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2D Replicator Classes

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2D Replicator Classes

Postby AbhpzTa » December 23rd, 2016, 4:58 am

7 classes (S,R,Q,U : 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-ac4eiy6
2bo$b3o$2ob2o$bobo$2bo!
x = 47, y = 47, rule = B3/S23-ac4eiy6
2bo41bo$b3o39b3o$2ob2o37b2ob2o$bobo39bobo$2bo41bo38$2bo$bobo$2ob2o$b3o
$2bo!

x = 3, y = 2, rule = B3-jny/S1c23
bo$3o!
x = 9, y = 7, rule = B3-jny/S1c23
bo5bo$3o3b3o4$3o$bo!

x = 9, y = 3, rule = B3578/S23-c
2o5b2o$2o5b2o$2o5b2o!
x = 25, y = 19, rule = B3578/S23-c
2o5b2o7b2o5b2o$2o5b2o7b2o5b2o$2o5b2o7b2o5b2o14$2o5b2o$2o5b2o$2o5b2o!

x = 7, y = 7, rule = B3578/S23
3o$obo$3o2$4b3o$4bobo$4b3o!
x = 15, y = 23, rule = B3578/S23
8b3o$8bobo$8b3o2$12b3o$9bo2bobo$12b3o2$3o$obo2bo$3o2$4b3o$4bobo$4b3o2$
8b3o$8bobo2bo$8b3o2$12b3o$12bobo$12b3o!

x = 9, y = 9, rule = B34ew/S23
3o$3o$3o4$6b3o$6b3o$6b3o!
x = 21, y = 33, rule = B34ew/S23
12b3o$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-c34ci6
b3o$o2bo$o2bo$3o5$9b3o$8bo2bo$8bo2bo$8b3o!
x = 26, y = 40, rule = B3-ckq6/S2-c34ci6
15b3o$14bo2bo$14bo2bo$14b3o5$23b3o$22bo2bo$22bo2bo$22b3o3$b3o$o2bo$o2b
o$3o5$9b3o$8bo2bo$8bo2bo$8b3o3$15b3o$14bo2bo$14bo2bo$14b3o5$23b3o$22bo
2bo$22bo2bo$22b3o!

x = 5, y = 3, rule = B34ej5y6n/S23
2bo$b3o$2o2bo!
x = 32, y = 18, rule = B34ej5y6n/S23
2bo$b3o$2o2bo3$7bobo$5b5o$5b3o$3b5o16bo$3bobo17b3o$22b2o2bo2$8bo2b2o$
9b3o17bobo$10bo16b5o$27b3o$25b5o$25bobo!
x = 35, y = 23, rule = B34ej5y6n/S23
2bo$b3o$2o2bo3$7bobo$5b5o$5b3o$3b5o$3bobo3$8bo2b2o$9b3o17bobo$10bo16b
5o$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/S123i4a
3o2$4bo$4bo$4bo!
x = 11, y = 16, rule = B3-c/S123i4a
5b3o2$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/S3a4a
2o$2o!

x = 4, y = 4, rule = B2ce3-ai/S01
bobo$o2$o!


Class U(unusual)

x = 3, y = 3, rule = B35a6ae78/S23
b2o$2o$bo!



FAILED


Class A(almost)

x = 9, y = 3, rule = B3578/S23
2o5b2o$2o5b2o$2o5b2o!
(see gen 29)

x = 3, y = 3, rule = B38/S2378
3o$obo$obo!
(see gens 26, 42)

x = 6, y = 6, rule = B34tw5y/S23
3o$obo$3o2$4b2o$4b2o!
(see gen 29)

x = 3, y = 3, rule = B34w/S23
bo$3o$3o!
(see gen 15)

x = 3, y = 4, rule = B34i5y/S23
bo$b2o$obo$bo!
(see gen 93)

x = 4, y = 4, rule = B3-kn5y8/S234i5i
b3o$o2bo$o2bo$3o!
(see gen 10)

x = 5, y = 6, rule = B3-ckq/S2-c34ci
3o$obo$obo$4bo$4bo$4bo!
(see gens 27, 159)


Class D(dirty)

x = 9, y = 9, rule = B34w/S23
3o$obo$3o4$6b3o$6bobo$6b3o!
(see gen 15)

x = 3, y = 2, rule = B34tw5y/S23
bo$3o!
(see gen 47)

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

Class F(space filling)

x = 3, y = 3, rule = B3-eq/S23-c4i
3o$obo$obo!

x = 3, y = 3, rule = B2cek/S02i
obo2$o!

x = 11, y = 11, rule = B3-q7c/S2-i3-q4q
5bo$4b3o$3bo3bo$2bo5bo$bo7bo$2o7b2o$bo7bo$2bo5bo$3bo3bo$4b3o$5bo!

x = 4, y = 3, rule = B2in3aeikn4city8/S23-a4city
2bo$b3o$o2bo!
Last edited by AbhpzTa on September 10th, 2017, 12:30 pm, edited 1 time 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).
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Re: 2D Replicator Classes

Postby toroidalet » December 25th, 2016, 4:07 pm

What about space-filling replicators?
x = 3, y = 3, rule = B3-eq/S23-c4i
3o$obo$obo!

