exist glider gun able of reconstruction in Life?
Genaro Juarez Martinez
I need the aid in Life.
Exist a collision where a glider gun takes a hit of a glider and is not
destroyed?, i.e., Is able to reconstruct the affected part and continue
being the same?.
Thanks.
-genaro
--
Posted via Mailgate.ORG Server - http://www.Mailgate.ORG
Markus Redeker
>Exist a collision where a glider gun takes a hit of a glider and is not
>destroyed?, i.e., Is able to reconstruct the affected part and continue
>being the same?.
That depends on how you define your glider gun. If you take any glider gun,
place an eater near it and declare _that_ the new glider gun, you can hit it
(i.e., the eater) with a glider and the whole thing recovers prefectly...
--
Markus Redeker Hamburg, Germany
Paul Chapman
To amplify: although self-repairing or self-defending patterns have been
discussed for many years, very little research has been done to my
knowledge.
It might well be possible to surround an object wth a "fence" of some kind,
made up of still lifes, and have "guards" which patrol the fence and repair
it when necessary. At best, a working pattern of this kind would only be
able to withstand repeated attacks provided they were infrequent enough to
allow repairs.
A glider gun would be a particularly difficult object to defend, since there
has to be a "gap" in the fence to allow gliders out. An attack through that
gap would at the very least stop the gun firing for a while during repairs.
It's an intersting line of research, but I don't see anyone stepping up to
the challenge just at the moment. :)
Cheers, Paul
Ilmari Karonen
>
> It might well be possible to surround an object wth a "fence" of some kind,
> made up of still lifes, and have "guards" which patrol the fence and repair
> it when necessary. At best, a working pattern of this kind would only be
> able to withstand repeated attacks provided they were infrequent enough to
> allow repairs.
This line of thought suggests another possibly interesting question:
are there any known patterns that are fully "glider-proof", in the
sense that they can withstand a collision with a single glider from
any direction and in any phase? (No, the trivial pattern of 0 live
cells does not count.)
I don't really care if the glider is eaten, passed through, reflected
or converted into something else, as long as said something else
escapes to infinity or otherwise has no effect on the glider-proofness
of the resulting pattern.
This is essentially a weaker version of "indestructibility" -- that
is, a finite pattern having the property that, once created, it cannot
be destroyed by any interaction with surrounding cells. There are
known CA's with indestructible patterns, but I'd be surprised if Life
had any. However, the weaker condition of "glider-proofness" doesn't
intuitively seem quite as impossible to me.
Note that requiring the pattern to withstand multiple simultaneous
glider impacts would probably require full indestructibility, since it
would effectively allow us to bombard the pattern with just about any
object that has a glider synthesis.
--
Ilmari Karonen
To reply by e-mail, please replace ".invalid" with ".net" in address.
Paul Chapman
> > It might well be possible to surround an object wth a "fence" of some
kind,
> > made up of still lifes, and have "guards" which patrol the fence and
repair
> > it when necessary. At best, a working pattern of this kind would only
be
> > able to withstand repeated attacks provided they were infrequent enough
to
> > allow repairs.
>
> This line of thought suggests another possibly interesting question:
> are there any known patterns that are fully "glider-proof", in the
> sense that they can withstand a collision with a single glider from
> any direction and in any phase? (No, the trivial pattern of 0 live
> cells does not count.)
In the large, the two things are equivalent: a fence-plus-patrol pattern
*would* be such a pattern. But I suspect you are asking if there any
"small" patterns which have this property. Again, none are known. One
might imagine a pattern which throws off large sparks (which may contain
gliders), such that those sparks always destroy incoming gliders without
mutating into patterns which destroy the core. It's a very interesting line
of research, but I haven't personally given any more than idle speculation
to it.
Cheers, Paul
Tim Tyler
> Paul Chapman <pa...@igblan.free-online.co.uk> kirjoitti 22.02.2005:
> This line of thought suggests another possibly interesting question:
> are there any known patterns that are fully "glider-proof", in the
> sense that they can withstand a collision with a single glider from
> any direction and in any phase? (No, the trivial pattern of 0 live
> cells does not count.)
>
> I don't really care if the glider is eaten, passed through, reflected
> or converted into something else, as long as said something else
> escapes to infinity or otherwise has no effect on the glider-proofness
> of the resulting pattern.
