ConwayLife.com

Posted: **January 12th, 2022, 6:13 am**

This rule by bibunsekibun has an infinite family of 1D replicators with an infinite number of distinct speeds:

x = 3, y = 1253, rule = B3aeiy4eqrty5cijn6ck7c8/S2-i3acein4cejkq5ir6cei7c8
bo$obo$bo4$bo$obo$bo48$bo$obo$bo8$bo$obo$bo63$bo$obo$bo13$bo$obo$bo77$
bo$obo$bo20$bo$obo$bo113$bo$obo$bo25$bo$obo$bo123$bo$obo$bo32$bo$obo$b
o164$bo$obo$bo37$bo$obo$bo180$bo$obo$bo44$bo$obo$bo216$bo$obo$bo49$bo$
obo$bo!

Separating the two tubs causes the speed to approach c/2, but never reaches it exactly.

The size of the separation between the two tubs that allows for clean replication does not seem to grow in a regular fashion (3, 7, 12, 19, 24, 31, 36, 43, 48, ...)

It's also possible to time-offset to allow for replication as well. I haven't investigated the separation values that these permit, though. Physically skewing the tubs may also allow for replication although I'm yet to find an explicit example.

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x = 3, y = 54, rule = B3aeiy4eqrty5cijn6ck7c8/S2-i3acein4cejkq5ir6cei7c8
bo$obo$bo49$bo$3o$bo!

My main question is: is it possible to find any simpler examples of adjustable-speed replicators? It certainly seems like a much more difficult task than finding adjustable spaceships, given that's been done plenty of times so far. The piston-like design of the original adjustable spaceships rule will probably be quite hard to capture, especially if we're to be able to copy the period information to an infinite number of successive copies and have them all cleanly annhialate. So I can't be too sure. But my main target right now is for an easy to describe and extend family of replicators to be found, such as, for example, all speeds c/2n below a given speed. Anyone up for this challenge?

Posted: **August 23rd, 2022, 3:59 pm**

Seeds technically has adjustable-speed replicators if bounded grids are permitted; I usually wouldn't but since there are so few cases of adjustable replicators these are going here anyway:

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x = 2, y = 1, rule = B2/S:T0,8
2o!

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x = 2, y = 1, rule = B2/S:T0,10
2o!

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x = 2, y = 1, rule = B2/S:T0,12
2o!

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x = 2, y = 1, rule = B2/S:T0,14
2o!

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x = 2, y = 1, rule = B2/S:T0,16
2o!

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x = 2, y = 1, rule = B2/S:T0,18
2o!

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x = 2, y = 1, rule = B2/S:T0,20
2o!

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x = 2, y = 1, rule = B2/S:T0,22
2o!

Posted: **August 23rd, 2022, 5:33 pm**

muzik wrote: January 12th, 2022, 6:13 am The size of the separation between the two tubs that allows for clean replication does not seem to grow in a regular fashion (3, 7, 12, 19, 24, 31, 36, 43, 48, ...)

I think it is quadratic but have not found the formula

Posted: **August 23rd, 2022, 9:25 pm**

Actually, ignoring the case of 3, it corresponds to either 7+12n or 12+12n. Given that a periodic fuse-like pattern is involved, it would make sense that the rule would be a few linear relations with some irregular cases. Also, for all cases with separation 0 or 3 mod 4, it is a replicator with puffer-like debris on the side (which doesn't affect the replication) except for 4, 8 and 15, which are puffers.

Posted: **August 24th, 2022, 10:58 am**

11 is strange:

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x = 3, y = 17, rule = B3aeiy4eqrty5cijn6ck7c8/S2-i3acein4cejkq5ir6cei7c8
bo$obo$bo12$bo$obo$bo!

16 is the same

Posted: **September 26th, 2023, 6:54 pm**

Adjustable speeds are hard to come by, but this rule has adjustable period 2D replicators: two dots an odd number of cells away from each other orthogonally will evolve into one.

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x = 83, y = 1, rule = B1c2i3e4c/S01c2n4cq8
o81bo!

This seems sufficiently far away from traditional unit cell behaviour to be notable in its own right as a single dot does not follow usual replication.

Posted: **September 13th, 2025, 5:09 pm**

Surprised this wasn't mentioned yet - I only found out about this while updating the collection zip:

FWKnightship wrote: April 2nd, 2024, 9:16 pm And adjustable W90 replicator of all orthogonal speed <= c/3!
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x = 102, y = 1, rule = ReplicatorsAndSnowflakes
2B2A2B8.2B2A3B8.3B2A3B9.2B2A4B2A3B11.15B2A15B!

Is there any possibility of finding a 2-state family that's this simple and straightforward to adjust?

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