Thread for basic questions
Re: Thread for basic questions
What types of symmetries can a periodic wick or agar have?
Parity Replicator Collection v1.6 is now live  please send all relevant discoveries here.
Re: Thread for basic questions
Has it ever been tabulated in how many places a single block can go that trigger either a Blocklaying or Gliderproducing Switch Engine from a single Switch engine?
 confocaloid
 Posts: 4111
 Joined: February 8th, 2022, 3:15 pm
 Location: https://catagolue.hatsya.com/census/b3s234c/C4_4/xp62
Re: Thread for basic questions
The first potentially related thing that comes to mind is "a search to find 4glider syntheses of glider producing switch engines, with the condition that none of them produce any nonforwardfacing gliders [...] hitting a 3G unstable switch engine synth with a glider":
viewtopic.php?p=153472#p153472
There were also several undocumented Catagolue censuses related to switch engines, among those listed in https://catagolue.hatsya.com/census/b3s23
127:1 B3/S234c User:Confocal/R (isotropic CA, incomplete)
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.
Re: Thread for basic questions
none filps to D2_x
Code: Select all
x = 9, y = 9, rule = B3/S23:T10,10
o7bo2$6bobo2$4bobo2$2bobo2$obo!
Code: Select all
x = 8, y = 8, rule = B3/S23:T8,8
3bo3bo$2bo3bo$o3bo$bo3bo$3bo3bo$2bo3bo$o3bo$bo3bo!
Code: Select all
x = 16, y = 16, rule = B3/S23:T16,16
obo5bobo$4bobo5bobo$o7bo$5bo7bo$bo5bobo5bo$3bobo5bobo$bo7bo$4bo7bo$ob
o5bobo$4bobo5bobo$o7bo$5bo7bo$bo5bobo5bo$3bobo5bobo$bo7bo$4bo7bo!
Code: Select all
x = 106, y = 106, rule = B3/S23:T106,106
b2o5bo24b3o2b2o7bob2obo2bo22b3o3bob2o11bo$2obo3b3o22bo2bob2obo7b2o2b3o
24bo5b2o7bo$bob2obo2bo22b3o3bob2o11bo7b2o5bo24b3o2b2o$2b2o2b3o24bo5b2o
7bo11b2obo3b3o22bo2bob2obo$7bo7b2o5bo24b3o2b2o7bob2obo2bo22b3o3bob2o$
2bo11b2obo3b3o22bo2bob2obo7b2o2b3o24bo5b2o$b3o2b2o7bob2obo2bo22b3o3bo
b2o11bo7b2o5bo$o2bob2obo7b2o2b3o24bo5b2o7bo11b2obo3b3o$3o3bob2o11bo7b
2o5bo24b3o2b2o7bob2obo2bo$bo5b2o7bo11b2obo3b3o22bo2bob2obo7b2o2b3o$15b
3o2b2o7bob2obo2bo22b3o3bob2o11bo7b2o5bo$14bo2bob2obo7b2o2b3o24bo5b2o7b
o11b2obo3b3o$14b3o3bob2o11bo7b2o5bo24b3o2b2o7bob2obo2bo$15bo5b2o7bo11b
