Smallest Spaceships Supporting Specific Speeds (5s) Project

[muzik]

I personally feel like these lists would work a lot better as a page/pages on the wiki, since that way multiple trusted people will be able to edit the page and update it at will. Also, I could pop a nice looking chart/table at the top of it that links you down to the respective speed, while highlighting speeds not yet discovered.

On a different note: Will generations and larger than life rules be allowed?

In which case, here are two 7-knightships:

c/17:

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x = 3, y = 4, rule = 2378/34578/4
2A$A.A$.BA$.2A!
[[ THEME Blues ]]

c/66:

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x = 8, y = 9, rule = 23578/3568/4
6.2A$6.2A3$.2A.C$2ACA$AC.A$ABA$C2A!
[[ THEME Blues ]]

[muzik]

Although this obviously doesn't count, c diagonal:

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x = 1, y = 1, rule = MAPAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
o!

[praosylen]

Are there any speeds and/or directions that would be completely impossible in all range-1 2-state CA, without the usage of universal construction technology?

I believe c diagonal is an example.

No:

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x = 1, y = 1, rule = MAPGAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
o!

[Naszvadi]

...
c/12 diagonal

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x = 4, y = 4, rule = B2cek3acijr5c6cik/S2-ck3inr
3bo2$3bo$obo!

...

Well, tie in minimal bounding box - c/12 diagonal:

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x = 4, y = 4, rule = B02/S1V
o$b2o$bobo$3bo!

[AforAmpere]

Are there any speeds and/or directions that would be completely impossible in all range-1 2-state CA, without the usage of universal construction technology?

I believe c diagonal is an example.

No:

Code: Select all

x = 1, y = 1, rule = MAPGAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
o!

Sorry, I read that wrong. a p1 knightship would be an actual answer.

[muzik]

Sorry, I read that wrong. a p1 knightship would be an actual answer.

But surely that would require a larger neighbourhood than my constraints would allow?

[AforAmpere]

Exactly, a p1 knightship is completely impossible in R1 Moore, you had no constraints for answers. I think (2,1)c/2 is also impossible, but within R1 Moore, because I think B1c in some direction would be required to make it work, and that would cause the knightship to fail. I can't say for sure without a better proof.

[BlinkerSpawn]

Sorry, I read that wrong. a p1 knightship would be an actual answer.

But surely that would require a larger neighbourhood than my constraints would allow?

Yes; by definition that would require a range-2 or higher CA.
While speeds >c technically answer the question, that's not really the answer muzik was looking for.
As for the actual answer, there are (presumably) infinitely many speeds and/or directions satisfying the criteria but a definitive proof for any particular speed is far beyond the reach of current computational machinery.

I think (2,1)c/2 is also impossible, but within R1 Moore, because I think B1c in some direction would be required to make it work, and that would cause the knightship to fail. I can't say for sure without a better proof.

This only disproves the existence of such ships for rules without B0.

[AforAmpere]

Can (2,1)c/2 be proved to be impossible?

[praosylen]

Can (2,1)c/2 be proved to be impossible?

I doubt it — one is likely possible by a similar mechanism to the 3c/4 diagonal B0 ship.

[AforAmpere]

How is this? Imagine there was a (2,1)c/2 ship. In one of the 2 generations, it would have to shift 1 cell diagonally, but also move up 1 at the same time, which seems to require B1c in one of the four diagonal directions. The problem is that with B1c, it can only support diagonal spaceships, even if non-symmetric, as everything has corners. Another way to look at it is this:

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x = 4, y = 5, rule = B1e2345678/S012345678History
3.D2$.2A$A.A$2.A!

Without B1c, the explosion can't even get to the red dot in 2 generations, but B1c is already impossible to use, even in non-symmetric rules, so it seems to be impossible.

[BlinkerSpawn]

How is this? Imagine there was a (2,1)c/2 ship. In one of the 2 generations, it would have to shift 1 cell diagonally, but also move up 1 at the same time, which seems to require B1c in one of the four diagonal directions. The problem is that with B1c, it can only support diagonal spaceships, even if non-symmetric, as everything has corners. Another way to look at it is this:

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x = 4, y = 5, rule = B1e2345678/S012345678History
3.D2$.2A$A.A$2.A!

Without B1c, the explosion can't even get to the red dot in 2 generations, but B1c is already impossible to use, even in non-symmetric rules, so it seems to be impossible.

It's true you can't shift diagonally with B1c and then orthogonally with B1e but you can move diagonally with B0 A*1c and then orthogonally with S7e.
Speaking of which, what's the status on non-totalistic B0 rules?

*A is short for abstain; in this case B1c is explicitly prohibited.

