For general discussion about Conway's Game of Life.
shouldsee
Posts: 406
Joined: April 8th, 2016, 8:29 am

### 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

dvgrn
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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].

calcyman
Posts: 2350
Joined: June 1st, 2009, 4:32 pm

### 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...

Code: Select all

1515 From: Richard Schroeppel <rcs@c...>
Date: Tue Aug 7, 2001 2:04pm
Subject: Coolout Conjecture counterexample

An outstanding question is the "Coolout Conjecture":

Given a partial Life pattern that's internally consistent
with being part of a still life (stable pattern), is there always
a way to add a stabilizing boundary? Is there an upper bound
to the required boundary size, perhaps 3 cells thick?
[Variations for stabilizing/completing partial oscillators are
also proposed.]

Counterexample:

xx..xx
x.xx.x

The pattern is internally self-consistent with stability:
Each cell has a number of live neighbors that, with possible
boundary help, makes it stable.

But there's no way to stabilize the top edge:
To preserve the xs adjacent to the corner cells, the row
above the top edge must have six consecutive OFF cells.
But this prevents stabilizing the two OFF cells in the
middle of the top edge, each of which needs one or more
ON neighbors in the stabilizing row.

This example shows that internal consistency is not enough
for stabilizability; some additional hypothesis is required.
The obvious extra hypothesis to try is "1-cell boundary
consistency": that the pattern have at least one possible
1-cell thick extension that's consistent with stability.

There probably also need to be some topological restrictions
on the pattern: connected, or perhaps some kind of convexity.

Rich
What do you do with ill crystallographers? Take them to the mono-clinic!

Scorbie
Posts: 1537
Joined: December 7th, 2013, 1:05 am

### 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

shouldsee
Posts: 406
Joined: April 8th, 2016, 8:29 am

### 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
lifespans2.png (115.86 KiB) Viewed 14356 times

NotLiving
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Joined: May 3rd, 2016, 3:47 pm

### Re: Thread for basic questions

Thanks for the responses!

Food for thought.

muzik
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Location: Scotland

### 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!

Sphenocorona
Posts: 510
Joined: April 9th, 2013, 11:03 pm

### 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.

muzik
Posts: 3943
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Thread for basic questions

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

Code: Select all

x = 14, y = 13, rule = LifeHistory
10.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:

Code: Select all

x = 5, y = 12, rule = LifeHistory
2A.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!

AbhpzTa
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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 :

Code: Select all

x = 384, y = 81, rule = LifeHistory
49D15.49D15.33D15.33D47.3D3C2D8B2DCDC3D16.3DCDC2D3B3C2B8D16.8D2BCBC3B
16.3BCBC2B3D3C2D\$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.D47.5DCDCBC4BCB3DC3DC16.8D3B3C2BD
C3DC2D16.2DC3DCD2BC4BC16.5B3C8D\$D5.5D11.D3.D12.D.D6.D15.D7.D13.5D11.D
3.D5.D15.D5.D3.D12.D.D6.D15.D7.D13.5D5.D47.C5D2CB2C2B2CB4DCDCD16.C6DC
3BC4BD2C5D16.5DCDC6BCB16.C6BC2D2C3DC\$D5.5D11.D3.D13.D7.D15.D5.5D11.5D
11.D3.D5.D15.D5.D3.D13.D7.D15.D5.5D11.5D5.D47.DC6D8B5D2CD16.C5DCDC7B
7DC16.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.DCD
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15.D3.D2.3D17.3D2.D15.D2.3D2.D14.3D2.D3.D47.4D2C2D3BC4B4DCDCD16.2D2C
4D5BCBC8D16.2D2C4D2BCBC3B16.8B5D2CD\$D.D3.D35.5D.D15.D.5D35.D3.D.D15.D
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D.D15.D3.D21.5D.D15.D.5D21.D3.D47.5BCB2C3DC3D32.8DCBC5B16.3B2C3B32.8B
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20.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.D
7.D13.5D11.D3.D5.D15.D5.D3.D12.D.D6.D15.D7.D13.5D5.D\$D5.5D11.D3.D13.D
7.D15.D5.5D11.5D11.D3.D5.D15.D5.D3.D13.D7.D15.D5.5D11.5D5.D\$D5.5D11.D
3.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.D
15.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).

NotLiving
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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:T0,5
o2bo\$o2bo\$b2o\$b2o!
May be easier to see when repeated:

Code: Select all

x = 4, y = 25, rule = B3/S23:T0,25
o2bo\$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!

codeholic
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### Re: Thread for basic questions

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

NotLiving
Posts: 19
Joined: May 3rd, 2016, 3:47 pm

### Re: Thread for basic questions

Ah ok.

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

muzik
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Location: Scotland

### 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?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

dvgrn
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Contact:

### 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?

rowett
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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!

muzik
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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!

Scorbie
Posts: 1537
Joined: December 7th, 2013, 1:05 am

### 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

muzik
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Location: Scotland

### 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!

drc
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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
\100\97\110\105

dvgrn
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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.

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### Re: Thread for basic questions

Are there any infinite waves with c/2 < (speed) < c?
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### Re: Thread for basic questions

Are there any guns that fire multiple types of spaceships?
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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.
What do you do with ill crystallographers? Take them to the mono-clinic!