2obo3b3o22bo2bob2obo7b2o2b3o$4bo24b3o2b2o7bob2obo2bo22b3o3bob2o11bo7b
2o$3b3o22bo2bob2obo7b2o2b3o24bo5b2o7bo11b2obo$obo2bo22b3o3bob2o11bo7b
2o5bo24b3o2b2o7bobo$2b3o24bo5b2o7bo11b2obo3b3o22bo2bob2obo7b2o$3bo7b2o
5bo24b3o2b2o7bob2obo2bo22b3o3bob2o$10b2obo3b3o22bo2bob2obo7b2o2b3o24b
o5b2o7bo$2b2o7bob2obo2bo22b3o3bob2o11bo7b2o5bo24b3o$b2obo7b2o2b3o24bo
5b2o7bo11b2obo3b3o22bo2bo$2bob2o11bo7b2o5bo24b3o2b2o7bob2obo2bo22b3o$
3b2o7bo11b2obo3b3o22bo2bob2obo7b2o2b3o24bo$11b3o2b2o7bob2obo2bo22b3o3b
ob2o11bo7b2o5bo$10bo2bob2obo7b2o2b3o24bo5b2o7bo11b2obo3b3o$10b3o3bob2o
11bo7b2o5bo24b3o2b2o7bob2obo2bo$11bo5b2o7bo11b2obo3b3o22bo2bob2obo7b2o
2b3o$o24b3o2b2o7bob2obo2bo22b3o3bob2o11bo7b2o$2o22bo2bob2obo7b2o2b3o24b
o5b2o7bo11b2obo3bo$bo22b3o3bob2o11bo7b2o5bo24b3o2b2o7bob2obo$o24bo5b2o
7bo11b2obo3b3o22bo2bob2obo7b2o2b2o$7b2o5bo24b3o2b2o7bob2obo2bo22b3o3b
ob2o11bo$6b2obo3b3o22bo2bob2obo7b2o2b3o24bo5b2o7bo$7bob2obo2bo22b3o3b
ob2o11bo7b2o5bo24b3o2b2o$o7b2o2b3o24bo5b2o7bo11b2obo3b3o22bo2bob2o$2o
11bo7b2o5bo24b3o2b2o7bob2obo2bo22b3o3bo$o7bo11b2obo3b3o22bo2bob2obo7b
2o2b3o24bo5bo$7b3o2b2o7bob2obo2bo22b3o3bob2o11bo7b2o5bo$6bo2bob2obo7b
2o2b3o24bo5b2o7bo11b2obo3b3o$6b3o3bob2o11bo7b2o5bo24b3o2b2o7bob2obo2b
o$7bo5b2o7bo11b2obo3b3o22bo2bob2obo7b2o2b3o$21b3o2b2o7bob2obo2bo22b3o
3bob2o11bo7b2o5bo$20bo2bob2obo7b2o2b3o24bo5b2o7bo11b2obo3b3o$20b3o3bo
b2o11bo7b2o5bo24b3o2b2o7bob2obo2bo$21bo5b2o7bo11b2obo3b3o22bo2bob2obo
7b2o2b3o$3b2o5bo24b3o2b2o7bob2obo2bo22b3o3bob2o11bo$2b2obo3b3o22bo2bo
b2obo7b2o2b3o24bo5b2o7bo$3bob2obo2bo22b3o3bob2o11bo7b2o5bo24b3o2b2o$4b
2o2b3o24bo5b2o7bo11b2obo3b3o22bo2bob2obo$9bo7b2o5bo24b3o2b2o7bob2obo2b
o22b3o3bob2o$4bo11b2obo3b3o22bo2bob2obo7b2o2b3o24bo5b2o$3b3o2b2o7bob2o
bo2bo22b3o3bob2o11bo7b2o5bo$2bo2bob2obo7b2o2b3o24bo5b2o7bo11b2obo3b3o
$2b3o3bob2o11bo7b2o5bo24b3o2b2o7bob2obo2bo$3bo5b2o7bo11b2obo3b3o22bo2b
ob2obo7b2o2b3o$17b3o2b2o7bob2obo2bo22b3o3bob2o11bo7b2o5bo$16bo2bob2ob
o7b2o2b3o24bo5b2o7bo11b2obo3b3o$16b3o3bob2o11bo7b2o5bo24b3o2b2o7bob2o
bo2bo$17bo5b2o7bo11b2obo3b3o22bo2bob2obo7b2o2b3o$o5bo24b3o2b2o7bob2ob
o2bo22b3o3bob2o11bo7bo$bo3b3o22bo2bob2obo7b2o2b3o24bo5b2o7bo11b2o$b2o
bo2bo22b3o3bob2o11bo7b2o5bo24b3o2b2o7bo$2o2b3o24bo5b2o7bo11b2obo3b3o22b
o2bob2obo$5bo7b2o5bo24b3o2b2o7bob2obo2bo22b3o3bob2o$o11b2obo3b3o22bo2b
