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Methuselah Definition

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Re: Methuselah Definition

Postby ssaamm » June 30th, 2011, 1:07 pm

Well, a Methuselah is defined by, essentially, the size of the original pattern versus the size of the reaction it creates, right?

If we make a standard for this, we will be able to give any pattern ratings based on this, and we can decide what rating makes the pattern a Methuselah.

We have not started talking about anything that does not concern the definition of a Methuselah directly or indirectly.

By suggesting that we have gone off-topic, you are bringing us back to where we started, using the outdated system of bounding boxes, and arguing about whether or not a Methuselah needs to stabilize, which it does.

What we need to do now is to figure out how to utilize the polyomino bounding box and stabilization time of a pattern for this definition.
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Re: Methuselah Definition

Postby Tropylium » June 30th, 2011, 11:18 pm

Hello LifeForums!
ssaamm wrote:Well, a Methuselah is defined by, essentially, the size of the original pattern versus the size of the reaction it creates, right?

If we make a standard for this, we will be able to give any pattern ratings based on this, and we can decide what rating makes the pattern a Methuselah.

I suppose the basic question is, is a Methuselah defined by its longevity (rel. to its size) period, or is exceptional longevity needed?

Things like R-pentomino, acorn and rabbits clearly qualify for both, but in going along the latter, the likes of B, Herschel, or century seem to not really belong. In my mind I actually group them into an intermediate category of "Seeds" — figures that arise "commonly" from a soup and last for "a while" before stabilizing. Familiar Fours also fall here. And speaking of familiar fours, if a Methuselah is defined by exceptional longevity, would the T-tetromino (and its precedessors, the bunny and the … "|·" one) also count? They do live for about twice as long as the next-longest lived 4-cell patterns (the pre-pond and a few beehive precedessors take 4 generations; a few sparks take 5). Not quite as impressiv as the lead the R and the pi and their kin have on other 5-cellers, but still clearly a neck.

It seems that any cutoff point will have to be arbitrary in some way, however.

Anyway, more on this in a while, I'm nearing completion on (a phase of) a project… 8)

ssaamm wrote:What we need to do now is to figure out (…) stabilization time of a pattern for this definition.

As for how to define "stabilization", I generally use the following (as in, how I actually inspect when a pattern has stabilized):
A pattern has stabilized once all of its components (any clusters of cells separated by at least two cells of empty space) are either periodic or infinite growth patterns, and its future development is the same as the future development of all of its sub-patterns taken individually.

(This allows for things like puffers, while exclucing stages where a pattern's activity has temporarily slowed down to one or more gliders heading towards some junk before igniting it. It still does not rigorously work for multiple-component things like queen bee shuttles or corderships… but really, that clause doesn't come up a lot.)
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Re: Methuselah Definition

Postby calcyman » July 1st, 2011, 11:44 am

need to compute the f(a, b) yourself.


It is straightforward to demonstrate that f(a,b) is uncomputable; indeed, there is a value k such that f(n,n) > BB(n) for all n > k.
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Re: Methuselah Definition

Postby Freywa » July 3rd, 2011, 4:15 pm

ssaamm wrote:What we need to do now is to figure out how to utilize the polyomino bounding box and stabilization time of a pattern for this (methuselah) definition.

Tropylium wrote:As for how to define "stabilization", I generally use the following (as in, how I actually inspect when a pattern has stabilized): A pattern has stabilized once all of its components (any clusters of cells separated by at least two cells of empty space) are either periodic or infinite growth patterns, and its future development is the same as the future development of all of its sub-patterns taken individually. (This allows for things like puffers, while exclucing stages where a pattern's activity has temporarily slowed down to one or more gliders heading towards some junk before igniting it. It still does not rigorously work for multiple-component things like queen bee shuttles or corderships… but really, that clause doesn't come up a lot.)


Basically, Tropylium is saying that a pattern has stabilised once all the objects are periodic/infinite growth and they don't interact anymore.

