For general discussion about Conway's Game of Life.

### Re: Thread for basic questions

I was measuring correlation of lifespan to the size of torus when I discovered this strange distribution.

Why is it discrete rather than smooth?
EDIT: It later came out to be an artifact as I logrithmised the integer type lifespan, leading to a distortion to the original discrete distribution.

And why are there strange overlapping on the right?
Lifespan of 30000 random soup at 35% on 10x10 torus.
lifespan_life.xlsx

By the way, I noticed the log(lifespan) is proportional to the width of a square torus, at least for a small torus. I can't say why it's the case.
lifespan_B1S01D1step, one of my customised generation rule

lifespan_life
shouldsee

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### Re: Thread for basic questions

NotLiving wrote:On a related note: is there an upper bound on the depth required to support an arbitrary row of still-life with only dead cells on the other side...?

Hmm. I thought at first this was the harder question about how many rows it might take to complete a still life, or stator, once you have a complete straight row of p1 cells.* I have a vague recollection of a discussion between people who were actually good at this kind of thing, years ago but I don't remember how many. In practice it seemed as if N rows were always needed, but it seemed possible that some yet-unseen weird configuration might need N+1 or N+2... for N somewhere between 3 and 5, if I recall correctly.

I think the answer is similar for an arbitrary row of still life with only emptiness beyond: seems to be single digits, but I don't know of a formal proof. There might possibly be a general method for constructing support, where it can be done -- in which case somebody has very likely solved the problem already, I just don't remember it or don't know about it. There aren't all that many cases to deal with, unless you allow ON cells in groups longer than two... but then to make it a still life you have to match it by an inductor on the other side, which is not "only dead cells". Are you intending to include length-3 and longer inductors in your question?

NotLiving wrote:...assuming there is a way to support said row...

Even with length-1 and length-2 chains of ON cells being all that is allowed, there are some configurations that can't actually be made stable if you're working from one side -- obobobo! and longer chains of alternating ON and OFF, right? Or am I missing a trick?

*EDIT: Vaguely related but not specifying any particular width: Richard Schroeppel's "Cool Out" Conjecture (from sometime before 1992) --

If a configuration C is locally stable over a rectangle R, then there exists a configuration C* such that (a) C* is locally equal to C over R; and (b) C* is globally stable.

-- which is still a conjecture as far as I know, EDIT but there's a lot I don't know [see next post].

dvgrn
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### Re: Thread for basic questions

dvgrn wrote:*EDIT: Vaguely related but not specifying any particular width: Richard Schroeppel's "Cool Out" Conjecture (from sometime before 1992) --

If a configuration C is locally stable over a rectangle R, then there exists a configuration C* such that (a) C* is locally equal to C over R; and (b) C* is globally stable.

-- which is still a conjecture as far as I know, and still probably true.

It was disproved almost 15 years ago, by RCS himself...

`1515 From: Richard Schroeppel <rcs@c...> Date: Tue Aug 7, 2001 2:04pmSubject: Coolout Conjecture counterexampleAn outstanding question is the "Coolout Conjecture":Given a partial Life pattern that's internally consistentwith being part of a still life (stable pattern), is there alwaysa way to add a stabilizing boundary? Is there an upper boundto the required boundary size, perhaps 3 cells thick?[Variations for stabilizing/completing partial oscillators arealso proposed.]Counterexample:xx..xxx.xx.xThe pattern is internally self-consistent with stability:Each cell has a number of live neighbors that, with possibleboundary help, makes it stable.But there's no way to stabilize the top edge:To preserve the xs adjacent to the corner cells, the rowabove the top edge must have six consecutive OFF cells.But this prevents stabilizing the two OFF cells in themiddle of the top edge, each of which needs one or moreON neighbors in the stabilizing row.This example shows that internal consistency is not enoughfor stabilizability; some additional hypothesis is required.The obvious extra hypothesis to try is "1-cell boundaryconsistency": that the pattern have at least one possible1-cell thick extension that's consistent with stability.There probably also need to be some topological restrictionson the pattern: connected, or perhaps some kind of convexity.Rich`
What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

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### Re: Thread for basic questions

calcyman wrote:It was disproved almost 15 years ago, by RCS himself...
Gosh! I keep learning new things every day!
Best wishes to you, Scorbie

Scorbie

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### Re: Thread for basic questions

Continuing the lifespan topic.
Seemingly "replicator" is the only rule that exhibit a statistical different characteristic in the lifespan-torus size distribution.
Attachments
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shouldsee

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### Re: Thread for basic questions

Thanks for the responses!

Food for thought.
NotLiving

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### Re: Thread for basic questions

What is the highest "dimension" of an infinite growth pattern created?