>
> This is essentially a weaker version of "indestructibility" -- that
> is, a finite pattern having the property that, once created, it cannot
> be destroyed by any interaction with surrounding cells. There are
> known CA's with indestructible patterns, but I'd be surprised if Life
> had any. However, the weaker condition of "glider-proofness" doesn't
> intuitively seem quite as impossible to me.
I think a sparse block minefield can protect any life structure from a
single glider.
IIRC, all possible colisions with a block die down in about a 50x50
square.
So - space the mines out by that much - and with enough of them, no
single glider will ever penetrate.
--
__________
|im |yler http://timtyler.org/ t...@tt1lock.org Remove lock to reply.
dv...@juno.com
by an incoming glider on any one of six adjacent paths, and none of the
possible collisions include any output gliders, so you can't get chain
reactions.
However, I think the intent of the original question was that a
"glider-proof" pattern has to be able to absorb any single glider
_without being permanently altered in any way_. Otherwise a pattern
consisting of nothing *but* a few widely spaced blocks might be said to
"withstand" a single glider.
So if a block gets destroyed, we have to put it back again -- which
means we have to test to see if it's there, and then rebuild it if it's
not (unless the rebuilding process is part of the test.)
It's actually pretty easy to find reactions like this -- I've run into
several of them while looking for something else.... The most common
kind seems to be an active pattern that throws out a spark near where
it's just about to build a block; the spark deletes the block if it's
there, and then the rest of the active pattern immediately rebuilds it
in the same place.
But combining the six annihilation paths with a test-and-rebuild
reaction fails to produce a viable defense mechanism because
1) gliders on paths *adjacent* to the six annihilating paths produce a
pi-heptomino and consequent large explosion -- and there's no way to
place blocks on nearby lanes to catch those gliders, because they'd
interact messily with gliders on some of the original six glider paths;
2) of course, there's no telling what will happen if a second glider
comes in while damage from glider #1 is being repaired -- or even if
glider #1 comes in and hits a block while that block's existence is
being tested by the maintenance system... It would be hard to avoid at
least a few generations' worth of vulnerability during the testing
process.
And once you get any kind of random explosion, of course, all bets are
off. It's hard for me to imagine a pattern that could "feel around"
for random junk and reliably clean it up without some likelihood of
causing a new (and much bigger) mess.
Keep the cheer,
Dave Greene
Dave Greene
> This line of thought suggests another possibly interesting
> question: are there any known patterns that are fully
> "glider-proof", in the sense that they can withstand a
> collision with a single glider from any direction and in
> any phase?
Among existing eater patterns in B3/S23 Life, I think the
successful-defense record is still held by the eater2, which can absorb
any number of gliders on any of four adjacent paths and emerge
undamaged:
#Life 1.05
..*
*.*
.**
......*
....*.*
.....**
..........*
........*.*
.........**
..............*
............*.*
.............**
.
...............**.*
...............**.***
.....................*
...............**.***
................*.*
................*.*
.................*
-- For many stable patterns, by the way, there are other input glider
lanes where the gliders are caught and turned into boats, which are
then cleanly deleted by another glider coming in on the same lane. I'm
not sure how to count those, though; if another glider then comes in on
a different "glider-proof" lane, a boat would sometimes get in the way
and cause an explosion.
So I suppose that's a different metric: any object will have a
glider-pair-invulnerability percentage (!) higher or equal to the
single-glider-invulnerability percentage. (Percentages could be
calculated from the number of input glider lanes that allow a complete
recovery, divided by the total number of input lanes that affect the
object in any way.)
There's a double-sided version of the eater2 which I thought at first
would have the highest known glider-invulnerability. By the above
metric, if my quick counts are right, the double-sided eater2 is
exactly 10% single-glider-proof, and 12.5% glider-pair-proof -- whereas
the single-sided eater2 above is only 6% glider-proof -- 1/17 of the
lanes are safe.
By comparison, a double-ended fishhook eater has a rating of 1/28
(3.6%) and a standard eater is down around 1/52 -- though the
slow-glider-pair-proof ratings go up to 1/14 and 3/52, respectively...
However, it appears that one can string together double-sided eater2
patterns and increase the percentage rating indefinitely: each new
eater2 added to the chain means that 18 more glider lanes will affect
the object, of which 8 lanes are safe. So the glider-proof rating of
these eater2 chains asymptotically approaches 4/9. Here's a 22%
glider-proof eater2 chain, for example:
#Life 1.05
........................**
.........................*
....................**.*
....................**.**
.
....................**.**
...............**.*..*.**
...............**.**
.
...............**.**
................*.**
...........**.*
...........**.**
.
