Your ultimate question for Game of Life

[Goldtiger997]

Two questions. Since they are related, but can have very different answers, either just one or both questions can be answered.

1. If you went to sleep and woke up in 100 years, and checked the forums, what would be the first question you would ask or the first discovery you would look for?
2. If you had access to a computer with “unlimited” processing power, and you could request exactly one pattern, what pattern would it be?

Here are three rules:

• Everything is in Game of Life only.
• This rule only applies to the second question. A pattern cannot be a single pattern containing many subpatterns. i.e. “All spaceships of the speed (43,71)c/127 in under 10^37 bits” is not allowed, but “The cheapest copperhead synthesis of the spaghetti monster” is.
• This rule also only applies to the second question. No adjustable patterns with "outputs", such that if the outputs were compiled into a collection of subpatterns, the existence of each subpattern absolutely has to be "explained" seperately. A cateloopillar-type pattern is allowed, but a pattern similar to biggiemac's is not (this rule is imprecisely defined)

[praosylen]

1. The highest-period non-c/2 and non-switch-engine-based spaceship on Catagolue (B3/S23 C1).

2. The smallest (2,1)c/6 knightship.

[biggiemac]

1. Oscillators of the missing periods.

2. As a preface, there exists an enumeration of triplets (A,B,D) ordered by A+B+D, ties broken by A then by B, with A/D and B/D rationals in lowest terms in a given bounded subset of Q2. My request from this unlimited computer would be the smallest (lowest population then bounding box) stable constellation that could be hit with gliders on N adjacent lanes, where for lane M the only remaining output was the smallest (A,B)c/D spaceship with (A,B,D) the Mth element of the enumeration above over the set of rationals with A/D nonzero, B/D nonnegative and A/D + B/D at most 1/2, and with N some absurdly large integer.

There would be a lot to watch, syntheses of every record smallest ship, circuitry we didn't know of yet, and who knows what else Even if all it spit out was the pattern file, leaving any simulation of it up to us, the fact that it is a stable constellation makes it tractable to add a glider and simulate it. I think I should also request a glider be present in the pattern on lane 1 of the N, just in case optimal highway robbers aren't as obvious to us as constructed ones!

Made some edits for clarity. With N=1 this is just a tiny G->LWSS one-time-converter. With N=2, there are two adjacent lanes. The first causes an LWSS to be output, the second outputs just the smallest c/3 spaceship, making it a switchable one-time converter. Beyond N=10 there exists a glider input giving the smallest (1,2)c/6 knightship, complete with a synthesis. I argue this isn't a pattern just consisting of a lot of subpatterns because taken as a whole it is an N-way switchable synthesis device. And I want N to be pretty large, but not so large that one couldn't load and simulate the pattern using any algorithm. Anyone else want to try to help me estimate an N such that the pattern file is just barely not beyond hope of simulation?

[Goldtiger997]

2. As a preface, there exists an enumeration of triplets (A,B,D) ordered by A+B+D, ties broken by A then by B, with A/D and B/D rationals in lowest terms in a given bounded subset of Q2. My request from this unlimited computer would be the smallest (lowest population then bounding box) stable constellation that could be hit with gliders on N adjacent lanes, where for lane M the only remaining output was the smallest (A,B)c/D spaceship with (A,B,D) the Mth element of the enumeration above over the set of rationals with A/D nonzero, B/D nonnegative and A/D + B/D at most 1/2, and with N some absurdly large integer.

There would be a lot to watch, syntheses of every record smallest ship, circuitry we didn't know of yet, and who knows what else Even if all it spit out was the pattern file, leaving any simulation of it up to us, the fact that it is a stable constellation makes it tractable to add a glider and simulate it. I think I should also request a glider be present in the pattern on lane 1 of the N, just in case optimal highway robbers aren't as obvious to us as constructed ones!

I see what you did there. Such a pattern would be awesome, but I feel that it is kind of cheating. I'll add another rule to prevent this kind of pattern (EDIT: rule added).

Made some edits for clarity. With N=1 this is just a tiny G->LWSS one-time-converter. With N=2, there are two adjacent lanes. The first causes an LWSS to be output, the second outputs just the smallest c/3 spaceship, making it a switchable one-time converter. Beyond N=10 there exists a glider input giving the smallest (1,2)c/6 knightship, complete with a synthesis. I argue this isn't a pattern just consisting of a lot of subpatterns because taken as a whole it is an N-way switchable synthesis device. And I want N to be pretty large, but not so large that one couldn't load and simulate the pattern using any algorithm. Anyone else want to try to help me estimate an N such that the pattern file is just barely not beyond hope of simulation?

At the moment, N=3 (EDIT: actually N=2 thanks biggiemac) is the maximum because no orthogonal c/4 ships currently have syntheses (this is not quite biggiemac's question). The pattern with even just N=2 would be very interesting to watch or construct!

