## Methuselah Definition

For general discussion about Conway's Game of Life.

### Methuselah Definition

As far as I know no two people agree on the same definition for methuselah. The purpose of this thread is to establish a formal agreed upon definition.
I propose:
A Methuselah is a pattern witch fits in a 20 by 20 Bounding box that takes more than 1000 generations to regularize, it can (but dosent have to) grow with out limit.
lifespeed

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Joined: December 7th, 2010, 10:56 pm

### Re: Methuselah Definition

Nah, I don't think that fits very well. The "mehtuselah"s with 150 cells that take up 20 by 20 boxes hardly seem small when compared to rabbits. Furthermore, exactly when a pattern "regularizes" is vaguely defined. Rather, a methuselah should stabilize, not grow without bounds. I think it should be:

--Contains 9 or fewer cells (to eliminate the possibility of infinite growth)
--Either contains 7 or fewer cells, or fits in a 20 by 20 box (to eliminate the glider+blinker which takes arbitrarily long to stabilize)
--Takes at least 1000 generations to stabilize

Alternatively, the condition of having fewer than 10 cells could be replaced with any of the following:
--fits in a 1 by 38 box
--fits in a 2 by 11 box
--fits in a 3 by 8 box
--fits in a 4 by 5 box

Any of those 5 conditions bar infinite growth, and limit the size.
137ben

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### Re: Methuselah Definition

Why limit the size of a methuselah? The main definition that I have heard is that a methuselah is any pattern that decays over a long period of time. I think a "long period of time" is relative to the size of the original pattern, since this:
`x = 3, y = 4, rule = B3/S23bo\$3o\$obo\$bo!`

is much shorter-lasting than this:
`x = 10, y = 11, rule = B3/S23o8bo\$b8o2\$b8o2\$b8o\$o8bo\$b8o2\$b8o\$o8bo!`

which is, in turn, shorter lasting than something that would take up a 60x60 square (in most cases).
Batmanifestdestiny

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### Re: Methuselah Definition

Batmanifestdestiny wrote:Why limit the size of a methuselah? The main definition that I have heard is that a methuselah is any pattern that decays over a long period of time. I think a "long period of time" is relative to the size of the original pattern, since this:
`x = 3, y = 4, rule = B3/S23bo\$3o\$obo\$bo!`

is much shorter-lasting than this:
`x = 10, y = 11, rule = B3/S23o8bo\$b8o2\$b8o2\$b8o\$o8bo\$b8o2\$b8o\$o8bo!`

which is, in turn, shorter lasting than something that would take up a 60x60 square (in most cases).

I like that idea. One thing we do need to settle is whether to limit size based only on population size (with some added clause to clear up the blinker+glider), only on bounding box, on some combination of the two, or something else entirely.

I actually thought of another way to measure size: the minimum size polyomino which contains the pattern. So for example acorn would be size 10:
`x = 7, y = 3, rule = lifehistory.A\$.2BA\$2A.B3A!`

I see no reason why the space that the pattern takes up should be limited to rectangular regions.

...come to think of it, this presents a new problem, more relevant in another thread...
137ben

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### Re: Methuselah Definition

One thing we do need to settle is whether to limit size based only on population size (with some added clause to clear up the blinker+glider)

The problem is that I can't think of anything that I think of any thing that solves the blinker+glider-esque issue, apart from limiting bounding box.
lifespeed

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### Re: Methuselah Definition

137ben wrote:Furthermore, exactly when a pattern "regularizes" is vaguely defined. Rather, a methuselah should stabilize

There is the same problem with the word "stabilize". It's vaguely defined as well. If it means "become stable" it should rule out any pattern with a blinker in the ash. A blinker is not stable in the normal sense of the word. It's changing. And if blinkers and gliders are considered "stable" (in a redifined sense of the word) you have to ask why a spaceship is considered "stable" but not a puffer. A spaceship is just a puffer with zero smoke.

Mats

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### Re: Methuselah Definition

A pattern "stabilizes" when its population becomes cyclic. I can tell you exactly when a pattern stablizes. You cannot, however, give me an exact generation in which a breeder "regularizes".
137ben

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### Re: Methuselah Definition

Mats wrote:
137ben wrote:Furthermore, exactly when a pattern "regularizes" is vaguely defined. Rather, a methuselah should stabilize

There is the same problem with the word "stabilize". It's vaguely defined as well. If it means "become stable" it should rule out any pattern with a blinker in the ash. A blinker is not stable in the normal sense of the word. It's changing. And if blinkers and gliders are considered "stable" (in a redifined sense of the word) you have to ask why a spaceship is considered "stable" but not a puffer. A spaceship is just a puffer with zero smoke.

