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## 2D Replicator Classes

For discussion of other cellular automata.

### 2D Replicator Classes

8 classes (S,R,Q,U,X : SUCCESSFUL)(A,D : FAILED)(F : SEMI-SUCCESSFUL ?)

SUCCESSFUL

Class S(strict){1,2,4,4,4,8,16,8,4,8, ...}(OEIS A173531)

`x = 5, y = 5, rule = B3/S23-ac4eiy62bo\$b3o\$2ob2o\$bobo\$2bo!`
`x = 47, y = 47, rule = B3/S23-ac4eiy62bo41bo\$b3o39b3o\$2ob2o37b2ob2o\$bobo39bobo\$2bo41bo38\$2bo\$bobo\$2ob2o\$b3o\$2bo!`

`x = 3, y = 2, rule = B3-jny/S1c23bo\$3o!`
`x = 9, y = 7, rule = B3-jny/S1c23bo5bo\$3o3b3o4\$3o\$bo!`

`x = 9, y = 3, rule = B3578/S23-c2o5b2o\$2o5b2o\$2o5b2o!`
`x = 25, y = 19, rule = B3578/S23-c2o5b2o7b2o5b2o\$2o5b2o7b2o5b2o\$2o5b2o7b2o5b2o14\$2o5b2o\$2o5b2o\$2o5b2o!`

`x = 7, y = 7, rule = B3578/S233o\$obo\$3o2\$4b3o\$4bobo\$4b3o!`
`x = 15, y = 23, rule = B3578/S238b3o\$8bobo\$8b3o2\$12b3o\$9bo2bobo\$12b3o2\$3o\$obo2bo\$3o2\$4b3o\$4bobo\$4b3o2\$8b3o\$8bobo2bo\$8b3o2\$12b3o\$12bobo\$12b3o!`

`x = 9, y = 9, rule = B34ew/S233o\$3o\$3o4\$6b3o\$6b3o\$6b3o!`
`x = 21, y = 33, rule = B34ew/S2312b3o\$12b3o\$12b3o4\$18b3o\$18b3o\$18b3o4\$3o\$3o\$3o4\$6b3o\$6b3o\$6b3o4\$12b3o\$12b3o\$12b3o4\$18b3o\$18b3o\$18b3o!`

`x = 12, y = 12, rule = B3-ckq6/S2-c34ci6b3o\$o2bo\$o2bo\$3o5\$9b3o\$8bo2bo\$8bo2bo\$8b3o!`
`x = 26, y = 40, rule = B3-ckq6/S2-c34ci615b3o\$14bo2bo\$14bo2bo\$14b3o5\$23b3o\$22bo2bo\$22bo2bo\$22b3o3\$b3o\$o2bo\$o2bo\$3o5\$9b3o\$8bo2bo\$8bo2bo\$8b3o3\$15b3o\$14bo2bo\$14bo2bo\$14b3o5\$23b3o\$22bo2bo\$22bo2bo\$22b3o!`

`x = 5, y = 3, rule = B34ej5y6n/S232bo\$b3o\$2o2bo!`
`x = 32, y = 18, rule = B34ej5y6n/S232bo\$b3o\$2o2bo3\$7bobo\$5b5o\$5b3o\$3b5o16bo\$3bobo17b3o\$22b2o2bo2\$8bo2b2o\$9b3o17bobo\$10bo16b5o\$27b3o\$25b5o\$25bobo!`
`x = 35, y = 23, rule = B34ej5y6n/S232bo\$b3o\$2o2bo3\$7bobo\$5b5o\$5b3o\$3b5o\$3bobo3\$8bo2b2o\$9b3o17bobo\$10bo16b5o\$27b3o\$25b5o\$25bobo3\$30bo2b2o\$31b3o\$32bo!`

Class R(rectangular only){1,2,4,4,4,8,16,8,4,8, ...}(OEIS A173531)

`x = 5, y = 5, rule = B3-c/S123i4a3o2\$4bo\$4bo\$4bo!`
`x = 11, y = 16, rule = B3-c/S123i4a5b3o2\$9bo\$9bo\$9bo\$o\$o\$o2\$2b3o2\$6bo\$6bo\$6bo2\$8b3o!`

Class Q(quadruple){1,4,4,16,4,16,16,64,4,16, ...}(OEIS A102376)

`x = 2, y = 2, rule = B2a/S3a4a2o\$2o!`

`x = 4, y = 4, rule = B2ce3-ai/S01bobo\$o2\$o!`

Class U(unusual)

