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Is there any unsimplified speed (x,y)c/p (2(|x|+|y|)<=p) that no spaceships exist?

https://conwaylife.com/wiki/LifeWiki:Sp ... tatus_Page


(1,1)c/6 https://www.conwaylife.com/wiki/C/6_diagonal
(4,0)c/9
(2,1)c/7
(3,1)c/8

Dylan Chen wrote: May 19th, 2021, 7:41 am https://conwaylife.com/wiki/LifeWiki:Sp ... tatus_Page
(1,1)c/6

? & still don’t understand the question.

Um... I'm not particularly well at engineering macro-spaceships, but there are a few things I can say.

• Speed Demonoids allow every possible diagonal speed.
  Orthogonoids can also allow every possible orthogonal speed.
  For oblique speeds, a macro-spaceship can theoretically be built if there is an appropriate helix.
  Also, adjustable oblique spaceships might also allow every possible oblique speed -- I see no theoretical difficulties, and I believe that such a family of adjustable oblique ships will very probably exist, just that no-one has built it yet.

shuich01 wrote: May 19th, 2021, 6:16 am Is there any unsimplified speed (x,y)c/p (2(|x|+|y|)<=p) that no spaceships exist?

Well, we definitely don't know of ships at all speeds, particularly not unsimplified as you stated (this rules out the macro-spaceships mentioned in the above post); but a proof of the nonexistence of a spaceship at a specific unsimplifed speed with the conditions you stated would be highly nontrivial (unless you count (0,0)c/n, though if you consider that a valid velocity for spaceships then it seems strange to say that oscillators aren't spaceships because they're called something else ).

By the way, in the future you might want to ask similar questions in the dedicated thread.

For all low periods that have been searched, long partial spaceships have been constructed, usually consisting of a working front end with a tail that rapidly degenerates (or sometimes a working tail with a head that rapidly degenerates), and there is no compelling reason why they should not be able to be completed. My personal opinion is that very large spaceships of all unsimplified speeds exist, but such a statement is nigh impossible to decide either way.

Moosey wrote: June 10th, 2021, 5:42 pma proof of the nonexistence of a spaceship at a specific unsimplifed (sic) speed with the conditions you stated would be highly nontrivial

Indeed, there are rules where it is undecidable whether a spaceship of that unsimplified speed exists. (proof: have the top row be the starting configuration of a universal Turing machine with the numbers a and b written somehow; the top row moves up a cells then waits b generations and further rows move up whenever they have room, provided that they locally correspond to the evolution of the Turing machine) Needless to say, Life is probably not one of these rules, but the fact that these rules exist suggests that without explicitly coming up with a ship or showing that all branches of the search reach dead ends, it will be very hard to reason one way or another.