10bo$8bo3bo$9bobo$6bo7bo$4bo2bob3obo2bo$4b2o3b3o3b2o$4bo2bob3ob
o2bo$6bo3bo3bo2$6bo3bo3bo$4bo2bob3obo2bo$4b2o3b3o3b2o$4bo2bob3obo2bo$
6bo7bo$9bobo$8bo3bo$10bo$9b3o!

ATPP has a lot of variants: viewtopic.php?t=3554

And this rule appears to have adjustable speeds to some extent: viewtopic.php?t=5529

[wwei47]

- Submitted replicators must also be proven to replicate strongly. For replicators in which both sides are the same period, this should be as easy as going through three replication cycles and then deleting one of the two middle replicators, and then showing it still co tinted to replicate cleanly.

This definition technically lets this 4c/15 through.

Code: Select all

x = 4, y = 3, rule = B3-cqy4ajq5ry6i8/S23-cejk4t5acj7c
b2o$o2bo$b2o!

Needless to say, it'll continue working if you delete either copy after 3 cycles.

Code: Select all

x = 28, y = 3, rule = B3-cqy4ajq5ry6i8/S23-cejk4t5acj7c
b2o22b2o$o2bo20bo2bo$b2o22b2o!

EDIT: Old result:

Code: Select all

x = 3, y = 3, rule = B2i3-cy4cj5cy6ek7e/S2-in3-aek4n5jnqr6n78
2o$obo$bo!

I don't even know how this replicates.

Code: Select all

x = 5, y = 3, rule = B2in3aijn4cen5eijny6in78/S2-ik3-aiq4nqrtwz5cejnq6cn7e8
bobo$obobo$bobo!

[Wyirm]

Code: Select all

x = 72, y = 143, rule = B2-a3j5q6cen/S12aek3y4t
35bo$36bo$35bo8$33bo3b2o$32bo$33bo3b2o8$30b4o4b3o$41bo$30b4o4b3o8$28b
2o4bo3b6o$27bo2bo2bo3bobo$28b2o4bo3b6o7$43bo$25b2o6b2o2b9o$32bo13bo$
25b2o6b2o2b9o$43bo7$23b9o2b6o3b2o2b2o$22bo2b2o5b2o11b2o$23b9o2b6o3b2o
2b2o8$20b2o2b2o3b2o4b10o2bo2bo$22b2o12b2o3bo3b2o4bo$20b2o2b2o3b2o4b10o
2bo2bo7$35bo$18bo2bo2b3o3bo3b4o4b2obo4b4o$17bo4b2o7bo14bo$18bo2bo2b3o
3bo3b4o4b2obo4b4o$35bo7$15b4o4b3o7b2o3bo7bo7b2o$22bo12bobo9bo5bo2bo$
15b4o4b3o7b2o3bo7bo7b2o8$13b2o7b6o3bo2bo2bo2bo3bo3b5o4b2o$12bo2bo5bo2b
o3bobo4b2o4bobo6bo$13b2o7b6o3bo2bo2bo2bo3bo3b5o4b2o8$10b2o4b5o2b4o4b2o
6b2o3b5o4bo3b4o$18bo2b2ob2o20bo2bo2bo3b3o2bo$10b2o4b5o2b4o4b2o6b2o3b5o
4bo3b4o7$26bo$8b4o3bo4b2o2b4o3b4o2b3o3b2o7bo2bo2b2o2b2o$7bo2b3o3bo2bo
2bo7b3o2b2o8bo5bo4bo3b2o$8b4o3bo4b2o2b4o3b4o2b3o3b2o7bo2bo2b2o2b2o$26b
o7$5b2o2b2o2bo2bo2b2o2b2o3b2o2b2o4bo3b2o2b11o5bo2bo$7b2o3bo4bo3b2o4bo
2bo6bo6b2o2bo4bo3bo3bo4bo$5b2o2b2o2bo2bo2b2o2b2o3b2o2b2o4bo3b2o2b11o5b
o2bo8$3bo2bo5b6o5b6o3b2o3b2o2b2o4b2o5b2o5b2o2b4o$2bo4bo3bo2b2o2bo3bo2b
2o2bobo2bobo19bo3bo$3bo2bo5b6o5b6o3b2o3b2o2b2o4b2o5b2o5b2o2b4o8$4o2b2o
5b4o7b4obo7b3o2bo4b3o3bo8b2o5b2o$8bo3bob2obo5bob2o3bo5bo6bo2b3o5bo6bo
6bo2bo$4o2b2o5b4o7b4obo7b3o2bo4b3o3bo8b2o5b2o!

I don't understand the difference between strong and weak replicators. Is the above a weak replicator?
Edit*
Even though this replicator looks 2-dimensional, count closely the total amount of replicators every cycle, and the number of replicators generated per replicator. This is technically a 1D replicator. In addition to displacements and periods, we now have to worry about rotation.

Code: Select all

x = 3, y = 4, rule = B3aijr4ciq7c/S2-i3-a4i5q
o$2o$b2o$2o!

Furthermore, there are a large number of replicators that also mirror their copies:

Code: Select all

x = 3, y = 2, rule = B2i3aij4a/S234i
3o$obo!  

Code: Select all

x = 5, y = 3, rule = B2i3aijn4a/S234i
2ob2o$o3bo$b3o!

[Wyirm]

Continued because character limit:
This next one makes me question how we classify replicators in the first place. Replicators naturally embed fractals, and fractals all have a hausdorff dimension associated with them. The sierpinski triangle, for example, has a hausdorff dimension of log(3)/Log(2). We have a basic square, iterate the dimension by adding squares around the edges to make a 4x4 square. do it again and we have 3x3. the area is the number of "iterations" raised to the power of 2, or it's dimensionality. With the sierpinski, we have a unit triangle, we add 2 triangles, and the iterations is 2, iterate it again, and we haev 9 triangles, for 4 iterations. This leads to a dimensionality of about 1.58. This part goes outside of the thread itself, but is important. A "2-dimensional" replicator emulates a 3-dimensional sierpinski pyramid, we have our base pyramid, 1 pyramid for 1, 5 pyramids for 2, 25 for 4. which is 5^sqrt(iterations). What we think is 2-dimensional, actually is log(x)(5^sqrt(x)) dimensional. So this thing that is somewhat in-between linear and quadratic, is going to break reality:

Code: Select all

x = 2, y = 4, rule = B2e3ijn6n/S1c2cek3n
o$bo$bo$2o!

It copies itself along not one, not 2, but some horrid 3-directional 1.5 dimensional oblique replicator explosion.

[wwei47]

Code: Select all

x = 3, y = 2, rule = B2i3aij4a/S234i
3o$obo!  

This one is a Pascal triangle modulo 3 replicator! It works differently from all the ones I found. Mine relied on a timing or spacial offset to replicate the way they did. This one simply flips over.
EDIT: Wait, no, but it's still pretty cool.

[Wyirm]

With 1D replicators also being able to make copies with rotations and reflections, I think the replicator notation should look like this:
F, R, L, or B for rotations of the copy in relation to the original replicator, x if the replicator copy mirrors itself, then it's displacement, then period. This replicator would be Bx(0,8)/42 , R(4,20)/46. (If I counted correctly)

Code: Select all

x = 3, y = 4, rule = B3aijr4ciq7c/S2-i3-a4i5q
o$2o$b2o$2o!

Edit* more stuff to worry about:
what about 1d replicators that do this:

Code: Select all

x = 1, y = 1, rule = R1,C0,S0-3,B1,3,N@07
o!

[LaundryPizza03]

what about 1d replicators that do this:

Code: Select all

x = 1, y = 1, rule = R1,C0,S0-3,B1,3,N@07
o!

Rule 150? There are at least three of these things in 2 dimensions, which are listed here. One of them works in an OT rule:

Code: Select all

x = 3, y = 1, rule = B026/S15
3o!