I'm pretty sure that stabilization implies a cyclic population.
Axaj

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### Re: Methuselah Definition

Generally, stabilization is not considered to be purely based on population. For example, the following pattern's population becomes cyclic (always 4) at generation 1, but does not stabilize until generation 2:
`x = 3, y = 7, rule = B3/S23obo\$2o3\$2bo\$bo\$o!`
-Matthias Merzenich
Sokwe
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### Re: Methuselah Definition

Axaj wrote:I'm pretty sure that stabilization implies a cyclic population.

Can you find a source to support that?

From the Life Lexicon:
stable A pattern is said to be stable if it is a parent of itself. See still life.

There is no entry for "stabilize" in the Lexicon so unless there is support for your interpretation I think "stabilize" should mean "become stable".

Mats

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Location: Stockholm, Sweden

### Re: Methuselah Definition

Mats wrote:
Axaj wrote:I'm pretty sure that stabilization implies a cyclic population.

Can you find a source to support that?

A reasonable source is the Life Lexicon definition of "methuselah", which lists seven example methuselahs, none of which produce final patterns that are stable in the sense of being period 1. They stabilize by evolving into large constellations of oscillators.

dvgrn
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### Re: Methuselah Definition

dvgrn wrote:
Mats wrote:
Axaj wrote:I'm pretty sure that stabilization implies a cyclic population.

Can you find a source to support that?

A reasonable source is the Life Lexicon definition of "methuselah", which lists seven example methuselahs, none of which produce final patterns that are stable in the sense of being period 1.

The Life Lexicon states that an ark is considered a Methuselah.
lifespeed

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### Re: Methuselah Definition

lifespeed wrote:The Life Lexicon states that an ark is considered a Methuselah.

There's some debate on whether an ark is an actual methuselah or not. I believe that a pattern is fully stabilized when the remaining debris reaches a state of oscillation, including escaping gliders and other escaping spaceships(implying that gliders don't collide with any other objects).

flipper77

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### Re: Methuselah Definition

flipper77 wrote:I believe that a pattern is fully stabilized when the remaining debris reaches a state of oscillation, including escaping gliders and other escaping spaceships(implying that gliders don't collide with any other objects).

Or escaping puffers, I would say. For example, switch engines occur fairly regularly in random ash, and escape to infinity. If someone happened to find a 15x9 13-cell pattern that evolved for 40,000 ticks, sent out a block-laying switch engine, and then stabilized, that would certainly be a real methuselah, and an unqualified improvement on Lidka. This kind of thing hasn't been found yet, I don't think, but it could show up any time.

If the switch engine is the last thing generated, the time of stabilization will be whenever the switch engine stops interacting with anything but its own exhaust -- i.e., the first generation G when the active part of the switch engine is exactly the same at G and at G+96.

dvgrn
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### Re: Methuselah Definition

If we're going to include puffers as stable, we may as well try to define "regularize." As you just said, something like
`x = 38, y = 53, rule = B3/S2334b4o\$33bo3bo\$37bo\$36bo3\$34bo\$35bo\$35bo\$34b2o\$28bo4bo\$27b2o3\$34b4o\$33bo3bo\$37bo\$36bo25\$11bo\$10b2o5\$bo8bo4bo\$o5bo2bo4bo\$o6b3o4bo\$o2bo10bo2bo\$3o11b3o!`

this could appear naturally, even if we haven't found it yet. I'd still say it is somewhat regularized eventually (even though the sequence of gliders is aperiodic), but when exactly this happens is very vague.

And then there's something that produces seemingly unlimited novelty. It doesn't mean it wouldn't be obviously regularized after 10^1000 generations (which we will never have enough processing power to run, of course), but it means that we would need a much more complicated definition of regularizing.
137ben

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### Re: Methuselah Definition

137ben wrote:If we're going to include puffers as stable, we may as well try to define "regularize." [A pattern with two interacting puffer trains] could appear naturally, even if we haven't found it yet. I'd still say it is somewhat regularized eventually (even though the sequence of gliders is aperiodic), but when exactly this happens is very vague.

A hashlife algorithm could possibly help with this kind of thing, to some extent. In hashlife mode, Golly "runs away" with some patterns after a while, meaning that in some sense it's seen everything before and is just looking up precalculated answers (and adding a few larger tiles now and again as the pattern grows). It might not be too difficult to write a dedicated methuselah analyzer to hunt for the first generation after which no novel combinations seem to appear.

But I wouldn't bet on this working for all cases: to a large extent, the hunt for a definition of "regularize" or "stabilize" is a wild-goose chase, because it's always possible to build patterns that challenge any definition. E.g., does Miscellaneous/fermat-primes.rle in Golly's pattern collection ever regularize?