`x = 3, y = 3, rule = B35a6ae78/S23b2o\$2o\$bo!`

Class X(4-fold XOR){1,4,8,16,16,32,32,64,32,64, ...}(OEIS A189007)

`x = 1, y = 1, rule = B1e2e3e/S0o!`

FAILED

Class A(almost)

`x = 9, y = 3, rule = B3578/S232o5b2o\$2o5b2o\$2o5b2o!`
(see gen 29)

`x = 3, y = 3, rule = B38/S23783o\$obo\$obo!`
(see gens 26, 42)

`x = 6, y = 6, rule = B34tw5y/S233o\$obo\$3o2\$4b2o\$4b2o!`
(see gen 29)

`x = 3, y = 3, rule = B34w/S23bo\$3o\$3o!`
(see gen 15)

`x = 3, y = 4, rule = B34i5y/S23bo\$b2o\$obo\$bo!`
(see gen 93)

`x = 4, y = 4, rule = B3-kn5y8/S234i5ib3o\$o2bo\$o2bo\$3o!`
(see gen 10)

`x = 5, y = 6, rule = B3-ckq/S2-c34ci3o\$obo\$obo\$4bo\$4bo\$4bo!`
(see gens 27, 159)

Class D(dirty)

`x = 9, y = 9, rule = B34w/S233o\$obo\$3o4\$6b3o\$6bobo\$6b3o!`
(see gen 15)

`x = 3, y = 2, rule = B34tw5y/S23bo\$3o!`
(see gen 47)

......................................................................

Class F(space filling)

`x = 3, y = 3, rule = B3-eq/S23-c4i3o\$obo\$obo!`

`x = 3, y = 3, rule = B2cek/S02iobo2\$o!`

`x = 11, y = 11, rule = B3-q7c/S2-i3-q4q5bo\$4b3o\$3bo3bo\$2bo5bo\$bo7bo\$2o7b2o\$bo7bo\$2bo5bo\$3bo3bo\$4b3o\$5bo!`

`x = 4, y = 3, rule = B2in3aeikn4city8/S23-a4city2bo\$b3o\$o2bo!`
Last edited by AbhpzTa on October 25th, 2017, 3:53 pm, edited 2 times in total.
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
AbhpzTa

Posts: 473
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: 2D Replicator Classes

What about space-filling replicators?
`x = 3, y = 3, rule = B3-eq/S23-c4i3o\$obo\$obo! `

Also some class Q replicators can be made into class S by adding another copy:
`x = 6, y = 6, rule = B2a/S3a4a4b2o\$4b2o3\$2o\$2o!`
`x = 22, y = 18, rule = B2a/S3a4a12b2o\$12b2o3\$8b2o4bo\$8b2o5bo\$12bo3bo\$13bo3bo\$4b2o8bo5b2o\$4b2o9bo4b2o3\$2o4bo9b2o\$2o5bo8b2o\$4bo3bo\$5bo3bo\$6bo\$7bo!`
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

toroidalet

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Location: my computer

### Re: 2D Replicator Classes

What class does this replicator fit into?

`x = 4, y = 5, rule = B34c/S2-i34wy5ay6ib2o\$2obo\$o2bo\$2obo\$b2o!`
SoL : FreeElectronics : DeadlyEnemies : 6a-ite : Rule X3VI
what is “sesame oil”?

Rhombic

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### Re: 2D Replicator Classes

Rhombic wrote:What class does this replicator fit into?

`x = 4, y = 5, rule = B34c/S2-i34wy5ay6ib2o\$2obo\$o2bo\$2obo\$b2o!`

That appears to be an S-class replicator.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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### Re: 2D Replicator Classes

Rhombic wrote:What class does this replicator fit into?

`x = 4, y = 5, rule = B34c/S2-i34wy5ay6ib2o\$2obo\$o2bo\$2obo\$b2o!`

That appears to be an S-class replicator.

`x = 13, y = 17, rule = B34c/S2-i34wy5ay6ib2o7b2o\$2obo5bob2o\$o2bo5bo2bo\$2obo5bob2o\$b2o7b2o8\$b2o\$2obo\$o2bo\$2obo\$b2o!`

`x = 16, y = 17, rule = B34c/S2-i34wy5ay6i4b2o7b2o\$3b2obo5bob2o\$3bo2bo5bo2bo\$3b2obo5bob2o\$4b2o7b2o8\$b2o\$ob2o\$o2bo\$ob2o\$b2o!`

it's S-class replicator (?).