[muzik]

This definition technically lets this 4c/15 through.

Code: Select all

x = 4, y = 3, rule = B3-cqy4ajq5ry6i8/S23-cejk4t5acj7c
b2o$o2bo$b2o!

Needless to say, it'll continue working if you delete either copy after 3 cycles.

Code: Select all

x = 28, y = 3, rule = B3-cqy4ajq5ry6i8/S23-cejk4t5acj7c
b2o22b2o$o2bo20bo2bo$b2o22b2o!

Not quite. Here's generation 180:

Code: Select all

x = 100, y = 3, rule = B3-cqy4ajq5ry6i8/S23-cejk4t5acj7c
b2o22b2o46b2o22b2o$o2bo20bo2bo44bo2bo20bo2bo$b2o22b2o46b2o22b2o!

If we delete one of the two inner units, the entire thing ends up exploding and therefore not following the replication habit.

Code: Select all

x = 100, y = 3, rule = B3-cqy4ajq5ry6i8/S23-cejk4t5acj7c
b2o22b2o70b2o$o2bo20bo2bo68bo2bo$b2o22b2o70b2o!

For comparison's sake, here's an ideal case of a Pascal-mod-3 replicator in a 3-state rule. An initial unit:

Code: Select all

x = 1, y = 2, rule = MarBlocks-3-rep
A$A!

Generation 12 (180/15):

Code: Select all

x = 25, y = 2, rule = MarBlocks-3-rep
A5.A11.A5.A$A5.A11.A5.A!

Generation 12, but we delete one of the middle units:

Code: Select all

x = 25, y = 2, rule = MarBlocks-3-rep
A5.A17.A$A5.A17.A!

As can be seen here, deleting the equivalent middle unit would not cause a "strong" mod-3 replicator from blowing up - it'd continue partitioning itself into twos, and then threes where the middle is inverted, and so on.

I don't even know how this replicates.

Code: Select all

x = 5, y = 3, rule = B2in3aijn4cen5eijny6in78/S2-ik3-aiq4nqrtwz5cejnq6cn7e8
bobo$obobo$bobo!

Since this is inherently chaotic we can't classify it under the standard rules.

[muzik]

Code: Select all

x = 72, y = 143, rule = B2-a3j5q6cen/S12aek3y4t
35bo$36bo$35bo8$33bo3b2o$32bo$33bo3b2o8$30b4o4b3o$41bo$30b4o4b3o8$28b
2o4bo3b6o$27bo2bo2bo3bobo$28b2o4bo3b6o7$43bo$25b2o6b2o2b9o$32bo13bo$
25b2o6b2o2b9o$43bo7$23b9o2b6o3b2o2b2o$22bo2b2o5b2o11b2o$23b9o2b6o3b2o
2b2o8$20b2o2b2o3b2o4b10o2bo2bo$22b2o12b2o3bo3b2o4bo$20b2o2b2o3b2o4b10o
2bo2bo7$35bo$18bo2bo2b3o3bo3b4o4b2obo4b4o$17bo4b2o7bo14bo$18bo2bo2b3o
3bo3b4o4b2obo4b4o$35bo7$15b4o4b3o7b2o3bo7bo7b2o$22bo12bobo9bo5bo2bo$
15b4o4b3o7b2o3bo7bo7b2o8$13b2o7b6o3bo2bo2bo2bo3bo3b5o4b2o$12bo2bo5bo2b
o3bobo4b2o4bobo6bo$13b2o7b6o3bo2bo2bo2bo3bo3b5o4b2o8$10b2o4b5o2b4o4b2o
6b2o3b5o4bo3b4o$18bo2b2ob2o20bo2bo2bo3b3o2bo$10b2o4b5o2b4o4b2o6b2o3b5o
4bo3b4o7$26bo$8b4o3bo4b2o2b4o3b4o2b3o3b2o7bo2bo2b2o2b2o$7bo2b3o3bo2bo
2bo7b3o2b2o8bo5bo4bo3b2o$8b4o3bo4b2o2b4o3b4o2b3o3b2o7bo2bo2b2o2b2o$26b
o7$5b2o2b2o2bo2bo2b2o2b2o3b2o2b2o4bo3b2o2b11o5bo2bo$7b2o3bo4bo3b2o4bo
2bo6bo6b2o2bo4bo3bo3bo4bo$5b2o2b2o2bo2bo2b2o2b2o3b2o2b2o4bo3b2o2b11o5b
o2bo8$3bo2bo5b6o5b6o3b2o3b2o2b2o4b2o5b2o5b2o2b4o$2bo4bo3bo2b2o2bo3bo2b
2o2bobo2bobo19bo3bo$3bo2bo5b6o5b6o3b2o3b2o2b2o4b2o5b2o5b2o2b4o8$4o2b2o
5b4o7b4obo7b3o2bo4b3o3bo8b2o5b2o$8bo3bob2obo5bob2o3bo5bo6bo2b3o5bo6bo
6bo2bo$4o2b2o5b4o7b4obo7b3o2bo4b3o3bo8b2o5b2o!

I don't understand the difference between strong and weak replicators. Is the above a weak replicator?

It's chaotic and therefore unclassifiable under the standards I've set out.

Edit*
Even though this replicator looks 2-dimensional, count closely the total amount of replicators every cycle, and the number of replicators generated per replicator. This is technically a 1D replicator. In addition to displacements and periods, we now have to worry about rotation.

Code: Select all

x = 3, y = 4, rule = B3aijr4ciq7c/S2-i3-a4i5q
o$2o$b2o$2o!

I love this replicator but classifying it under this system would be tricky at best. I've tried deleting individual units at certain times and whether it continues to replicate as expected is kind of hit or miss, so I can't be certain if this is a strong replicator at some scale level. It'd probably be a good idea to try and simplify the behaviour of this replicator into a fundamental rule of sorts, like how common replicators can be simplified down to Rule 6/Rule 90, before we think about including it in the notation.

Furthermore, there are a large number of replicators that also mirror their copies:

Code: Select all

x = 3, y = 2, rule = B2i3aij4a/S234i
3o$obo!  

Code: Select all

x = 5, y = 3, rule = B2i3aijn4a/S234i
2ob2o$o3bo$b3o!

This should be pretty easy to deal with - we just wait until the replicator becomes an exact copy of itself in such a way that rotation or flipping doesn't matter, as is done with oscillators and spaceships. This should be easy enough for linear replicators (although we may run into problems for quadratic cases).

[muzik]

Continued because character limit:
This next one makes me question how we classify replicators in the first place. Replicators naturally embed fractals, and fractals all have a hausdorff dimension associated with them. The sierpinski triangle, for example, has a hausdorff dimension of log(3)/Log(2). We have a basic square, iterate the dimension by adding squares around the edges to make a 4x4 square. do it again and we have 3x3. the area is the number of "iterations" raised to the power of 2, or it's dimensionality. With the sierpinski, we have a unit triangle, we add 2 triangles, and the iterations is 2, iterate it again, and we haev 9 triangles, for 4 iterations. This leads to a dimensionality of about 1.58. This part goes outside of the thread itself, but is important. A "2-dimensional" replicator emulates a 3-dimensional sierpinski pyramid, we have our base pyramid, 1 pyramid for 1, 5 pyramids for 2, 25 for 4. which is 5^sqrt(iterations). What we think is 2-dimensional, actually is log(x)(5^sqrt(x)) dimensional. So this thing that is somewhat in-between linear and quadratic, is going to break reality:

Code: Select all

x = 2, y = 4, rule = B2e3ijn6n/S1c2cek3n
o$bo$bo$2o!

It copies itself along not one, not 2, but some horrid 3-directional 1.5 dimensional oblique replicator explosion.

A small selection of three-directional replicators does exist, both of which replicate strongly from what I can see:

Code: Select all

x = 3, y = 2, rule = B2a3iry4y5aiky7e/S2k4cz
3o$obo!

