ConwayLife.com

Posted: **August 7th, 2024, 10:37 am**

What types of symmetries can a periodic wick or agar have?

Posted: **August 7th, 2024, 3:43 pm**

Has it ever been tabulated in how many places a single block can go that trigger either a Block-laying or Glider-producing Switch Engine from a single Switch engine?

Posted: **August 7th, 2024, 4:10 pm**

WhiteHawk wrote: ↑
August 7th, 2024, 3:43 pm
Has it ever been tabulated in how many places a single block can go that trigger either a Block-laying or Glider-producing Switch Engine from a single Switch engine?

The first potentially related thing that comes to mind is "a search to find 4-glider syntheses of glider producing switch engines, with the condition that none of them produce any non-forward-facing 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

Posted: **August 7th, 2024, 11:25 pm**

muzik wrote: ↑
August 7th, 2024, 10:37 am
What types of symmetries can a periodic wick or agar have?

none filps to D2_x

Code: Select all

x = 9, y = 9, rule = B3/S23:T10,10
o7bo2$6bobo2$4bobo2$2bobo2$obo!

D2_x(?) filps to D4_x4

Code: Select all

x = 8, y = 8, rule = B3/S23:T8,8
3bo3bo$2bo3bo$o3bo$bo3bo$3bo3bo$2bo3bo$o3bo$bo3bo!

D2_x filps to D4_x4

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!

D4+4 to D4+4?

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!

D2+1 filps to D4+4

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!

Posted: **August 8th, 2024, 10:44 am**

Is a 1-2-3-4-5 and beyond known?

Posted: **August 8th, 2024, 11:26 am**

Haycat2009 wrote: ↑
August 8th, 2024, 10:44 am
Is a 1-2-3-4-5 and beyond known?

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 1-2-...-p-1-2-...-p-... (period p).
For p>4, this is impossible, because the birth of a cell in generation p-1 (active cells count p-1 -> 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).

Posted: **August 9th, 2024, 10:20 am**

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.)

Posted: **August 9th, 2024, 1:54 pm**

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.

Posted: **August 10th, 2024, 5:57 am**

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.

Posted: **August 10th, 2024, 4:28 pm**

muzik wrote: ↑
August 10th, 2024, 5:57 am
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.

Linking and pinging a related forum discussion thread: viewtopic.php?f=3&t=1133

hkoenig wrote: ↑
October 5th, 2022, 12:12 am

Posted: **August 10th, 2024, 6:59 pm**

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 pseudo-objects?

Posted: **August 10th, 2024, 9:12 pm**

muzik wrote: ↑
August 10th, 2024, 6:59 pm
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 pseudo-objects?

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.

Posted: **August 12th, 2024, 5:44 am**

Is Motor Grader really the first non-monotonic c/7 spaceship? I remember seeing a smaller non-monotonic c/7 spaceship once with the exact same frontend.

Posted: **August 12th, 2024, 3:43 pm**

Haycat2009 wrote: ↑
August 12th, 2024, 5:44 am
Is Motor Grader really the first non-monotonic c/7 spaceship?

It's the first elementary non-monotonic c/7 spaceship, but not the first overall, because the c/7 Caterloopillar is also non-monotonic.

Haycat2009 wrote: ↑
August 12th, 2024, 5:44 am
I remember seeing a smaller non-monotonic c/7 spaceship once with the exact same frontend.

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.

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!

Posted: **August 13th, 2024, 2:26 am**

Do you have a list of glider turners in Life?

Posted: **August 13th, 2024, 8:12 am**

Citation needed wrote: ↑
August 13th, 2024, 2:26 am
Do you have a list of glider turners in Life?

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, tub-with-tails, integrals, aircraft carriers, ship-ties, shillelaghs, eleveners, and maybe a few other still lifes from farther down on the commonness scale.

Posted: **August 13th, 2024, 4:47 pm**

When were period-3 oscillators up to 18 cells enumerated, and by who?

Posted: **August 14th, 2024, 4:53 am**

May13 wrote: ↑
August 8th, 2024, 11:26 am

Haycat2009 wrote: ↑
August 8th, 2024, 10:44 am
Is a 1-2-3-4-5 and beyond known?
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 1-2-...-p-1-2-...-p-... (period p).
For p>4, this is impossible, because the birth of a cell in generation p-1 (active cells count p-1 -> 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).

Including those with multiple islands and non-interacting rotors?

Posted: **August 14th, 2024, 11:57 am**

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?

Posted: **August 14th, 2024, 12:46 pm**

WhiteHawk wrote: ↑
August 14th, 2024, 11:57 am
A couple of questions about SKOPs in life:

FWIW, I see six questions in your post, which doesn't quite match my understanding of what constitutes 'a couple of questions'.

WhiteHawk wrote: ↑
August 14th, 2024, 11:57 am
What is the average proportional size decrease for SKOPs in life (from 1st known oscillator to current SKOP)?

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. pentadecathlon-based glider shuttles, closed Herschel tracks, Snark-based glider loop oscillators, rectifier-based 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.

WhiteHawk wrote: ↑
August 14th, 2024, 11:57 am
How many oscillator periods have SKOPs with minimum population less than or equal to their period? Maximum?

Infinitely many, to both questions. High-period glider loop oscillators that are SKOPs have bounded population and unbounded period.

WhiteHawk wrote: ↑
August 14th, 2024, 11:57 am
What is the highest period SKOP in life with a minimum population greater than it's period? Maximum?

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 (minimum|maximum) population fails to exceed their period, then as a consequence there would be infinitely many oscillator periods with SKOPs whose (minimum|maximum) population does exceed their period, and as a consequence there would be no highest period SKOP in Conway's Life with a (minimum|maximum) 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!

WhiteHawk wrote: ↑
August 14th, 2024, 11:57 am
Finally, how many periods of oscillators are known to be currently represented by the true SKOP (e.g. the blinker can easily be proven to be the smallest p2 SKOP)?

The wording "the smallest p2 SKOP" is unnecessarily awkward, because "SKOP" means "smallest known oscillator of such-and-such period".
Further, "the SKOP" is ill-defined 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 period-n oscillator is known?"
I think there are at least three such periods (2, 3, 4).

Posted: **August 14th, 2024, 12:53 pm**

confocaloid wrote: ↑
August 14th, 2024, 12:46 pm

WhiteHawk wrote: ↑
August 14th, 2024, 11:57 am
How many oscillator periods have SKOPs with minimum population less than or equal to their period? Maximum?
Infinitely many, to both questions. High-period glider loop oscillators that are SKOPs have bounded population and unbounded period.

Whoops. Meant greater than.

Posted: **August 14th, 2024, 12:57 pm**

WhiteHawk wrote: ↑
August 14th, 2024, 12:53 pm
Whoops. Meant greater than.

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 up-to-date.

Posted: **August 14th, 2024, 12:58 pm**

The table regularly gets updated, but the userpage doesn't.

Posted: **August 14th, 2024, 5:23 pm**

muzik wrote: ↑
August 10th, 2024, 6:59 pm
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 pseudo-objects?

Chris857 wrote: ↑
August 10th, 2024, 9:12 pm

muzik wrote: ↑
August 10th, 2024, 6:59 pm
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 pseudo-objects?
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.

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.

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 period-n 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 period-n oscillator that's a single object.

Posted: **August 15th, 2024, 4:53 am**

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!

ConwayLife.com

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