The Parity Replicator Collection

[muzik]

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

This is obviously already in the collection under c orthogonal:

Code: Select all

x = 2, y = 1, rule = B1e/S1e
2o!

Code: Select all

x = 8, y = 1, rule = B1e/S1e
4o2b2o!

[haaaaaands]

oh right, i should check the rle in posts more often xd

[LaundryPizza03]

I'm not sure how to process these 4737 results automatically, all with displacement a divisor of 20 and most of which are likely 20c/40o replicators.

b3-y4kw5inys2-i3-ay4i@10_x20_backup.txt

(168 Bytes) Downloaded 128 times

[Aleph]

Posting this old pattern I found in case it didn't make it here:

Code: Select all

x = 4, y = 5, rule = B3-ceky4aijnqtw5jqy6aci/S2-ac3-ce4ijkt
bo$o2bo$o2bo$o2bo$b3o!

[muzik]

I'm not sure how to process these 4737 results automatically, all with displacement a divisor of 20 and most of which are likely 20c/40o replicators.
b3-y4kw5inys2-i3-ay4i@10_x20_backup.txt

Honestly, it's about time that someone wrote a script that can identify replicators, just like how oscar and LifeViewer can reliably identify still lifes, oscillators and spaceships. Even if we limit ourselves to the 1D case, we have a big enough sample size with the collection zip so far - how difficult could it be?

Anyway, crossposting these for later inclusion:

Surprise, surprise. The rule has another replicator, this time a clean one. It forms when what would be a traffic light predecessor is sparked in a certain way:

Code: Select all

x = 7, y = 5, rule = B3-cek4-iqry5jr6n8/S2-a3-ky4cky
b3o2bo$o3bo$o3bo$o3bo$b3o!

Code: Select all

x = 5, y = 4, rule = B3acei4aq5aejr6aen7e/S2aen3-acy4iqt5aekn6kn7c8
2b2o$bob2o$2obo$b2o!

Code: Select all

x = 5, y = 9, rule = B2ein3cijn4cnrwy5cnq6e/S1c2-ai3acny4anqy5c6ek8
b3o$o3bo$2bo4$2bo$o3bo$b3o!

Code: Select all

x = 3, y = 3, rule = B2e3-cnqr4i5-iy/S1c2-in3ny4c
bo$obo$3o!

Code: Select all

x = 3, y = 4, rule = B3ai4ai/S2e34aeiwz5iqr6a
bo$3o$3o$bo!

Code: Select all

x = 3, y = 3, rule = B3aijq4aeqr5a6c/S2ae3cijnr4aciq5aei7e
b2o$obo$3o!

Code: Select all

x = 7, y = 3, rule = B3aeij4ajkrt5-er6-in78/S23
2o3b2o$2o3b2o$2o3b2o!

Code: Select all

x = 12, y = 12, rule = B3aijry4z5ery6c7c8/S2-ci3-aky4einrtyz5cejqr6cn
$6b2o$5b5o$5b2o3bo$10bo$2b2o5b2o$b3o3b2o$b2o3bo$2bo3bo$2bo2bo$3b3o!

Code: Select all

x = 9, y = 9, rule = B2-an3a5ac6an7e8/S1c2-n3enr4er5cej6ai
6bobo$6bobo$6bobo4$3o2$3o!

Code: Select all

x = 13, y = 13, rule = B2ei3aeij4ckt5kry6i7/S1c2ace3jkn4aeijtw5ekry6in7e
3bo$2bobo$b5o$obobobo$b5o$2bobo$3bo5bo$8bobo$7b5o$6bobobobo$7b5o$8bobo
$9bo!

Code: Select all

x = 12, y = 3, rule = B2-ai/S12-k
b3o4b3o$o3bo2bo3bo$b3o4b3o!

[muzik]

Posting this old pattern I found in case it didn't make it here:

Code: Select all

x = 4, y = 5, rule = B3-ceky4aijnqtw5jqy6aci/S2-ac3-ce4ijkt
bo$o2bo$o2bo$o2bo$b3o!

