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...?
NotLiving wrote:...assuming there is a way to support said row...
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.
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
Gosh! I keep learning new things every day!calcyman wrote:It was disproved almost 15 years ago, by RCS himself...
muzik wrote:What is the highest "dimension" of an infinite growth pattern created?
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$11.3A!
x = 5, y = 12, rule = LifeHistory
2A.2A$A3.A$.3A7$2D.2D$D3.D$.3D!
NotLiving wrote:What about patterns that are aperiodic, be it in space, time, or both? Does this still hold?
x = 384, y = 81, rule = LifeHistory
49D15.49D15.33D15.33D47.3D3C2D8B2DCDC3D16.3DCDC2D3B3C2B8D16.8D2BCBC3B
16.3BCBC2B3D3C2D$D47.D15.D47.D15.D31.D15.D31.D47.5DC2D2B4C2B2DC5D16.
4DC3D6BCB2D4C2D16.2D4C2DBCBC4B16.4BC3B5DC2D$D6.3D13.3D22.D15.D7.D14.
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15.D31.D47.4B2C2B3D2C3D32.3DCDC2D2BC5B16.2BC5B32.4B2C2B$D31.17D15.17D
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8B$256.8B2D2C4D32.4DC3D2B2C4B16.5BC2B32.2B4C2B$256.8B8D32.8D8B16.8B
32.2BC2BC2B$256.3B2C3B8D32.7D2C6BC16.2CBC3BC32.8B$256.C2BC4B2D2C2D2C
32.DC5DCBC4BCB16.2B2C2BCB32.C6BC$256.BCBC4B3DC2DCD32.2C6DCBC3BCB16.C
5BCB32.BCBC3BC$256.2BC5B2DC5D32.8DB2C2B2CB16.5B2CB32.2B2C4B$256.5B2CB
2D2C4D32.6DCD8B16.8B32.8B$256.4DC2DC3BC4B8D16.3D3C2D5BCBC8D16.8D3BCBC
2B16.2BCBC3B8D$256.4DC2DC3BCBC2B2D4C2D16.6DCD4BCBCB8D16.8D4BC3B16.2BC
5B8D$256.5D2CD4B2C2B2DC2DC2D16.2DCDCDCD3BCBC2B3DC3DC16.2DC5D8B16.3BC
4B8D$256.C7D8B3D2C3D16.3CD2C2D4BC3B2DCDCDCD16.DCDC4DB2C5B16.3C5BD2C5D
$256.C7D8B7DC16.8D8B3D2CDCD16.2DC2D2CDB2C4BC16.8BDC4D2C$256.5DC2D4B2C
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2C3D2B2C4B5DC2D16.4DC3D8B16.8B2D2C4D$256.2DC5D4B2C2B3D2C3D16.2DC2DC2D
2BC5B4D2C2D16.4D2C2D3B2C3B16.4B2C2B2DC5D$33D47.33D15.17D47.17D$D31.D
47.D31.D15.D15.D47.D15.D$D6.3D22.D47.D7.D14.3D6.D15.D6.3D6.D47.D6.3D
6.D$D5.D3.D12.D.D6.D47.D7.D13.5D5.D15.D5.5D5.D47.D5.D3.D5.D$D5.D3.D
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20.D3.D.D15.D.D3.D20.D.D2.D$D2.3D.3D13.3D17.3D2.D15.D2.3D2.D14.3D13.
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7.D13.5D11.D3.D5.D15.D5.D3.D12.D.D6.D15.D7.D13.5D5.D$D5.5D11.D3.D13.D
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15.D47.D15.D31.D15.D31.D$49D15.49D15.33D15.33D!
x = 4, y = 5, rule = B3/S23:T0,5
o2bo$o2bo$b2o$b2o!
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$b2o!
muzik wrote:Are there patterns that are simply guns "by definition" and require no stabilisation components?
NotLiving wrote:(Also: why does the viewer miss a row of cells?)
dvgrn wrote:What do you think of the period-156 multi-barrel gun? That's kind of made out of four identical pieces, but it could also be considered one piece. Would it count, if it wasn't for the four stabilizing blocks at the corners?
The point of dvgrn's question was not to explicitly build one, but just checking what we are looking for precisely. To put dvgrn's question in another way:muzik wrote:Probably not. Those four blocks are pretty much required.
Scorbie wrote:The point of dvgrn's question was not to explicitly build one, but just checking what we are looking for precisely. To put dvgrn's question in another way:muzik wrote:Probably not. Those four blocks are pretty much required.
Let us say that we found something similar to the p156 double barrelled gun, but with no external support. The gun has 4 identical units that mutually support each other. Would that count?
And from your reply, I guess the answer is "yes", right?
muzik wrote:I was thinking about something else earlier: are there any infinite growth patterns that are a polyplet in at least one phase?
drc wrote:@muzik
Depends on what you mean. In B1/S, a single cell is a p2 c diagonal 2D replicator
Sphenocorona wrote:But we can still make things that act like what you've described. For example, I found a quadratic-growth MMMM 'super-breeder' in an old rule known as aurora19 a few years back. I'm sure there's some other examples out there.
bobo2b3o2b2o2bo3bobo$obobobo3bo2bobo3bobo$obobob2o2bo2bobo3bobo$o3bobo3bo2bobobobo$o3bob3o2b2o3bobo2bo!
muzik wrote:Are there any guns that fire multiple types of spaceships?
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