PHPBB12345

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Joined: August 5th, 2015, 11:55 pm

### Re: 2D Replicator Classes

`x = 117, y = 7, rule = B1357/S1357obobo2bo3bo4bo4b5o6b5o3b4o7b5o2b4o4b3o3bo3bo8b4o3bo3bo3b4o2b5o3b2o\$obobo2bo3bo3bobo5bo10bo4bo13bo4bo3bo2bo3bo2bo3bo8bo3bo2bo3bo2bo8bo4bo2bo\$obobo2bo3bo2bo3bo4bo10bo4bo13bo4bo3bo2bo3bo2b2o2bo8bo3bo2bo3bo2bo8bo7bo\$obobo2b5o2bo3bo4bo10bo5b3o10bo4b4o3bo3bo2bobobo8b4o3bo3bo3b3o5bo6bo\$obobo2bo3bo2b5o4bo10bo8bo9bo4bobo4bo3bo2bo2b2o8bobo4bo3bo6bo4bo5bo\$obobo2bo3bo2bo3bo4bo10bo8bo9bo4bo2bo3bo3bo2bo3bo8bo2bo3bo3bo6bo4bo\$2ob2o2bo3bo2bo3bo4bo8b5o2b4o8b5o2bo3bo3b3o3bo3bo8bo3bo3b3o3b4o5bo5bo!`

PHPBB12345

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Joined: August 5th, 2015, 11:55 pm

### Re: 2D Replicator Classes

Would this be a U?
`x = 3, y = 1, rule = B2i34w5eq7/S1e2ikn34ci3o!`
If you're the person that uploaded to Sakagolue illegally, please PM me.
`x = 17, y = 10, rule = B3/S23b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5bo2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!`

(Check gen 2)

Saka

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Location: In the kingdom of Sultan Hamengkubuwono X

### Re: 2D Replicator Classes

Saka wrote:Would this be a U?

No, it would be Q, because starting from generation 20 it replicates into 1, 4, 4, 16, 4, 16, 16, 64... copies every 90 generaions.

This sequence, by the way, is a(n) = 4^A000120(n), where A000120 is the number of 1's in the binary expansion of n.

gameoflifeboy

Posts: 474
Joined: January 15th, 2015, 2:08 am

### Re: 2D Replicator Classes

A failed one-see gen 22
`x = 7, y = 7, rule = B34-a5aek/S232b3o\$bo3bo\$o5bo\$o5bo\$o5bo\$bo3bo\$2b3o!`

EDIT:A dirty one
`x = 3, y = 3, rule = B34-a5ak/S233o\$obo\$3o!`
Current status: outside the continent of cellular automata. Specifically, not on the plain of life.

GUYTU6J

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### Re: 2D Replicator Classes

A failed one
`x = 2, y = 3, rule = B2e3aei4wyz6/S2-e34-cjkbo\$2o\$bo!`
Current status: outside the continent of cellular automata. Specifically, not on the plain of life.

GUYTU6J

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Joined: August 5th, 2016, 10:27 am
Location: My Glimmering Garden

### Re: 2D Replicator Classes

Here's a dirty replicator:
`x = 4, y = 3, rule = B3-cenq/S23-cy4ib3o\$o2bo\$2o!`
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

toroidalet

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Location: my computer

### Re: 2D Replicator Classes

B2-e/S, failed:
`x = 3, y = 1, rule = B2-e/Sobo!`

B23n/S, failed:
`x = 3, y = 1, rule = B23n/Sobo!`

B3/S23, failed:
`x = 9, y = 3, rule = B3/S23bo5bo\$2o5b2o\$bo5bo!`

PHPBB12345

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Joined: August 5th, 2015, 11:55 pm

### Re: 2D Replicator Classes

What about the types you see in the Replicator rule? I personally like to call these "Dry Out" replicators.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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Location: Scotland

### Re: 2D Replicator Classes

muzik wrote:What about the types you see in the Replicator rule? I personally like to call these "Dry Out" replicators.
I believe they are irregular. Take a single dot, for example:
`x = 1, y = 1, rule = B1357/S1357o!`

It replicates at 1,8,8,24,8,64,24,112,8,64,64,192,24,192,112,416,8...
If you're the person that uploaded to Sakagolue illegally, please PM me.
`x = 17, y = 10, rule = B3/S23b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5bo2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!`

(Check gen 2)

Saka

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Location: In the kingdom of Sultan Hamengkubuwono X

### Re: 2D Replicator Classes

You know how on a lot of these replicators, when all the clones in the centre die, there's always a few survivors at the very edges for a few generations? I would like to see ones that do not do this.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3466
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: 2D Replicator Classes

muzik wrote:You know how on a lot of these replicators, when all the clones in the centre die, there's always a few survivors at the very edges for a few generations? I would like to see ones that do not do this.

