Stable and Periodic discussion

[confocaloid]

(Edited) I changed "oscillates with period" to "has period", because I think "oscillates with period" is commonly used only for oscillators or for a subset of cells of a pattern.

(For what it's worth) I do not like the repetition in "periodic with period". If the pattern is an oscillator, or when talking about a subset of cells of a pattern, I think an alternative way to say it would be "oscillates with period...".

I'll replace it with this:

A periodic pattern oscillates with period p if it repeats every p generations. This includes still lifes (trivially, with p=1), oscillators, and spaceships.

[Wyirm]

You can't talk about motion in an endless void with no reference to position without talking about relativity.
Even the definition of CA are relativistic in a sense. Objects act without regard to other objects unless they directly come into contact. Imagine this:
You're busy emulating cgol, and a spceship flies by. You could reasonably deduce that from your TEMPORAL viewframe that the spaceship is moving at 2c/4, and you are standing completely still. From the spaceship's perspective, you and your emulator are also moving at 2c/4, with some altered version of cgol. The spaceship sees itself as a p4 oscillator, and in it's TEMPORAL viewframe, this is completely reasonable. In fact, purely looking at the pattern cannot define it as a spaceship, it functions essentially the same as an oscillator. If you are given a spaceship and an oscillator of the same period, the only way we define a spaceship is through looking at it through a SPATIAL viewframe, and in the endless abyss of dead cells, that doesn't actually exist.
This is not to say that oscillators and spaceships are the same, but spaceships act as oscillators in a void.

[dvgrn]

(Edited) I changed "oscillates with period" to "has period", because I think "oscillates with period" is commonly used only for oscillators or for a subset of cells of a pattern.

Good call -- thanks!

n to p?
makes sense to me

Okay, done.
That was fun.

[Book]

I'd like to turn back now to "stable" and go back to basics, see if we can get agreement on fundamental concepts.

In the context of "is pattern X stable" or "is X a stable pattern" (I assume these are two ways of saying the same thing):

If X is a still life, the answer is yes.

If X is an oscillator, is it stable?
If X is a spaceship is it stable?
If X is a gun is it stable?

For each of these cases (obviously there are others), if the answer is no, do we want to say X is unstable? That is, is stable a binary attribute, you either are or you aren't? Or is there a continuum, perhaps with stable at one extreme and chaotic at another, and some other gradations (labels) in between? Or what?

Similarly, if X is the predecessor of a still life, is it unstable?

[dvgrn]

Similarly, if X is the predecessor of a still life, is it unstable?

That one seems easy. Yes, there will be general agreement that the predecessor is unstable -- it turns into something else, and never turns back into itself again.

The rest of these questions kind of worry me a little bit. The word "stable" has at least a couple of mutually contradictory common uses.

Notably, ash can become "stable" after N ticks, even when the "stable ash" includes p2 stuff or even more exotic stuff, possibly including guns and .puffers. This is a common use of "stable", so the article needs to acknowledge it.

In other usage, "stable" can be a synonym for "p1", notably in the context of "stable circuitry". Gotta acknowledge that too. So far so good.

Whenever there are mutually contradictory definitions, there's no way that a term can be a binary attribute. It seems a little dangerous to logically derive a new term, "unstable", that's the "opposite of stable", and then try to deduce what it might mean, on the basis of a contradictory foundation.

Seems like the only thing you can safely do is document actual common usage of terms that are actually commonly used... in which case, "unstable" should not be applied to spaceships or guns (for example) because it doesn't seem like anybody uses the word "unstable" to refer to spaceships or guns.

[wirehead]

I'd like to turn back now to "stable" and go back to basics, see if we can get agreement on fundamental concepts.

In the context of "is pattern X stable" or "is X a stable pattern" (I assume these are two ways of saying the same thing):

If X is a still life, the answer is yes.

If X is an oscillator, is it stable?
If X is a spaceship is it stable?
If X is a gun is it stable?

For each of these cases (obviously there are others), if the answer is no, do we want to say X is unstable? That is, is stable a binary attribute, you either are or you aren't? Or is there a continuum, perhaps with stable at one extreme and chaotic at another, and some other gradations (labels) in between? Or what?

Similarly, if X is the predecessor of a still life, is it unstable?

I think one definition of "stable" would be that the population doesn't grow off to infinity if you run it long enough and the bounding box doesn't also run off to infinity, and there is at least one cell that will forever remain in the bounding box. So that would eliminate guns and spaceships.

If something is a predecessor of a stable pattern, the predecessor stabilizes.

I would call an "unstable" pattern one that eventually will stabilize, but is not stabilized yet.

Then we get into the world of "predictable." I would call something "predictable" if you can reverse-engineer it and create a logic circuit that would be simpler than just a grid of Life unit cells that just simulates the pattern. I.e. the p46 PRNG (see OP of this thread) would just be a toggle latch, an inverter, and a delay line wired into each other.

[confocaloid]

...
In the context of "is pattern X stable" or "is X a stable pattern" (I assume these are two ways of saying the same thing):
...

No - these are not always equivalent. For example, as already mentioned earlier in this very thread, current revisions of many articles about methuselahs have sections named "Stable pattern", and use "stable pattern" to refer to the resulting remaining settled ash. E.g. Acorn currently contains statement:

The stable pattern that results from the acorn has 633 cells and covers an area of 215 by 168 cells; it consists of 41 blinkers (including four traffic lights), 34 blocks, 30 beehives (including one honey farm), 13 gliders, eight boats, five loaves, three ships, two barges, two ponds and a mango.

However, I believe it would be incorrect to replace "stable pattern" with "pattern is stable" in this case, because the ash of the acorn is not stable - it contains blinkers, and blinkers are p2.

(An alternative way to refer to the resulting ash of a methuselah is to say that it is the final pattern - see e.g. Lifeline vol.3 page 8. The final pattern is not required to be stable - it may be stable, or it may be periodic.)

Long story short: I would oppose interpreting "is pattern X stable" and "is X a stable pattern" as two equivalent ways to say the same thing - I believe these are two different distinct wordings, which are commonly used in different contexts with distinct meanings.

...
For each of these cases (obviously there are others), if the answer is no, do we want to say X is unstable? That is, is stable a binary attribute, you either are or you aren't? Or is there a continuum, perhaps with stable at one extreme and chaotic at another, and some other gradations (labels) in between? Or what?
...

I believe that this discussion is not about logically deriving something. Neither it is about finding some good generalisation. Instead, this discussion is about the actual ways how words and combinations of words are actually used, when people discuss Conway's Game of Life (e.g. on these forums). The wiki should attempt to reflect the common usage - rather than trying to make things polished, logical and general.

[Book]

I appreciate the discussion. I agree that common usage is the guiding principle. It would be great if we could document these nuances (ok, maybe they are not nuances, but...) in the wiki article. Because I think the "innocent" questions I posed reveal necessary distinctions in usage and somehow exposing them would reveal much about even why there are different usages of this seemingly simple word (and its offshoots). And those differences reveal important concepts behind the usage.