Code: Select all

x = 4, y = 4, rule = B2o3op4m5/S13m4p6H
2bo$bobo$o2bo$b2o!

This could be considered three-directional as well if we permit copies to be collinear and stationary (which I would):

Code: Select all

x = 1, y = 5, rule = B2a/S1e3eiy5i
o$o2$o$o!

[muzik]

Time for another dump of unsorted replicators, dating back to after Feb 2022:

Code: Select all

x = 3, y = 3, rule = B3-kqy4cejr5k6in7c/S2-i3-acky4cinqrz5cek6cn
bo$2bo$3o!

Code: Select all

x = 4, y = 3, rule = B2aci3jq4y/S1c2i5i6c8
o2bo$b2o$o2bo!

Code: Select all

x = 9, y = 9, rule = B3-knqr4t6n/S2-in3-acy4iz5q6c
5bo$5b2obo$5bo3$3o$bo2$bo!

Code: Select all

x = 192, y = 12, rule = B3-cn4w5a/S23-r4k
173bo$4bo13bo41bo14bo96b3o$3b3o11b3o39b3o12b3o41bo52b5o11bo$2b5o9b5o37b
5o10b5o39b3o12bo37b2o3b2o9b3o$b2o3b2o7b2o3b2o35b2o3b2o8b2o3b2o37b5o10b
3o35b3o3b3o7b5o$3o3b3o5b3o3b3o33b3o3b3o6b3o3b3o35b2o3b2o8b5o35b2o3b2o
7b2o3b2o$b2o3b2o7b2o3b2o35b2o3b2o8b2o3b2o35b3o3b3o6b2o3b2o35b5o7b3o3b
3o$2b5o9b5o37b5o10b5o37b2o3b2o6b3o3b3o35b3o9b2o3b2o$3b3o11b3o39b3o12b
3o39b5o8b2o3b2o37bo11b5o$4bo13bo41bo14bo41b3o10b5o51b3o$118bo12b3o53b
o$132bo!

Code: Select all

x = 15, y = 17, rule = B2e3aijky4acjr5aik6ce7/S1c2-in3nr4acekn5-acqy6ci78
o3bo5bo3bo$5o5b5o$2bo9bo$2bo9bo10$2bo9bo$2bo9bo$5o5b5o$o3bo5bo3bo!

Code: Select all

x = 3, y = 3, rule = B3-q4w5cry8/S2-i3-k4cwz7c
bo$3o$2o!

Code: Select all

x = 2, y = 3, rule = B3-nr4t5eiy78/S234q5e
2o$2o$2o!

Code: Select all

x = 7, y = 4, rule = B2n3air4c5cy6e/S2-i3-ay4aikq5a
bo3bo$obobobo$3ob3o$bo3bo!

Code: Select all

x = 3, y = 4, rule = B3-enr4cz5cen6cen7c/S23-ckq4int5aej6ck7e
bo$3o$3o$bo!

Code: Select all

x = 4, y = 3, rule = B3-r4art5ci6kn8/S2e3-cqy4-cny6in7c
4o$o2bo$4o!

Code: Select all

x = 3, y = 4, rule = B2n3-cqr4acnqtyz5eikqr6cei7c/S2-ik3ijknr4aeiw5nqr6k
bo$3o$3o$bo!

Code: Select all

x = 5, y = 4, rule = B3aeijq4qyz5jk6ei/S23-k4cknqz5jk6ae8
b3o$o3bo$o3bo$b3o!

Code: Select all

x = 5, y = 21, rule = B35a6i/S23
o2bo$o2bo$obo$3b2o14$3b2o$obo$o2bo$o2bo!

Code: Select all

x = 4, y = 4, rule = B2ac3a4twz5j/S12in3ay4a6ac78
b2o$4o$b2o$b2o!

Code: Select all

x = 8, y = 5, rule = B3-ckq4cj5ey/S23-cky4w
b2o2b2o$b2o2b2o$o6bo$b2o2b2o$b2o2b2o!

Code: Select all

x = 5, y = 4, rule = B34e5ck/S2-i3-acky4iz
b3o$o2bo$o$2o2bo!

Code: Select all

x = 6, y = 4, rule = B3-jny4-cik5ar6a/S2eik3airy8
4bo$6o$2b3o$2b2o!

Code: Select all

x = 2, y = 12, rule = B34t6a/S2-ei3-ai4aeijr5einqy6i
o$2o$o7$o$2o$o!

Code: Select all

x = 3, y = 17, rule = B3-k4tw/S23
3o$obo$3o12$3o$obo$3o!

Code: Select all

x = 3, y = 2, rule = B3-y4e5y6ci8/S23-n4t6ce8
3o$bo!

Code: Select all

x = 5, y = 5, rule = B3-j/S1c2-e3
b3o$b3o$o3bo$b3o$b3o!

Code: Select all

x = 8, y = 7, rule = B3acei5j6i/S2-i3-a4ity6c
b3o$o2bo$o2bo$3o2b3o$4bo2bo$4bo2bo$4b3o!

Code: Select all

x = 3, y = 3, rule = B2n3-e5ck6e/S234i5a
3o$2bo$3o!

Code: Select all

x = 3, y = 4, rule = B2in3aijqr4ckqz5kr6i7c/S2aek3-ae4eiyz5akn6a7e8
bo$obo$obo$3o!

Code: Select all

x = 4, y = 3, rule = B3ai4acq5a6e/S34aw5aiyq6acn7c
b2o$4o$b2o!

Code: Select all

x = 3, y = 19, rule = B34n/S234w
bo$3o$obo14$obo$3o$bo!

Code: Select all

x = 11, y = 11, rule = B34k/S2-a3-n4aeny5y
b2o5b2o$3o5b3o$b2o5b2o6$b2o5b2o$3o5b3o$b2o5b2o!

Code: Select all

x = 9, y = 3, rule = B2i3-cen4k5nr6i8/S2-i3-ac4iyz6a7c8
bo5bo$3o3b3o$ob2ob2obo!

Code: Select all

x = 1, y = 4, rule = B3-kq4tz5y/S23-k4twyz5e
o$o$o$o!

Code: Select all

x = 5, y = 6, rule = B3-kq4tz5y/S23-k4twyz5e
2bo$b3o$2ob2o$2ob2o$b3o$2bo!

Code: Select all

x = 12, y = 17, rule = B3-eky4-eiqrz5ry/S2-a3-y4q7e
3$5bo2bo$4bo4bo$4bo4bo$4b6o4$4b6o$4bo4bo$4bo4bo$5bo2bo!

Code: Select all

x = 4, y = 3, rule = B2in35ey6ikn/S23-a4t6c
b2o$o2bo$b2o!

Code: Select all

x = 4, y = 3, rule = B2e3-y4w/S1c2-i3-en
b2o$o2bo$b2o!

Code: Select all

x = 7, y = 7, rule = B2a/S2k
2o2b2o$2b2o2bo$2b2o2bo$4b2o$4b2o$6bo$6bo!

Code: Select all

x = 4, y = 4, rule = B2e3aij4aqr/S1c2aek3jknry4a7c
3o$o2bo$o2bo$b3o!

Code: Select all

x = 3, y = 9, rule = B3-cq5ej6c/S2-ci3-aek4it5c8
bo$2bo$2bo$3o2$3o$2bo$2bo$bo!

Code: Select all

x = 6, y = 44, rule = B3-j5y/S234t6c
3b2o$2b4o$3b2o2$3b2o$2b4o$3b2o7$3b2o$2b4o$3b2o2$3b2o$2b4o$3b2o18$b2o$
4o$b2o2$b2o$4o$b2o!

Code: Select all

x = 3, y = 19, rule = B34n/S234w
bo$3o$obo14$obo$3o$bo!

Code: Select all

x = 4, y = 3, rule = B3-knqy4ce5y6ci/S2-i3-a4iqtz5ir6ci8
o2bo$4o$o2bo!