...........**.**
......**.*..*.**
......**.**
.
......**.**
.......*.**
..**.*
..**.**
.
..**.**
*..*.**
**
It takes one or two more eater2s to reach 25% (depending on whether
glider-pair invulnerability is good enough) and further improvement
gets slower and slower.
So it looks like maybe the first challenge would be to find something
that breaks the 50% barrier. There might possibly be some clever way
of getting those absorbing blocks one step closer together, but it
doesn't look too likely to me...
Dave Greene
all this before:
Ilmari Karonen wrote:
>... There are known CA's with indestructible patterns, but I'd be
> surprised if Life had any. However, the weaker condition of
> "glider-proofness" doesn't intuitively seem quite as impossible
> to me.
There's an even weaker form of the question which has the virtue of
having a positive answer: it is technically possible to build an eater
(of sorts) that can safely handle a wider "glider highway" than the
eater2's four adjacent lanes. In fact, it can be shown that any given
width of highway can be made single-glider-proof with a stable pattern
-- or even multiple-glider-proof, as long as there's enough space
between the gliders.
Last March I cobbled together a miscellaneous collection of stable
Herschel conduits into a pattern that I called a "highway robber": it
can absorb a glider coming in on one particular path -- let's call it
"lane 0" -- and recover its initial configuration (very slowly!). It
can also send out one or more output gliders to signal a capture from
the highway. But in this case the important thing is that it allows
gliders on adjacent lanes 1, 2, 3, ... of the highway to pass by
unharmed.
[Conventional small eaters based on boats or tub-with-tails
(tubs-with-tail?) can *almost* manage this last trick --
#C 7x9 boat-based eater
.....*
......*
....***
.
.
**...*
*...*.*
.*...**
..*
*.*****
**....*
...***
**.*
*.*
-- they can absorb a glider on lane 0 and leave lanes 2, 3, 4 ...
unaffected. As it happens, they also usually work on gliders coming in
at 90 degrees from lane 0, that strike the eater at the same point. But
they reliably blow up if a glider comes in on lane 1.]
A row of highway robbers watching adjacent lanes of a glider highway
can absorb any slow glider salvo traveling along that highway. And
setting several highway robbers to watch the same lane could reduce the
minimum time between gliders by quite a bit.
But guarding a wide highway this way is hideously expensive -- the
current highway-robber pattern is close to 400x400, though it could be
made a good bit smaller. And it can only watch for gliders coming from
one direction, of course -- if gliders can travel in both directions on
the highway, you have to double the number of robbers so they can watch
each others' backs.
Basically, every glider lane that you have to guard with this method
just makes a pattern that much bigger and adds more unguarded lanes
somewhere else. Figuring out how to build a complete glider-proof
perimeter is very much an unsolved problem, as Paul said.
-------------------------------
So to return briefly to the original question: my instinct is that a
stable pattern will never be 100% glider-proof -- there are too many
possible lanes of attack -- and that even with an active pattern, it's
going to be very hard to avoid having an Achilles' heel somewhere, at
least during the detect-and-repair process. But it might at least be
possible to design an active defense system with a reasonably high
_probability_ (above 99.99%, let's say) of recovering from a single
random glider impact.
-- Just don't throw any orthogonal spaceships at it, or all bets are
off!
Keep the cheer,
Dave Greene
P.S. My last message was apparently duplicated, though I don't remember
doing anything to send it twice. My apologies, anyway; I'll pay extra
attention this time around...
Paul Chapman
> Basically, every glider lane that you have to guard with this method
> just makes a pattern that much bigger and adds more unguarded lanes
> somewhere else. Figuring out how to build a complete glider-proof
> perimeter is very much an unsolved problem, as Paul said.
I, too, was going to mention the possibility of finding a fence which would
guard a one-way highway of indefinite width. I'd forgotten about highway
robbers.
Another more pleasing approach might be this: one might imagine a shotgun
producing a convoy of giders which can absorb any incoming orthogonal glider
and clean up any debris. The convoy could either be eaten at the other end,
or left to continue to infinity, thus protecting half the plane from
intrusion. Four such shotguns arranged back-to-back-to-back-to-back could
thus protect an indefinitely large proportion of the plane from attack from
two antiparallel directions.
Something for the to-do list.
Cheers, Paul
gena...@correo.unam.mx
Right, self-repair in glider gun is not known in Life and too in Rule
110 (making an exhaustive search by binary collisions).