By this I mean:

guns (SM), puffers (MS), and rakes (MM) are 2d, consisting of two main things,

breeders (MMS, MSM, SMM and MMM in most cases), consisting of 3 main things and are therefore 3D

So, have any 4d (for example, MMMM) "superbreeders" or the like been constructed?

On a similar topic, have MSS or SSS (things that make infinite bricklayers/blockstackers) been created?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Thread for basic questions

muzik wrote:What is the highest "dimension" of an infinite growth pattern created?

There isn't really any limit to this as far as I'm aware, though it must be remembered that the actual long-term population growth rate in an n-dimensional CA cannot exceed nth degree polynomial growth (2nd degree is quadratic, 3rd degree is cubic, etc). But we can still make things that act like what you've described. For example, I found a quadratic-growth MMMM 'super-breeder' in an old rule known as aurora19 a few years back. I'm sure there's some other examples out there.
Sphenocorona

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### Re: Thread for basic questions

The switch engine produces a replica of itself, and keeps doing so, at c/12 orthogonal:

`x = 14, y = 13, rule = LifeHistory10.D\$.D.D5.D.D\$D\$.D2.D4.D2.D\$3.3D5.2D\$12.D4\$9.A.A\$8.A\$9.A2.A\$11.3A!`

Of course, we already know how to stabilise this into a spaceship.

House, similarly, produces a replica of itself:

`x = 5, y = 12, rule = LifeHistory2A.2A\$A3.A\$.3A7\$2D.2D\$D3.D\$.3D!`

however it dies much quicker.

Can this be stabilised into a 9c/30 ship?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Thread for basic questions

NotLiving wrote:What about patterns that are aperiodic, be it in space, time, or both? Does this still hold?

