Talk:Spaceship

Edits and prospective splitting

I have made some major edits to this page as I found that the old page was somewhat difficult to read. I would like to see more added to the history section of this page, especially more references. My initial idea for that section was to provide information on the various searches that people had made, as well as the discovery of new spaceship speeds, but other information on the history of spaceships would also be nice. Also, if somebody would rewrite some of this page so that it used the word "spaceship" somewhat less, I believe that would be helpful.

I was wondering if separate pages should be made for each spaceship speed, in addition to the categories of patterns that travel at those speeds, as I find that the category pages don't provide the necessary information that one might be looking for when going to such a page. I also believe that pages should be made for individuals who have made significant contributions to life.

More in relation to this page, I was wondering if the table of smallest known spaceships for a given speed should get its own section in this article, or whether it should be put in a new sub-section with other information. I am assuming that the table of spaceship speed discoveries will be in the history section.

Update: I added more to the history section, I am also going to create a "Spaceship types" section (with a link to Types of spaceships) to describe things like greyships and tagalongs, as well as to put the table of smallest spaceships in.

Update 2: I added names for several unnamed spaceships missing from the tables on this page. These additions are, to the best of my knowledge, correct. The names refer to the following patterns:

295P5H1V1	25P3H1V0.1	25P3H1V0.2	46P4H1V0	30P5H2V0	67P5H1V1

I also added a new section (Spaceship types).

02:11, 19 April 2009 (UTC)

Update 3: Pages for all of these unnamed spaceships have been created, thanks to Nathaniel.

04:07, 23 April 2009 (UTC)

~Sokwe 17:36, 18 April 2009 (UTC)

Personally, I would rather see the category pages themselves expanded to include any relevant information about the spaceships of that speed (the first one found, the smallest one known to date, etc) rather than creating a separate page for that information and then having the category as well. Similarly with the user contribution pages, though that might be more questionable if we have a lot of information for a particular Life guru (such as Conway, Hickerson and Bell). I protected some categories early on but I don't know why I did that, so I'll remove the protection from the speed category pages, and feel free to ask me to remove protection from any other page you'd like to expand/alter. Category pages can have text added in the exact same way as normal text pages.

Also, just so you know you can sign your post automatically by typing four tildes: ~~~~ will be replaced automatically by your name and timestamp. Also, I'll add some pattern pages for the spaceships that you added to this page. My thinking is that if a pattern holds a record that is notable enough that it's mentioned on another page, then that pattern probably deserves its own page. Nathaniel 03:56, 19 April 2009 (UTC)

I noticed that the tables with spaceship speeds are organized by the size of their denominator. I was wondering if perhaps they should be ordered by relative speed (still keeping the directions separate), thus making the order: Diagonal: c/4, c/5, c/6, c/12; Orthogonal: c/2, 2c/5, 17c/45, c/3, 2c/7, c/4, c/5, c/6 (The first discoveries table could possibly be ordered by date of discovery). I've noticed that the convention in the life community seems to be the way in which the tables are currently ordered.

~Sokwe 06:09, 19 April 2009 (UTC)

The mathematician in me agrees that in general things like this should be sorted by their actual value, but I personally think it's easier to read the way it is, since it's not completely trivial to determine whether or not 2/7 is faster or slower than 1/3 in your head. I don't care a whole lot either way though.

Also, I've found most of the other spaceships, but can I ask where you found 295P5H1V1? I'd like to add a page for it and it would be a lot easier to do so if I could track down an RLE file (or similar file) for it. Nathaniel 23:09, 22 April 2009 (UTC)

Nevermind, I found it in Jason Summers' pattern collections. Nathaniel 23:25, 22 April 2009 (UTC)

Sorting

It would be nice if someone could sort the orthogonal spaceships by their speed (c/2, 2c/5, 17c/45, c/3).

Also, why the hell are shield bug and centipede not with the rest of the orthogonal spaceships? AwesoMan3000 (talk) 11:28, 18 February 2016 (UTC)

I've done this for the second table. Feel free to revert if needed. - AwesoMan3000 (talk) 08:41, 19 February 2016 (UTC)

Should weekender distaff be included in the engineered spaceships section?

