Miscellaneous Discoveries in Other Cellular Automata

[77topaz]

A p8009 (!) gun:

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x = 17, y = 17, rule = 235678/3456/9
7.3A$7.3A$4.HG5AGH$3.11A$2.H11AH$2.G11AG$2.13A$17A$17A$17A$2.13A$2.G
11AG$2.H11AH$3.11A$4.HG5AGH$7.3A$7.3A!

Its minimum population is 181 cells.

[77topaz]

A p30 oscillator, two copies of which can phase shift each other to produce a p31 or a p32:

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x = 26, y = 10, rule = B2c3-i5i6ac78/S2378
12b2o10b2o$12bo12bo$12b2o10b2o5$2o9b2o11b2o$bo10bo12bo$2o9b2o11b2o!

[KittyTac]

A peculiar replicator:

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x = 2, y = 2, rule = B02345/S12
bo$o!

[AforAmpere]

A rule with three unique relativistic speeds, can someone find one with more?

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x = 29, y = 7, rule = B2-ek4aiw5-anry6aei8/S1c2ak3eik4einwz5-cnqr6ace7
bob2obo8bo8b2ob2o$2b4o9b2obo7bo$13b2o$o6bo6bo$2bo2bo7bo5bo$bob2obo$2b
4o!

EDIT, found one with 3c/5, 2c/3, 3c/4 and 4c/5:

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x = 40, y = 9, rule = B2-ek4aiqtwz5cijq6ein/S1c2ak3eik4einwyz5eijny6-k7
o5bo5bob2obo8bo8b2ob2o$b2ob2o7b4o9b2obo7bo$2bobo19b2o$b5o5bo6bo6bo$13b
o2bo7bo5bo$3bo8bob2obo$3bo9b4o$o2bo2bo$bo3bo!

[77topaz]

By "relativistic", I assume you mean "between c/2 and c"?

[AforAmpere]

By "relativistic", I assume you mean "between c/2 and c"?

Yeah, A for Awesome defined that a while ago, it is a pretty handy term instead of writing out the description every time.

[KittyTac]

I often call relativistic ships "fast".

[77topaz]

I often call relativistic ships "fast".

That's an even vaguer term.

[KittyTac]

I often call relativistic ships "fast".

That's an even vaguer term.

And c spaceships "very fast".

[KittyTac]

Is this known?

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#CXRLE Pos=-5,-3 Gen=565
x = 6, y = 6, rule = B3/S238:T10,10
2bo$5o$2ob3o$2o2bo$b3o$2bo!

[77topaz]

And c spaceships "very fast".

What are above-c ships in LtL rules, then?

[KittyTac]

And c spaceships "very fast".

What are above-c ships in LtL rules, then?

"Ridiculously fast".

[Apple Bottom]

What are above-c ships in LtL rules, then?

Impossible, since -- as I pointed out before -- "speed of light" does not mean "one cell per generation", and faster-than-c ships are impossible even in LtL rules. You guys had better come up with some different terminology for that.

That said, just for the context of this thread and this question, surely those ships would be called tachyons, in analogy to photons?

[77topaz]

Well, in a recent discussion the consensus seemed to be to reserve the usage of "c" to mean "one cell per generation", and to use a different term, possible "relative c", to refer to the (higher) speed limit in LtL rules.

[Apple Bottom]

Well, in a recent discussion the consensus seemed to be to reserve the usage of "c" to mean "one cell per generation", and to use a different term, possible "relative c", to refer to the (higher) speed limit in LtL rules.

Well, if by "consensus" you mean that four people chimed in at all, of which two agreed we should stick to the established definition, where "c" denotes the maximum at which information can travel in a given CA, and two thought it should instead always refer to a speed of one cell per generation -- then sure!

But you're of course free to use terms such as "c" and "speed of light" in any way you want. I'm merely pointing out that what you seem to think they mean isn't what they actually mean. You might as well go and re-declare what "space ship" or "oscillator" means. Perhaps there are indeed rules where the standard definitions aren't a good fit, somehow; but if so, surely it would be a better idea to come up with new terms, rather than co-opting and redefining terms that have been in use for almost 50 years.