Ammann A2 / Wang 24 :
`x = 384, y = 81, rule = LifeHistory49D15.49D15.33D15.33D47.3D3C2D8B2DCDC3D16.3DCDC2D3B3C2B8D16.8D2BCBC3B16.3BCBC2B3D3C2D\$D47.D15.D47.D15.D31.D15.D31.D47.5DC2D2B4C2B2DC5D16.4DC3D6BCB2D4C2D16.2D4C2DBCBC4B16.4BC3B5DC2D\$D6.3D13.3D22.D15.D7.D14.3D13.3D6.D15.D6.3D22.D15.D7.D14.3D6.D47.5DCDCBC4BCB3DC3DC16.8D3B3C2BDC3DC2D16.2DC3DCD2BC4BC16.5B3C8D\$D5.5D11.D3.D12.D.D6.D15.D7.D13.5D11.D3.D5.D15.D5.D3.D12.D.D6.D15.D7.D13.5D5.D47.C5D2CB2C2B2CB4DCDCD16.C6DC3BC4BD2C5D16.5DCDC6BCB16.C6BC2D2C3DC\$D5.5D11.D3.D13.D7.D15.D5.5D11.5D11.D3.D5.D15.D5.D3.D13.D7.D15.D5.5D11.5D5.D47.DC6D8B5D2CD16.C5DCDC7B7DC16.C5DCD6BCB16.C7B2D2C2DCD\$D5.5D11.D3.D12.D.D6.D15.D7.D13.5D11.D3.D5.D15.D5.D3.D12.D.D6.D15.D7.D13.5D5.D47.C7D8B7DC16.7DC5B2CB7DC16.DCD3C2D3BC3BC16.8B6DCD\$D2.3D.3D13.3D17.3D2.D15.D2.3D2.D14.3D13.3D.3D2.D15.D3.D2.3D17.3D2.D15.D2.3D2.D14.3D2.D3.D47.4D2C2D3BC4B4DCDCD16.2D2C4D5BCBC8D16.2D2C4D2BCBC3B16.8B5D2CD\$D.D3.D35.5D.D15.D.5D35.D3.D.D15.D3.D21.5D.D15.D.5D21.D3.D47.3DC2DCD2BCBC3B4D2C2D16.2DC5D6B2C8D16.8D2BC2BC2B16.3B2C3B8D\$D.D3.D35.5D.D15.D.5D35.D3.D.D15.D.5D19.5D.D15.D.5D19.5D.D47.4BCBCB3DCDC2D32.8D2C6B16.8B32.8B\$D.D3.D35.5D.D15.D.5D35.D3.D.D15.D3.D21.5D.D15.D.5D21.D3.D47.5BCB2C3DC3D32.8DCBC5B16.3B2C3B32.8B\$D2.3D33.3D.3D2.D15.D2.3D.3D33.3D2.D15.D3.D19.D2.3D2.D15.D2.3D22.D3.D47.B2C3BCBDC6D32.3D2C3DB2C5B16.3B2C3B32.5BCBC\$D37.D3.D5.D15.D5.5D37.D15.D23.D7.D15.D6.D.D22.D47.BC5BCDC4D2C32.4DC3D8B16.C7B32.B2C2B2CB\$D37.D3.D5.D15.D5.5D37.D15.D21.5D5.D15.D7.D23.D47.BC6BC5DCD32.CDC5D6B2C16.C5B2C32.2BC5B\$D37.D3.D5.D15.D5.5D37.D15.D23.D7.D15.D6.D.D22.D47.C7B8D32.D3C4D6BCB16.6BCB32.2C3B3C\$D38.3D6.D15.D6.3D38.D15.D23.D7.D15.D31.D47.4B2C2B8D32.4DC3D2B2C4B16.2B2C4B32.4BC3B\$D47.D15.D47.D15.D31.D15.D31.D47.4B2C2B3D2C3D32.3DCDC2D2BC5B16.2BC5B32.4B2C2B\$D31.17D15.17D31.D15.D15.17D15.17D15.D\$D31.D47.D31.D15.D15.D47.D15.D\$D31.D47.D31.D15.D15.D47.D15.D\$D31.D47.D31.D15.D15.D47.D15.D\$D31.D47.D31.D15.D15.D47.D15.D\$D31.D47.D31.D15.D15.D47.D15.D\$D27.D3.D47.D3.D27.D15.D2.3D10.D47.D10.3D2.D\$D2.D.D22.D3.D47.D3.D22.D.D2.D15.D.5D4.D.D2.D47.D2.D.D4.5D.D\$D3.D21.5D.D47.D.5D21.D3.D15.D.5D5.D3.D47.D3.D5.5D.D\$D2.D.D22.D3.D47.D3.D22.D.D2.D15.D.5D4.D.D2.D47.D2.D.D4.5D.D\$D6.3D18.D3.D47.D3.D3.D14.3D6.D15.D2.3D.3D6.D47.D6.3D.3D2.D\$D5.D3.D12.D.D6.D47.D7.D13.5D5.D15.D5.5D5.D47.D5.D3.D5.D\$D5.D3.D13.D7.D47.D5.5D11.5D5.D15.D5.5D5.D47.D5.D3.D5.D\$D5.D3.D12.D.D6.D47.D7.D13.5D5.D15.D5.5D5.D47.D5.D3.D5.D\$D6.3D22.D47.D7.D14.3D6.D15.D6.3D6.D47.D6.3D6.D\$D31.D47.D31.D15.D15.D47.D15.D\$33D47.33D15.17D47.17D47.8B2DCDC3D32.3DCDC2D3BC4B16.3B3C2