2D Replicator Classes

[jimmyChen2013]

I would say this is a replicator

Code: Select all

x = 6, y = 3, rule = B2i3-r4ceit5ce6-c7e8/S2-a3-cj4cet5cei6-i78
bo2bo$6o$bo2bo!

or breeder?

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x = 10, y = 5, rule = B3ai4e5cei678/S2-ai34cet5ci678
2bo5b2o$b3o4b2o$5o2b3o$b3o4b2o$2bo5b2o!

[77topaz]

I'd go more with "breeder" than "replicator" for both of those, yes.

[77topaz]

I feel like people may have forgotten about this rule, with one of the weirdest replicators in Life-like CA:

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x = 78, y = 3, rule = B36/S245
6o7b6o38b6o9b6o$o4bo7bo4bo38bo4bo9bo4bo$b4o9b4o40b4o11b4o!

Note that single half-replicator breaks, but a pair works the same at separation 7 and 9. They can even be offset in the other direction:

Code: Select all

x = 12, y = 17, rule = B36/S245
9b2o$9bobo$9bobo$9bobo$9bobo$9b2o6$2o$obo$obo$obo$obo$2o!

Or with a time offset:

Code: Select all

x = 17, y = 7, rule = B36/S245
b2o$b2o$o2bo8b4o$4o9b2o$11b6o$13b2o$13b2o!

[dani]

That's not a 2d replicator though...

[77topaz]

Okay, technically you're correct, but aren't linear replicators a subset of 2D replicators anyway? I think the regular ones like HighLife's replicator could even be considered their own class. Anyway, I thought this was a nice replicator whose unusual, difficult-to-classify behaviour might be of interest to this thread.

[wwei23]

Code: Select all

x = 3, y = 3, rule = B2cek5e8/S01e3y8
obo2$2bo!

[KittyTac]

Code: Select all

x = 3, y = 3, rule = B2cek5e8/S01e3y8
obo2$2bo!

Dirty. Creates a chaotic mess, but still expands at the edges using replication.

[muzik]

Code: Select all

x = 3, y = 5, rule = B2e3aijkq4ac7c/S2-an3-a
bo$obo$3o$obo$bo!

[muzik]

There are a few "Q-like" replicator classes that exist:

Q90edge,90diag:

Code: Select all

x = 1, y = 1, rule = B1c/S
o!

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x = 1, y = 1, rule = B1e/S
o!

Q90edge,150diag:

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x = 1, y = 1, rule = B1c/S04c
o!

Code: Select all

x = 1, y = 1, rule = B1e/S04e
o!

Q150edge,90diag:

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x = 1, y = 1, rule = B13ci/S
o!

Q150edge,150diag:

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x = 1, y = 1, rule = B13i/S08
o!

This one has an oddball diag value:

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x = 1, y = 1, rule = B13i/S
o!

as does this:

Code: Select all

 x = 1, y = 1, rule = B13ai/S0
o!

Looks like rule 22:

Code: Select all

x = 1, y = 1, rule = B13ci/S0
o!

Also, is there really any difference between class-S and class-Q9090 replicators? Skipping the right amount of generations on a class-S causes it to replicate exactly like a class-Q9090, so is there any need for a distinction?

[muzik]

Class U, does it match any of the other two?:

Code: Select all

x = 3, y = 3, rule = B3ai4ct5aj7c8/S1e2eik3ikry4i8
bo$3o$bo!

[PHPBB12345]

Class U, does it match any of the other two?:

Code: Select all

x = 3, y = 3, rule = B3ai4ct5aj7c8/S1e2eik3ikry4i8
bo$3o$bo!

Sone oscillators:

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x = 91, y = 42, rule = B3ai4ct5aj7c8/S1e2eik3ikry4i8
76b2o12$44b2o$62bo27bo$62bo12b3o12bo$26b2o$11b2o60bo5bo$b2o35bo11bo$
38bo4b3o4bo20bo9bo$3o5bob3o12b3o14bo3bo23bo11bo$8bo5bo7bo7bo13bo$11bo
2bo7bo7bo9bo7bo19bo15bo$2o65bo17bo$38bo2bo5bo2bo$10b2o26bo11bo14bo10bo
10bo$40bo7bo$25b2o17bo$42bo3bo15bo10bo5bo10bo$62bo27bo$43b2o$65bo10bo
10bo2$67bo17bo$68bo15bo$10b2o$23b2o3b2o40bo11bo$10b3o58bo9bo$7bo2bo3bo
5bo2bo$7bo2bo3bo5bob3o7bo40bo5bo$11bo11bo8bo2$10b2o11b2o3b2o45b2o!