Code: Select all

x = 9, y = 9, rule = B34n/S23-n
7bo$7bo$6bobo$7bo$7bo2$2bo$2ob2o$2bo!

Code: Select all

x = 6, y = 4, rule = B2e3aij4ajkqr5ejy6-a78/S1c2aek3-aciq4ainz7c8
b4o$o4bo$o4bo$b4o!

Code: Select all

x = 3, y = 7, rule = B34j5eik7c8/S2-i3-a4iz5aeik
3o$obo$3o2$3o$obo$3o!

Code: Select all

x = 4, y = 3, rule = B2e3/S2-ai34a
b2o$o2bo$b2o!

Code: Select all

x = 3, y = 3, rule = B3-j4z5e8/S2-in3-a4i5eik67
3o$obo$obo!

Code: Select all

x = 3, y = 2, rule = B2cek6i/S0
bo$obo!

Code: Select all

x = 15, y = 27, rule = B3ai4ekqty5cy6cn/S2-c3-ace4ainr5enqry6an78
6b3o$6bobo$6b2o3$b3o$bobo9b2o$b2o9bobo$12b3o3$8b2o$7bobo$7b3o2$2b2o$b
obo$o2bo$3o5$9b3o$8bo2bo$8bobo$8b2o!

Code: Select all

x = 4, y = 4, rule = B2n3-jqry4cein5acry6-ak7/S2ce3-kq4-ajq5einy6-an78
2bo$b3o$3o$bo!

Code: Select all

x = 5, y = 3, rule = B3aeiry4eqtwz5acen6c/S1c2-kn3-akr4-aejw5-i6-n7
o3bo$5o$o3bo!

Code: Select all

x = 3, y = 3, rule = B2cei3ai4j/S12-ak
2o$obo$2o!

Code: Select all

x = 0, y = 4, rule = B3-r5cey/S2-a3
o$o$o$o!

Code: Select all

x = 5, y = 5, rule = B37/S345
b3o$bobo$2ob2o$bobo$b3o!

Code: Select all

x = 10, y = 3, rule = B2i34cw5ay6n/S23
b2o4b2o$o8bo$b2o4b2o!

Code: Select all

x = 9, y = 3, rule = B2e3-ej/S1c23-cnq
3o3b3o$obo3bobo$bo5bo!

Code: Select all

x = 7, y = 7, rule = B35c678/S3567
2o3b2o$7o$3ob3o$2bobo$3ob3o$7o$2o3b2o!

Code: Select all

x = 2, y = 4, rule = B35cq68/S245
o$2o$2o$o!

Code: Select all

x = 12, y = 19, rule = B3ai4ekq5cy6n/S2-ci3-ace4inr5eqry
10bo$9b3o$8b2obo$9b2o4$2b2o$bobo$o2bo$3o5$9b3o$8bo2bo$8bobo$8b2o!

Code: Select all

x = 4, y = 4, rule = B3aei5/S23-a4i
3o$o$o2bo$b3o!

Code: Select all

x = 5, y = 5, rule = B3ai4a5ai6a78/S2aei4-cknqy5-ejk6-e
b3o$b3o$5o$2ob2o$o3bo!

Code: Select all

x = 6, y = 1, rule = B2n3/S2ai35
6o!

I might start work on a zip some time soon.

[muzik]

And here the first version of that zip is. I've created subfolders for orthogonal, diagonal and oblique replicators, as well as an "unbalanced" folder that should cover migratory replicators, directionally biased replicators and those weird Lorentz-shifted cases. In that folder, we use the full notation with two different velocities.

Do inform me if this contains any errors, if there are any replicators I missed, or if there are any replicators in existence that may necessitate a redoing of the notation itself (provided they are 1D - I'm not at the point of classifying replicators with three or more copies yet, but that might come soon.)

[muzik]

Some more replicators I found through more in-depth forum browsing:

6c/40

Code: Select all

x = 5, y = 11, rule = B2ein3cijn4cnrwy5cnq6e/S1c2-ai3acny4anqy5c6ek8
b3o$o3bo8$o3bo$b3o!

32c/32

Code: Select all

x = 45, y = 3, rule = B2a3ijry4ity5ey/S3i4ent5er6i
obobobo3bobobo3bobo3bobo3bobobo3bobobobo$obobobo3bo3bo3bobo3bobo3bo3b
o3bobobobo$obobobo3bobobo3bobo3bobo3bobobo3bobobobo!

7c/20

Code: Select all

x = 4, y = 3, rule = B3-kqry4n5ry6ek8/S23-qy4qt5acnq6n
o2bo$o2bo$o2bo!

20c/116:

Code: Select all

x = 21, y = 41, rule = B36cin7/S2-in3-a4cqy5c6ei8
3b2o11b2o$4b2o9b2o$2b2obo9bob2o$4b2o9b2o$3b2o11b2o2$10bo$9bobo$8bo3bo
$5bo3bobo3bo$5bo3b3o3bo2$3b2o11b2o$3b2o11b2o$4bob3o3b3obo$6bo2bobo2bo
$7bobobobo$7b3ob3o2$7bo5bo$6b3o3b3o$5b2o2bobo2b2o$4bo2b3ob3o2bo$6bo7b
o$9bobo$8b5o$6b2o2bo2b2o$7bo5bo$7bo5bo$8b2ob2o$9bobo$10bo$3b3o9b3o$2b
o2bo9bo2bo$bo4b2o5b2o4bo$7bo5bo$o3b3obo3bob3o3bo$7bo5bo$bo4b2o5b2o4bo
$2bo2bo9bo2bo$3b3o9b3o!

6c/19

Code: Select all

x = 4, y = 3, rule = B3-ejnr4city5ik6ain8/S23-a4city5e6c
o2bo$4o$o2bo!

6c/56d

Code: Select all

x = 3, y = 3, rule = B2i3-cny4jr5ny6in8/S2-i3-ack4ciyz5n6a
3o$o$o!

10c/24

Code: Select all

x = 8, y = 3, rule = B2ce/S1
bo4bo$o6bo$bo4bo!

17c/132d

Code: Select all

x = 14, y = 14, rule = B34city5eqry6n8/S23-a4city6a7
2b3o$b2obo$ob2o4$b2o2b2o$b3obobo$6b2o$12b2o$6bo4bobo$6b2o3b3o$6b2o4bo
$11bo!

10c/36

Code: Select all

x = 5, y = 3, rule = B2i3aijn4a/S234i
2ob2o$o3bo$b3o!

7c/14

Code: Select all

x = 4, y = 13, rule = B2e3cei4-acnr5ajy7e8/S1c2ck3-ijqy4aetwz5ckqry6k8
b2o$o2bo$b2o8$b2o$o2bo$b2o!

9c/33

Code: Select all

x = 1, y = 3, rule = B2aei3ay4airty5ci6i8/S01e2in3ejqr4r5aey6ci8
o2$o!

8c/30

Code: Select all

x = 1, y = 3, rule = B2-ck3r4airy5ciy6i/S01e2i3enqr4jr5e6ci8
o2$o!

20c/105

Code: Select all

x = 10, y = 9, rule = B2ei3-acjk4cew5-acer6-a7e/S1c2-ik3ay4cikrw5aekq6ae8
2o6b2o$o2bo2bo2bo$ob2o2b2obo$obo4bobo$4b2o$obo4bobo$ob2o2b2obo$o2bo2b
o2bo$2o6b2o!

17c/67

Code: Select all

x = 6, y = 3, rule = B2ei3-ajk4cew5-acer6cik7e/S1c2-ik3ay4cikrwz5aejq6an7c8
bo2bo$o4bo$bo2bo!