[muzik]

32c/320:

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x = 111, y = 148, rule = B3/S23
66b2o$65b2ob2o5b3o$65bo2b2o10bo$65b4o6b2o3b3o$65b2o4b2o3b2o2bobo$65b2o
4b2o3b2o2bobo$65b4o6b2o3b3o$65bo2b2o10bo$45b2o18b2ob2o5b3o$45bobo6b2o
2bo7b2o18b2o$44bo2b2o5b2obo2bo25bobo6b2o2bo$22b2o21b2o3bo4bo4bo24bo2b
2o5b2obo2bo$22bobo6b2o2bo9bo5bo4bo2bobo24b2o3bo4bo4bo$21bo2b2o5b2obo2b
o7bo5bo4bo2bobo24bo5bo4bo2bobo$22b2o3bo4bo4bo7b2o3bo4bo4bo25bo5bo4bo2b
obo$22bo5bo4bo2bobo5bo2b2o5b2obo2bo25b2o3bo4bo4bo$22bo5bo4bo2bobo6bobo
6b2o2bo26bo2b2o5b2obo2bo$22b2o3bo4bo4bo7b2o39bobo6b2o2bo$21bo2b2o5b2ob
o2bo48b2o$b2o19bobo6b2o2bo$bobo6b2o2bo7b2o$o2b2o5b2obo2bo$b2o3bo4bo4bo
$bo5bo4bo2bobo8b2o8b2o20b2o$bo5bo4bo2bobo8b2o8b2o20b2o$b2o3bo4bo4bo$o
2b2o5b2obo2bo77b2o$bobo6b2o2bo79bobo6b2o2bo$b2o90bo2b2o5b2obo2bo$94b2o
3bo4bo4bo$94bo5bo4bo2bobo$13b2o6b2o22b2o6b2o39bo5bo4bo2bobo$13b2o6b2o
22b2o6b2o39b2o3bo4bo4bo$93bo2b2o5b2obo2bo$94bobo6b2o2bo$94b2o$34b2o$
34b2o2$82bo$17b2o63b2o$17bobo6b2o2bo50bobo$16bo2b2o5b2obo2bo$17b2o3bo
4bo4bo$17bo5bo4bo2bobo$17bo5bo4bo2bobo$17b2o3bo4bo4bo$16bo2b2o5b2obo2b
o$17bobo6b2o2bo$17b2o17$57bobo$58b2o$58bo30$17b2o$17bobo6b2o2bo$16bo2b
2o5b2obo2bo$17b2o3bo4bo4bo$17bo5bo4bo2bobo$17bo5bo4bo2bobo$17b2o3bo4bo
4bo$16bo2b2o5b2obo2bo$17bobo6b2o2bo$17b2o5$94b2o$94bobo6b2o2bo$93bo2b
2o5b2obo2bo$5b2o22b2o6b2o30b2o23b2o3bo4bo4bo$5b2o22b2o6b2o30b2o23bo5bo
4bo2bobo$94bo5bo4bo2bobo$94b2o3bo4bo4bo$b2o90bo2b2o5b2obo2bo$bobo6b2o
2bo47bobo29bobo6b2o2bo$o2b2o5b2obo2bo44bo3bo28b2o$b2o3bo4bo4bo43bo4bo$
bo5bo4bo2bobo24b2o16bo4bo8b2o$bo5bo4bo2bobo24b2o16bo3bo9b2o$b2o3bo4bo
4bo44bo2bo$o2b2o5b2obo2bo$bobo6b2o2bo7b2o$b2o19bobo6b2o2bo$21bo2b2o5b
2obo2bo48b2o$22b2o3bo4bo4bo7b2o39bobo6b2o2bo$22bo5bo4bo2bobo6bobo6b2o
2bo26bo2b2o5b2obo2bo$22bo5bo4bo2bobo5bo2b2o5b2obo2bo25b2o3bo4bo4bo$22b
2o3bo4bo4bo7b2o3bo4bo4bo25bo5bo4bo2bobo$21bo2b2o5b2obo2bo7bo5bo4bo2bob
o24bo5bo4bo2bobo$22bobo6b2o2bo9bo5bo4bo2bobo24b2o3bo4bo4bo$22b2o21b2o
3bo4bo4bo24bo2b2o5b2obo2bo$44bo2b2o5b2obo2bo25bobo6b2o2bo$45bobo6b2o2b
o7b2o18b2o$45b2o18b2ob2o5b3o$65bo2b2o10bo$65b4o6b2o3b3o$65b2o4b2o3b2o
2bobo$65b2o4b2o3b2o2bobo$65b4o6b2o3b3o$65bo2b2o10bo$65b2ob2o5b3o$66b2o
!