B32.8B\$256.8B2D2C4D32.4DC3D2B2C4B16.5BC2B32.2B4C2B\$256.8B8D32.8D8B16.8B32.2BC2BC2B\$256.3B2C3B8D32.7D2C6BC16.2CBC3BC32.8B\$256.C2BC4B2D2C2D2C32.DC5DCBC4BCB16.2B2C2BCB32.C6BC\$256.BCBC4B3DC2DCD32.2C6DCBC3BCB16.C5BCB32.BCBC3BC\$256.2BC5B2DC5D32.8DB2C2B2CB16.5B2CB32.2B2C4B\$256.5B2CB2D2C4D32.6DCD8B16.8B32.8B\$256.4DC2DC3BC4B8D16.3D3C2D5BCBC8D16.8D3BCBC2B16.2BCBC3B8D\$256.4DC2DC3BCBC2B2D4C2D16.6DCD4BCBCB8D16.8D4BC3B16.2BC5B8D\$256.5D2CD4B2C2B2DC2DC2D16.2DCDCDCD3BCBC2B3DC3DC16.2DC5D8B16.3BC4B8D\$256.C7D8B3D2C3D16.3CD2C2D4BC3B2DCDCDCD16.DCDC4DB2C5B16.3C5BD2C5D\$256.C7D8B7DC16.8D8B3D2CDCD16.2DC2D2CDB2C4BC16.8BDC4D2C\$256.5DC2D4B2C2B7DC16.C7D8B5DCDC16.2C4DCD7BC16.C7B3DC2DCD\$256.3D3C2D3BC2BCB8D16.3D2C3D2B2C4B5DC2D16.4DC3D8B16.8B2D2C4D\$256.2DC5D4B2C2B3D2C3D16.2DC2DC2D2BC5B4D2C2D16.4D2C2D3B2C3B16.4B2C2B2DC5D\$33D47.33D15.17D47.17D\$D31.D47.D31.D15.D15.D47.D15.D\$D6.3D22.D47.D7.D14.3D6.D15.D6.3D6.D47.D6.3D6.D\$D5.D3.D12.D.D6.D47.D7.D13.5D5.D15.D5.5D5.D47.D5.D3.D5.D\$D5.D3.D13.D7.D47.D5.5D11.5D5.D15.D5.5D5.D47.D5.D3.D5.D\$D5.D3.D12.D.D6.D47.D7.D13.5D5.D15.D5.5D5.D47.D5.D3.D5.D\$D3.D2.3D22.D47.D7.D14.3D2.D3.D15.D2.3D.3D2.D3.D47.D3.D2.3D.3D2.D\$D3.D22.D.D2.D47.D2.D.D22.D3.D15.D.D3.D5.D3.D47.D3.D5.D3.D.D\$D.5D21.D3.D47.D3.D21.5D.D15.D.D3.D3.5D.D47.D.5D3.D3.D.D\$D3.D22.D.D2.D47.D2.D.D22.D3.D15.D.D3.D5.D3.D47.D3.D5.D3.D.D\$D3.D27.D47.D27.D3.D15.D2.3D6.D3.D47.D3.D6.3D2.D\$D31.D47.D31.D15.D15.D47.D15.D\$D31.D47.D31.D15.D15.D47.D15.D\$D31.D47.D31.D15.D15.D47.D15.D\$D31.D47.D31.D15.D15.D47.D15.D\$D31.D47.D31.D15.D15.D47.D15.D\$D31.17D15.17D31.D15.D15.17D15.17D15.D\$D47.D15.D47.D15.D31.D15.D31.D\$D38.3D6.D15.D6.3D38.D15.D23.D7.D15.D31.D\$D37.D3.D5.D15.D5.5D37.D15.D23.D7.D15.D6.D.D22.D\$D37.D3.D5.D15.D5.5D37.D15.D21.5D5.D15.D7.D23.D\$D37.D3.D5.D15.D5.5D37.D15.D23.D7.D15.D6.D.D22.D\$D2.3D33.3D.3D2.D15.D2.3D.3D33.3D2.D15.D23.D2.3D2.D15.D2.3D26.D\$D.5D35.D3.D.D15.D.D3.D35.5D.D15.D2.D.D20.D3.D.D15.D.D3.D20.D.D2.D\$D.5D35.D3.D.D15.D.D3.D35.5D.D15.D3.D21.D3.D.D15.D.D3.D21.D3.D\$D.5D35.D3.D.D15.D.D3.D35.5D.D15.D2.D.D20.D3.D.D15.D.D3.D20.D.D2.D\$D2.3D.3D13.3D17.3D2.D15.D2.3D2.D14.3D13.3D.3D2.D15.D6.3D17.3D2.D15.D2.3D2.D14.3D6.D\$D5.5D11.D3.D12.D.D6.D15.D7.D13.5D11.D3.D5.D15.D5.D3.D12.D.D6.D15.D7.D13.5D5.D\$D5.5D11.D3.D13.D7.D15.D5.5D11.5D11.D3.D5.D15.D5.D3.D13.D7.D15.D5.5D11.5D5.D\$D5.5D11.D3.D12.D.D6.D15.D7.D13.5D11.D3.D5.D15.D5.D3.D12.D.D6.D15.D7.D13.5D5.D\$D6.3D13.3D22.D15.D7.D14.3D13.3D6.D15.D6.3D22.D15.D7.D14.3D6.D\$D47.D15.D47.D15.D31.D15.D31.D\$49D15.49D15.33D15.33D!`
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
AbhpzTa