I do not know other CA's with that characteristic, as Ilmari says::
"there are known CA's with indestructible patterns." Includes glider
gun?.
Nevertheless, in Rule 54 if it exist a binary collision where glider
gun is self-repair. Receiving a hit against a w-> or w<- glider.
http://microcomputadoras.buap.mx/~automatas/imagenes/regla110/gliderGunSelfRepairR54.gif
w glider must approach gradually in each collision, and in two cases
glider gun is only able to self-repair. Because the w glider crosses
glider gun as soliton and both structures continue undergoing only a
displacement in their trajectory.
Eight collisions exist between a w-> glider vs glider gun, and in two
different cases glider gun is only able to self-repair
Another question, glider gun the Life can arise through a periodic
region or like product of a chaotic decomposition?, i.e.,
spontaneously.
In Rule 110 exist some initial conditions (very rare) that they produce
a glider gun from chaotic regions, but nonperiodic or another type of
ether. Several of very short history.
Then Rule 54 we can produce his glider gun from periodic regions, i.e,
from another type of ether.
http://microcomputadoras.buap.mx/~automatas/imagenes/regla110/gliderGunArisingR54.gif
A construction that helps to maintain the existence of a glider gun
with other objects, as Dave says, makes reflect on a construction who
must be very complicated, a complete black hole.
Exiten black holes in Rule 110 and Rule 54, but they single absorb a
type of glider, in Life can be a eater.
Nevertheless, we can think about constructing a mechanism made up of
several objects Life and then can absorb everything!, i.e., a complete
black hole.
Absorbing all type of gliders or another construction. In Rule 110 and
Rule 54 it must be very complicated and I do not see so far as it can
be constructed. But about Life, seeing the constructions of Dave, I
think that the possibility exists of constructing it.
-genaro
Paul Chapman
> I do not know other CA's with that characteristic, as Ilmari says::
> "there are known CA's with indestructible patterns." Includes glider
> gun?.
After a little thought, I see that it is straightforward to engineer a CA
with an indestructible glider gun, even a Life glider gun.
Split state-space into two halves: static and dynamic. Static space
completely ignores dynamic space, while dynamic space can be affected by
static space. Furthermore, the cells in static space also completely ignore
neighbour cells: each cell depends only on its own previous state. Thus
static space implements nothing more than some finite number of cyclic
counters.
In our example, let's have dynamic space be a 2-state space with Life's
rules. Let's give static space 31 states, with the following rule table:
Old New
0 0 period-1 cycle
1 2 \
2 3 |
: : } period-30 cycle
29 30 |
30 1 /
One final rule affecting dyanimic space: if the static-space state of a cell
is 30, the next dynamic-space state of the cell will always be 1.
Thus we have a 62-state CA.
Our glider gun is thus the following 3x3 static-space pattern:
0 1 0
0 0 1
1 1 1
with 0s elsewhere. Every 30 generations, this pattern will force the
creation of a glider. It thus emulates the period-30 Gosper gun.
Clearly the gun is indestructible. If any other activity in the Life
state-space occurs in the region of the glider gun, it's actual affect on
Life space might be different. If you want to guarantee that genuine
gliders are always produced, you can extend static space with a further 30
states, giving another P30 cycle. In this case, have state 60 force a 0 in
Life space, and start with a static-space pattern like:
31 31 31 31 31
31 31 1 31 31
31 31 31 1 31
31 1 1 1 31
31 31 31 31 31
with 0s elsewhere. Every 30 generations, this will force this region of
Life space to have:
0 0 0 0 0
0 0 1 0 0
0 0 0 1 0
0 1 1 1 0
0 0 0 0 0
Cheers, Paul
Markus Redeker
>To amplify: although self-repairing or self-defending patterns have been
>discussed for many years, very little research has been done to my
>knowledge.
On the other hand, there _is_ a kind of self-repairing pattern that occurs
naturally: it is the "ether" of rule 110 and other linear automata.
Unfortunately, nobody seems ot understand why the ether arises, so this
doesn't lead to a solution of Genaro's question. But at least it suggests
that these problems should be considered together.
[Does or did someone research on the ether and why it arises? I am very
interested.]
The analogon to the ether in Life is the debris that inevitably occurs when
one starts with a random pattern, consisting mainly of blinkers, blocks,
boats, beehives, and other small objects with a period of at most two. It is
a lot more complicated than the periodic patterns that arise in
one-dimensional CAs, but it shares with them the stability.
So I imagine an almost indestructible glider gun, guarded by carefully
placed debris...