So we should define a methuselah to be (stabilisation time)/(polyomino bounding box) > 11.8, based on the Diehard (130/11 = 11.81 recurring). None of the patterns classified as "methuselah" on LifeWiki have lower such ratios than the Diehard. Are you willing to accept this definition :?:
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Re: Methuselah Definition

Postby knightlife » July 24th, 2011, 9:32 am

In another thread it was implied that there are two types of methuselahs, which I would call simple (compact) and compound (non-compact). The excellent distinction is made that there is a single cluster of cells or there are multiple clusters of cells in the methuselah. A cluster of cells is defined here as cells connected to each other in the sense that there is never a gap of two or more empty cells between islands of cells. A gap of one empty cell is OK. One way to find out if you have a single cluster or multiple clusters is by turning on all eight neighboring bits of each original "on" cell regardless of their initial state. If the result is a single polyomino of "on" cells then the original pattern is a single cluster, otherwise there are multiple clusters. Acorn is one cluster and diehard is two. The wiki even points out that diehard is a collision.

For a simple methuselah the number of “on” cells is enough said, no bounding box or bounding polyomino is needed in its description. The compound methuselah can also be called a collision methuselah because the multiple clusters will interact (if they don’t all interact, then you have more than one starting pattern).

Unfortunately, the bounding box issue still exists for a compound or collision methuselah, and stabilization still needs a solid definition. Ratios should be avoided, as they always seem to be at the center of conflict. In the spirit of the original definition of methuselah (at or near the time when the outcome of an R-pentomino was still unknown) I think the overriding parameter for size is the number of cells. For a simple Methuselah just leave it at that so lifespans can be compared directly for methuselahs of the same size.
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Re: Methuselah Definition

Postby 137ben » July 24th, 2011, 10:45 am

One way to find out if you have a single cluster or multiple clusters is by turning on all eight neighboring bits of each original "on" cell regardless of their initial state. If the result is a single polyomino of "on" cells then the original pattern is a single cluster, otherwise there are multiple clusters.

I think that should be polyplet, not polyomino.
Aside from that, I agree. Population is the primary measurement of size.
Actually, by limiting population to 7 cells or fewer, even compound methuselahs need not have any other restrictions.
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Re: Methuselah Definition

Postby Tropylium » July 24th, 2011, 12:27 pm

knightlife wrote:In another thread it was implied that there are two types of methuselahs, which I would call simple (compact) and compound (non-compact). The excellent distinction is made that there is a single cluster of cells or there are multiple clusters of cells in the methuselah. A cluster of cells is defined here as cells connected to each other in the sense that there is never a gap of two or more empty cells between islands of cells. A gap of one empty cell is OK. One way to find out if you have a single cluster or multiple clusters is by turning on all eight neighboring bits of each original "on" cell regardless of their initial state. If the result is a single polyomino of "on" cells then the original pattern is a single cluster, otherwise there are multiple clusters. Acorn is one cluster and diehard is two. The wiki even points out that diehard is a collision.

This definition of compactness is close but not quite the definition I would have used. I count objects separated by one-cell gaps as two clusters, as long as the development of any one cluster does not depend on the presence of the others; thus, block on block, rabbits, or (the final pattern of) traffic lights are all noncompact in my view.

knightlife wrote:For a simple methuselah the number of “on” cells is enough said, no bounding box or bounding polyomino is needed in its description.

Agreed.

knightlife wrote:The compound methuselah can also be called a collision methuselah because the multiple clusters will interact (if they don’t all interact, then you have more than one starting pattern).

Unfortunately, the bounding box issue still exists for a compound or collision methuselah, and stabilization still needs a solid definition.

The core of the problem is collisions involving spaceships + still lifes/oscillators. For any such example, we can generate an ancestor that is larger, longer-lived, and has the same components. I think this suggests that the "bounding box threshold" should simply grow faster than the speed of spaceships: a m×n methuselah with lifespan K is only equally good (or possibly worse) than a m×(n-1) methuselah with lifespan K-2.

By contrast, the same problem does not apply to spaceship + smaller methuselah collisions, any "sufficiently" long-lived examples which I would be happy to count as bigger methuselahs in their own right.
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Re: Methuselah Definition

Postby edwardfanboy » December 3rd, 2011, 5:21 am

I think a methuselah is any pattern that lasts more than 1000 gens before becoming periodic, and has a population that does not keep increasing forever. Therefore a pattern that creates a switch engine does not count.
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Re: Methuselah Definition

Postby NotAvailableCooper » August 10th, 2014, 9:14 pm

edwardfanboy wrote:I think a methuselah is any pattern that lasts more than 1000 gens before becoming periodic, and has a population that does not keep increasing forever. Therefore a pattern that creates a switch engine does not count.