[toroidalet]

44-cell 8c/26 diagonal

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x = 19, y = 19, rule = B2cei3aeiny/S2-i3-a4citz
5bo$6bo$7bo$4bo$3bo$o$bo$2bo10bobo$16bo$16bo$10b2o3bo$10b2o$14bobo$7bo
5b3obo$12b2o3b2o$7bo2bo2bo3b2o$8b2o2bo4bo$13b5o$14b2o!

[BlinkerSpawn]

44-cell 8c/26 diagonal

Code: Select all

x = 19, y = 19, rule = B2cei3aeiny/S2-i3-a4citz
5bo$6bo$7bo$4bo$3bo$o$bo$2bo10bobo$16bo$16bo$10b2o3bo$10b2o$14bobo$7bo
5b3obo$12b2o3b2o$7bo2bo2bo3b2o$8b2o2bo4bo$13b5o$14b2o!

Adding B6n tames the rear spark, cutting minimum population and dimensions in right around half:

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x = 9, y = 9, rule = B2cei3aeiny6n/S2-i3-a4citz
4b2o$b3ob2o$bo4bo$bo$o7bo$2o5bo$b2o5bo$5bo2bo$4bob3o!

[muzik]

drc discovered this one a while ago, not sure if it's in the collection.

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x = 12, y = 12, rule = B35/S234i
11bo$11bo$9b3o7$2bo$2bo$3o!

[toroidalet]

Adding B6n tames the rear spark, cutting minimum population and dimensions in right around half:

Code: Select all

ship

Nice catch!
Smaller c/30

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x = 3, y = 7, rule = B3/S1c2-ck35i
2bo$bo3$bo$2o$o!

6 cells

[wwei23]

c/7 diagonal:

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x = 5, y = 5, rule = B2ce3-ai/S23
4bo$b2obo$bo2bo2$3o!

[wildmyron]

Smaller c/30

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x = 3, y = 7, rule = B3/S1c2-ck35i
2bo$bo3$bo$2o$o!

6 cells

c/7 diagonal:

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x = 5, y = 5, rule = B2ce3-ai/S23
4bo$b2obo$bo2bo2$3o!

Both these diagonal speeds already have 3-cell examples.

Also, to wwei23, please observe the canonical direction for ships posted in this thread which is given in the original post.

[toroidalet]

Both these diagonal speeds already have 3-cell examples.

My mistake, I was looking at the population for the 3c/30 diagonal ship. (the layout is confusing)
18-cell 4c/5 to attone for my mistakes

Code: Select all

x = 11, y = 7, rule = B2ac5a/S01e
7bo$2b3o4b2o$bo2bo$o3bo$bo2bo$2b3o4b2o$7bo!

[Bullet51]

22c/61:

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x = 7, y = 5, rule = B3-q4-a5y8/S23-ijn4a5aj
b3o$o3b2o$o5bo$o3b2o$b3o!

[AforAmpere]

I still haven't logged all of the 4-cell ships that I lost after the crash, because I have had a lot of other things to do lately. This still has a bunch more new ships, and I will finish looking through the 4-cell results eventually.

the layout is confusing)

How is it confusing? I tried to lay it out so that specific periods were easy to look up, so just scroll down to p30 in the diagonal ships file and look for 3c/30. Please feel free to tell me why it is confusing.

18-cell 4c/5 to attone for my mistakes

Code: Select all

x = 11, y = 7, rule = B2ac5a/S01e
7bo$2b3o4b2o$bo2bo$o3bo$bo2bo$2b3o4b2o$7bo!

How was this found? I did one soup of the rule, and it just popped out, but was this discovery on accident? That fills in all ships up to p5 that are possible in Non-totalistic rules. I have a feeling that 5c/6 will not be found for a while though.

EDIT, that rule actually has two 4c/5 ships:

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x = 11, y = 31, rule = B2ac5a/S01e
7bo$2b3o4b2o$bo2bo$o3bo$bo2bo$2b3o4b2o$7bo10$3bobo$2bo2$2bo$7bo$3b3o3b
2o$2bo2bo$bo3bo$2bo2bo$3b3o3b2o$7bo$2bo2$2bo$3bobo!

[muzik]

What are your opinions on maybe hosting the collection on the wiki, so that it can be updated by anyone?

[AforAmpere]

I don't know how I would really do that, and I am worried that spammers would start editing it with fake or irrelevant stuff. If there was a way to allow certain people to edit it or something, maybe, but I am really unsure. The problem is, I know someone would add in their "discovery", and not actually check before adding it.

[muzik]

and I am worried that spammers would start editing it with fake or irrelevant stuff.

Strongly doubt this would happen, since the wiki requires your account be trusted for anyone to edit.