Thread for basic questions

[drc]

Define "interesting".

A lot of the spaceships are symmetric, and oscillators too. nt/zfind generally reports more results for symmetric searches rather than asymmetric.

[BlinkerSpawn]

Define "interesting".

A lot of the spaceships are symmetric, and oscillators too. nt/zfind generally reports more results for symmetric searches rather than asymmetric.

Symmetric objects aren't inherently more interesting, they just have fewer degrees of freedom for their size and are thus far easier to search for.
Because of this, you'll see a lot of symmetric objects show up when people search for them.
I believe, however, that asymmetry comes with its own level of "exotic-ness":
Oblique spaceships/replicators don't have symmetry.
RROs don't have symmetry.
Conduits don't have symmetry.

[muzik]

Oblique spaceships/replicators don't have symmetry.

They can have rotational symmetry:

Code: Select all

x = 2, y = 3, rule = B02346/S023
o2$bo!

[Apple Bottom]

Why are symmetric objects generally more interesting?

In addition to what's already been said, symmetry (or near-symmetry) is also generally perceived as beautiful, which may explain why people are drawn on some immediate level to symmetric objects.

Consider, if you will, Beluchenko's p51 and 92p51. Nonwithstanding the fact that the latter hasn't appeared on Catagolue in the first place (and is unlikely to for a long time to come), I think the former is simply more aesthetically pleasing.

[dvgrn]

Define "interesting".

A lot of the spaceships are symmetric, and oscillators too. nt/zfind generally reports more results for symmetric searches rather than asymmetric.

Symmetric objects aren't inherently more interesting, they just have fewer degrees of freedom for their size and are thus far easier to search for.
Because of this, you'll see a lot of symmetric objects show up when people search for them.

I actually agree with all this completely, but also want to say that the opposite is true in a sense:

Symmetric objects are inherently more interesting, because symmetry makes certain things probable that otherwise are so improbable that they never actually show up.

Take Rich's p16 for example. It's technically possible that another p16 pattern might exist, identical to Rich's p16 on one side, but on the other side it's a mostly-all-different reaction that just happens to produce the same p16 pattern of ON and OFF cells. Or it might be a somewhat different pattern, I suppose, but it has the same effect of suppressing all gutter-cell births.

That other half-oscillator pattern could even be completely asymmetrical, no time-delayed vertical mirror symmetry (or whatever we're calling that these days) as long as it produces the right cells next to the gutter.

However, there are something like 2^128 different possible p16 patterns of those eight cells next to the gutter. So that might mean we'd have to collect around 2^127 different mirror-symmetric p16 oscillators with a length-8 gutter, before we'd be likely to find a new one that could be matched to half of a Rich's p16. Two to the power of any three-digit number is one of those "way way way too unlikely, never mind" probabilities that only show up in the Hitchhiker's Guide to the Galaxy... especially since it's a fairly tough job to find just one more such oscillator.

----------------------------------------------

Another way of thinking about it is that symmetry can create small patches of the Life universe where the rules are effectively different. The cells in the gutter of Rich's p16 might as well be running B/S2 instead of B3/S23.

That seems pretty darn exotic! It's kind of similar to the way filling the B3/S23 universe with zebra stripes makes it act like a totally different rule, one that supports lightspeed signals and 2c/3 orthogonal signals and suchlike that are impossible in plain vanilla empty-space Life.

[AforAmpere]

Is a 2c/3 diagonal, or any speed between c/2 and c diagonal possible in a non-isotropic MAP rule? C and c/2 diagonal are possible, but I can't think of a way to implement, say a 3c/4 diagonal.

[praosylen]

I can't think of a way to implement, say a 3c/4 diagonal.

There's one in a B0 outer-totalistic rule, but I can't find it for some reason.

[AforAmpere]

I mean non-B0, but I know what you are talking about:

Code: Select all

x = 3, y = 6, rule = B023457/S023456
b2o$o$obo$b2o$b2o$b2o!

[drc]

Has a mango ever been used in a conduit?