This definition I can agree with myself. There is something about interacting clusters than seems to not have been considered here, which is the footprint of the reaction of each individual cluster. For example, upon generation 1103 the R pentomino has a much larger "bounding box" for it's debris field than the initial figure.
That is what I believe should be considered along with the above quoted definition. As for ships activating junk, I believe as long as the debris field's bounding box at initial time of the stabilization or entrance of cycling population numbers (which I will refer to from now on as the "area of effect") interact then that pattern should qualify as well.
One addendum that could be required without any issue would be to subtract the number of generations that it takes for a ship to escape an initial reaction to when said ship collides with junk or otherwise triggers another reaction.
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Re: Methuselah Definition

Postby c0b0p0 » August 20th, 2014, 10:11 pm

@NotAvailableCooper: The clause you mentioned was suggested before by ssaamm.
Well, a Methuselah is defined by, essentially, the size of the original pattern versus the size of the reaction it creates, right?

You are thinking in terms of bounding boxes, which he considered to be outdated, while he used what he called the size of the reaction. Under both criteria, the diehard methuselah could be called into question.

I think that the bounding cluster would be a good measurement of size, and thus that [lifespan]/ln([bounding cluster])^2 would be a pretty good measurement, thus excluding elaborately designed patterns with growth rate O(sqrt(log(t))).
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Re: Methuselah Definition

Postby NotAvailableCooper » August 21st, 2014, 10:49 pm

c0b0p0 wrote:@NotAvailableCooper: The clause you mentioned was suggested before by ssaamm.
Well, a Methuselah is defined by, essentially, the size of the original pattern versus the size of the reaction it creates, right?

You are thinking in terms of bounding boxes, which he considered to be outdated, while he used what he called the size of the reaction. Under both criteria, the diehard methuselah could be called into question.

I think that the bounding cluster would be a good measurement of size, and thus that [lifespan]/ln([bounding cluster])^2 would be a pretty good measurement, thus excluding elaborately designed patterns with growth rate O(sqrt(log(t))).


Ehh, that quote doesn't quite represent what I was attempting to communicate, though it does come close to one aspect. The definition I was proposing is primarily of two parts: part 1 being the "size of the reaction" (or much more clearly, the area and shape of cells highlighted at the generation of stabilization or cycling population numbers in the LifeHistory rule in Golly) and part 2 being the lifetime. The lifetime we seem to agree on, so I won't go into that. I'm specifically trying to avoid bounding boxes entirely since they only refer to the starting configuration and have a way of being far too restrictive for reactions.

The point I'm trying to convey with this proposition is that if we define methuselahs in this particular manner then we don't need any mathematical sieves or other more complex filters, from my work with methuselahs it appears that this definition is sufficiently restrictive. Though in fact, if you can show me a pattern that fits my definition that defies the "spirit" of the definition, I'm perfectly open to modifying it more.

As for diehards, I don't consider them truly useful. They are more a curiosity than anything; in fact I don't consider them to be a type of methuselah at all. So I guess another addendum to the definition already present is that the final generation of stabilization or cycling population numbers has to have a nonzero cell quantity.
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Re: Methuselah Definition

Postby c0b0p0 » August 23rd, 2014, 10:31 pm

c0b0p0 wrote:I think that the bounding cluster would be a good measurement of size, and thus that [lifespan]/ln([bounding cluster])^2 would be a pretty good measurement, thus excluding elaborately designed patterns with growth rate O(sqrt(log(t))).

Corrected: [lifespan]/2^([bounding cluster]*2).
NotAvailableCooper wrote:The point I'm trying to convey with this proposition is that if we define methuselahs in this particular manner then we don't need any mathematical sieves or other more complex filters, from my work with methuselahs it appears that this definition is sufficiently restrictive.

NotAvailableCooper wrote:One addendum that could be required without any issue would be to subtract the number of generations that it takes for a ship to escape an initial reaction to when said ship collides with junk or otherwise triggers another reaction.

Isn't the addendum above a pretty complex filter?
NotAvailableCooper wrote:... in fact I don't consider them to be a ... methuselah ...