80c/420

Code: Select all

x = 82, y = 9, rule = B2ei3-acjk4cewz5-acer6-ae7e/S1c2-ik3ay4cikr5aenq6an8
3bo15bo2b2o4bo24bo4b2o2bo15bo$18bo5bo3b3o20b3o3bo5bo$17bob4o2bo3bo22b
o3bo2b4obo$o18bo2bo7b2o18b2o7bo2bo18bo$bo15b2o3bobobo2b2o20b2o2bobobo
3b2o15bo$o18bo2bo7b2o18b2o7bo2bo18bo$17bob4o2bo3bo22bo3bo2b4obo$18bo5b
o3b3o20b3o3bo5bo$3bo15bo2b2o4bo24bo4b2o2bo15bo!

18c/54

Code: Select all

x = 22, y = 17, rule = B3-cekq4iq6ekn/S2-i3-aeky4ciqyz5r6n
10b2o$9bo2bo$8b2o2b2o$7bob4obo$8bo4bo2$b2o6bo2bo6b2o$o2bo14bo2bo$o2bo
6b2o6bo2bo$o2bo14bo2bo$b2o6bo2bo6b2o2$8bo4bo$7bob4obo$8b2o2b2o$9bo2bo
$10b2o!

39c/180

Code: Select all

x = 16, y = 3, rule = B2ei3-ajk4cewz5ijkqy6-a/S1c2-ik3ay4cikrz5aenq6ae8
b2o10b2o$o2bo8bo2bo$b2o10b2o!

9c/36

Code: Select all

x = 4, y = 3, rule = B2ek3einqy4-aijnw5-aij6ik8/S1c2aci3airy5cery6e7c
b2o$o2bo$b2o!

16c/64

Code: Select all

x = 10, y = 7, rule = B2ein3-jkqy4cewz5acjry6c8/S1c2ac3-ceqr4aer5akry6ck
4b2o$3bo2bo$2obo2bob2o$2o6b2o$2obo2bob2o$3bo2bo$4b2o!

18c/36

Code: Select all

x = 8, y = 3, rule = B2e3-acny4knrw5-nq6cei7c8/S1c2ac3ajk4eikn5ck6i7e
o2b2o2bo$3o2b3o$o2b2o2bo!

6c/26

Code: Select all

x = 3, y = 8, rule = B2e3/S1c2-k3-er
3o2$bo3$bo2$3o!

5c/48

Code: Select all

x = 3, y = 4, rule = B34et5y6i7e/S235j
bo$obo$obo$bo!

8c/48

Code: Select all

x = 3, y = 4, rule = B34t5ey6i7e/S23
bo$obo$obo$bo!

(16,4)c/22

Code: Select all

x = 11, y = 5, rule = B3-kq4jt5jy6-e7c/S2-i3-k4it5ar7e8
2bo$b3o5b2o$o9bo$2o5b3o$8bo!

8c/28

Code: Select all

x = 6, y = 5, rule = B3-cky4ejwz5y/S23-q
bo2bo$o4bo$o4bo$o4bo$bo2bo!

7c/28

Code: Select all

x = 3, y = 16, rule = B3aij4ai/S34ajknryz5
3o$obo$obo$obo$obo$obo$obo$obo$obo$obo$obo$obo$obo$obo$obo$3o!

(37,4)c/96

Code: Select all

x = 5, y = 6, rule = B3-ceky4aijnqtw5jqy6aci/S2-ac3-ce4ijkt
3bo$b4o$b2obo$ob2o$4o$bo!

56c/56

Code: Select all

x = 7, y = 4, rule = B2-ck3jq4cejrt5eijry6ekn7e/S1e2eik3cekry4aeiqryz5-eny6c8
bo3bo$7o$o5bo$bo3bo!

22c/710d

Code: Select all

x = 8, y = 8, rule = B3-cq4cekq5ery6ik/S2-ci3-aek4i6ck
4b3o$4bo2bo$4bo2bo$5b3o$3o$o2bo$o2bo$b3o!

5c/17

Code: Select all

x = 4, y = 3, rule = B2in35ey6ikn7e/S23-a4t6c
b2o$4o$b2o!

Unbalanced: 6c/16 left, 8c/16 right

Code: Select all

x = 2, y = 3, rule = B2ce3-ciqy4acijnrt5j6cik/S01c
bo$o$bo!

Unbalanced: c/16 left, 7c/16 right

Code: Select all

x = 2, y = 3, rule = B2-ai3nqy4acejqry5ij7e8/S1
o$bo$o!

Unbalanced, to be determined:

Code: Select all

x = 4, y = 3, rule = B2i3-cen5nr8/S2-i3-ac4iyz6a7e8
bo$3o$ob2o!

Unbalanced, p58:

Code: Select all

x = 3, y = 3, rule = B36cn78/S2-in3-a4cqy7e8
obo$obo$3o!

Unbalanced: (30,24)c/168

Code: Select all

x = 5, y = 3, rule = B2e3aeijn4cj5cnqy6ckn7e/S1c2-cn3ceij4aeijkq5cejnq6k
o3bo$5o$2ob2o!

Unbalanced: (29,16)c/217

Code: Select all

x = 7, y = 3, rule = B2e3-cjk4j5cjr6k/S1c2ae3eijy4ijnq5cekn6i
o2bo2bo$3ob3o$2obob2o!

Unbalanced: c/12 left, 6c/12 right

Code: Select all

x = 2, y = 3, rule = B2e3aiy4ce5ey/S12ace3ay4c5i
o$bo$o!

Unbalanced: stationary and 4c/8

Code: Select all

x = 2, y = 3, rule = B2a3ejy4ciy5iny6-kn/S1c2ce3aeiqy4acrw5iny6i
bo$o$bo!

Unbalanced: (3,0)

Code: Select all

x = 3, y = 3, rule = B1e2cek3j4j5y6c/S1c2kn3cnqy4q
2o$obo$bo!

Unbalanced: (21,9)c/93

Code: Select all

x = 18, y = 18, rule = B2n3-cy4eqz5cer/S2-in3-a4iknz5q8
6b2obo3b3o$4b2o7bo2b2o$4bo5bobo4bo$7bob2ob2o3bo$b2o3b2o2bo2bob2o$bo$o
3bo$o2b2o2$o2bo$2b3o2$2b2o$2ob2o$o$o3bo$bo2bo$b3o!

Unbalanced, p107:

Code: Select all

x = 26, y = 26, rule = B2n3-ck4ez5cekry/S2-in3-a4iknyz5q
4b5o3b5o$3bobob3ob3obobo$4b5o3b5o$bobo$obobo$3o$obo20bo$3o15b3o2b2o$3o
15bob2o2b2o$bo17b3o2bo$20b2obo$bo13b2obo$3o16bo$3o$obo12b3o$3o8bo2b2o
$obo8bo2bo$bo12bo$7b2o2bo$7bobo2bo$7b4o$8b3o2$6b2o2bo$7b3o$8bo!

Unbalanced: (4,8)c/8

Code: Select all

x = 3, y = 3, rule = B01e2ci3-ikqy4acinz5c6ac7c/S012en3cijqy4eijry5ky6k7e
3o$obo$bo!

Unbalanced, to be determined:

Code: Select all

x = 4, y = 3, rule = B35ny78/S2-c3-aky4it6a
bo$3o$ob2o!

Unbalanced: (25,8)c/82

Code: Select all

x = 4, y = 4, rule = B3-cjn4cjktz5cj7c/S2-ci3-ae4eit6i
b2o$o2bo$o2bo$b3o!

Unbalanced, 14c/47:

Code: Select all

x = 3, y = 3, rule = B3aeijr4jk6n7c/S2-ci3-aky4einrz5j6c7e
b2o$2o$o!

Unbalanced: (9,7)c/50

Code: Select all

x = 11, y = 9, rule = B3-kqy4cejr5k6in7c/S2-i3-acky4cinqrz5cek6cn
5bo$3b5o$2b2o3b2o$3b2ob2o$2obo3bob2o$b2ob3ob2o$o2b2ob2o2bo$4b3o$5bo!