[biggiemac]

At the moment, N=3 is the maximum because no orthogonal c/4 ships currently have syntheses (this is not quite biggiemac's question). The pattern with even just N=2 would be very interesting to watch or construct!

An attempt at N=2 is the maximum we could construct, since the enumeration goes (1,0,2), (1,0,3), (1,0,4); we would need the c/4 orthogonal before the glider. But I was suggesting estimating an N such that given a pattern with the perfect solution for that N, we mere mortals could even run it.

Also another edit I missed: I said A/D nonzero but I meant A/D positive. If we only get one shot with this magic computer then I better not have an input error! Or as my girlfriend put it when I ran this scenario past her, "with infinite power comes infinite responsibility." Also, she suggested encoding an NP-complete problem into a computer running in CGoL, giving the oracle that pattern and requesting from it the same pattern evolved some sufficient amount of generations that the solution is contained in the output, which I thought was pretty clever. But we agreed that it's hard to know which single instance of an NP-complete problem is relevant for a one-shot deal!

While I'm sanity checking my inputs, I'll change the ordering of the enumeration: order by D first, then A+B, then A. That best corresponds to the way I would list spaceship speeds in CGoL.

I'll add another rule to prevent this kind of pattern.

That's kind of a tricky rule to write without excluding other suggestions that won't themselves feel cheaty. I'm always going to try to push rules given a hypothetical situation with bizarrely restricted yet otherwise infinite power

[Saka]

1. The small, stable, "side shooting" heisenburp of my dreams.
2. I wouldn't request a pattern, but rather the perfect program to find any desired pattern.

If it has to be a pattern, a slope 3 or 4 elementary knightship

[calcyman]

2. As a preface, there exists an enumeration of triplets (A,B,D) ordered by A+B+D, ties broken by A then by B, with A/D and B/D rationals in lowest terms in a given bounded subset of Q2. My request from this unlimited computer would be the smallest (lowest population then bounding box) stable constellation that could be hit with gliders on N adjacent lanes, where for lane M the only remaining output was the smallest (A,B)c/D spaceship with (A,B,D) the Mth element of the enumeration above over the set of rationals with A/D nonzero, B/D nonnegative and A/D + B/D at most 1/2, and with N some absurdly large integer.

There would be a lot to watch, syntheses of every record smallest ship, circuitry we didn't know of yet, and who knows what else Even if all it spit out was the pattern file, leaving any simulation of it up to us, the fact that it is a stable constellation makes it tractable to add a glider and simulate it. I think I should also request a glider be present in the pattern on lane 1 of the N, just in case optimal highway robbers aren't as obvious to us as constructed ones!

You would be very disappointed with the result: if N is sufficiently large, the oracle would return the following:

A stable constellation, P, which is a universal computer programmed to run a naively simplistic search program which, when inputted a glider encoding (A, B, D), brute-forces every possible pattern, in increasing size order, until it finds an (A,B)c/D spaceship. Then, it would brute-force simulate n-glider collisions (probably simeksian one-channel constructions for simplicity) until it finds one that generates the exact (A,B)c/D spaceship and nothing else within 2^n generations, increasing n until it finds a solution. Then, it would emit that simeksian synthesis, firing it at a suitably-placed block.

So you would have exactly what you wish for, but it would take a long time (on the order of 10^1000 generations) to produce the output.

If you change 'smallest constellation' to 'fastest constellation', then you won't get this abominable disappointment P. (Of course, you'd be able to salvage really small stable logic gates from P, so it wouldn't be completely useless.)

[muzik]

1. Where are those elementary knightships at?

Question I would ask after 1: What other speeds have been successfully searched for/constructed?

Question I would ask after that second one: I'm officially the oldest living human in Earth, how am I still functioning?

[dvgrn]

1. Have fast 90-degree signal elbows or splitters been found, recovery time p19 or below?

2. Show me the quadratic self-replicating pattern with the smallest bounding box. (We'll get to quadratic self-replicators eventually, and smallest-GoE and fastest signal elbow and things like that aren't absolutely impossible for humans to find unaided... but we'll never know what the smallest possible quadratic replicator looks like, unless this Plato's Cave ultracomputer tells us.)

But I hope we each get to ask the computer a question, because I want to see answers to other people's questions as well...!

[Goldtiger997]

An attempt at N=2 is the maximum we could construct, since the enumeration goes (1,0,2), (1,0,3), (1,0,4); we would need the c/4 orthogonal before the glider.

I've actually created the pattern for N=2. It uses the glider to 25P3H1V0.2 converter I posted in the "Construction pratice" topic. I've attached below as it goes over the character limit.