Also some class Q replicators can be made into class S by adding another copy:
x = 6, y = 6, rule = B2a/S3a4a
4b2o$4b2o3$2o$2o!
x = 22, y = 18, rule = B2a/S3a4a
12b2o$12b2o3$8b2o4bo$8b2o5bo$12bo3bo$13bo3bo$4b2o8bo5b2o$4b2o9bo4b2o3$
2o4bo9b2o$2o5bo8b2o$4bo3bo$5bo3bo$6bo$7bo!
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Re: 2D Replicator Classes

Postby Rhombic » December 30th, 2016, 3:01 pm

What class does this replicator fit into?

x = 4, y = 5, rule = B34c/S2-i34wy5ay6i
b2o$2obo$o2bo$2obo$b2o!
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Re: 2D Replicator Classes

Postby BlinkerSpawn » December 30th, 2016, 5:40 pm

Rhombic wrote:What class does this replicator fit into?

x = 4, y = 5, rule = B34c/S2-i34wy5ay6i
b2o$2obo$o2bo$2obo$b2o!

That appears to be an S-class replicator.
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Re: 2D Replicator Classes

Postby PHPBB12345 » December 30th, 2016, 11:53 pm

BlinkerSpawn wrote:
Rhombic wrote:What class does this replicator fit into?

x = 4, y = 5, rule = B34c/S2-i34wy5ay6i
b2o$2obo$o2bo$2obo$b2o!

That appears to be an S-class replicator.

x = 13, y = 17, rule = B34c/S2-i34wy5ay6i
b2o7b2o$2obo5bob2o$o2bo5bo2bo$2obo5bob2o$b2o7b2o8$b2o$2obo$o2bo$2obo$b
2o!

x = 16, y = 17, rule = B34c/S2-i34wy5ay6i
4b2o7b2o$3b2obo5bob2o$3bo2bo5bo2bo$3b2obo5bob2o$4b2o7b2o8$b2o$ob2o$o2b
o$ob2o$b2o!

it's S-class replicator (?).
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Re: 2D Replicator Classes

Postby PHPBB12345 » December 31st, 2016, 12:36 am

x = 117, y = 7, rule = B1357/S1357
obobo2bo3bo4bo4b5o6b5o3b4o7b5o2b4o4b3o3bo3bo8b4o3bo3bo3b4o2b5o3b2o$obo
bo2bo3bo3bobo5bo10bo4bo13bo4bo3bo2bo3bo2bo3bo8bo3bo2bo3bo2bo8bo4bo2bo$
obobo2bo3bo2bo3bo4bo10bo4bo13bo4bo3bo2bo3bo2b2o2bo8bo3bo2bo3bo2bo8bo7b
o$obobo2b5o2bo3bo4bo10bo5b3o10bo4b4o3bo3bo2bobobo8b4o3bo3bo3b3o5bo6bo$
obobo2bo3bo2b5o4bo10bo8bo9bo4bobo4bo3bo2bo2b2o8bobo4bo3bo6bo4bo5bo$obo
bo2bo3bo2bo3bo4bo10bo8bo9bo4bo2bo3bo3bo2bo3bo8bo2bo3bo3bo6bo4bo$2ob2o
2bo3bo2bo3bo4bo8b5o2b4o8b5o2bo3bo3b3o3bo3bo8bo3bo3b3o3b4o5bo5bo!
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Re: 2D Replicator Classes

Postby Saka » January 1st, 2017, 11:35 pm

Would this be a U?
x = 3, y = 1, rule = B2i34w5eq7/S1e2ikn34ci
3o!
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Re: 2D Replicator Classes

Postby gameoflifeboy » January 1st, 2017, 11:58 pm

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.
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Re: 2D Replicator Classes

Postby GUYTU6J » January 8th, 2017, 12:30 am

A failed one-see gen 22
x = 7, y = 7, rule = B34-a5aek/S23
2b3o$bo3bo$o5bo$o5bo$o5bo$bo3bo$2b3o!