ob2obo7b2o2b3o24bo5b2o$2o2b2o7bob2obo2bo22b3o3bob2o11bo7b2o5bo24bo$bo
b2obo7b2o2b3o24bo5b2o7bo11b2obo3b3o22bo$o3bob2o11bo7b2o5bo24b3o2b2o7b
ob2obo2bo22b2o$5b2o7bo11b2obo3b3o22bo2bob2obo7b2o2b3o24bo$13b3o2b2o7b
ob2obo2bo22b3o3bob2o11bo7b2o5bo$12bo2bob2obo7b2o2b3o24bo5b2o7bo11b2ob
o3b3o$12b3o3bob2o11bo7b2o5bo24b3o2b2o7bob2obo2bo$13bo5b2o7bo11b2obo3b
3o22bo2bob2obo7b2o2b3o$2bo24b3o2b2o7bob2obo2bo22b3o3bob2o11bo7b2o$b3o
22bo2bob2obo7b2o2b3o24bo5b2o7bo11b2obo$o2bo22b3o3bob2o11bo7b2o5bo24b3o
2b2o7bob2o$3o24bo5b2o7bo11b2obo3b3o22bo2bob2obo7b2o$bo7b2o5bo24b3o2b2o
7bob2obo2bo22b3o3bob2o$8b2obo3b3o22bo2bob2obo7b2o2b3o24bo5b2o7bo$2o7b
ob2obo2bo22b3o3bob2o11bo7b2o5bo24b3o$obo7b2o2b3o24bo5b2o7bo11b2obo3b3o
22bo2bobo$ob2o11bo7b2o5bo24b3o2b2o7bob2obo2bo22b3o$b2o7bo11b2obo3b3o22b
o2bob2obo7b2o2b3o24bo$9b3o2b2o7bob2obo2bo22b3o3bob2o11bo7b2o5bo$8bo2b
ob2obo7b2o2b3o24bo5b2o7bo11b2obo3b3o$8b3o3bob2o11bo7b2o5bo24b3o2b2o7b
ob2obo2bo$9bo5b2o7bo11b2obo3b3o22bo2bob2obo7b2o2b3o$23b3o2b2o7bob2obo
2bo22b3o3bob2o11bo7b2o5bo$22bo2bob2obo7b2o2b3o24bo5b2o7bo11b2obo3b3o$
22b3o3bob2o11bo7b2o5bo24b3o2b2o7bob2obo2bo$23bo5b2o7bo11b2obo3b3o22bo
2bob2obo7b2o2b3o$5b2o5bo24b3o2b2o7bob2obo2bo22b3o3bob2o11bo$4b2obo3b3o
22bo2bob2obo7b2o2b3o24bo5b2o7bo$5bob2obo2bo22b3o3bob2o11bo7b2o5bo24b3o
2b2o$6b2o2b3o24bo5b2o7bo11b2obo3b3o22bo2bob2obo$11bo7b2o5bo24b3o2b2o7b
ob2obo2bo22b3o3bob2o$6bo11b2obo3b3o22bo2bob2obo7b2o2b3o24bo5b2o$5b3o2b
2o7bob2obo2bo22b3o3bob2o11bo7b2o5bo$4bo2bob2obo7b2o2b3o24bo5b2o7bo11b
2obo3b3o$4b3o3bob2o11bo7b2o5bo24b3o2b2o7bob2obo2bo$5bo5b2o7bo11b2obo3b
3o22bo2bob2obo7b2o2b3o$19b3o2b2o7bob2obo2bo22b3o3bob2o11bo7b2o5bo$18b
o2bob2obo7b2o2b3o24bo5b2o7bo11b2obo3b3o$18b3o3bob2o11bo7b2o5bo24b3o2b
2o7bob2obo2bo$19bo5b2o7bo11b2obo3b3o22bo2bob2obo7b2o2b3o!
Code: Select all
x = 24, y = 24, rule = B3/S23:T24,24
o5bo5bo5bo$3bo5bo5bo5bo$bo3bobo3bobo3bobo3bo$3bo5bo5bo5bo$o5bo5bo5bo$
2bobo3bobo3bobo3bobo$o5bo5bo5bo$3bo5bo5bo5bo$bo3bobo3bobo3bobo3bo$3bo
5bo5bo5bo$o5bo5bo5bo$2bobo3bobo3bobo3bobo$o5bo5bo5bo$3bo5bo5bo5bo$bo3b
obo3bobo3bobo3bo$3bo5bo5bo5bo$o5bo5bo5bo$2bobo3bobo3bobo3bobo$o5bo5bo
5bo$3bo5bo5bo5bo$bo3bobo3bobo3bobo3bo$3bo5bo5bo5bo$o5bo5bo5bo$2bobo3b
obo3bobo3bobo!