[dvgrn]

Has a mango ever been used in a conduit?

Pretty sure not. They're a horrible combination of unnecessarily big. painfully fragile, and relatively rare.

We definitely know how to turn one into a traffic light, though, while using up any spare gliders that happen to be flying past.

If we hunted long enough, we could find a place where a mango could suppress births next to a length-5 or length-6 line... but then we'd just replace it with a tub or a block or beehive. Unless we had to suppress another similar-length line on the other side, at a one-cell offset, at exactly the right distance -- then a mango might be the only thing that works.

Maybe we should make a conduit with a (painfully slow to recover) transparent mango in it, just so that future Google searches for "transparent mango" will return more variety than just endless clip-art images of fruit.

[gameoflifemaniac]

Is there a formula for how many n-bit still lives exist in Conway's Game of Life? Or just give me the first 20 values.

[Apple Bottom]

Is there a formula for how many n-bit still lives exist in Conway's Game of Life? Or just give me the first 20 values.

There's no known formula -- and an exact formula and a proof of its correctness would be very big news I'm sure --, but all the values known(*) are listed on the LifeWiki, and in sequence A019473 in Sloane's OEIS.

If you only want a very rough approximation, the number increases by a factor of about 2.48 for each bit added. If you wanted to you could do an explicit fit to arrive at an approximate formula, too.

(*) "Known" currently means "up to 32 bits". Last thing I heard Nathaniel was working on enumerating the 33-bitters, but he remarked he wasn't yet sure he'd finish that.

[drc]

Related: Is it posssible for a still life count of a higher number to be less than a lower number in life? (excluding 4-5)

[Apple Bottom]

Related: Is it posssible for a still life count of a higher number to be less than a lower number in life? (excluding 4-5)

Yes, there's fewer 7-bit still lifes (four) than 6-bit still lifes (five).

If you only consider still lifes 7 bits and up, though, I'm sure the answer is "no", but I don't know if there's a proof. Perhaps it could be done by describing a method of extending n-bit still lifes to (n+1)-bit still lifes so that no two n-bit still lifes are extended to the same (n+1)-bit still life (an injective function, in other words). Further showing that there is an (n+1)-bit still life not thus constructed would make the inequality strict.

It might be worth checking the relevant literature, though, there's bound to be results. (And if you find any... post about 'em so we can update the LifeWiki accordingly.)

[Apple Bottom]

(Apologies for double-posting.)

Does the following count as a basic question? I'm not sure, but since this thread is the closest we seem to have to a reference desk, I figure I might as well ask here.

Over in the thread for accidental discoveries, gmc_nxtman wrote:

[...]

EDIT: This also gives 21.41458 in 9 gliders.

21.41458 is obviously the identifier of a still life in Mark Niemiec's database. In this particular case, 21.41458 is actually shown as one of the 47 chosen 21-bitters on Mark's site, but in general, no complete, exhaustive lists of still lifes are provided by Mark for populations 19 and up. In particular, it's not generally possible to know what still life any given number refers to.

So, my question is: is this really true? ARE these files not available anywhere? Or have I just not found them?

(Mind, it's not just about getting full lists of still lifes. Simon Ekström's still life enumerator handily takes care of that; I'm more interested in knowing which still life has which number in Mark's DB.)

[muzik]

Is it possible for a pattern to not be constructible via gliders, aside from GoEs, grandfather problem variants, and unique father problem variants?

[dvgrn]

Is it possible for a pattern to not be constructible via gliders, aside from GoEs, grandfather problem variants, and unique father problem variants?

Nobody knows for sure, and it's going to be really hard to prove anything one way or another. There was some discussion back in May of the possibility of non-synthesizable still lifes. But even if we come up with a candidate counterexample, it's going to be nearly impossible to come up with an airtight proof that a method will never be found to construct it with gliders.

Specifically, just for example, nobody currently has the tools that would be needed to collide gliders to incrementally construct this horrible sample thing I made. That's the pattern that the other link above is talking about -- it was made with the idea of being hard to deconstruct rather than hard to construct, but there tends to be a lot of overlap.