In the pattern there is a big arrow that points to two gliders that are 1 glider-lane apart. One turns in a LWSS and the other turns into a 25P3H1V0.2.

[superstrijder15]

Im fretty new to CGOL, but for question 2. I'd like to know if there is any finite sized pattern which can stop an infinite amount of each concievable spaceship from any direction(a kind of ultimate eater)! And if there isn't, is there a finite pattern which can stop one or multiple spaceships from any direction.
For one I'd probably wanna look up stuff about colonization of the solar system.

[drc]

Im fretty new to CGOL, but for question 2. I'd like to know if there is any finite sized pattern which can stop an infinite amount of each concievable spaceship from any direction(a kind of ultimate eater)! And if there isn't, is there a finite pattern which can stop one or multiple spaceships from any direction.
For one I'd probably wanna look up stuff about colonization of the solar system.

That's most likely impossible. However, there are eaters that eat infinite spaceships from multiple positions, such as the TWIT eater:

Code: Select all

x = 9, y = 13, rule = B3/S23
6bo$6bobo$6b2o2$bobo$2b2o$2bo$7b2o$3bo3b2o$2bobo$bobo$bo$2o!

[dvgrn]

Im [p]retty new to CGOL, but for question 2. I'd like to know if there is any finite sized pattern which can stop an infinite amount of each concievable spaceship from any direction(a kind of ultimate eater)! And if there isn't, is there a finite pattern which can stop one or multiple spaceships from any direction...

That's most likely impossible...

To be a little more specific: people have spent quite a bit of time trying to come up with the most likely defense mechanism for something like a quadratic replicator.

The theoretical question is something like this: in a Life universe with very sparse initial conditions -- most cells OFF, but each cell with a tiny chance of being ON -- all sorts of different patterns will spontaneously come into existence very very very far apart from each other. Here and there on an infinite Life grid you'll even see spontaneous replicators. Would there be a replicator with a good enough defense mechanism, that it would eventually outcompete all other replicators and take over the whole Life plane... after a very very very very long time?

Simple Stuff Works Better
So far it seems as if a simple passive defense is the only thing that would be moderately useful. For example, if I haven't made a mistake in setting this up, three rows of carefully spaced blocks can successfully absorb a glider on any lane from any direction, with no possibility of starting a chain reaction.

Code: Select all

x = 746, y = 746, rule = LifeHistory
72.2A$72.2A35$72.2A46.2A$72.2A46.2A35$72.2A46.2A46.2A34.2A34.2A34.2A
34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A$72.
2A46.2A46.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A
34.2A34.2A34.2A34.2A34.2A35$72.2A46.2A46.2A$72.2A46.2A46.2A11$204.2A
34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.
2A$204.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A
34.2A34.2A23$72.2A46.2A46.2A$72.2A46.2A46.2A23$204.2A34.2A34.2A34.2A
34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A$204.2A34.2A34.2A
34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A11$72.2A46.2A
46.2A$72.2A46.2A46.2A23$576.2A46.2A46.2A$576.2A46.2A46.2A11$72.2A46.
2A46.2A$72.2A46.2A46.2A23$576.2A46.2A46.2A$576.2A46.2A46.2A11$72.2A
46.2A46.2A$72.2A46.2A46.2A23$576.2A46.2A46.2A$576.2A46.2A46.2A11$72.
2A46.2A46.2A$72.2A46.2A46.2A23$576.2A46.2A46.2A$576.2A46.2A46.2A11$
72.2A46.2A46.2A$72.2A46.2A46.2A23$576.2A46.2A46.2A$576.2A46.2A46.2A
11$72.2A46.2A46.2A$72.2A46.2A46.2A23$576.2A46.2A46.2A$576.2A46.2A46.
2A11$72.2A46.2A46.2A$72.2A46.2A46.2A23$576.2A46.2A46.2A$576.2A46.2A
46.2A11$72.2A46.2A46.2A$72.2A46.2A46.2A23$576.2A46.2A46.2A$576.2A46.
2A46.2A11$72.2A46.2A46.2A$72.2A46.2A46.2A23$576.2A46.2A46.2A$576.2A
46.2A46.2A11$72.2A46.2A46.2A$72.2A46.2A46.2A23$576.2A46.2A46.2A$576.
2A46.2A46.2A11$72.2A46.2A46.2A$72.2A46.2A46.2A23$576.2A46.2A46.2A$
576.2A46.2A46.2A11$72.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A
34.2A34.2A34.2A34.2A$72.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.
2A34.2A34.2A34.2A34.2A23$576.2A46.2A46.2A$576.2A46.2A46.2A23$36.2A34.
2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A$
36.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.
2A34.2A11$576.2A46.2A46.2A$576.2A46.2A46.2A35$2A34.2A34.2A34.2A34.2A
34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A46.2A46.
2A$2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.2A34.
2A34.2A34.2A34.2A46.2A46.2A35$624.2A46.2A$624.2A46.2A35$672.2A$672.2A
!