 Posts: 892
 Joined: April 26th, 2023, 5:47 am
 Location: Bahar Junction, Zumaland
Re: Thread for basic questions
Is a 12345 and beyond known?
~ Haycat Durnak, a hardworking editor
Also, support Conway and Friends story mode!
I mean no harm to those who have tested me. But do not take this for granted.
Also, support Conway and Friends story mode!
I mean no harm to those who have tested me. But do not take this for granted.
Re: Thread for basic questions
As far as I understand, you are interested in oscillators that have a rotor with p cells and number of alive cells in rotor changing like 12...p12...p... (period p).
For p>4, this is impossible, because the birth of a cell in generation p1 (active cells count p1 > p) should affect the death of more than 3 cells (p > 1), but there are only 3 cells that can be affected immediately  3 neighbours that turned it into alive state (this cell cannot die due to S3).
The latest version of hexgliders.db have 668 gliders from OT hexagonal rules.
The latest version of newgliders.db (28991 gliders): here
My scripts: newglider.py v0.2, nbsearch2a.py, collector.py v0.3
Dmitry Maitak
The latest version of newgliders.db (28991 gliders): here
My scripts: newglider.py v0.2, nbsearch2a.py, collector.py v0.3
Dmitry Maitak
Re: Thread for basic questions
Is "iron" an established term?
https://catagolue.hatsya.com/object/xs1 ... x11/b3s23/
Second question: regarding cis/trans: is the way I'm calculating it how it's supposed to be done? (Catagolue made the correct decision according to the graphic below.)
https://catagolue.hatsya.com/object/xs1 ... x11/b3s23/
Second question: regarding cis/trans: is the way I'm calculating it how it's supposed to be done? (Catagolue made the correct decision according to the graphic below.)
 Attachments

 Screenshot 20240809 at 7.21.07 AM.png (36.79 KiB) Viewed 3147 times
User:HotdogPi/My discoveries
Periods discovered: 516,⑱,⑳G,㉑G,㉒㉔㉕,㉗㉛,㉜SG,㉞㉟㊱㊳㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,6266,68,70,73,74S,75,76S,80,84,88,90,96
100,02S,06,08,10,12,14G,16,17G,20,26G,28,38,44,47,48,54,56,72,74,80,92,96S
217,300,486,576
S: SKOP
G: gun
Periods discovered: 516,⑱,⑳G,㉑G,㉒㉔㉕,㉗㉛,㉜SG,㉞㉟㊱㊳㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,6266,68,70,73,74S,75,76S,80,84,88,90,96
100,02S,06,08,10,12,14G,16,17G,20,26G,28,38,44,47,48,54,56,72,74,80,92,96S
217,300,486,576
S: SKOP
G: gun
Re: Thread for basic questions
Does the line that the orthogonal loopship reflects across pass through cell centers or cell vertices? Likewise for the orthogonoid and the speed orthogonal loopship.
Parity Replicator Collection v1.6 is now live  please send all relevant discoveries here.
Re: Thread for basic questions
Is there a full archive of pentadecathlon.com anywhere? The site no longer appears to be active and many links from the wiki now 404 even with the wayback machine.
Parity Replicator Collection v1.6 is now live  please send all relevant discoveries here.
 confocaloid
 Posts: 4111
 Joined: February 8th, 2022, 3:15 pm
 Location: https://catagolue.hatsya.com/census/b3s234c/C4_4/xp62
Re: Thread for basic questions
Re: Thread for basic questions
For a given period n, is it possible for an infinite number of distinct oscillators with period n to exist which all have the same minimum population, discounting pseudoobjects?
Parity Replicator Collection v1.6 is now live  please send all relevant discoveries here.