In LifeWiki there is a page named "Diehard Methuselah". Would you consider renaming that page to "Longest-lived diehard under eight cells" (more correct under your definition of methuselah)?
NotAvailableCooper wrote: Though in fact, if you can show me a pattern that fits my definition that defies the "spirit" of the definition, I'm perfectly open to modifying it more.

x = 1506, y = 26, rule = B3/S23
20b3o3b3o$19bo2bo3bo2bo$4o18bo3bo18b4o$o3bo17bo3bo17bo3bo$o8bo12bo3bo
12bo8bo$bo2bo2b2o2bo25bo2b2o2bo2bo$6bo5bo7b3o3b3o7bo5bo$6bo5bo8bo5bo8b
o5bo$6bo5bo8b7o8bo5bo$bo2bo2b2o2bo2b2o4bo7bo4b2o2bo2b2o2bo2bo$o8bo3b2o
4b11o4b2o3bo8bo$o3bo9b2o17b2o9bo3bo$4o11b19o11b4o$16bobo11bobo$19b11o$
19bo9bo$20b9o$24bo$20b3o3b3o$22bo3bo2$21b3ob3o$21b3ob3o$20bob2ob2obo
1476bo$20b3o3b3o1476bo$21bo5bo1477bo!
The farther the blinker is from the spacefiller, the more amazing the pattern is according to your definition, and extending your addendum doesn't do much good.
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Re: Methuselah Definition

Postby NotAvailableCooper » September 17th, 2014, 2:17 pm

@c0p0b0 I'm not sure how subtracting the travel time of a triggering spaceship is "complex" in the same manner as the mathematical sieves previously presented, perhaps we are working with different definitions of complex?

Yes, I think that the name you suggested for the "Diehard" would be more appropriate.

The pattern you present has a pattern within it that grows to infinity. Any pattern that has this property should not be a methuselah. So yes, that would mean another addendum to the definition I am offering would be that no isolated island of any proposed methuselah may grow infinitely.
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Re: Methuselah Definition

Postby Gpennder_____409 » December 12th, 2014, 9:39 pm

x = 103, y = 79, rule = B3/S23
48bo5bo$47b3o3b3o$47bob2ob2obo$48b3ob3o$48b3ob3o2$49bo3bo$47b3o3b3o$
51bo$47b9o$46bo9bo$46b11o$44bo13bo$44b15o$42bo17bo$42b19o$40bo21bo$40b
23o$38bo25bo$38b27o$36bo29bo$36b31o$34bo33bo$34b35o$32bo37bo$32b39o$
30bo41bo$30b43o$2b2o24bo45bo24b2o$b4o23b47o23b4o$2ob2o21bo49bo21b2ob2o
$b2o6bo16b51o16bo6b2o$8b2o14bo53bo14b2o$6b2o4b2o10b55o10b2o4b2o$6b3o3b
3o7bo57bo7b3o3b3o$6b2o4b3o7b59o7b3o4b2o$8b2o3bob2o3bo61bo3b2obo3b2o$b
2o6bo4bo5b63o5bo4bo6b2o$2ob2o9bo3bo65bo3bo9b2ob2o$b4o10bo3b32ob32o3bo
10b4o$2b2o12b2o67b2o12b2o$19b65o$20bo61bo$21b61o$22bo57bo$23b57o$24bo
53bo$25b53o$26bo49bo$27b49o$28bo45bo$29b45o$30bo41bo$31b41o$32bo37bo$
33b37o$34bo33bo$35b33o$36bo29bo$37b29o$38bo25bo$39b25o$40bo21bo$41b21o
$42bo17bo$43b17o$44bo13bo$45b13o$46bo9bo$47b9o$51bo$48b3ob3o$49bo3bo$
48bobobobo$48bobobobo$47bo7bo$47bo7bo$47bo2bobo2bo$47b3o3b3o!
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Re: Methuselah Definition

Postby turtleguy1134 » December 28th, 2014, 12:00 pm

I was thinking "The generation when the methuselah stabilizes is when it contains only guns, spaceships, and oscillators (including still lifes, because they are period 1 oscillators at heart) but the puffer thing kills all that. :cry:
So maybe we can kill the puffer problem by saying "Any pattern that exhibits infinite growth is disqualified from being a methuselah.
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Re: Methuselah Definition

Postby Prokaryotic Life » December 2nd, 2016, 7:35 pm

turtleguy1134 wrote:I was thinking "The generation when the methuselah stabilizes is when it contains only guns, spaceships, and oscillators (including still lifes, because they are period 1 oscillators at heart) but the puffer thing kills all that. :cry:
So maybe we can kill the puffer problem by saying "Any pattern that exhibits infinite growth is disqualified from being a methuselah.


