## B3478/S15678

For discussion of other cellular automata.
AforAmpere
Posts: 1079
Joined: July 1st, 2016, 3:58 pm

### Re: B3478/S15678

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?
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

Posts: 1942
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: B3478/S15678

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.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

wildmyron
Posts: 1346
Joined: August 9th, 2013, 12:45 am

### Re: B3478/S15678

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?
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

wildmyron
Posts: 1346
Joined: August 9th, 2013, 12:45 am

### Re: B3478/S15678

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.
The latest version of the 5S Project contains over 226,000 spaceships. There is also a GitHub mirror of the collection. Tabulated pages up to period 160 (out of date) are available on the LifeWiki.

moony
Posts: 8
Joined: October 22nd, 2017, 10:55 pm

### Re: B3478/S15678

Does this rule have an actual name yet?
Just curious.

Majestas32
Posts: 524
Joined: November 20th, 2017, 12:22 pm
Location: 'Merica

### Re: B3478/S15678

Hi moony
Last edited by Majestas32 on April 12th, 2018, 7:04 pm, edited 1 time in total.
Please, stop spam searching Snowflakes.

77topaz
Posts: 1467
Joined: January 12th, 2018, 9:19 pm

### Re: B3478/S15678

Majestas32 wrote:Hi moony search b2e3-ajs23
...That's completely irrelevant to this thread, Majestas, which is about B3478/S15678. It's borderline spam.

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: B3478/S15678

moony wrote:Does this rule have an actual name yet?
Just curious.
It's just called B3478/S15678 for now
Airy Clave White It Nay

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``````x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o\$11b4obo\$2bob3o2bo2b3o\$bo3b2o4b2o\$o2bo2bob2o3b4o\$bob2obo5b
o2b2o\$2b2o4bobo2b3o\$bo3b5ob2obobo\$2bo5bob2o\$4bob2o2bobobo!
``````
(Check gen 2)