Tony Finch
>
>The analogon to the ether in Life is the debris that inevitably occurs when
>one starts with a random pattern, consisting mainly of blinkers, blocks,
>boats, beehives, and other small objects with a period of at most two.
You occasionally get period 3 patterns in such debris, most commonly the
pulsar. This appears at the end of Gosper's P20 puffer:
http://mathworld.wolfram.com/gifs/puffertr.gif
The p14 Tumbler is also fairly common:
http://home.interserv.com/~mniemiec/p14-16.gif
Tony.
--
f.a.n.finch <d...@dotat.at> http://dotat.at/
WHITBY TO THE WASH: NORTHWEST 4 OR 5. FAIR, ISOLATED SHOWERS. GOOD OR
MODERATE. SLIGHT TO MODERATE.
Ilmari Karonen
>
> I do not know other CA's with that characteristic, as Ilmari says::
> "there are known CA's with indestructible patterns." Includes glider
> gun?.
I was mostly thinking of some cyclic CA rules when I wrote that, but
there are also plenty of trivial examples: for instance, in any rule
where live cells never die, any pattern of live cells is obviously
indestructible.
I don't know of any specific rule that would have an indestructible
glider gun, but I'm sure some do exist. I particular, I've seen rules
with guns that fire rakes in all directions, creating a quadratically
growing glider swarm that is at least pretty hard to penetrate. I'd
be willing to bet that some rules exist where "pretty hard" actually
does mean "impossible".
Finding a rule with such a gun, and proving its indestructibility, is
left as an exercise for the reader.
McIntosh Harold V.
news:mehh0d...@ID-219982.user.uni-berlin.de
> "Paul Chapman" <pa...@igblan.free-online.co.uk> writes:
>
> > To amplify: although self-repairing or self-defending
> > patterns have been discussed for many years, very
> > little research has been done to my knowledge.
Wouldn't these be the limiting configurations, which all
cellular automata possess? However, unless what you're
looking for happens to be one of them, knowing about them
wouldn't seem to be very helpful. Except for knowing that
they are not likely to be the kind of small, local
arrangement that one would be likely to want to defend.
> On the other hand, there _is_ a kind of self-repairing
> pattern that occurs naturally: it is the "ether" of rule
> 110 and other linear automata.
>
> Unfortunately, nobody seems to understand why the ether
> arises, so this doesn't lead to a solution of Genaro's
> question. But at least it suggests that these problems
> should be considered together.
>
> [Does or did someone research on the ether and why it
> arises? I am very interested.]
There are some empirical considerations (otherwise known
as handwaving arguments) that point towards an ether. Or
a vacuum, for that matter. Evolution can be expansive,
contractive, or neutral, respect to the invasion of a
pattern of one type by another. The type of pattern which
could be of interest for this discussion is one of the
shift-periodic lattices (what the Life people have called
agars and their putrefaction)
Rule 110 is left expansive (live cells invade the vacuum
which is otherwise stable), but it also has macrocells
and semipermeable membranes (x1y -> 1 except for 111 -> 0).
Isosceles right triangles are therefore favored. However
the density predicted by mean field theory greatly favors
the T3's, which constitute the ether; they also comprise
one of the regular shiftperiodic lattices. Empirically, of
course, we see that ultimate evolution tends toward this
lattice while admitting certain defects (the gliders).
With this, you can run into a tiling problem; one of many
but slightly more elegant than most. But thinking about
these things involves a lot of work, which may be why
progress has been slow.
- hvm
McIntosh Harold V.
news:422b6d4d$0$87549$ed26...@ptn-nntp-reader01.plus.net
> After a little thought, I see that it is straightforward to engineer a CA
> with an indestructible glider gun, even a Life glider gun.
Actually I had seen something similar to the example which follows
this remark years ago when I was first playing with Life. Given
limited memory it is a temptation to run Life on a small torus. A
variant is to enforce a fixed state on a boundary. Sometimes one
would come across initial configurations which would feature a
steady stream of gliders boiling off from a hot spot on one of the
boundaries.
I never recorded the configuration, but one suspects that given
how quickly one was found, a similar one could be captured. Some
engineering might give a permanent gun, although lying out in the
open, the framework might be susceptible to disruption. Making two
spaces clearly enough solves *that* problem.
- hvm
Markus Redeker
>Markus Redeker <c...@ibp.de> wrote:
>>
>>The analogon to the ether in Life is the debris that inevitably occurs when
>>one starts with a random pattern, consisting mainly of blinkers, blocks,
>>boats, beehives, and other small objects with a period of at most two.