On that note, and to make a constructive suggestion -- how about "speed of sound" for "1 cell per generation"? It's just as catchy, and there's no potential for confusion (that I can see anyway).

[77topaz]

The main thread for Larger than Life developments is here. In it, there are numerous posted spaceships, the speeds of which are frequently discussed. Here are some examples from the most recent page of the thread. I'll even exclude the ones posted by me for you:

• 1224,15c/284
• 406c/148d
• 128c/88d
• 5c/2o
• 1029c/239o
• (2718614,375678)c/245714
• 3934c/148
• 3788c/669o
• 4c/2 and 12c/6
• 67c/220d
• (4327,88)c/508
• 6c/84 diagonal
• 8c/26
• 2c/10o
• 4c
• c diagonal
• C/2 d
• (19,6)c/28

Notice something about all these speeds? Yep, they're all written using "c" to mean "one cell per generation". So, as a matter of fact, the consensus amongst people who actually investigate LtL rules does seem to be to use "c" in that way. So, your comments about "the established definition" and "what you seem to think they mean isn't what they actually mean" seem to be a bit inaccurate.

[AforAmpere]

So, as a matter of fact, the consensus amongst people who actually investigate LtL rules does seem to be to use "c" in that way.

Yeah, Golly itself, when using oscar, shows two cells per generation as 2c, regardless of range. If anything, c as being one cell per generation is the one that is established. Golly says this is 8c/4, with oscar:

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x = 7, y = 7, rule = R4,C0,M1,S2..4,B7..7,NM
2ob2o$5bo$6bo$6bo$6bo$5bo$2ob2o!

Wikipedia says that C is one cell per generation as well, and the only spot that seems not to is the LifeWiki page that you edited to say that C is relative.

[Apple Bottom]

Wikipedia says that C is one cell per generation as well, and the only spot that seems not to is the LifeWiki page that you edited to say that C is relative.

I didn't intend to reply again, but there is a misunderstanding here that I'd like to address. So let me give some historical background, as I see it.

The term "speed of light" has been in use for a long time, and was chosen because it naturally suggests itself for the maximum speed at which information can propagate. (I don't know if it precedes Conway's invention (discovery?) of Life -- perhaps there's something in the early LifeLines, or in Gardner's articles in Scientific American, I haven't checked.)

For Life, and generally for Life-like CAs (outer-totalistic CAs using the range-1 Moore neighborhood), the speed of light in the above sense is equal to one cell per generation, and people used the two interchangably. There was no reason to distinguish, after all, any more than there is a reason to distinguish between the physical speed of light (in a vaccuum) and "299,792,458 meters per second". The LifeWiki article, when it was originally created in 2009 by Nathaniel, also made no attempt to distinguish between the two.

When people on this forum later became interested in isotropic non-totalistic Life-like CAs (someone should really come up with a shorter moniker for these!), one user changed the article, apparently without realizing that two distinct concepts had even been conflated in the first place. That's OK -- but it added to the confusion. My recent edit was merely to clarify the situation, and (at the very least!) clarify that those two concepts, the speed at which information can propagate in a given CA and "one cell per generation", are in fact distinct.

Now, of course maybe I'm wrong, and maybe "speed of light" was meant to mean "one cell per generation" all along, no matter which CA was being considered, and the fact that this also happened to be the maximum speed at which information could be transmitted was merely a curious coincidence. But names are usually chosen for a reason, and it strikes me as more likely that whoever came up with this term was inspired by the physical speed of light, and its (apparent) quality of being an upper limit on the speed at which information can travel.

That said, for now, I'll stand by my interpretation, which is (in a nutshell) that a) "speed of light" refers to the maximum speed at which information can travel, b) the use of the term for a speed of one cell per generation is due to this being the speed of light in Life-like CAs, and c) the use of the term in that sense for CAs in which information can travel faster is due to confusion on the part of those using it, no doubt aided by the confusion also present in most reference sources who (due to b)) have also conflated the terms.

Perhaps someone who (unlike me) possesses a modicum of authority can shed some light on this -- Dvgrn, maybe?