I believe this one's been in the folder since the first release: (37,4)c/96

[muzik]

Here's version 1.5 of the collection, now accounting for modulo-3 replicators since we finally now have one strong example.

[LaundryPizza03]

I think we should catalog B0 ones separately, like this (±51,33)c/102 migratory orthogonal replicator:

Code: Select all

x = 73, y = 3, rule = B01e2ace34ajy5akq6ci7e/S01e234a5cinq
33bo5bo$o3bo29bo3bo29bo3bo$bobo65bobo!

[muzik]

I think we should catalog B0 ones separately, like this (±51,33)c/102 migratory orthogonal replicator:

Code: Select all

x = 73, y = 3, rule = B01e2ace34ajy5akq6ci7e/S01e234a5cinq
33bo5bo$o3bo29bo3bo29bo3bo$bobo65bobo!

Is there a dedicated collection for B0 5s stuff? We could definitely set up one for this collection as well (although I probably won't be the one maintaining it).

I should point out that we don't have any true knight-replicators in a non-B0 rule yet:

Code: Select all

x = 2, y = 3, rule = B02346/S023
bo2$o!

[Aleph]

Is this in the collection? It seems to follow a fixed rule but I don't see it listed under 3c/13 anywhere.

Code: Select all

x = 5, y = 3, rule = B3-ejq4einrtwz5-ery6-k78/S2ace3cinr4ijnqwz5ceqy6c7
bobo$obobo$bobo!

[LaundryPizza03]

I think we should catalog B0 ones separately, like this (±51,33)c/102 migratory orthogonal replicator:

Code: Select all

x = 73, y = 3, rule = B01e2ace34ajy5akq6ci7e/S01e234a5cinq
33bo5bo$o3bo29bo3bo29bo3bo$bobo65bobo!

Is there a dedicated collection for B0 5s stuff? We could definitely set up one for this collection as well (although I probably won't be the one maintaining it).

I should point out that we don't have any true knight-replicators in a non-B0 rule yet:

Code: Select all

x = 2, y = 3, rule = B02346/S023
bo2$o!

Here's the current version. B0 5s is also accessible through jedlimlx's applet at https://gliderdb-reader.vercel.app/.

[muzik]

Is this in the collection? It seems to follow a fixed rule but I don't see it listed under 3c/13 anywhere.

Code: Select all

x = 5, y = 3, rule = B3-ejq4einrtwz5-ery6-k78/S2ace3cinr4ijnqwz5ceqy6c7
bobo$obobo$bobo!

Given that this replicator never ends up becoming just two copies an infinite number of times at twice, four times, eight times, etc. its period, it obviously doesn't fit here.

[Aleph]

Is this in the collection? It seems to follow a fixed rule but I don't see it listed under 3c/13 anywhere.

Code: Select all

x = 5, y = 3, rule = B3-ejq4einrtwz5-ery6-k78/S2ace3cinr4ijnqwz5ceqy6c7
bobo$obobo$bobo!

Given that this replicator never ends up becoming just two copies an infinite number of times at twice, four times, eight times, etc. its period, it obviously doesn't fit here.

Doesn't it just replicate under a different rule?

[muzik]

Is this in the collection? It seems to follow a fixed rule but I don't see it listed under 3c/13 anywhere.

Code: Select all

x = 5, y = 3, rule = B3-ejq4einrtwz5-ery6-k78/S2ace3cinr4ijnqwz5ceqy6c7
bobo$obobo$bobo!

Given that this replicator never ends up becoming just two copies an infinite number of times at twice, four times, eight times, etc. its period, it obviously doesn't fit here.

Doesn't it just replicate under a different rule?

It's not a parity rule, so it doesn't fit in the collection.

