Adjustable-speed replicators

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muzik
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Adjustable-speed replicators

Post by muzik » January 12th, 2022, 6:13 am

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

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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?

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muzik
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Re: Adjustable-speed replicators

Post by muzik » 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!

HotWheels9232
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Re: Adjustable-speed replicators

Post by HotWheels9232 » 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
My rules:
B34q/S23-k(ObliquePufferLife) and
B2n3-n4c5c/S234cz5cPM me to get some help on making rules!

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x = 8, y = 5, rule = B3-k/S23
2o3b2o$obo2bobo$2bo2bo$bo$b2o!

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toroidalet
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Re: Adjustable-speed replicators

Post by toroidalet » 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.
Step back from that cliff, you idiots! Yes, you! Every last one of you! We wouldn't want to do something regrettable, do we now?

HotWheels9232
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Re: Adjustable-speed replicators

Post by HotWheels9232 » 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
My rules:
B34q/S23-k(ObliquePufferLife) and
B2n3-n4c5c/S234cz5cPM me to get some help on making rules!

Code: Select all

x = 8, y = 5, rule = B3-k/S23
2o3b2o$obo2bobo$2bo2bo$bo$b2o!

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