I think that puffers shouldn't disqualify. Any generations with no chaotic behavior (like a glider towards a blinker) does not count towards the lifespan. Things like puffers count as stabilized, given their debris doesn't interact with anything else and the puffer won't collide with anything.

Additionally, the system I was using to grade methuselahs took into account the lifespan, the bounding box, the number of cells, and the end state. I usually consider methuselahs to be the "elite" so patterns like Herschel fall short. Those are long lived, but they're not special enough to be considered methuselahs

This doesn't solve the problem of spacefillers reaching blinkers though.
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Re: Methuselah Definition

Postby Rhombic » December 15th, 2016, 7:08 pm

So this is what you get when you create an ill-defined word for a concept that is both ambiguous and unreliable to explain. The thing is, I think nobody ever thought about defining methuselah when it was first used, and it was certainly used liberally for any pattern that took kind of long to stabilise.
Unfortunately, it's impossible to avoid this concept altogether and forget the descriptor "methuselah" to a pattern. After all, if we did so, what would the first posts of all new users be? "I have found a pattern that takes somewhat longer than other patterns to stabilise into a bounded-population constellation of various still lifes, oscillators and diverging spaceships!"

...or maybe "Is this 34c/117 spaceship known?" (there might be bugs in wfind) ~~wdr



back on topic
Puffers:
  • they can counted as bounded growth population, hence ignored and assumed to be stable since their formation as long as they don't react any more... rakes interacting periodically with puffers are included in the same category because it's a translation-adjusted oscillating linear-growth pattern! Think spaceships always keep expanding the final bounding box, but it's obviously stabilised
  • either that or don't accept them, but to be fair, it is a stable pattern and once it's formed, you are not accounting for any further generations (which means that a puffer itself has a stabilisation lifespan of 0)
  • corollary: non-interacting quadratic growth that is naturally(!) formed would also be counted as a stabilised endpoint, so if it's the last object to stabilise, le lifespan of the methuselah would end as soon as it appeared
    Pros: this accounts perfectly for all cases of growth patterns in an unambiguous systematic way, as long as we are in non-explosive rules and we avoid pathological growths; this is fine since this is not DryLife or HighLife but regular CGoL, we're good to go

In my opinion, the polyomino bb approach is sensible, but the number of cells in that polyomino should be raised to some fractional power to account for how there is significant less interest if the lifespan is extended just by moving a cluster away. Adjusting the parameters would manage to yield numbers that, like us, would sneer at infinite growth colliding with distant blinkers.
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Re: Methuselah Definition

Postby wwei23 » July 16th, 2017, 12:29 pm

Here's one, it emits two gliders on the same path!
x = 6, y = 6, rule = LifeHistory
4.A$3.A$3.3A3$3A!
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Re: Methuselah Definition

Postby Majestas32 » November 27th, 2017, 8:01 pm

My definition is a pattern such that:
# of generations until stabilizing is G
initial bounding box is AxB
G > (A+B)^2
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Re: Methuselah Definition

Postby dvgrn » November 27th, 2017, 8:25 pm

Majestas32 wrote:My definition is a pattern such that:
# of generations until stabilizing is G
initial bounding box is AxB
G > (A+B)^2

If you run Patterns\Life\Oscillators\p103079214841.rle for 101,000 ticks, then delete almost any of the still lifes in the protruding area along the south edge, or add obstructions in that region... you'll end up with a pattern that fits the above definition. Are you allowing these kinds of large engineered pattern as methuselahs, or is there a way to modify your definition of "methuselah" to exclude them?

-- Sorry, I'm probably just being annoying and playing devil's advocate here. Precise definitions of "methuselah" always seem to have exceptional cases that many people find hard to accept. It almost seems as if no two people in the history of Life have ever quite agreed on a definition of the term.
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Re: Methuselah Definition

Postby Macbi » November 27th, 2017, 8:44 pm

If you run Patterns\Life\Oscillators\p103079214841.rle for 101,000 ticks, then delete almost any of the still lifes in the protruding area along the south edge, or add obstructions in that region... you'll end up with a pattern that fits the above definition. Are you allowing these kinds of large engineered pattern as methuselahs, or is there a way to modify your definition of "methuselah" to exclude them?