EDIT:A dirty one
x = 3, y = 3, rule = B34-a5ak/S23
3o$obo$3o!
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Re: 2D Replicator Classes

Postby GUYTU6J » January 13th, 2017, 12:06 pm

A failed one
x = 2, y = 3, rule = B2e3aei4wyz6/S2-e34-cjk
bo$2o$bo!
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Re: 2D Replicator Classes

Postby toroidalet » January 14th, 2017, 1:19 am

Here's a dirty replicator:
x = 4, y = 3, rule = B3-cenq/S23-cy4i
b3o$o2bo$2o!
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Re: 2D Replicator Classes

Postby PHPBB12345 » January 14th, 2017, 11:16 pm

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

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

B3/S23, failed:
x = 9, y = 3, rule = B3/S23
bo5bo$2o5b2o$bo5bo!
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Re: 2D Replicator Classes

Postby muzik » January 17th, 2017, 4:30 am

What about the types you see in the Replicator rule? I personally like to call these "Dry Out" replicators.
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Re: 2D Replicator Classes

Postby Saka » January 17th, 2017, 4:36 am

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/S1357
o!

It replicates at 1,8,8,24,8,64,24,112,8,64,64,192,24,192,112,416,8...
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Re: 2D Replicator Classes

Postby muzik » January 27th, 2017, 5:23 am

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.
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Re: 2D Replicator Classes

Postby Saka » January 29th, 2017, 5:48 am

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/S
3bo$3bo$3bo$3o!

x = 1, y = 3, rule = B2acin/S
o$o$o!
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Re: 2D Replicator Classes

Postby GUYTU6J » February 2nd, 2017, 11:23 am

x = 5, y = 5, rule = B2a/S3
2o$obo$bobo$2bobo$3b2o!

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Re: 2D Replicator Classes

Postby AbhpzTa » February 2nd, 2017, 2:09 pm

Class A, non-explosive:
x = 3, y = 3, rule = B3-cky4q7c/S23-y
2bo$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).
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Re: 2D Replicator Classes

Postby GUYTU6J » February 3rd, 2017, 5:23 am

A rule which has a true one,a dirty one and a kind of space-filling loaf
x = 4, y = 4, rule = B2a3a/S024
2b2o$2b2o$2o$2o!

x = 2, y = 2, rule = B2a3a/S024
2o$2o!

x = 3, y = 3, rule = B2a3a/S024
b2o$b2o$o!
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Re: 2D Replicator Classes

Postby muzik » February 8th, 2017, 4:20 am

That's more of a dirty 1D replicator that moves out of the way.
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Re: 2D Replicator Classes

Postby Saka » February 8th, 2017, 4:22 am

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

It's a sierspinski
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Re: 2D Replicator Classes

Postby muzik » February 8th, 2017, 5:13 pm

That I know.
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Re: 2D Replicator Classes

Postby muzik » February 28th, 2017, 2:22 pm

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/S
3bo$3bo$3bo$3o!

x = 1, y = 3, rule = B2acin/S
o$o$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):

Image
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Re: 2D Replicator Classes

Postby toroidalet » July 15th, 2017, 5:52 pm

U-class replicator (?)
x = 3, y = 2, rule = B34ek5-ey7e8/S234j
3o$bo!

Fractal-filling replicators:
x = 3, y = 3, rule = B2cek/S02i
obo2$o!

x = 3, y = 3, rule = B2cek3-aij5y/S0
obo2$o!

S-class replicator:
x = 9, y = 9, rule = B34e5-ey7e8/S23
7bo$7b2o$7bo5$3o$bo!

x = 21, y = 33, rule = B34e5-ey7e8/S23
19bo$18b3o5$13bo$12b2o$13bo4$7bo$6b3o5$bo$2o$bo4$19bo$19b2o$19bo5$12b
3o$13bo!
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Re: 2D Replicator Classes

Postby toroidalet » August 6th, 2017, 12:15 pm

bump
Class Q replicator:
x = 5, y = 2, rule = B34tw5y7e/S234k
b3o$o3bo!

Related class S:
x = 16, y = 16, rule = B34tw5y7e/S234k
b3o$o3bo10$14bo$15bo$15bo$15bo$14bo!

x = 66, y = 42, rule = B34tw5y7e/S234k
bo$o$o50b3o$o49bo3bo$bo9$64bo$11bo3bo49bo$12b3o50bo$65bo$64bo9$27bo$
26bo$26bo$26bo$27bo10$37bo3bo$38b3o!
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