To be determined:

Code: Select all

x = 251, y = 185, rule = B2i3ai4ceiw5aceqr6cik7/S2k3-jkqr4cejnq5ik6cei7c8
85bo79bo$84b3o77b3o$83b5o75b5o$82b7o73b7o$81b9o71b9o$80b11o69b11o$79b
3o2b3o2b3o67b3o2b3o2b3o$78b3o4bo4b3o65b3o4bo4b3o$77bobobo7bobobo63bob
obo7bobobo$76bo7bobo7bo61bo7bobo7bo14$10bo229bo$9b3o227b3o$8b5o96bo31b
o96b5o$7b7o94b3o29b3o94b7o$6b9o92b5o27b5o92b9o$5b11o90b7o25b7o90b11o$
4b13o88b9o23b9o88b13o$3b15o86b11o21b11o86b15o$2b17o84b13o19b13o84b17o
$b19o82b15o17b15o82b19o$21o80b17o15b17o80b21o$b19o80b19o13b19o80b19o$
2b17o80b21o11b21o80b17o$3b15o82b19o13b19o82b15o$4b13o84b17o15b17o84b13o
$5b11o86b15o17b15o86b11o$6b9o88b13o19b13o88b9o$7b7o90b11o21b11o90b7o$
8b5o92b9o23b9o92b5o$9b3o94b7o25b7o94b3o$10bo96b5o27b5o96bo$108b3o29b3o
$109bo31bo22$11bo49bo127bo49bo$10bo51bo125bo51bo$9bo53bo123bo53bo$8b3o
51b3o121b3o51b3o$7b4o2bo45bo2b4o119b4o2bo45bo2b4o$6b6o49b6o117b6o49b6o
$7b4o2bo45bo2b4o119b4o2bo45bo2b4o$8b3o51b3o121b3o51b3o$9bo53bo123bo53b
o$10bo51bo125bo51bo$11bo49bo127bo49bo30$11bo49bo127bo49bo$10bo51bo125b
o51bo$9bo53bo123bo53bo$8b3o51b3o121b3o51b3o$7b4o2bo45bo2b4o119b4o2bo45b
o2b4o$6b6o49b6o117b6o49b6o$7b4o2bo45bo2b4o119b4o2bo45bo2b4o$8b3o51b3o
121b3o51b3o$9bo53bo123bo53bo$10bo51bo125bo51bo$11bo49bo127bo49bo22$109b
o31bo$108b3o29b3o$10bo96b5o27b5o96bo$9b3o94b7o25b7o94b3o$8b5o92b9o23b
9o92b5o$7b7o90b11o21b11o90b7o$6b9o88b13o19b13o88b9o$5b11o86b15o17b15o
86b11o$4b13o84b17o15b17o84b13o$3b15o82b19o13b19o82b15o$2b17o80b21o11b
21o80b17o$b19o80b19o13b19o80b19o$21o80b17o15b17o80b21o$b19o82b15o17b15o
82b19o$2b17o84b13o19b13o84b17o$3b15o86b11o21b11o86b15o$4b13o88b9o23b9o
88b13o$5b11o90b7o25b7o90b11o$6b9o92b5o27b5o92b9o$7b7o94b3o29b3o94b7o$
8b5o96bo31bo96b5o$9b3o227b3o$10bo229bo14$76bo7bobo7bo61bo7bobo7bo$77b
obobo7bobobo63bobobo7bobobo$78b3o4bo4b3o65b3o4bo4b3o$79b3o2b3o2b3o67b
3o2b3o2b3o$80b11o69b11o$81b9o71b9o$82b7o73b7o$83b5o75b5o$84b3o77b3o$85b
o79bo!

[muzik]

Here's an amended zip which contains the replicators from the post above. I've also amended the "unbalanced" folder so that it's split into four categories, which should make navigating its contents much more intuitive.

[wwei47]

If we delete one of the two inner units, the entire thing ends up exploding and therefore not following the replication habit.

Code: Select all

x = 100, y = 3, rule = B3-cqy4ajq5ry6i8/S23-cejk4t5acj7c
b2o22b2o70b2o$o2bo20bo2bo68bo2bo$b2o22b2o70b2o!

<snip>

As can be seen here, deleting the equivalent middle unit would not cause a "strong" mod-3 replicator from blowing up - it'd continue partitioning itself into twos, and then threes where the middle is inverted, and so on.

I think I know what's going on, and I also want to establish some replicator theory. Almost all pascal mod 3 replicators in isotropic rules do so not with two different STATES; instead, what would be a different state is done with a replicator copy that is shifted in time, space, or both. For example, with that replicator, its "state 2" is just a copy of the original replicator shifted forwards in 3 generations.

Code: Select all

x = 52, y = 5, rule = B3-cqy4ajq5ry6i8/S23-cejk4t5acj7c
25b2o$o2bo20bo2bo20bo2bo$o2bo19bo4bo19bo2bo$o2bo20bo2bo20bo2bo$25b2o!

This led me to making "tables" describing how replicators replicate. They're not perfect, but they work for the vast majority of well-behaved 1D replicators. First, we describe an unshifted copy using A, and the lack of a copy using 0. Then we enumerate all relevant collisions.
Most replicators are just sierpinski replicators. In this case, we have 0+0=0, 0+A=A, but A+A=0.
But with this replicator, we instead get a time-shifted copy. Since it's shifted 3 generations ahead, I denote this with Avvv (or A3v). If it were shifted 3 cells left, I'd use ALLL (or A3L). If it were shifted 3 generations behind, I'd use A^^^ (or A3^). If it were shifted 3 cells up, I'd use AUUU (or A3U). So, what does the table itself look like?
0+0=0
0+A=A
A+A=A3v
A+A3v=0
As a result, this happens.

Code: Select all

                  A
                A   A
              A   A3v A
            A           A
          A   A       A   A
        A   A3v A   A   A3v A
      A           A3v         A
    A   A       A3v A3v     A   A
  A   A3v A   A3v A6v A3v A   A3v A
A                                   A

Wait. A6v? Where did that come from? That's not in the table! To answer this, we have to remember that the absolute phases don't matter; only the relative phases do. A3v and A3v are in the same phase, so they collide in the same way that A and A do. Since they're already shifted 3 generations ahead, this collision shifts them another 3 generations ahead, making A6v. At the end, all the timings are "orchestrated" to annihilate everything in the middle. The phase shift between A3v and A6v is still 3 generations, so they still annihilate like with A and A3v.
With all of that theory established, let's go back to the exploding pattern and go 9 cycles or 405 generations in, when the failure happens.

Code: Select all

x = 316, y = 9, rule = B3-cqy4ajq5ry6i8/S23-cejk4t5acj7c
171b2o18b2o$119bo28bo22bobo16bobo$97b2o18b5o24b5o19b4o16b4o23b2o48bo20b
o$b2o22b2o69b4o16b2obo3bo20bo3bob2o19b2o18b2o23b4o21b2o22b3ob2o14b2ob
3o22b2o$o2bo20bo2bo67b2o2b2o15bo6bo20bo6bo15b3o24b3o18b2o2b2o19bo2bo20b
3o3bo14bo3b3o20bo2bo$b2o22b2o69b4o16b2obo3bo20bo3bob2o19b2o18b2o23b4o
21b2o22b3ob2o14b2ob3o22b2o$97b2o18b5o24b5o19b4o16b4o23b2o48bo20bo$119b
o28bo22bobo16bobo$171b2o18b2o!

Here, two replicators collide, but instead of producing nothing or another replicator, they instead explode. Why? Because A+A6v=boom. As long as you don't delete any replicators, things work like usual. But as soon as you do, you can get pathological collisions that would have never happened otherwise. This is why removing one replicator unit broke the whole thing.
A strong pascal mod 3 replicator should be possible with an asymmetric unit that flips when two of them collide. If we label a flipped unit as A' and use 0+0=0; 0+A=A; A+A=A'; A+A'=0, then the flipped unit really does act like a state 2, since collisions between flipped units simply flip them back (A'+A'=A), giving us a strong pascal mod 3 replicator.