[Macbi]

While we're on the topic, can I complain that a "Garden of Eden" is a pattern with no parents, while an "orphan" is a bounded region that can only occur in the initial state of the universe.

[77topaz]

[snip]
Now, of course maybe I'm wrong, and maybe "speed of light" was meant to mean "one cell per generation" all along, no matter which CA was being considered, and the fact that this also happened to be the maximum speed at which information could be transmitted was merely a curious coincidence.
[snip]

Yes, the term "speed of light" was originally defined as the speed of information, which is one cell per generation in CGoL. But in LtL, the vast majority of people use "c" in its geometrical sense of meaning one cell per generation (which is easier to visualise and consistent across different ranges), so that insisting upon the other meaning seems a bit pedantic. It's not due to "confusion on the part of those using it", it's rather used because it's more convenient, for the reasons in the previous sentence.

While we're on the topic, can I complain that a "Garden of Eden" is a pattern with no parents, while an "orphan" is a bounded region that can only occur in the initial state of the universe.

Why is that something to complain about? A Garden of Eden is simply any pattern that contains an orphan, with possibly additional cells surrounding it.

EDIT: Oh wait, I see, you'd want "orphan" to be something without "parents" and "Garden of Eden" to only be able to exist in the initial state of the universe. But that is true of the terms in their current definitions, too.

EDIT 2:

isotropic non-totalistic Life-like CAs (someone should really come up with a shorter moniker for these!)

"Non-tot rules" or "nt rules" are sometimes used for those.

[dani]

I agree that c should be used to mean one cell per generation, because it is much easier to compare spaceship speeds among rules with varying ranges. A c/2 spaceship in r1 suddenly being a c/4 spaceship in r2 is much more confusing. Worse, a c/3 spaceship in r2 would be a 2c/3 spaceship in r1, making perfect speeds imperfect depending on the rule. But that's just my opinion/old man rant

[calcyman]

I think someone suggested uppercase C for theoretical maximum speed of information propagation, and lowercase c for cell-per-generation, which I find to be very intuitive. Does anyone have arguments against this being adopted as the unambiguous standard?

[77topaz]

I think someone suggested uppercase C for theoretical maximum speed of information propagation, and lowercase c for cell-per-generation, which I find to be very intuitive. Does anyone have arguments against this being adopted as the unambiguous standard?

Yeah, that was something I'd suggested in the other thread I linked earlier. In that thread, AforAmpere had the counterargument that C is sometimes used interchangeably with c at the moment (as is true of one of the descriptions in that list from the LtL thread). Still, I think it's a good option, as would be AforAmpere's suggestion of "RC" for "relative c".

[AforAmpere]

I think someone suggested uppercase C for theoretical maximum speed of information propagation, and lowercase c for cell-per-generation, which I find to be very intuitive. Does anyone have arguments against this being adopted as the unambiguous standard?

The only problem I have with that system is that C and c are currently used interchangeably. Do you think instead of capital C, maybe use RC, for relative c? I feel personally that the two need to have some sort of obvious distinction, to determine meaning more easily, without having to check for capitalization every time.

EDIT, I started writing this before 77topaz had posted, sorry for the redundancy.

EDIT 2, as an actual Miscellaneous Discovery, the fastest (that I know of) known wickstretcher slower than c, at 3c/4:

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x = 19, y = 50, rule = B2-ik3nqr4cejntw5-ckq678/S02ain3-iknr4anry5acei678
bo3bo7bo3bo$obobobo5bobobobo$2obob2o5b2obob2o$2o3b2o5b2o3b2o$ob3obo5bo
b3obo$b5o7b5o$b5o7b5o3$8bobo$5bob5obo$4bo2b2ob2o2bo$4bobobobobobo$4b2o
2b3o2b2o$2bo2b9o2bo$b3o3b5o3b3o$3o2b9o2b3o$b17o$b17o$b17o$b17o$b17o$b
17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o$b
17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o$b17o!

[calcyman]

My argument in favour of using C and c is that even though they have been used interchangeably in the past, the vast majority of research in cellular automata has been in range-1 where the concepts do coincide. You only need to be careful with capitalisation in LtL and other large-range neighbourhoods.