To me that seems like a perfectly good methuselah. Normally we're used to seeing "natural" methuselahs that are chaotic over the course of their entire evolution. But we allow engineered ships as well as natural ones, so why not engineered methuselahs as well?

Also, has anyone ever done statistics on the distribution of times-to-stabilization of soups? Is it log-normal? Exponential? Poisson? EDIT: http://www.njohnston.ca/2009/07/the-max ... e-of-life/
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Re: Methuselah Definition

Postby Apple Bottom » November 28th, 2017, 1:56 am

dvgrn wrote:-- Sorry, I'm probably just being annoying and playing devil's advocate here. Precise definitions of "methuselah" always seem to have exceptional cases that many people find hard to accept. It almost seems as if no two people in the history of Life have ever quite agreed on a definition of the term.


Do we even need a formal definition? The informal one I'm using -- "a small pattern that takes a disproportionate number of generations to settle down" -- has worked enough well for me. I knows 'em when I sees 'em!
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Re: Methuselah Definition

Postby A for awesome » November 28th, 2017, 12:27 pm

If we have to formally define "methuselah", it seems like defining "lifespan" is necessary first. Possible definitions include:

  1. The number of generations until each individual separate pattern that lasts until infinity and no others are present and have begun their first periodic cycles.

    • This is, in effect, the "canonical" definition of lifespan, but it has some shortcomings. First, it is not always clear with infinite growth patterns whether they or their output are considered "separate" or "periodic"; it is often possible to intuitively define when a pattern containing infinite growth has stabilized, but that is more of an informal process. Second, the "begun their first periodic cycles" part, while consistent with existing lifespan counts of methuselahs, isn't always immediately clear, for instance if a previously unknown pattern appears, where it must be run until it completes its "first periodic cycle" to determine its true lifespan. Therefore, the following definition seems slightly more intuitive:
  2. The number of generations until each individual separate object that lasts until infinity and no others are present and have completed their first periodic cycles.

    • This seems slightly preferable because it assumes no prior knowledge about how periodic patterns will behave, but it shares the rest of the prior definition's downsides as well as being incompatible with the canonical definition for non-diehards. A possibly better definition might be:
  3. The number of generations of initial evolution that must be known to compute the following evolution of the pattern without invoking the basic rule of evolution.

    • In effect, this is the point at which no "new" reactions occur within a pattern, or the "chaotic lifespan" of a pattern. This definition has certain compelling advantages, but also has its share of problems. First, it is defined for all patterns except infinite novelty generators (and in fact offers a simple definition of "infinite novelty generator":
      a pattern for which the "chaotic lifespan" is undefined), including linear, quadratic, and other types of growth as well as most of the patterns in Golly's HashLife folder. Second, it is fairly simple and non-arbitrary, although both (1) and (2) meet this criterion to some extent. However, it is
      1. Difficult to compute,
      2. Somewhat unclear, as the rule of evolution itself can be computed in some cases from the evolutionary history of a pattern, and
      3. Raises new complexities for existing methuselahs — for many, it is identical to (2), but for others, such as those terminating in a common evolutionary sequence, the "chaotic lifespan" is over before the pattern reaches even its lifespan per (1).
Finally, a very simple metric, that, while not equivalent to any other definition including the canonical one, is unambiguously defined for every pattern that does not grow infinitely and is unambiguously undefined for every pattern that does, is the first generation at which a pattern reaches its maximum population. This may or not be a useful metric.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

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Re: Methuselah Definition

Postby Macbi » November 28th, 2017, 2:24 pm

A for awesome wrote:This seems slightly preferable because it assumes no prior knowledge about how periodic patterns will behave

We don't really need that though, do we? We can always evolve forward for one period to see how the periodic pattern behaves and the work backwards to find the point at which it started behaving that way.
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Re: Methuselah Definition

Postby Majestas32 » November 28th, 2017, 7:56 pm

Macbi wrote:
A for awesome wrote:This seems slightly preferable because it assumes no prior knowledge about how periodic patterns will behave

We don't really need that though, do we? We can always evolve forward for one period to see how the periodic pattern behaves and the work backwards to find the point at which it started behaving that way.

That was my thinking. Of course there's always sqrt(t) growth things etc but let's ignore that pathological stuff
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