Weekender distaff is just an engineless rake. We have such rakes for many other speeds (c/3, c/4, c/5, 2c/5 orthogonal and c/4, c/5 diagonal). It seems we should either include all of these or none of them in the table.
~Sokwe 18:57, 24 October 2018 (UTC)

You're right, it's a stretch to fit the weekender distaff into this table. The "specific active reaction that travels at one particular speed" would have to be the weekenders, which can travel unsupported. So an engineless rake (or high-period traveling loop, whatever you call that, if it's like an engineless rake but doesn't emit any gliders) shouldn't be in quite the same category as a supported active reaction.

That said, it seems like a reasonably good idea to add an "engineless rakes" section at the bottom of the engineered-spaceships table, with all seven known types. They do share some commonality with engineered spaceships. Dvgrn (talk) 10:40, 25 October 2018 (UTC)

False statement in "In other rules"

In any rule with B23/S0, the trailing edge of a pattern cannot die.

The veracity of this statement (assumedly intended as a disproof of the existence of spaceships in a subset of the OT rulespace, given the other items in the list) is dubious. For instance, the glider works in B23/S023. Before removing it, is there anything it could have been intended to mean? DroneBetter (talk) 14:40, 11 August 2023 (UTC)

The linked Catagolue object page shows the glider working in B3/S023. I don't think it works with B2: link. Confocal (talk) 14:51, 11 August 2023 (UTC)

Terribly sorry, my mistake, let us never speak of it again. (I'm glad the LifeWiki doesn't store permanent records of all conversations :-)

I do, however, have some less incorrect things to say.

In any rule with S01234a, the trailing edge of a pattern cannot die.

This is true, but can be strengthened. Since the bounding box and diamond must be able to recede, in an S0123 rule with B2, B3 or their union, if one is to create a configuration such that every cell dies from overpopulation, they cannot prevent a cell neighbouring those from being born (since the only way to make all cells on a receding edge of the bounding box die in one iteration is to have them all under the S4a or S5i transitions, the S5i ones depend upon the existence of S4a's, and S4a causes B2a, and if the rule contains B3, S5i causes B3i and S4a causes B3a adjacent to it). This is corroborated by all spaceships in the extension of David Eppstein's glider database, but so too would have been until the work of Layz Boi in 2021 finding six counterexamples, so I'd like someone else to convince themselves of my reasoning also.

However, I venture to motion that a non-B0 rule having all transitions within S1234a precludes spaceships also, and the statement ought to be split into excluding the union of S0123 and S1234a, not the intersection. Since B1 is already excluded, there must either be B2 or B3. The proof here instead relies on the fact that a cell at the end of a line of contiguous cells on the edge of the bounding box may not die. In B3 rules, it can be seen that it takes only two generations for such an edge (with the necessary maximal support cells behind it) to propagate itself by one cell outwards. In both B2 and B3 rules, the receding edge cannot produce dot sparks at all, which are prerequisite to its receding.

Over the strobing rules (B0 without S8), we have some equivalents of these facts.

"There must not be B1" is slightly more subtle, for there do exist spaceships with the equivalent of B1 in alternate phases. Nonetheless, the equivalent of B1 in both iterations (the absence of B1 and the presence of S7) preclude them for the same reason of uncontrollable omnidirectional B1c growths. (This disproves 2¹⁴ rules, a quarter of the strobing rulespace.)

"There must be at least one of B1, B2 or B3" becomes "There must be one of the absences of B1, B2 and B3, or the presences of S7, S6 and S5." (This disproves another 2¹⁰.)

"There must not be all of S01234" becomes "Not all of S01234 can be absent and there must be at least one absence from B87654"

If my previous proof is correct, this may be strengthened to separate conditions for spaceships

At least one of S1234, and not all of B7654.

If a rule has both S0 absent and B8 present (meaning its equivalent alternating pair both have S0), it must have at least one of (S1 and B7), (S2 and B6), and (S3 and B5). This seems to have counterexamples, I know not why.