[PHPBB12345]

P14:

Code: Select all

x = 8, y = 7, rule = B3ai4ct5aj7c8/S1e2eik3ikry4i8
3b2o$2o3$2b3o$6b2o$3b2o!

P156:

Code: Select all

x = 68, y = 29, rule = B3ai4ct5aj7c8/S1e2eik3ikry4i8
13b2o11b2o11b2o11b2o13$53bo13bo$o51b3o12bo$o52bo13$14b2o11b2o11b2o11b
2o!

Very big P52:

Code: Select all

x = 83, y = 83, rule = B3ai4ct5aj7c8/S1e2eik3ikry4i8
40b2o12$27bo27bo$27bo27bo13$41bo$12b2o26b3o26b2o$41bo12$27bo27bo26bo$o
25b3o25b3o25bo$o26bo27bo12$41bo$12b2o26b3o26b2o$41bo13$27bo27bo$27bo
27bo12$41b2o!

[Saka]

I dont know if this counts, but it's cool anyway

Code: Select all

x = 1, y = 1, rule = B1e2i4e/S
o!

[77topaz]

Sone oscillators:

Code: Select all

x = 91, y = 42, rule = B3ai4ct5aj7c8/S1e2eik3ikry4i8
76b2o12$44b2o$62bo27bo$62bo12b3o12bo$26b2o$11b2o60bo5bo$b2o35bo11bo$
38bo4b3o4bo20bo9bo$3o5bob3o12b3o14bo3bo23bo11bo$8bo5bo7bo7bo13bo$11bo
2bo7bo7bo9bo7bo19bo15bo$2o65bo17bo$38bo2bo5bo2bo$10b2o26bo11bo14bo10bo
10bo$40bo7bo$25b2o17bo$42bo3bo15bo10bo5bo10bo$62bo27bo$43b2o$65bo10bo
10bo2$67bo17bo$68bo15bo$10b2o$23b2o3b2o40bo11bo$10b3o58bo9bo$7bo2bo3bo
5bo2bo$7bo2bo3bo5bob3o7bo40bo5bo$11bo11bo8bo2$10b2o11b2o3b2o45b2o!

Found in the stable interior ash of an explosion:

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x = 12, y = 12, rule = B3ai4ct5aj7c8/S1e2eik3ikry4i8
5b2o$8b2o2$3b3o$obo2bo$obo2bo4b2o$2b3obo$5bo3bo$5bo3bo$5b2o$8bo$8bo!

[wwei23]

It's failed, but it fails gracefully.
It doesn't leave behind chaos, only blocks.
As it does so, it creates a beautiful fractal pattern.
To understand sone more, you should see for yourself.

Code: Select all

x = 3, y = 3, rule = B2e3eijky4acen5ijnqy6cn/S1c2ckn3acj4acejrz5ejy6i7e8
bo$obo$bo!

It was isolated from the ash of this very-ungracefully-failed 1D replicator.

Code: Select all

x = 4, y = 3, rule = B2e3eijky4acen5ijnqy6cn/S1c2ckn3acj4acejrz5ejy6i7e8
b2o$o2bo$b2o!

[Layz Boi]

B2e3eijky4acen5ijnqy6cn/S1c2ckn3acj4acejrz5ejy6i7e8

Here's another replicator found in that ash. It also leaves behind a fractal pattern, but made of tiny oscillators.

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x = 7, y = 7, rule = B2e3eijky4acen5ijnqy6cn/S1c2ckn3acj4acejrz5ejy6i7e8
4.2A$6.A$4.2A$$A.A$A.A$.A$!

A clean 1D replicator.

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x = 7, y = 7, rule = B2e3eijky4acen5ijnqy6cn/S1c2ckn3acj4acejrz5ejy6i7e8
.2A6.2A$A2.A4.A2.A$.2A6.2A$!

A couple of oscillators.

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x = 27, y = 22, rule = B2e3eijky4acen5ijnqy6cn/S1c2ckn3acj4acejrz5ejy6i7e8
2A14.2A7.2A$2A13.A2.A6.2A$16.2A9.17$2.A.A$.A2.A$A.2A$!

[KittyTac]

Here's another replicator found in that ash. It also leaves behind a fractal pattern, but made of tiny oscillators.

