Period infinity oscillators and spaceships?

 Posts: 3138
 Joined: June 19th, 2015, 8:50 pm
 Location: In the kingdom of Sultan Hamengkubuwono X
Period infinity oscillators and spaceships?
I just want to ask if they exist
I know that if it is period infinity it wouldn't really be an "oscillator"...
I know that if it is period infinity it wouldn't really be an "oscillator"...
Airy Clave White It Nay
(Check gen 2)
Code: Select all
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
Re: Period infinity oscillators and spaceships?
There is no meaning in period infinity oscillator. There is no such thing as "almost oscillator".Saka wrote:I know that if it is period infinity it wouldn't really be an "oscillator"...
Re: Period infinity oscillators and spaceships?
I agree with the first of these statements, but not the second. Consider the following line of reasoning:simsim314 wrote:There is no meaning in period infinity oscillator. There is no such thing as "almost oscillator".Saka wrote:I know that if it is period infinity it wouldn't really be an "oscillator"...
For finitelysupported 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.
Now, if you allow patterns with infinite population, an example of a periodinfinity 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 periodinfinity almostoscillator 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
Code: Select all
x = 1, y = 1, rule = UnboundedCounter
C!
What do you do with ill crystallographers? Take them to the monoclinic!
Re: Period infinity oscillators and spaceships?
But this pattern isn't really a strict oscillator, right? What name should we call patterns like this very pattern?calcyman wrote: Then every cell is periodic, but the pattern has infinite period. Someone such as Dave Greene could probably implement this in b3/s23.
Call me "Dannyu NDos" in Forum. Call me "Park Shinhwan"(박신환) in Wiki.
Re: Period infinity oscillators and spaceships?
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 notoscillator 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 postpriory the meaning of some ill defined terminology.
If you define infinite oscillator is notoscillator 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 postpriory the meaning of some ill defined terminology.

 Posts: 3138
 Joined: June 19th, 2015, 8:50 pm
 Location: In the kingdom of Sultan Hamengkubuwono X
Re: Period infinity oscillators and spaceships?
Ok what about infinite period spaceships?
Airy Clave White It Nay
(Check gen 2)
Code: Select all
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
Re: Period infinity oscillators and spaceships?
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.
Tanner Jacobi
Re: Period infinity oscillators and 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 wrote: about infinite period spaceships?

 Posts: 3138
 Joined: June 19th, 2015, 8:50 pm
 Location: In the kingdom of Sultan Hamengkubuwono X
Re: Period infinity oscillators and spaceships?
A spaceship that never repeats its original pattern/configuration/state but remaining in a determined bounding boxsimsim314 wrote: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 wrote: about infinite period spaceships?
Airy Clave White It Nay
(Check gen 2)
Code: Select all
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
Re: Period infinity oscillators and spaceships?
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.Saka wrote:A spaceship that never repeats its original pattern/configuration/state but remaining in a determined bounding box
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.
Re: Period infinity oscillators and spaceships?
I'm currently thinking about 2 arrays of ships, with 2 different velocities bot none of them is c/2:Saka wrote: A spaceship that never repeats its original pattern/configuration/state but remaining in a determined bounding box
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.
This is game of life, this is game of life!
Loafin' ships eaten with a knife!
Loafin' ships eaten with a knife!
Re: Period infinity oscillators and spaceships?
I used the definition that every cell is periodic, not merely eventually periodic.If you define infinite oscillator is notoscillator but eventually each cell will be periodic after some time, you can take glider gun as example.
Well, I used the term 'almostoscillator', but perhaps 'local oscillator' is more descriptive.David wrote:But this pattern isn't really a strict oscillator, right? What name should we call patterns like this very pattern?calcyman wrote: Then every cell is periodic, but the pattern has infinite period. Someone such as Dave Greene could probably implement this in b3/s23.
What do you do with ill crystallographers? Take them to the monoclinic!