Anyway, practically speaking, it's a bit of a leap from considering a single instance of a rare puffer that has actually been seen "in the wild", to worrying about multiple simultaneous instances of a much more improbable puffer that has never actually been observed to appear in random ash. Clearly we're wandering into disputed "ark" territory here. Nick Gotts has found objects along these lines that stabilize only after millions of ticks.

137ben wrote:And then there's something that produces seemingly unlimited novelty. It doesn't mean it wouldn't be obviously regularized after 10^1000 generations (which we will never have enough processing power to run, of course), but it means that we would need a much more complicated definition of regularizing.

This thread started with the observation that "no two people agree on the same definition for methuselah". For the last forty-odd years that's pretty much been true, despite plenty of spirited discussions on the subject (the argument spontaneously breaks out again somewhere every half-decade or so, at least). Unfortunately, that means that this thread is most unlikely to produce The Authoritative Definition that will make everybody happy.

The definition in the LIfe Lexicon is pretty good, really -- short and sweet, without getting too bogged down in the messy details. Beyond that, people who want to make extensive collections of methuselahs simply have to decide for themselves what limiting parameters to use. See Dean Hickerson's methuselah page, for example.

dvgrn
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### Re: Methuselah Definition

Unfortunately, that means that this thread is most unlikely to produce The Authoritative Definition that will make everybody happy.

Agreed. In fact, I think it is unlikely that we will ever find a definition that everyone agrees on.

E.g., does Miscellaneous/fermat-primes.rle in Golly's pattern collection ever regularize?

This highlights another potential problem: even if we agree on a definition of a methuselah, we can't necessarily easily determine whether a pattern will eventually stabilize.
137ben

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### Re: Methuselah Definition

My way would be to state it in terms of the "L/I" (lifespan divided by initial population) but have no idea what number it should be!

In terms of stablilize if it becomes either a series (or one) other known patturns that have repetition of any form
wintersolstice

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### Re: Methuselah Definition

Using the recently proposed polynomino bounding box, I think that system is dependent both on population and on distance (bounding box).

The start pattern should be judged by the polyomino bounding box.
The end pattern should be judged by the smallest size polyomino bounding box for all periods.

So the inital pattern divided by the result pattern should be the methuselah index; this would be a good measure of how large any methuselah is.

ssaamm

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### Re: Methuselah Definition

So the inital pattern divided by the result pattern should be the methuselah index;

I disagree: One can create patterns with arbitrarily high values of (final size)/f(initial size), for any computable function f.
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calcyman

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### Re: Methuselah Definition

(time to stabilise)/(minimal covering polyplet size for initial state) seems like a pretty good measure to me.

Macbi

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### Re: Methuselah Definition

It really just depends on your definition of "size" then. I guess size of end pattern is important, but it can be caused by a short reaction. At the same time, a pattern that lasts a long time can produce a small end result...

I think that they should be measured for averages, and then averaged with weighting to ensure that they have equal status.

ssaamm

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### Re: Methuselah Definition

I suggest size to be the area of the bounding box.
Comparison of long and short lived Methuselahs in terms of this Methuselah definition. (.xls file)
When will a 2x2 gun be discovered...?
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eaglgenes101

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### Re: Methuselah Definition

eaglgenes101 wrote:I suggest size to be the area of the bounding box.
Comparison of long and short lived Methuselahs in terms of this Methuselah definition. (.xls file)

This is a chart without a reason. I could make a chart comparing methuselahs based on the amount of anything, and it would still have this much authority.

If you have a reason for the validity of this measurement, aside from the fact that it is possible to use, you can tell us.

Anyway.

In order to properly measure size, the gliders should all be let away. We would not want to count them, because they are very far away by the time the pattern ends. It would be most useful to run the pattern for the amount of generations as the largest dimension of the bounding box * 2 after it has stabilized. If a slower ship can naturally occur, we would want to use its speed to multiply by instead of the speed of a glider or SS.

ssaamm

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### Re: Methuselah Definition

OK, the topic is getting way astray. The original purpose of this thing was to define a methuselah, and then you are discussing things about cyclic populations and all the paraphernalia?

I'll need to refresh your memory by quoting the definition given at the very first post on this topic:

lifespeed wrote:A methuselah is a pattern witch fits in a 20-by-20 bounding box that takes more than 1000 generations to regularize. It can (but doesn't have to) grow without limit.

Since it proposed a certain bounding box and lifespan, I propose a definition generalised from this:

A methuselah is a pattern that fits in an a-by-b bounding box that takes more than f(a, b) generations to regularise. It can (but doesn't have to) grow without limit.

Where f(a, b) refers to the average time for a random pattern that has an a-by-b bounding box to regularise. You'll need to compute the f(a, b) yourself. Any comments?
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Freywa

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