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Re: B3478/S15678

Posted: March 14th, 2018, 7:44 pm
by AforAmpere
wildmyron wrote:Nevertheless, here's the first 2c/5 orthogonal ship I have found in this rule (making good use of the above fuse):

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2c/5 ship
Nice! That is smaller than I thought it would be to be honest. I can't find any frontends for C/2, but I have no proof that they are impossible yet. Is there some way to prove it?

Re: B3478/S15678

Posted: March 14th, 2018, 8:21 pm
by BlinkerSpawn
AforAmpere wrote:
wildmyron wrote:Nevertheless, here's the first 2c/5 orthogonal ship I have found in this rule (making good use of the above fuse):

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2c/5 ship
Nice! That is smaller than I thought it would be to be honest. I can't find any frontends for C/2, but I have no proof that they are impossible yet. Is there some way to prove it?
Let's assume symmetry for simplicity.
The width of the leading edge of a c/2 engine alternates either between 1 and 3 or between 2 and 4.
Regardless of which, the only possibility that allows the center to survive and contribute to the next advancement is one bit followed by one bit:

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.o. 
.o.
Since the leading bit must remain alive to become the trailing bit 2 generations later, all four dots must experience birth and the trailing bit must survive to give S5.
But ensuring the front tip's survival via S1 leaves only three undeclared neighbors for the trailing which cannot be on since S234 isn't there.
We have two options for our frontend:

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...o...        ..ooo..
.o.o.o.        o.ooo.o
oo...oo

...o...        ..ooo..
.o.o.o.        .ooooo.
??...??
(exactly one of the ?'s on each side is ON)

It looks improbable that c/2 exists.
When I started writing this post I thought maybe I'd end up with an argument that could be extended inductively into an interminable ribbon (similar to infinite lines in GoL needed for lightspeed) but I'm not sure if anything concrete is reachable from there now.

Re: B3478/S15678

Posted: March 14th, 2018, 11:42 pm
by wildmyron
The options available for a p2 c/2 engine are probably covered by the two examples in B3478/S1568 and B3478/S1578 I posted earlier. They fit nicely with this consideration (for the odd symmetry case) and obviously one doesn't work with S6 and the other doesn't work with S7. @BlinkerSpawn: I suspect you're probably not too far off a proof that there's no p2 c/2 engine. But what about higher period engines? p4 and p6 look similarly unlikely as those searches finish pretty quickly too. Can anything be said about the existence of higher period c/2 engines if we know that p2 c/2 engines don't exist?

Re: B3478/S15678

Posted: March 20th, 2018, 1:53 am
by wildmyron
Here are some vaguely promising leads on 4c/8 which at the very least show that there's no simple proof of their non-existence.

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x = 44, y = 31, rule = B3478/S15678
3bo$3bo28bobo$3b2o28b2o$4b2o28b2o$4b3o28bo$35b3o$3b3o2bo24bobobo$bob2o
2b4o20bob3o2b2o$bo2bobo24bo2bobo6bo$bo3b2o24bo3b2o2b4o$2b2o2b2o2b3o19b
2o2b2o$3b4o26b4o5bo$3b3o27b3o$4b2o28b2o$2bo29bo$obo27bobo$2bo29bo$4b2o
28b2o$3b3o27b3o$3b4o26b4o5bo$2b2o2b2o2b3o19b2o2b2o$bo3b2o24bo3b2o2b4o$
bo2bobo24bo2bobo6bo$bob2o2b4o20bob3o2b2o$3b3o2bo24bobobo$35b3o$4b3o28b
o$4b2o28b2o$3b2o28b2o$3bo28bobo$3bo!
The idea is to find a wing shaped ship with a symmetrical leading edge that is supported by long wings. I'm not sure yet if this is feasible, but it's a start.

Re: B3478/S15678

Posted: April 12th, 2018, 2:03 pm
by moony
Does this rule have an actual name yet?
Just curious.

Re: B3478/S15678

Posted: April 12th, 2018, 2:48 pm
by Majestas32
Hi moony

Re: B3478/S15678

Posted: April 12th, 2018, 4:25 pm
by 77topaz
Majestas32 wrote:Hi moony search b2e3-ajs23
...That's completely irrelevant to this thread, Majestas, which is about B3478/S15678. It's borderline spam.

Re: B3478/S15678

Posted: April 12th, 2018, 7:31 pm
by Saka
moony wrote:Does this rule have an actual name yet?
Just curious.
It's just called B3478/S15678 for now