>You occasionally get period 3 patterns in such debris, most commonly the
>pulsar. This appears at the end of Gosper's P20 puffer:
>http://mathworld.wolfram.com/gifs/puffertr.gif
>The p14 Tumbler is also fairly common:
>http://home.interserv.com/~mniemiec/p14-16.gif
I knew of the pulsar but left it out to simplify things (a bit too much).
But the tumbler surprises me. I had hoped for a kind of universal law --
that almost everything you get is either static or has period 2.
I think someone has done statistics of all the stuff that is the result of
random configurations. It must be somewhere on the net but I have lost the
link.
Paul Chapman
> random configurations. It must be somewhere on the net but I have lost the
> link.
Try
http://wwwhomes.uni-bielefeld.de/achim/freq_top_life.html
Cheers, Paul
Markus Redeker
>Try
>http://wwwhomes.uni-bielefeld.de/achim/freq_top_life.html
Thanks. Not what I had in mind, but quite impressive.
Markus Redeker
>"Markus Redeker" <c...@ibp.de> wrote in message
>news:mehh0d...@ID-219982.user.uni-berlin.de
>> [Does or did someone research on the ether and why it arises? I am very
>> interested.]
>There are some empirical considerations (otherwise known as handwaving
>arguments) that point towards an ether. Or a vacuum, for that matter.
The question I am interested in is, more precisely, "Why _this_ ether?"
>Evolution can be expansive, contractive, or neutral, respect to the
>invasion of a pattern of one type by another. The type of pattern which
>could be of interest for this discussion is one of the shift-periodic
>lattices (what the Life people have called agars and their putrefaction)
Ah, the agar. It is mentioned in Martin Gardner's original article but I
haven't seen anything else about it. Are there new results?
>Rule 110 is left expansive (live cells invade the vacuum which is otherwise
>stable), but it also has macrocells and semipermeable membranes (x1y -> 1
>except for 111 -> 0). Isosceles right triangles are therefore favored.
Here the question is why there arises a _periodic_ pattern of triangles.
>However the density predicted by mean field theory greatly favors the T3's,
>which constitute the ether; they also comprise one of the regular
>shiftperiodic lattices.
>Empirically, of course, we see that ultimate evolution tends toward this
>lattice while admitting certain defects (the gliders).
One can see a bit more from the evolution of random configurations. Before a
piece of ether arises, it doesn't a arise directly from the original chaos
but from a periodic pattern of T1 (or gliders of type A). So there seems to
be a two-step mechanism.
McIntosh Harold V.
> "McIntosh Harold V." <mcin...@servidor.unam.mx> writes:
>> [ ... skipping ove3r most of the posting ... ]
> Ah, the agar. It is mentioned in Martin Gardner's original
> article but I haven't seen anything else about it. Are
> there new results?
So far as I know, not too many. The agars are essentially
Hedlund's shift-periodic lattices; even in one dimension
there are huge numbers of them. Actually for each (p,s) a
few only, but p and s can be any integer, and that grows
fast enough. However, if one sifts through de Bruijn
diagrams to get them, the number of de Bruijn diagrams
grows exponentially, even before you get some agars to
play with. But then they can be perturbed in many weays,
so I would say that this has never been investigated
systematically.
For Life, Rule 22 is a one dimensional projection, so it
is possible to look at Rule 22 instead. Two dimensions
tends to be undecidable, but de Bruijn diagrams can be
used to get shift periodicity which is 1) periodic or 2)
quiescent at infinity. Actually a few other joinings are
possible, but in any event, two generations involves 32
million cases, and three generations would be up in the
billions. Doing two generations ten years ago just to
get phoenix or c/2 space ships took weeks, even months.
As for Rule 110, we have examined up to a dozen
generations; to go beyond that requires more computer
capacity than we have been willing or able to invest.
On can look over the results to see how triangles are
involved, but if one believes in mean field theory even
marginally, the only favored densities tend toward the
traditional ether; "triangles" in everything else are
either too big or too small, and hence too sparse or
too dense.
I understand that Matthew Cook investigated some Rule
110 agar decomposition, and thereby found some of his
reaction, but I have only hints and don't think he has
published about that. As for ourselves, something
similar is true; decompositions were studied and gave
some interesting reactions amongst the general chaos.
But we have never attacked the problem systematically,
meaning, to try out all possible inserts within some
range, and examining the results.