Additionally, strobing rules with B1 and not B2, S6 or S7, may not support spaceships. In the equivalent alternating pair, this is equivalent to (B2, S6, S7 and not B1) and (B1, B2, S7 and no S6). The high-neighbour survival transitions matter not, so this is equivalent to the statement that if B2 is present, B1 may not be on alternate iterations. Consider again a line of cells on a receding edge, in the iteration in which B1 is active. If there is only one cell in this line, it creates two cells diagonally adjacent, which on the next iteration grow further due to B2, forming a perpetual lightspeed outgrowth. If there are two, they will grow to a line of four, and three (or indeed, any higher length) will grow into two lines of two. On iterations without B1, two will propagate themselves outwards due to B2. (This disproves another 2¹² rules.)

Furthermore, there is another pair of disproven regions that exhibit a duality with the previous two.

The presence of B1, S5 and S6, and absence of B2, B3 and S7, preclude spaceships. This may strike you as familiar, because it disproves 2¹⁰ rules, similarly to the earlier one about bounding box/diamond growth. In the alternating pair, these correspond with (B2, B3, S5 and not B1, S7 or S6) and (B1, S6, S5 and not B2, B3 or S7).

The presence of B1, B2, and S7, and absence of S6, preclude spaceships. This comprises 2¹² rules, like the other earlier one. Its alternating pair conditions are (S6 and not B1, B2 or S7) and (B1, S7, S6, and not B2). Importantly, B2 is not allowed in either and B1 exists in alternate iterations. This one I am not sure of, so I am not including it.

This all pertains specifically to the OT rulespace, to the ends of a map I have made.

It iterates over birth conditions in a Gray code rightwards (B0 having the highest precedence) and survival ones downwards (S0 having the highest in the left half, and S8 (equivalent to B0 in the rules' duals) in the right), green has an explicit example, red has a disproof, black and grey are unknown (though grey ones are strobing).

It has each of these lines of reasoning implemented within it, the ith bit of b or s (ie. b>>i&1) represents the current rule's Bi or Si transition. It isn't very efficient (it could use multiple bitmasks and SWAR methods for the image generation, and probably the iteration over the vertices of the hypercubes of rule ranges within the 18-dimensional OT rulespace cube by Cartesian products is very inefficient), but the 34415 spaceships and 262144 rules don't take very long to iterate over on my computer (about three or four seconds). Do you know of any other spaceship collections, and would it be worth including the map in this page?

If you are curious, the six rules in the vertical band with both B2 and B3 each have single spaceships in the collection, each OT-endemic and found by Layz Boi in 2021, namely b23578s14678, b23678s24678, b2358s14678, b2357s14678, b23578s3678 and b2357s14678.

I'm not sure whether it would be disrespectful, so will ask you first. In the aim of making this talk page useful for future visitors, what say you we remove my original blunder and your response (and make this the parent post)? DroneBetter (talk) 16:43, 12 August 2023 (UTC)

I think the previous replies provide context, and generally help the future curious reader to understand where discussions and ideas came from. I much prefer it this way and would like if it were to stay as such. Confocal (talk) 17:05, 12 August 2023 (UTC)

In any case, I have added a few more green ones from black/white reversals of strobing rules, as well as regions of disproof from LaundryPizza03, who had proven the statement about the presence of B1, B2, and S7 and absence of S6, I was only becoming confused with myself. A few more self-complementary rules in the "death zone" of B23 without S0 could be proven to be the strobing duals of those in a known block of impossible strobing rules, I wonder whether this generalises to other death zone rules.

The images are both on this page now (under a tab bar to switch them), as you may have seen. I wonder whether it will one day be continued and turned entirely red and green. DroneBetter (talk) 20:31, 20 August 2023 (UTC)

Regarding the existence of a 4c/14 spaceship and maximum diagonal speed

There does not appear to be a 4c/14 spaceship in Life listed here, only 6c/21 from the doo-dah. Are there no period-doubling tagalongs known? Also, regarding the line

Certain range-1 non-isotropic rules can harbour c/1 diagonal spaceships, giving a limit of 2.

it is obviously true (since it requires B1c), but is there a known maximum diagonal speed? It appears as though the statement

In rules with S4w and/or S5a, the diagonal speed limit is c/3, not c/4.

answers this question, but has it been proven, and if so, may this proof be cited? Does it pertain over all INT rules? DroneBetter (talk) 20:31, 20 August 2023 (UTC)