Re: Thread for basic questions
Not sure what you might have in mind, but I'm not sure how to have infinitely many anything of a given period and population if it's going to remain well connected i.e. not pseudo. Like a sufficiently large snark loop can adjust the sides of the rectangle of the glider paths, but there's only a finite number of combinations for any finite period. Likewise, it feels like any oscillator of a given period has some well definable max bounding box based on the speed of light, and only a finite number of patterns of any sort can fit in that bounding box.

 Posts: 892
 Joined: April 26th, 2023, 5:47 am
 Location: Bahar Junction, Zumaland
Re: Thread for basic questions
Is Motor Grader really the first nonmonotonic c/7 spaceship? I remember seeing a smaller nonmonotonic c/7 spaceship once with the exact same frontend.
~ Haycat Durnak, a hardworking editor
Also, support Conway and Friends story mode!
I mean no harm to those who have tested me. But do not take this for granted.
Also, support Conway and Friends story mode!
I mean no harm to those who have tested me. But do not take this for granted.
Re: Thread for basic questions
It's the first elementary nonmonotonic c/7 spaceship, but not the first overall, because the c/7 Caterloopillar is also nonmonotonic.Haycat2009 wrote: ↑August 12th, 2024, 5:44 amIs Motor Grader really the first nonmonotonic c/7 spaceship?
There was a c/7 orthogonal wave with a similar front end (one half of motor grader's front end), but no complete spaceship with that front end.Haycat2009 wrote: ↑August 12th, 2024, 5:44 amI remember seeing a smaller nonmonotonic c/7 spaceship once with the exact same frontend.
Code: Select all
#C c/7 orthogonal wave
x = 13, y = 53, rule = B3/S23
4bo$6bo$bo5bo$8bo$2ob3ob2o2$4bo$3bobo$2bo4b2o$2o3b4o$o3bo$2bo$2bo2$3b
5o$7bo$8bo4$4bo3b2o$2b2ob3o2bo$3bo6bo$4b2obobo$6bo$4bo3bo$2bob2o3bo$b
2obo2bo2bo$5bob3o$3b2o3bo$4b3obo$4b3o$10bo$9b2o3$7b3o$5b6o$5b7o$4b2o5b
2o3$7b3o$7b2o2bo$7b6o$3b4o$5b2o3bo2$7bo2bo$11bo$7b2obobo2$11b2o!
Matthias Merzenich

 Posts: 279
 Joined: April 1st, 2021, 1:03 am
Re: Thread for basic questions
Do you have a list of glider turners in Life?
Re: Thread for basic questions
I think Hippo.69's recent work is by far the best collection that has been made so far  much better documented and more comprehensive than my attempt at sorting a different enumeration earlier in that thread.
Back almost a decade ago, simsim314 posted a collection (also in that same thread) based on an enumeration of constellations that included some different still lifes (e.g., mangoes). Hippo.69's turners also include mangoes, tubwithtails, integrals, aircraft carriers, shipties, shillelaghs, eleveners, and maybe a few other still lifes from farther down on the commonness scale.
Re: Thread for basic questions
When were period3 oscillators up to 18 cells enumerated, and by who?
Parity Replicator Collection v1.6 is now live  please send all relevant discoveries here.

 Posts: 892
 Joined: April 26th, 2023, 5:47 am
 Location: Bahar Junction, Zumaland
Re: Thread for basic questions
Including those with multiple islands and noninteracting rotors?May13 wrote: ↑August 8th, 2024, 11:26 amAs far as I understand, you are interested in oscillators that have a rotor with p cells and number of alive cells in rotor changing like 12...p12...p... (period p).
For p>4, this is impossible, because the birth of a cell in generation p1 (active cells count p1 > p) should affect the death of more than 3 cells (p > 1), but there are only 3 cells that can be affected immediately  3 neighbours that turned it into alive state (this cell cannot die due to S3).
~ Haycat Durnak, a hardworking editor
Also, support Conway and Friends story mode!
I mean no harm to those who have tested me. But do not take this for granted.
Also, support Conway and Friends story mode!
I mean no harm to those who have tested me. But do not take this for granted.
Re: Thread for basic questions
I have several questions about SKOPs in life:
What is the average proportional size decrease for SKOPs in life (from 1st known oscillator to current SKOP)  either up to a fixed value or infinity?