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### Re: Thread for basic questions

Is there a name for patterns that would be spaceships, but require an infinite linear chain (not 2d tiling) of repeats to work?

Think of it as a subclass of a linear agar, or a generalization of a wick to allow non-stilllife.

For instance:

Code: Select all
`x = 4, y = 5, rule = B3/S23:T0,5o2bo\$o2bo\$b2o\$b2o!`

May be easier to see when repeated:

Code: Select all
`x = 4, y = 25, rule = B3/S23:T0,25o2bo\$o2bo\$b2o\$b2o2\$o2bo\$o2bo\$b2o\$b2o2\$o2bo\$o2bo\$b2o\$b2o2\$o2bo\$o2bo\$b2o\$b2o2\$o2bo\$o2bo\$b2o\$b2o!`

(Also: why does the viewer miss a row of cells?)

Also, neat tiling!
NotLiving

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### Re: Thread for basic questions

It is still called a wick. In particular, this one is called ants.
Ivan Fomichev

codeholic
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### Re: Thread for basic questions

Ah ok.

Is there a specific name for non-stilllife wicks, then?
NotLiving

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### Re: Thread for basic questions

Are there patterns that are simply guns "by definition" and require no stabilisation components?

The Gosper glider gun consists of two queen bees and two blocks, and therefore is a "composite" gun. The Simkin gun similarly consists of blocks to stabilise it, etc. Whereas the b38/s23 gun I posted here earlier is just a pattern of its own with no stabilisation agents.

Could guns like that exist within normal life?
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muzik

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### Re: Thread for basic questions

muzik wrote:Are there patterns that are simply guns "by definition" and require no stabilisation components?

Could certainly happen. We've only searched 0% of the total space of B3/S23 pattern possibilities so far, even with Catagolue -- so how could we possibly know that something like that isn't out there?

I suspect there's probably a p14 pattern out there somewhere that's all one piece, looks like a supervolcano or a pipsquirter except probably bigger, but it spits out gliders instead of sparks. It's going to be mighty hard to find, is all.

What do you think of the period-156 multi-barrel gun? That's kind of made out of four identical pieces, but it could also be considered one piece. Would it count, if it wasn't for the four stabilizing blocks at the corners?

dvgrn
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### Re: Thread for basic questions

NotLiving wrote:(Also: why does the viewer miss a row of cells?)

This is a bug which will be fixed in the next released build of LifeViewer. Thanks for spotting it!

rowett
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### Re: Thread for basic questions

dvgrn wrote:What do you think of the period-156 multi-barrel gun? That's kind of made out of four identical pieces, but it could also be considered one piece. Would it count, if it wasn't for the four stabilizing blocks at the corners?

Probably not. Those four blocks are pretty much required.

Now perhaps, if we were able to link many of these guns onto each other in a way that would make them not require those blocks...
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Thread for basic questions

muzik wrote:Probably not. Those four blocks are pretty much required.
The point of dvgrn's question was not to explicitly build one, but just checking what we are looking for precisely. To put dvgrn's question in another way:

Let us say that we found something similar to the p156 double barrelled gun, but with no external support. The gun has 4 identical units that mutually support each other. Would that count?

Best wishes to you, Scorbie

Scorbie

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### Re: Thread for basic questions

Scorbie wrote:
muzik wrote:Probably not. Those four blocks are pretty much required.
The point of dvgrn's question was not to explicitly build one, but just checking what we are looking for precisely. To put dvgrn's question in another way:

Let us say that we found something similar to the p156 double barrelled gun, but with no external support. The gun has 4 identical units that mutually support each other. Would that count?

Probably.

I was thinking about something else earlier: are there any infinite growth patterns that are a polyplet in at least one phase?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Thread for basic questions

@muzik

Depends on what you mean. In B1/S, a single cell is a p2 c diagonal 2D replicator
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### Re: Thread for basic questions

muzik wrote:I was thinking about something else earlier: are there any infinite growth patterns that are a polyplet in at least one phase?

drc wrote:@muzik

Depends on what you mean. In B1/S, a single cell is a p2 c diagonal 2D replicator

Even if you stick with B3/S23, a switch engine is infinite-growth, and it's a polyplet in quite a few of its phases.

If you meant "polyomino" (rookwise connected cells) instead of "polyplet" (kingwise connected cells), the answer is still "Sure!" -- if I'm understanding the question correctly. Just write a script to enumerate polyominoes, and run them through apgsearch. Sooner rather than later a switch engine will show up in the census. In fact, that was how Charles Corderman found the switch engine, back in 1971 (apparently by enumerating nonominoes, that is, not by using apgsearch).

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### Re: Thread for basic questions

Sphenocorona wrote:But we can still make things that act like what you've described. For example, I found a quadratic-growth MMMM 'super-breeder' in an old rule known as aurora19 a few years back. I'm sure there's some other examples out there.

That is indeed a rake that creates rakes that create rakes.
Well then.
`bobo2b3o2b2o2bo3bobo\$obobobo3bo2bobo3bobo\$obobob2o2bo2bobo3bobo\$o3bobo3bo2bobobobo\$o3bob3o2b2o3bobo2bo!`

SuperSupermario24

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### Re: Thread for basic questions

Are there any infinite waves with c/2 < (speed) < c?
I Like My Heisenburps! (and others)

Extrementhusiast

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### Re: Thread for basic questions

Are there any guns that fire multiple types of spaceships?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: Thread for basic questions

muzik wrote:Are there any guns that fire multiple types of spaceships?

Yes, there are even configurations which fire an infinite sequence of distinct spaceships.
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calcyman

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