So there's a safe area in the middle of the above square... until a second glider comes along. Even having six rows of blocks (or more) instead of three won't necessarily provide safety from a second glider impact -- the second glider might hit an ongoing pi explosion from the first impact and set off a large uncontrollable reaction. A quick automated search could pick out the most explosive combinations.

Also of course this particular setup will stop a single glider, but it's terrible at guarding against orthogonal spaceships. You could fix that, but there would be other vulnerabilities. Each type of spaceship allows for new chain-reaction threats, and there are an infinite number of different spaceships. For any given defense wall, an automated search utility (with a large spaceship library) could take as long as it needed to find the exact attack point that would do the most damage.

What If It's Not Passive?
It's tempting to consider an active defense -- maybe a similar wall of blocks, but one that is monitored from inside the wall and repaired when it gets damaged. But it turns out that any possible repair mechanism is probably more vulnerable to attack than the simple static wall would be. Let's say the monitoring reaction takes N ticks to reach out, make sure a block is in the right place, and fade away. Our theoretical search utility now has N times as many possible targets to try hitting with spaceships, making it (most likely) about N times more likely to find a devastating weakness.

Possibly the perimeter could be patrolled by very cleverly designed salvos of gliders, where each salvo is designed to fade away cleanly if it hits Spaceship X, and fade away cleanly using a different mechanism if it hits Spaceship Y, and so on. But again, the bigger and cleverer the salvo is, the more different ways there are to hit it with something that the salvo designers didn't guard against...!

[83bismuth38]

period infinity oscillator. obviously.

[Rhombic]

period infinity oscillator. obviously.

A bounded pattern cannot fulfil this.

Mine:

1) All natural knightships known and all (p,q)c/n knightships known to date (then) so that p>2*q and p,q are prime.
2) a) Cheapest glider synthesis of a very very large Caterloopillar, Gemini or, i.e., any of the largest known engineer[ed/able] spaceships to date --> this would probably show some amazing shortcuts in synthesis and amazing ways to be clever with certain explosions (it would optimise all possible uses of explosions!)
b) Shallowest* elementary knightship that fits within the bounding box of Gemini.
* Maximise q/p for a (p,q)c/n knightship.

[testitemqlstudop]

The maximum value of q of a (1,q)/(2q+2)c ship, and the ship itself.

[Gustone]

1. Is there an elementary replicator yet?
2.a stabilisation for an underweight spaceship
UWSS

Code: Select all

x = 4, y = 4, rule = B3/S23
bobo$o$o2bo$3o!

[PkmnQ]

A 2c/3 signal turner.

[Macbi]

A synthesis of a block using Geminis.

[calcyman]

A synthesis of a block using Geminis.

Ouch! It took me a while to even convince myself that this exists.

When two Geminis collide, there will be a huge messy explosion radiating lots of gliders.

Now, three of those positioned huge distances apart could be arranged to produce a cleanly escaping isolated orthogonal spaceship (by a 3-glider collision), and two of those could be arranged to produce an isolated glider. So, we can arrange an arbitrary synthesis, except for lots of junk and escaping gliders.

Additional Geminis 'from infinity' could absorb these gliders in passing. At this point, therefore, it becomes possible to synthesise a Reverse Caber Tosser which cleans up the static junk and systematically hunts down and cleanly destroys each of these extra Geminis, before finally self-destructing to leave just a block.

[testitemqlstudop]

A 2c/3 signal turner.

Technically that already exists: there are already 2c/3 -> G, G -> 2c/3, and G reflectors.

A 2c/3 signal turner that works at p19 or under.

[Hunting]

1. Is Life omniperiodic yet?
2. p19 oscillator.

[Moosey]

A synth for 44P5H2V0, the fabled "tough nut to crack".

Anyone up for 44P5H2V0?

Code: Select all

#N 44P5H2V0
#O Dean Hickerson
#C The first 2c/5 spaceship to be discovered
#C http://www.conwaylife.com/wiki/index.php?title=44P5H2V0
x = 15, y = 11, rule = b3/s23
4bo5bo4b$3b3o3b3o3b$2bo2bo3bo2bo2b$b3o7b3ob$2bobo5bobo2b$4b2o3b2o4b$o
4bo3bo4bo$5bo3bo5b$2o3bo3bo3b2o$2bo2bo3bo2bo2b$4bo5bo!

I guess this isn’t the original theme of the thread but I think this is the best place to do this.

[Hdjensofjfnen]

period infinity oscillator. obviously.

http://conwaylife.com/wiki/Total_aperiodic