How many oscillator periods have SKOPs with minimum population greater than their period? Maximum? (This number is finite since eventually dependent loops set constant limits on population)
What is the highest period SKOP in life with a minimum population greater than it's period? Maximum?
Finally, how many periods of oscillators are known to be currently represented by the smallest possible SKOP/SKOPs?
What is the average proportional size decrease for SKOPs in life (from 1st known oscillator to current SKOP)  either up to a fixed value or infinity?
How many oscillator periods have SKOPs with minimum population greater than their period? Maximum? (This number is finite since eventually dependent loops set constant limits on population)
What is the highest period SKOP in life with a minimum population greater than it's period? Maximum?
Finally, how many periods of oscillators are known to be currently represented by the smallest possible SKOP/SKOPs?
Last edited by WhiteHawk on August 14th, 2024, 12:55 pm, edited 5 times in total.
 confocaloid
 Posts: 4111
 Joined: February 8th, 2022, 3:15 pm
 Location: https://catagolue.hatsya.com/census/b3s234c/C4_4/xp62
Re: Thread for basic questions
FWIW, I see six questions in your post, which doesn't quite match my understanding of what constitutes 'a couple of questions'.
You may need to clarify the intended question.
If you mean the average of (minpop(SKOP(n)) / minpop(first known oscillator(n))) for periods n up to some fixed positive integer (say n <= 100), then that's a function of both the current knowledge and the highest period to take into account. It could be computed from available data, but I'm not sure if I understand the purpose.
If you mean the average of (minpop(SKOP(n)) / minpop(first known oscillator(n))) for all positive integer periods n, then one could consider what happens with the infinite families of oscillators (e.g. pentadecathlonbased glider shuttles, closed Herschel tracks, Snarkbased glider loop oscillators, rectifierbased glider loop oscillators, etc.) and how those affect the answer. Again, one could attempt to answer this from existing data, but it is unclear why the answer would be interesting.
Infinitely many, to both questions. Highperiod glider loop oscillators that are SKOPs have bounded population and unbounded period.
Firstly, the statement of these two questions implicitly assumes that the answer to previous two questions is "infinity" (making it unclear why the preceding two questions were asked at all).
Indeed, if there were only finitely many oscillator periods with SKOPs whose (minimummaximum) population fails to exceed their period, then as a consequence there would be infinitely many oscillator periods with SKOPs whose (minimummaximum) population does exceed their period, and as a consequence there would be no highest period SKOP in Conway's Life with a (minimummaximum) population that exceeds their period. But the questions assume that such highest period does exist.
For the minimum population question, the answer may be 142 due to the following glider shuttle (period 142, minpop 144):
Code: Select all
#C Two Jubjub reflectors shuttling a glider
x = 38, y = 39, rule = B3/S23
19b2o$20bo$19bo$19b2o11bo$17b2o11b3o$16bo2b2o8bo$17bobo9b2o$16b2obobo4bo7b2o$
20b2o3bobo6bo$24bo2bo4bobo$25b2o5b2o4$17bo$4b2o9b3o$b2o2bo8bo19b2o$o2b2o3bo5b
2o15b2o2bo$obo2b4o22b2obo$bobo30bobo$3bob2o22b4o2bobo$2bo2b2o15b2o5bo3b2o2bo$
2b2o19bo8bo2b2o$20b3o9b2o$20bo$11b2o$10b2o$11b2o$4b2o$3bobo$3bo13bo$2b2o12bob
ob2o$7b2o7bobobo$8bo7b3o2bo$5b3o11b2o$5bo11b2o$18bo$17bo$17b2o!
The wording "the smallest p2 SKOP" is unnecessarily awkward, because "SKOP" means "smallest known oscillator of suchandsuch period".
Further, "the SKOP" is illdefined in general, because it may not be unique.
If I understand correctly, the above question can be reworded as
"How many are there periods n for which the minimum population of a periodn oscillator is known?"
I think there are at least three such periods (2, 3, 4).
127:1 B3/S234c User:Confocal/R (isotropic CA, incomplete)
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.
