Period infinity oscillators and spaceships?

[Saka]

I just want to ask if they exist
I know that if it is period infinity it wouldn't really be an "oscillator"...

[simsim314]

I know that if it is period infinity it wouldn't really be an "oscillator"...

There is no meaning in period infinity oscillator. There is no such thing as "almost oscillator".

[apg]

I know that if it is period infinity it wouldn't really be an "oscillator"...

There is no meaning in period infinity oscillator. There is no such thing as "almost oscillator".

I agree with the first of these statements, but not the second. Consider the following line of reasoning:

For finitely-supported patterns, the following two definitions are equivalent:

• There exists a period, P, such that the pattern returns to its original state after P generations.
• Every cell in the universe is periodic.

In general, the first definition (which is the usual definition of an oscillator, so 'period-infinity oscillator' is indeed meaningless) is stronger than the second. So we could call a pattern that satisfies the second definition an 'almost-oscillator'.

Now, if you allow patterns with infinite population, an example of a period-infinity almost oscillator is the disjoint union of oscillators of periods {1, 2, 3, 4, ...}. But usually we don't consider these to be patterns by the usual definition.

More subtly, it is possible to build a period-infinity almost-oscillator which has a finite population in all generations. This can be accomplished in b3/s23, but it's quite difficult to implement, so I shall instead exhibit such a pattern in a custom rule. Firstly, copy and paste this rule into Golly:

Code: Select all

@RULE UnboundedCounter

@TABLE

n_states:4
neighborhood:vonNeumann
symmetries:none

var a={0,1,2,3}
var b={0,1,2,3}
var c={0,1,2,3}
var d={0,1,2,3}
var e={0,1,2,3}

0,a,b,c,2,1
1,a,b,c,2,2
2,a,b,c,d,0
0,a,b,c,3,2

Now copy and paste this pattern into Golly:

Code: Select all

x = 1, y = 1, rule = UnboundedCounter
C!

Then every cell is periodic, but the pattern has infinite period. Someone such as Dave Greene could probably implement this in b3/s23.

[David]

Then every cell is periodic, but the pattern has infinite period. Someone such as Dave Greene could probably implement this in b3/s23.

But this pattern isn't really a strict oscillator, right? What name should we call patterns like this very pattern?

[simsim314]

Well I don't like to have some amorphic therm like infinite oscillator and start guessing what it means.

If you define infinite oscillator is not-oscillator but eventually each cell will be periodic after some time, you can take glider gun as example. And yet again there is no point in guessing post-priory the meaning of some ill defined terminology.

[Saka]

Ok what about infinite period spaceships?

[Kazyan]

Infinity, no, but it's fairly simple to modify Gemini so that it's period is as high as you want. I think you just space out the constructors more.

[simsim314]

about infinite period spaceships?

Please define the therm "infinite period spaceships". I have no clue what you mean by that, for me it's total nonsense like still life spaceship or P19 empty space.

[Saka]

about infinite period spaceships?

Please define the therm "infinite period spaceships". I have no clue what you mean by that, for me it's total nonsense like still life spaceship or P19 empty space.

A spaceship that never repeats its original pattern/configuration/state but remaining in a determined bounding box

[simsim314]

A spaceship that never repeats its original pattern/configuration/state but remaining in a determined bounding box

Such doesn't exist for simple reason, the number of setups in limited bounding box is finite. Each pattern limited by determined bounding box will eventually repeat itself.

To give rough estimate of the maximal possible period: pattern inside bounding box of size NxN will repeat itself after maximum 2^(N*N) generations.

[towerator]

A spaceship that never repeats its original pattern/configuration/state but remaining in a determined bounding box

I'm currently thinking about 2 arrays of ships, with 2 different velocities bot none of them is c/2:
The "fast array", let's say 2c/5, gets collided from behind by a LWSS, and transforms it into a block. Later, thethe c/3 array collects the block, recreate the LWSS and sends it flinging back to the first array. It would create a growing spaceship easily moddable into a caber tosser, and it would have a higher and higher period.

[apg]

If you define infinite oscillator is not-oscillator but eventually each cell will be periodic after some time, you can take glider gun as example.

I used the definition that every cell is periodic, not merely eventually periodic.

Then every cell is periodic, but the pattern has infinite period. Someone such as Dave Greene could probably implement this in b3/s23.

But this pattern isn't really a strict oscillator, right? What name should we call patterns like this very pattern?

Well, I used the term 'almost-oscillator', but perhaps 'local oscillator' is more descriptive.