Replicator thread

[WhiteHawk]

simple replicator in a rule similar to seeds.

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Known

EDIT:

Can you elaborate on your statement that it's known? For example, how would one find that out?

I don't know low long it's been known for, but any mere investigation of the evolution of the domino in any rule between B2a/S & B2-e. The B2a transition is already notable for being one of the transitions confirmed to allow for growth beyond the bounding box, especially chaotic growth due to being triggered by any 2-cell edge.

Alternatively, read the domino page on the wiki, confirming my previous assertation. Reading the wiki will also provide a lot of base information about what is known about simple patterns, though slight variations on simple pattern evolution may not always be included for obvious reasons. In those cases, asking in "basic questions' threads will likely give good answers

[ThePlayzr]

simple replicator in a rule similar to seeds.

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Known

2 more replicators in rules similar to seeds.

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 x = 0, y = 0, rule = b2-cs
o$o2$o$o!
[[ AUTOSTART AUTOFIT GPS 20 ]]

Code: Select all

 x = 0, y = 0, rule = b2-ks
o$o!
[[ AUTOSTART AUTOFIT GPS 20 ]]

[ec1263f3]

simple replicator in a rule similar to seeds. [...]

Known

Can you elaborate on your statement that it's known? For example, how would one find that out? Posting the word "known" is too terse. It doesn't tell how one would come to know that the observation is indeed well-known or established (and whether the claim of "known" is well-supported).

Also, it seems to me that the same objection can be made about several of your own posts as well.
In viewtopic.php?f=11&t=3557&p=212867#p212867 you reposted a well-known p424 gun from B38/S23.
In viewtopic.php?p=212868#p212868 you reposted Karel's p177 and the maximum volatility gun; both are already known.
I don't see usefulness of reposting patterns that are already known; that "it works here too" is not a sufficient reason.

[Aleph]

6c/12 replicator:

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x = 7, y = 3, rule = B2n3aeiry4ektwz5-a6akn7c/S2ae34-qr5-aijn
b5o$3ob3o$b5o!

EDIT: 11c/146d failed quadratic replicator:

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x = 3, y = 3, rule = B2n3-jknq4etwz5-a6-e/S2ae34-er5ckqr
3o$3o$bo!

Edit: 6c/31 replicator:

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x = 3, y = 4, rule = B3578/S23ae4
3o$3o$3o$3o!

[LuveelVoom]

Oblique replicator.

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x = 18, y = 21, rule = B2ein3-aj4w578/S1c2-a35aek
2$11b3o$11bobo$10b3obo$12b2o$9bo2b2o$8b5obo$8b7o$8bob5o$9b2o2bo$9b2o$
8bob3o$9bobo$9b3o!

[Aleph]

12c/45 replicator by Luveel:

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x = 4, y = 3, rule = B35y/S23-e
b2o$o2bo$b2o!

[Naszvadi]

12c/45 replicator by Luveel:

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x = 4, y = 3, rule = B35y/S23-e
b2o$o2bo$b2o!

Corderized, a 2-engine glider forerake capped with a 3rd replicator instance:

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x = 45, y = 16, rule = B35y/S23-e
12b3o2b3o15b2o6b2o$35bobo4bobo$b2o32b2o6b2o$b2o9b3o2b3o3$6b4o20b4o$6b
4o20b4o$6b4o20b4o$2bo$obo$b2o2$4b2o2b3obo4bob3o2b2o$3b3o2b2o2bo4bo2b2o
2b3o$4b2o2b3obo4bob3o2b2o!

[yyh_baboon]

an interesting one:

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x = 1, y = 1, rule = B3-n6n7/S2-n34i7
3o$o2bo$ob2o!
[[ THEME INVERSE ]]

EDIT:another one

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x = 11, y = 11, rule = B3-n5cky6n7c/S2-n34i
b3o$obo$2o$o4$10bo$9b2o$8bobo$7b3o!
[[ THEME INVERSE ]]

[73times137]

5c/21 quadratic replicator:

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x = 8, y = 8, rule = B2i3-q4kt/S23-k4w7c8
3o$obo$3o3$5b3o$5bobo$5b3o!

made of two p13 oscillators:

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x = 3, y = 3, rule = B2i3-q4kt/S23-k4w7c8
3o$obo$3o!

[Aleph]

2c/6 sierpinski replicator by sylvie:

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x = 4, y = 3, rule = B3aijn/S2ace34t56
o2bo$4o$o2bo!

[Naszvadi]

2c/6 sierpinski replicator by sylvie:

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x = 4, y = 3, rule = B3aijn/S2ace34t56
o2bo$4o$o2bo!

Corderized:

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x = 19, y = 18, rule = B3aijn/S2ace34t56
2b2ob2o$b2o3b2o$b2o3b2o$2b2ob2o4$3o13b3o$bo15bo$bo15bo$3o13b3o4$2b2ob
2o$b2o3b2o$b2o3b2o$2b2ob2o!

[WhiteHawk]

2c/6 sierpinski replicator by sylvie:

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Corderized:

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Gunnified (adjustable)

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x = 9, y = 10, rule = B3aijn/S2ace34t56
7bo$6bobo$7bo$b5o$o2b2obo$b6o2$b6o$o2b2o2bo$b6o!

EDIT: Thumb and period-specific period-doubler

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x = 31, y = 10, rule = B3aijn/S2ace34t56
27b2o$bo16bo8b2o$obo14bobo$bo15bobo$5bo11b3o$4bobo10b3o$4bobo10bobo$b
o3bo11bobo9bo$obobobo11bo9bobo$bo2b3o22bo!