Code: Select all

x = 7, y = 7, rule = B2e3eijky4acen5ijnqy6cn/S1c2ckn3acj4acejrz5ejy6i7e8
4.2A$6.A$4.2A$$A.A$A.A$.A$!

That's a Sierpinski Triangle. Easy to find in CA if you know where to look.

[wwei23]

NOT GRACEFUL

Code: Select all

x = 3, y = 3, rule = B2en3-aek4nq5ce6ein8/S1c2cek3ijnqy4ekyz5ck6i8
bo$obo$bo!

[muzik]

Centered 3-way

Code: Select all

x = 1, y = 1, rule = MAPSACAAAAAAABIAAAAAAAAAKQAAAAAAAAAAAAAAAAAAABIAAAAAAAAAAAAIQAAAAAAAAAAAAAAAAAAAAAAAAAAAA
o!

7-way:

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x = 1, y = 1, rule = MAPaYAAAIAAAABAgAAAAAAAAIAAAAAAAAAAgAAAAAAAAACEAAAACAAAAIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
o!

[Majestas32]

I suppose a class A stops replicating and turns into another pattern, and a class D continues replicating at its outer edges but leaves behind chaos in its centre, but even the OP doesn't really make this distinction clear - the second posted class D looks like it could be class A. The first example class D suggests it's supposed to be a sort of "class F but messier".

I'd suggest class A is failed replicators that eventually become some sort of finite or linear-growth pattern, class D is failed repliators that expand infinitely with chaos penetrating near the center of the pattern for all time, and class F is class D but with the region of stability near the center expanding over time.

So wwei's first replicator on this page is class F and his second one is class D.

[Saka]

An oblique replicator

Code: Select all

x = 4, y = 3, rule = B3ai4a5/S234a
bo$obo$ob2o!

[toroidalet]

Is this replicator a D or U?

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x = 3, y = 3, rule = B3aijnq7c/S23-ckq
o$o$3o!

[77topaz]

Is this replicator a D or U?

Code: Select all

x = 3, y = 3, rule = B3aijnq7c/S23-ckq
o$o$3o!

I'd consider that a class U. It's not as messy as the class D examples, as the interior has a clear structure - the replicators and blocks actually seem to be simulating another cellular automaton!

[toroidalet]

I made a p40 glider gun in the above rule (EDIT: smaller):

Code: Select all

x = 18, y = 31, rule = B3aijnq7c/S23-ckq
6bob2o$6b2obo2$2o$bo$o$2o14b2o$16bo$17bo$16b2o$6b3o$6bobo$6b2o6$14bo$
2b3o8bobo$4bo9bo$4bo8$8bob2o$8b2obo!

It's fun to enclose a replicator in snakes and watch it evolve and it reminds me of extinction turmites:

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x = 74, y = 54, rule = B3aijnq7c/S23-ckq
52b2o$52bo$53bo$52b2o13$36b2o$36bo$37bo$36b2o$70b2obo$70bob2o3$4b2o6b
2o6b2o6b2o36bob2o$4bo7bo7bo7bo37b2obo$5bo7bo7bo7bo$4b2o6b2o6b2o6b2o6$
19bo$19bo$17b3o$62b2obo$62bob2o5$2o6b2o6b2o6b2o6b2o6b2o$bo7bo7bo7bo7bo
7bo$o7bo7bo7bo7bo7bo21b2obo$2o6b2o6b2o6b2o6b2o6b2o20bob2o5$48b2o$49bo$
48bo$48b2o!

I also found a turner for a pair of replicator signals (separated by 40 generations), but I lost it.

But that's a digression from the topic of collecting miscellaneous (wow, I typed that word right!) replicators. To reconcile that, here is a funky class-R replicator which is also a failed replicator (see generations 12,13, 24, and 25):

Code: Select all

x = 4, y = 2, rule = B2ce3aky4acer5jknry6-ac7c8/S2-cn3-cinq4ceikr5-anry6-ck
ob2o$4o!

(It is funky because the copies are not in sync with each other and if you zoom out and simulate it then you can see cool patterns right as everything starts to die)
I don't think it's even a sawtooth.

[dani]

2c/18 ship in that rule:

Code: Select all

x = 9, y = 5, rule = B2ce3aky4acer5jknry6-ac7c8/S2-cn3-cinq4ceikr5-anry6-ck
2bo$2ob2ob3o$2ob2o2b2o2$7bo!