[muzik]

A strong pascal mod 3 replicator should be possible with an asymmetric unit that flips when two of them collide. If we label a flipped unit as A' and use 0+0=0; 0+A=A; A+A=A'; A+A'=0, then the flipped unit really does act like a state 2, since collisions between flipped units simply flip them back (A'+A'=A), giving us a strong pascal mod 3 replicator.

I was actually thinking about this earlier today. This, for example, was a close call:

Here's another cool one (it's so tantalisingly close to working in a rule containing gliders and having replicator ships):

Code: Select all

x = 3, y = 2, rule = B2i3aij4a/S234i
3o$obo!

Notice that the copies it produces that violate Rule 90 are shifted downward by 1 cell.

If, instead of the "state 2" units being shifted downwards by one cell, they were instead vertically flipped, and everything else relating to annihilation worked out, this would be a prime example of strong mod-3 replication.

[muzik]

It's been a month now, so here's the next iteration of the replicator collection. The scope has been expanded to replicators with more than two copies, including 4-copy (quadratic) replicators, provided that they replicate strongly.

So far, replicators with four copies are classified into one of five folders: diagonal (in which the units move diagonally, creating a square), orthogonal (in which the units move orthogonally, creating a square rotated 90 degrees), oblique (in which the units move in an oblique direction, creating a square rotated by some other angle), rectangular (in which the units move in an oblique direction, creating a rectangle) and rhombic (in which there are two distinct displacements at play, resulting in a rhombus).

There's also folders for replicators with three, five, eight or nine copies, all following the strength requirements.

If there's anything to add, do pitch in!

[muzik]

Time for another update - I've combed through the discord server for every mention of "rep" for things to include in this release. There's some comically high period examples, slow B2a cases, and more oblique 1D and 2D replicators to enjoy, bringing the file up to 99KB total.

Still wondering as to what else is yet to be discovered. Do 2D replicators with a trapezoidal envelope exist? Lorentzian 2D replicators? The fabled strong modulo-3 replicator so we can stop only counting the omnipresent modulo-2 patterns? 1D replicators with four or more copies? As far as we've come with isotropic non-totalistic rules over the past ten years, there's still a lot to discover.

[LaundryPizza03]

More replicators

On the symmetric speeds of XOR type:

2c/2o, 2 cells

Code: Select all

x = 14, y = 1, rule = B1e/S1e
2o2b2o6b2o!

3c/3o, 2 cells

Code: Select all

x = 19, y = 2, rule = B2a/S1e
o5bo11bo$o5bo11bo!

2c/3o, 3 cells; 2 cells is impossible.

Code: Select all

x = 14, y = 5, rule = B2ack5i/S03j5i
o3bo7bo2$bo3bo7bo2$o3bo7bo!

The only other 3-cell replicator of this speed is:

Code: Select all

x = 14, y = 5, rule = B2ack/S03j4i
o3bo7bo2$bo3bo7bo2$o3bo7bo!

You can use EnumPattEvo to identify patterns that replicate once at the given speed, and then try to make it replicate strongly. The ones later in this post that are period multiples of 3c/4o are byproducts of such a search.

1c/3o, 3 cells:

Code: Select all

x = 7, y = 3, rule = B2a4ir5i8/S1e2i3ei4i6i
obo3bo$obo3bo$obo3bo!

4c/4o, 2 cells:

Code: Select all

x = 25, y = 2, rule = B2a3a/S1e3a
o7bo15bo$o7bo15bo!

Does this count as c/2d or 2c/4d?

Code: Select all

x = 10, y = 10, rule = B2ac3a/S1c2ae3ak
3bo$b2o$b2o2bo$o2b2o$3b2o$2bo$9bo$7b2o$7b2o$6bo!

6c/8o, 6 cells:

Code: Select all

x = 43, y = 4, rule = B2ac4ir5y6i/S02aik5i6ce
o5bo5bo5bo17bo5bo2$o5bo5bo5bo17bo5bo$o5bo5bo5bo17bo5bo!

9c/12o, 6 cells:

Code: Select all

x = 61, y = 4, rule = B2-kn3e4i5e7e/S1c2ai4i
o5bo11bo5bo29bo5bo2$o5bo11bo5bo29bo5bo$o5bo11bo5bo29bo5bo!

12c/16o, 26 cells:

Code: Select all

x = 85, y = 15, rule = B2ac3ky4cr5ijy/S02aik4in
6bo23bo47bo$o4bobo4bo11bo4bobo4bo35bo4bobo4bo$o5bo5bo11bo5bo5bo35bo5bo
5bo2$o5bo5bo11bo5bo5bo35bo5bo5bo$5bobo21bobo45bobo4$5bobo21bobo45bobo$
o5bo5bo11bo5bo5bo35bo5bo5bo2$o5bo5bo11bo5bo5bo35bo5bo5bo$o4bobo4bo11bo
4bobo4bo35bo4bobo4bo$6bo23bo47bo!

[muzik]

A much smaller update today, bringing a few new speeds, updates to existing speeds, and classification changes to the 4-copy folder to account for the weird rule-27030 migratory diagonal "annoying replicator".

How would I go about filling in gaps in replicator speeds using LLS? I've tried getting EPE to work, but there's weird compilation errors I'm yet to work out.

[LaundryPizza03]

A much smaller update today, bringing a few new speeds, updates to existing speeds, and classification changes to the 4-copy folder to account for the weird rule-27030 migratory diagonal "annoying replicator".

How would I go about filling in gaps in replicator speeds using LLS? I've tried getting EPE to work, but there's weird compilation errors I'm yet to work out.

You need to build a custom input file, which might look like:

Code: Select all

x = 112, y = 30, rule = LifeHistory
10B$10B$10B$4B2A4B$4B2A4B$4B2A4B$4B2A4B$10B$10B$10B$30.E20.E$29.2E20.
E$30.E8.E3.E.E.2E2.E2.E2.E.2E3.3E2.E.E.E.E.2E15.3E2.E.2E3.4E$5.E4.E6.
E.2E9.E8.E3.E.2E2.E.E.E3.2E2.E.E3.E.E.E.E.2E2.E8.2E.E.E3.E.2E2.E.E$9.
E7.2E2.E.5E2.E8.E3.E.E3.E.2E4.E3.E.E3.E.E.E.E.E3.E7.E2.2E.5E.E3.E2.3E
$5.E2.7E2.E3.E8.E8.E2.2E.E3.E.E.E3.E3.E.E3.E.E.E.E.E3.E7.E3.E.E5.E3.E
5.E$9.E7.4E8.3E8.2E.E.E3.E.E2.E2.E3.E2.3E3.E.E2.E3.E8.4E2.4E.E3.E.4E
2.E$5.E4.E6.E73.E$17.E69.E3.E$17.E70.3E$10B$10B$10B$B2A4B2AB$B2A4B2AB
$B2A4B2AB$B2A4B2AB$10B$10B$10B!

EDIT: (±3,1)c/4 migratory replicator, 10 cells:

Code: Select all

x = 23, y = 5, rule = B2ace3e4acj5i8/S1e2c3y4r
2bo5bo11bo$obobobobobo7bobobo$bobo3bobo9bobo$o3bobo3bo7bo3bo$bobo3bobo
9bobo!

There are no 3c/4o or (3,1)c/4 replicators proper with the shape o2$o$o!

EDIT2: Lots more orthogonal ones. Most of these are derived from EnumPattEvo, including a 3c/4o run and a search in pB2-acek3aeijq-y4kw-acinqrt5iy-akq6-acik8/S2acekn-i3eijnqr-y4i-ajknw5-ceiy6-ac78 for rules where the pattern b3o$o3bo$o3bo$5o2$5o$o3bo$o3bo$b3o! replicates once, displaced by 20 cells each direction. I've still got more results to go through, and will share the latter dump file once I'm done with it.