[yyh_baboon]

Something:(its front end has speed (37,2)c/204)

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x = 4, y = 3, rule = B3-n4c7c/S2-n34ei5k
3o$o2bo$ob2o!
[[ THEME INVERSE ]]

Hope someone can make a spaceship using this.

[yyh_baboon]

Interesting:

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 x = 3, y = 3, rule = B3-cnqy4j5e6c/S2-ci3-aky4einrtyz6cn
3o$obo$2bo!

What rule does it emulate?

[Neocaridina]

Weird:

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x = 7, y = 59, rule = B3-cnqy4j5e6n7c/S2-c3-ay4einryz6c
b4o$bo2b2o$b2o2b2o$3b3o2$3b3o$b2o2b2o$bo2b2o$b4o19$2o$bo$2o2$2o$bo$2o
17$b4o$bo2b2o$b2o2b2o$3b3o2$3b3o$b2o2b2o$bo2b2o$b4o!

[bailandiCA]

Recently I'm interested in B1357/S1357 replicator on a bounded plane (rule=B1357/S1357:Pm,n where m and n are integers). Apparently a torus created with T suffix is beautiful and commonly used, but P suffix also generates many interesting things.

Just now I let a program place a cell in the top-left corner of the grid, run the rule and find the period after reaching steady state. Below are data for all rectangles with length <= 20 (in ascending order of width):

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1: 1,
2: 2,2,
3: 1,2,1,
4: 6,2,12,6,
5: 4,2,4,12,4,
6: 14,2,28,126,28,14,
7: 1,2,1,24,4,56,1,
8: 14,2,28,126,28,14,56,14,
9: 12,2,12,12,12,252,24,252,12,
10: 62,2,124,2046,124,65534,248,65534,4092,62,
11: 8,2,8,24,8,56,8,56,24,248,8,
12: 126,2,252,126,252,126,504,126,252,2147483646,504,126,
13: 28,2,28,252,28,28,56,28,252,131068,56,252,28,
14: 30,2,60,30,60,1638,120,8190,60,2097150,120,8190,16380,30,
15: 1,2,1,48,4,112,1,112,48,496,8,1008,112,240,1,
16: 30,2,60,30,60,8190,120,8190,60,2097150,120,8190,16380,30,240,30,
17: 28,2,28,252,28,28,56,28,252,131068,56,252,28,16380,112,16380,28,
18: 1022,2,2044,174762,2044,1022,4088,1022,349524,TooLong,4088,524286,2044,TooLong,8176,TooLong,2044,1022,
19: 24,2,24,24,24,504,24,504,24,8184,24,504,504,120,48,120,504,699048,24,
20: 126,2,252,126,252,126,504,126,252,2147483646,504,126,252,8190,1008,8190,252,524286,504,126,

Here "TooLong" means the period is longer than 2^32 generations and my program gave up.

This table has many interesting points:

• Most of the numbers in the table are the difference of two powers of 2. e.g. the 4th number in the 6th row, 126, equals to 2^7-2.

• The table doesn't seem to follow any simple patterns, or say it's hard to write down a formula that generates the whole table.

• There are sometimes extremely long periods. e.g. 2147483646=2^31-2 for P12,10.

• The position of the first cell most of the time doesn't affect the final period. I found this with some manual attempts.

• You may notice several "1"s in the table. They indicate that all cells are finally dead. By looking at the table, I conjecture that this happens if and only if the size of the rectangle has the form (2^a-1)x(2^b-1), where a and b are positive integers. e.g. set a=b=4, we get P15,15 and it seems like any initial placement eventually dies in this grid.

Sadly I didn't find these numbers in https://oeis.org/. Maybe it's worthwhile to do more research on it? I don't know if it's proper to post such things here, but I'm too excited not to share this.

[addition] Just now I found that the first column of this table is recorded in OEIS as A268754: https://oeis.org/A268754.

[yyh_baboon]

Oblique replicator:

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x = 3, y = 3, rule = B3-cnqy4ejk5c/S2-ci3-ak4einryz5a6ce
3o$obo$2bo!

[yyh_baboon]

Code: Select all

 x = 3, y = 3, rule = B3aijkr4ej5c6in/S2-ci3-aky4einryz5jn
3o$obo$2bo!

[yyh_baboon]

Double post
Really strange displacement:

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 x = 3, y = 3, rule = B2i3-jkny4qz5cy6cn8/S2aek3-aky4iyz5cj6ace7e8
3o$obo$2bo!

[aengmore]

There should also be a thread for engineered replicators, especally those based on universal constructors, like those in JvN, Codd, Devore, Flow6, etc. So I collected them as much as possible:

• By islptng: https://conwaylife.com/forums/viewtopic.php?t=6577
• Sticky: https://conwaylife.com/forums/viewtopic ... 79#p186079
• Devore2: Mahler-rep https://conwaylife.com/forums/viewtopic.php?t=4163
• TernaryJvN60: https://conwaylife.com/forums/viewtopic ... 80#p210880
• JvN29: https://conwaylife.com/forums/viewtopic ... 421#p61421
• Flow6: https://conwaylife.com/forums/viewtopic ... 221#p87221
• WWEJ3: https://conwaylife.com/forums/viewtopic ... 491#p84491
• JVNWWE: https://conwaylife.com/forums/viewtopic ... 2159#12159
• WWEJ: https://conwaylife.com/forums/viewtopic.php?t=1868

Also see: https://github.com/gollygang/ruletabler ... i/TheRules

[silversmith]

There should also be a thread for engineered replicators

Why? I personally disagree, since that would group two very different kinds of patterns together, just because they are (unfortunately) named similarly. I think it makes sense for engineered replicators to be posted in whichever thread documents the technology used to build it, such as the thread for the rule itself.

Additionally, most of those don't replicate into identical patterns, and seem to be linear propagators or puffers.