However, when you hunt for predecessors, that pattern isn't immediately a GoE, and there's no particular reason to suspect that it's a great^N-grandfatherless pattern either.

If it's not great^N-grandfatherless, then it has an unlimited number of predecessors, as far back in time as you want to go. The obvious way to make that happen is to rewind the pattern back to a standard glider recipe... somehow. But there are other possibilities. There might be a Ring of Chaos that converges to produce that object -- a big hollow square, let's say, that always has a bigger hollow square as a predecessor, but never has a predecessor that's all gliders.

I don't think that non-glider-constructible non-great^N-grandfatherless Rings of Chaos are very likely to exist, but how would one go about proving that they absolutely don't exist?

An even more difficult case would be greyship-constructible objects (TM). Out of all the possible weird greyships out there, what if there's a case where a head-on collision between two of them would leave a large stabilized agar of some kind? Maybe these things could be quasi-greyships that stabilize a periodic agar, and when the collision happens the escorting edges settle into a permanent support structure.

(This is terribly unlikely, of course, but maybe not as unlikely as it seems for higher-period agars. If you imagine that a universal-constructor-based greyship exists, then the crash might just disable the constructors, leaving the supported agar in place indefinitely.)

If the individual greyships in the collision can't be constructed by gliders, and the resulting hypothetical agar is also construction-proof, then this is a greyship-constructible object is not a glider-constructible object. Here again, if we were trying to prove that no such object exists, or conversely if we were trying to build an example, where could we even start?

Maybe some greyship could be a solution to the unique-father problem somehow -- set it up so that any predecessor is provably great^N-grandfatherless, unless it contains the entire functional greyship? Seems like a tall order, but intuition is a lousy guide for a lot of these problems.

That seems like it might be the only possible angle of attack for proving that some theoretical greyship is really not glider-constructible. Otherwise, if it really is not glider-constructible, it's going to be tricky to complete the proof without doing an infinitely long backtracking search...!

[AforAmpere]

Is it possible for there to be a p6 ship in a B0 rule that looks like it is p3, if strobing is not shown, similar to how this looks p1?

Code: Select all

x = 2, y = 4, rule = B01367/S0124
o$bo$bo$o!

[muzik]

Is it possible for there to be a p6 ship in a B0 rule that looks like it is p3, if strobing is not shown, similar to how this looks p1?

Code: Select all

x = 2, y = 4, rule = B01367/S0124
o$bo$bo$o!

This I doubt, since the fact that the ship only moves once every two generations is due to the fact that every single cell turns on once every two generations.

I do think that something like this could be extended to make a p4 ship appear as p2, though.

[calcyman]

Is it possible for there to be a p6 ship in a B0 rule that looks like it is p3, if strobing is not shown, similar to how this looks p1?

Of course:

Code: Select all

x = 5, y = 5, rule = B01245/S0125
b3o$ob3o$2o$2o$bo!

In general, for odd k, choose a period-k ship in a rule with black/white reversal (Day and Night in this case) and negate every transition in the rule; the result is a period-2k ship.

[AforAmpere]

Interesting, I never realized that, thanks. Was this discovered by experimentation, or just an analysis of B0 rules?

[gameoflifemaniac]

Related: how many two-state black-white reversal rules are there (rules like Day & Night)?

[Saka]

What's the steepest known knightship in any 2 state rule?

[AforAmpere]

What's the steepest known knightship in any 2 state rule?

This is the steepest I know of, a (23,1)c/157:

Code: Select all

x = 33, y = 18, rule = B3-r/S2aei3aeijr4eijrtyz5-ejkq6c7e
2ob2o$bobo$bobo$2ob2o$bobo$bobo$2ob2o8$20bo9bo$19b3o7b3o$18b4o7b4o$19b
2o9b2o!

[Apple Bottom]

Related: how many two-state black-white reversal rules are there (rules like Day & Night)?

Rules that are their own black/white reversal? According to the wiki, 512.