3c4o-replicator-candidates.txt

(5.92 KiB) Downloaded 2 times

I don't expect any smaller 3c/4o replicators than what I've presented thus far, but higher period multiples might admit replicators from these rulespaces. There are a few other interesting phenomena as well, including at least two that can be turned into spaceships.

3c/4o, 14 cells:

Code: Select all

x = 23, y = 7, rule = B2ace4e6i/S1e4cr5i
bobo3bobo9bobo$obobobobobo7bobobo$bobo3bobo9bobo2$bobo3bobo9bobo$obobo
bobobo7bobobo$bobo3bobo9bobo!

10c/20o, 24 cells:

Code: Select all

x = 65, y = 9, rule = B3-q4kw5iy/S2-i3-ay4i
b3o17b3o37b3o$o3bo15bo3bo35bo3bo$o3bo15bo3bo35bo3bo$5o15b5o35b5o2$5o
15b5o35b5o$o3bo15bo3bo35bo3bo$o3bo15bo3bo35bo3bo$b3o17b3o37b3o!

11c/22o, 28 cells:

Code: Select all

x = 73, y = 11, rule = B3-y4kw5iny/S2-i3-ay4i
3bo21bo43bo$bo3bo17bo3bo39bo3bo$o5bo15bo5bo37bo5bo$o5bo15bo5bo37bo5bo$
7o15b7o37b7o2$7o15b7o37b7o$o5bo15bo5bo37bo5bo$o5bo15bo5bo37bo5bo$bo3bo
17bo3bo39bo3bo$3bo21bo43bo!

12c/24o, 22 cells:

Code: Select all

x = 77, y = 9, rule = B34ckw5iy/S2-i3-ay4i
2bo23bo47bo$b3o21b3o45b3o$2ob2o19b2ob2o43b2ob2o$b3o21b3o45b3o2$b3o21b
3o45b3o$2ob2o19b2ob2o43b2ob2o$b3o21b3o45b3o$2bo23bo47bo!

14c/28o, 22 cells:

Code: Select all

x = 89, y = 9, rule = B3-y4ckw5iny/S2-i3-ay4i
2bo27bo55bo$b3o25b3o53b3o$2ob2o23b2ob2o51b2ob2o$b3o25b3o53b3o2$b3o25b
3o53b3o$2ob2o23b2ob2o51b2ob2o$b3o25b3o53b3o$2bo27bo55bo!

17c/34o, 22 cells:

Code: Select all

x = 107, y = 9, rule = B34cw5iy/S2-i3-a4i
2bo33bo67bo$b3o31b3o65b3o$2ob2o29b2ob2o63b2ob2o$b3o31b3o65b3o2$b3o31b
3o65b3o$2ob2o29b2ob2o63b2ob2o$b3o31b3o65b3o$2bo33bo67bo!

20c/40o, 22 cells:

Code: Select all

x = 125, y = 9, rule = B3-nry4kw5ijnry/S2-i3-aky4ci5akn6kn
2bo39bo79bo$b3o37b3o77b3o$2ob2o35b2ob2o75b2ob2o$b3o37b3o77b3o2$b3o37b
3o77b3o$2ob2o35b2ob2o75b2ob2o$b3o37b3o77b3o$2bo39bo79bo!

23c/46o, 34 cells:

Code: Select all

x = 7, y = 11, rule = B3-r4w5iny/S2-i3-ay4i
3bo$2bobo$b5o$2obob2o$b2ob2o2$b2ob2o$2obob2o$b5o$2bobo$3bo!

26c/52o, 24 cells:


Code: Select all

x = 161, y = 9, rule = B34w5iry/S2-i3-ay4i
b3o49b3o101b3o$o3bo47bo3bo99bo3bo$o3bo47bo3bo99bo3bo$5o47b5o99b5o2$5o
47b5o99b5o$o3bo47bo3bo99bo3bo$o3bo47bo3bo99bo3bo$b3o49b3o101b3o!

20c/59o, 14 cells:

Code: Select all

x = 123, y = 7, rule = B3-ry4kw5iry/S2-i3-acky4it5ak6in
b2o37b2o78b2o$2o2bo33bo2b2o75bo2b2o$b2o37b2o78b2o2$b2o37b2o78b2o$2o2bo
33bo2b2o75bo2b2o$b2o37b2o78b2o!

20c/61o, 12 cells:

Code: Select all

x = 123, y = 7, rule = B3-knry4jkwz5ijry6n/S2-i3-aky4i5a6k
2o39b2o78b2o$b2o37b2o78b2o$2o39b2o78b2o2$2o39b2o78b2o$b2o37b2o78b2o$2o
39b2o78b2o!

20c/64o, 12 cells:

Code: Select all

x = 117, y = 7, rule = B3-ry4kw5eijny6n/S2-i3-aky4iy5a6in
2bo31bo79bo$b2o31b2o78b2o$3o31b3o77b3o2$3o31b3o77b3o$b2o31b2o78b2o$2bo
31bo79bo!

20c/70o, 18 cells:

Code: Select all

x = 123, y = 9, rule = B3-cry4kwz5iry/S2-i3-aky4ity5akn6n
2b2o35b2o78b2o$bobo35bobo77bobo$ob2o35b2obo76b2obo$2o39b2o78b2o2$2o39b
2o78b2o$ob2o35b2obo76b2obo$bobo35bobo77bobo$2b2o35b2o78b2o!

20c/76o, 16 cells:

Code: Select all

x = 123, y = 7, rule = B3-ckry4ejkwz5ijy6n/S2-i3-aky4ity5akn8
3o37b3o77b3o$obo37bobo77bobo$3o37b3o77b3o2$3o37b3o77b3o$obo37bobo77bob
o$3o37b3o77b3o!

20c/88o, 14 cells:

Code: Select all

x = 111, y = 11, rule = B3-ckry4jkwz5ijny6n/S2-i3-aky4ity5ak6n
3bo23bo79bo$3bo23bo79bo$o2bo23bo2bo76bo2bo$3o25b3o77b3o4$3o25b3o77b3o$
o2bo23bo2bo76bo2bo$3bo23bo79bo$3bo23bo79bo!

20c/92o, 12 cells:

Code: Select all

x = 123, y = 7, rule = B3-knry4ejkwz5eijy/S2-i3-aky4it5an6kn
b2o37b2o78b2o$2o39b2o78b2o$b2o37b2o78b2o2$b2o37b2o78b2o$2o39b2o78b2o$b
2o37b2o78b2o!

20c/94o, 16 cells:

Code: Select all

x = 123, y = 7, rule = B3-cry4kwz5iry/S2-i3-acky4i5ak6in
3o37b3o77b3o$obo37bobo77bobo$3o37b3o77b3o2$3o37b3o77b3o$obo37bobo77bob
o$3o37b3o77b3o!

20c/95o, 12 cells:

Code: Select all

x = 123, y = 7, rule = B3aeijq4jkw5iry6n/S2-i3-acky4ity5a6k
2o39b2o78b2o$b2o37b2o78b2o$2o39b2o78b2o2$2o39b2o78b2o$b2o37b2o78b2o$2o
39b2o78b2o!

20c/126o, 12 cells:

Code: Select all

x = 3, y = 7, rule = B3aeijq4ekw5iry6n/S2-i3-aky4it5a6ik
2o$b2o$2o2$2o$b2o$2o!

[haaaaaands]

the tiny thing:

Code: Select all

x = 2, y = 1, rule = B1e2-a4k/S134
2o!

strength proof:

Code: Select all

x = 14, y = 1, rule = B1e2-a4k/S134
2o6b2o2b2o!

and this was originally found by accident xd