[confocaloid]

In that case, probably the thread title should be changed to clarify the scope, otherwise it seems a bit misleading?
Additionally, check this terminology-related discussion affecting the first post of this thread. Non-totalistic CA aren't Life-like.

[muzik]

Smaller update today - just adding about five or so new replicators. I've also added a simple collection of higher-range replicators in a separate zip I probably won't be maintaining as much. There are still plenty missing from it, such as these.

[R2INT]

6 cells make a 16c/36 replicator in R3, C2, S9-11, B6:

Code: Select all

x = 2, y = 3, rule = R3,C2,S9-11,B6
2o$2o$2o![/pattern

[CARuler]

puffer/replicator

Code: Select all

x = 14, y = 12, rule = 345/2/11|345/24/11
2$5.2A$4.3A$5.3A$4.BC2A$4.3ADA$4.D2EBAB$4.CDEBC3A$4.FGCBC3A$4.2EFHB.A
$4.H2IG!

[R2INT]

Replicator:

Code: Select all

x = 2, y = 3, rule = B2ce3j4c5e/S12e3a4i
o$bo$2o!

What speed is it?

[muzik]

Replicator:

Code: Select all

x = 2, y = 3, rule = B2ce3j4c5e/S12e3a4i
o$bo$2o!

What speed is it?

Should be easy enough to figure out: every 11 generations it translates 4 cells orthogonally and 2 cells vertically, for a total of (4,2)c/11.

[muzik]

It's been a while since the last update, so here's version 1.7 with what I've found posted on the forums since last time.

There are definitely some interesting things possibly worth analyzing to see if they pass strength tests and can be classified using the one-displacement-and-time-per-copy system, such as the following:

Similar to some of the previous 'insane' ones, but in a diamond shape:

Code: Select all

x = 3, y = 4, rule = B3aijry4ciqz5ry6ci7c/S2-i3-ay4i5ceijq6aei7c8
2o$b2o$2o$o!

EDIT, another weird one:

Code: Select all

x = 3, y = 4, rule = B3aijry4eiqz5e6c7c/S2-i3-ay4i5-ejny6aik7e
2o$b2o$2o$o!

EDIT2, another clean, but unusual triangle:

Code: Select all

x = 3, y = 4, rule = B3aijry4eiq5y6c7c/S2-i3-a4i5eijq6ak7e
2o$b2o$2o$o!

There are also, of course, replicators on the hexagonal and triangular grids, which wouldn't fit into the collection as it currently exists, but very well could have a section if I can bother to figure out the coordinate systems:

An interesting replicator in a hexagonal rule:

Code: Select all

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

Common Rule 150 replicator:

Code: Select all

x = 9, y = 5, rule = B13/SLV
bobo$b3o!

I probably won't bother maintaining a B0 collection, but if anyone else is up for that then feel free to do so:

Code: Select all

x = 3, y = 1, rule = B02aci6i/S1e5i
3o!

Code: Select all

x = 2, y = 3, rule = B02346/S023
bo2$o!

Do tell me if there are any mistakes in the new or updated replicators included in version 1.7.

[rabbit]

A simple 2D replicator that makes a rhombus shape:

Code: Select all

x = 4, y = 3, rule = B3-j4-a5ay/S2-cn3
2o$b2o$2b2o!

Chaos placed inside tends to spread very slowly relative to the expanding replicators.

[Rhombicubocta]

It would be nice if we kept track by the 1d rule instead of the number of copies the replicator produces.
edit: Muzik you are missing some replicators you yourself found.

Code: Select all

x = 7, y = 7, rule = B3578/S23
3o$obo2bo$3o2$4b3o$4bobo$4b3o!

...

Proof of parity

Code: Select all

x = 41, y = 35, rule = B3578/S23
3$23b3o$23bobo$23b3o2$27b3o$24bo2bobo$27b3o10$7b3o$7bobo2bo$7b3o2$11b
3o$11bobo$11b3o2$15b3o$15bobo2bo$15b3o2$19b3o$19bobo$19b3o!