Here ya go (If I understand)
`x = 4, y = 4, rule = B2acin/S3bo\$3bo\$3bo\$3o!`

`x = 1, y = 3, rule = B2acin/So\$o\$o!`
If you're the person that uploaded to Sakagolue illegally, please PM me.
`x = 17, y = 10, rule = B3/S23b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5bo2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!`

(Check gen 2)

Saka

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Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: 2D Replicator Classes

`x = 5, y = 5, rule = B2a/S32o\$obo\$bobo\$2bobo\$3b2o!`

We need a way to deal with those leaking oil from the ship!
Current status: outside the continent of cellular automata. Specifically, not on the plain of life.

GUYTU6J

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### Re: 2D Replicator Classes

Class A, non-explosive:
`x = 3, y = 3, rule = B3-cky4q7c/S23-y2bo\$b2o\$2o!`
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
AbhpzTa

Posts: 473
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: 2D Replicator Classes

A rule which has a true one,a dirty one and a kind of space-filling loaf
`x = 4, y = 4, rule = B2a3a/S0242b2o\$2b2o\$2o\$2o!`

`x = 2, y = 2, rule = B2a3a/S0242o\$2o!`

`x = 3, y = 3, rule = B2a3a/S024b2o\$b2o\$o!`
Current status: outside the continent of cellular automata. Specifically, not on the plain of life.

GUYTU6J

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### Re: 2D Replicator Classes

That's more of a dirty 1D replicator that moves out of the way.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: 2D Replicator Classes

muzik wrote:That's more of a dirty 1D replicator that moves out of the way.

It's a sierspinski
If you're the person that uploaded to Sakagolue illegally, please PM me.
`x = 17, y = 10, rule = B3/S23b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5bo2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!`

(Check gen 2)

Saka

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Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: 2D Replicator Classes

That I know.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: 2D Replicator Classes

Saka wrote:
muzik wrote:You know how on a lot of these replicators, when all the clones in the centre die, there's always a few survivors at the very edges for a few generations? I would like to see ones that do not do this.

Here ya go (If I understand)
`x = 4, y = 4, rule = B2acin/S3bo\$3bo\$3bo\$3o!`

`x = 1, y = 3, rule = B2acin/So\$o\$o!`

As amazing as that is, that's not actually what I'm referring to. I mean these formations (seen with the B3578/S23 replicator):

Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: 2D Replicator Classes

U-class replicator (?)
`x = 3, y = 2, rule = B34ek5-ey7e8/S234j3o\$bo!`

Fractal-filling replicators:
`x = 3, y = 3, rule = B2cek/S02iobo2\$o!`

`x = 3, y = 3, rule = B2cek3-aij5y/S0obo2\$o!`

S-class replicator:
`x = 9, y = 9, rule = B34e5-ey7e8/S237bo\$7b2o\$7bo5\$3o\$bo!`

`x = 21, y = 33, rule = B34e5-ey7e8/S2319bo\$18b3o5\$13bo\$12b2o\$13bo4\$7bo\$6b3o5\$bo\$2o\$bo4\$19bo\$19b2o\$19bo5\$12b3o\$13bo!`
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

toroidalet

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Location: my computer

### Re: 2D Replicator Classes

bump
Class Q replicator:
`x = 5, y = 2, rule = B34tw5y7e/S234kb3o\$o3bo!`

Related class S:
`x = 16, y = 16, rule = B34tw5y7e/S234kb3o\$o3bo10\$14bo\$15bo\$15bo\$15bo\$14bo!`

`x = 66, y = 42, rule = B34tw5y7e/S234kbo\$o\$o50b3o\$o49bo3bo\$bo9\$64bo\$11bo3bo49bo\$12b3o50bo\$65bo\$64bo9\$27bo\$26bo\$26bo\$26bo\$27bo10\$37bo3bo\$38b3o!`
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

toroidalet

Posts: 1002
Joined: August 7th, 2016, 1:48 pm
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