The 1D 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 4 times

[wwei47]

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:

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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!

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

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

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

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

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

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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!

[wwei47]

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.

[wwei47]

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.