Re: Thread for basic questions
Whoops. Meant greater than.confocaloid wrote: ↑August 14th, 2024, 12:46 pmInfinitely many, to both questions. Highperiod glider loop oscillators that are SKOPs have bounded population and unbounded period.
 confocaloid
 Posts: 4111
 Joined: February 8th, 2022, 3:15 pm
 Location: https://catagolue.hatsya.com/census/b3s234c/C4_4/xp62
Re: Thread for basic questions
There are pages Table of oscillators by period and User:Galoomba/Skopje, which might allow to get some estimates for those questions. Those pages may not be uptodate.
127:1 B3/S234c User:Confocal/R (isotropic CA, incomplete)
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.
Re: Thread for basic questions
The table regularly gets updated, but the userpage doesn't.
User:HotdogPi/My discoveries
Periods discovered: 516,⑱,⑳G,㉑G,㉒㉔㉕,㉗㉛,㉜SG,㉞㉟㊱㊳㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,6266,68,70,73,74S,75,76S,80,84,88,90,96
100,02S,06,08,10,12,14G,16,17G,20,26G,28,38,44,47,48,54,56,72,74,80,92,96S
217,300,486,576
S: SKOP
G: gun
Periods discovered: 516,⑱,⑳G,㉑G,㉒㉔㉕,㉗㉛,㉜SG,㉞㉟㊱㊳㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,6266,68,70,73,74S,75,76S,80,84,88,90,96
100,02S,06,08,10,12,14G,16,17G,20,26G,28,38,44,47,48,54,56,72,74,80,92,96S
217,300,486,576
S: SKOP
G: gun
 confocaloid
 Posts: 4111
 Joined: February 8th, 2022, 3:15 pm
 Location: https://catagolue.hatsya.com/census/b3s234c/C4_4/xp62
Re: Thread for basic questions
I think there are only finitely many possibilities in any case. The number of possibilities grows with the period, and also grows with the minimum population, but remains finite.Chris857 wrote: ↑August 10th, 2024, 9:12 pmNot sure what you might have in mind, but I'm not sure how to have infinitely many anything of a given period and population if it's going to remain well connected i.e. not pseudo. Like a sufficiently large snark loop can adjust the sides of the rectangle of the glider paths, but there's only a finite number of combinations for any finite period. Likewise, it feels like any oscillator of a given period has some well definable max bounding box based on the speed of light, and only a finite number of patterns of any sort can fit in that bounding box.
Let the period be n, and let the minimum population be p. There are only finitely many possible ways to decompose the number p as a sum of populations of connected "islands". (For example, 6 can be decomposed as 6 = 5 + 1 = 4 + 2 = 4 + 1 + 1 = 3 + 3 = 3 + 2 + 1 = 3 + 1 + 1 + 1 = 2 + 2 + 2 = 2 + 2 + 1 + 1 = 2 + 1 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1 + 1.) There are also only finitely many different "islands" of a specific population. Hence there are only finitely many ways to choose a multiset of "islands" with total population p.
For a chosen multiset, there can be infinitely many ways to arrange the "islands" in the Life universe so that no two "islands" are currently adjacent or overlapping, and no two "islands" will interact in the next tick. However, if some "island" happens to be located too far from any other "island", then it will be impossible for the resulting configuration to be a phase of a periodn oscillator that's a single object (impossible, because the speed of light limit will prevent any interaction between the distant "island" and any other part of the pattern, earlier than the same configuration is supposed to be repeated n ticks later).
Hence there's an upper bound on distances between any "island" and the set of other "islands". There are only finitely many ways to arrange the "islands" in the Life universe so that no two "islands" are currently adjacent or overlapping, no two "islands" will interact in the next tick, and every "island" is sufficiently close to the set of remaining alive cells to allow the resulting pattern to be a phase of a periodn oscillator that's a single object.
127:1 B3/S234c User:Confocal/R (isotropic CA, incomplete)
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.
Re: Thread for basic questions
Is this W22 emulator onmiperiodic?
Code: Select all
x = 85, y = 4, rule = B45/S12345
85o$o83bo$o83bo$85o!
Code: Select all
x = 87, y = 4, rule = B2a/S1Investigator
87E$ED83.DE$ED83.DE$87E!