Thread for basic non-CGOL questions

[MEisSCAMMER]

MAPAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA as a ruletable (symmetries: none)

Python:

Code: Select all

code

That should do it

RULETABLE please!

The script creates the ruletable, run it and it should create it as "aaa.rle"

[unname4798]

Python:

Code: Select all

aaa.py

That should do it

RULETABLE please!

The script creates the ruletable, run it and it should create it as "aaa.rule"

I don't have computer.

[confocaloid]

Please don't spam.

[get_Snacked]

could i have some non-totalistic oscillator search programs, and their pros and cons?

[Naszvadi]

Is there a constructed Life-like reflectorless rotating oscillator in other rule than CGoL?

[unname4798]

Is there a constructed Life-like reflectorless rotating oscillator in other rule than CGoL?

Yes, but I don't know.

[Period1GliderGun]

Is there a constructed Life-like reflectorless rotating oscillator in other rule than CGoL?

Here's one that I found from the forums.

[confocaloid]

Is there a constructed Life-like reflectorless rotating oscillator in other rule than CGoL?

Here's one that I found from the forums.

That one is in an INT rule, rather than Life-like, right?

[Period1GliderGun]

Is there a constructed Life-like reflectorless rotating oscillator in other rule than CGoL?

Here's one that I found from the forums.

That one is in an INT rule, rather than Life-like, right?

Oops. Forgot my definitions for a minute. However, a lot of known CGoL circuitry works in B38/S23, so it would probably be possible to construct an RRO. I'm not sure about the status of technological advancement in rules farther from Life, such as Morley.

[unname4798]

What is the multi-generation parent of this?

Code: Select all

x = 24, y = 23, rule = B35y/S23
b2o$obo$2bo6$7bo8bo$5b2ob2o4b2ob2o$7bo8bo2$7bo8bo$5b2ob2o4b2ob2o$7bo8b
o6$2bo18bo$obo18bobo$b2o18b2o!

[confocaloid]

What is the parent of this?

Code: Select all

x = 24, y = 23, rule = B35y/S23
b2o$obo$2bo6$7bo8bo$5b2ob2o4b2ob2o$7bo8bo2$7bo8bo$5b2ob2o4b2ob2o$7bo8b
o6$2bo18bo$obo18bobo$b2o18b2o!

If by "the parent of this" you mean "where this pattern comes from", then I saw the mechanism last time in rule's thread viewtopic.php?f=11&t=5718 "B35y/S23 (hatlife)", but it was known years before that: viewtopic.php?p=22861#p22861

If you mean a parent, then there's no unique parent, but it's naturally rewindable by running it for 51 ticks and deleting two gliders:

Code: Select all

x = 24, y = 23, rule = B35y/S23
bo$b2o$obo6$6bobo6bobo$6bo2bo4bo2bo$6bobo6bobo2$6bobo6bobo$6bo2bo4bo2b
o$6bobo6bobo6$obo18bobo$b2o18b2o$bo20bo!

[Naszvadi]

Here's one that I found from the forums.

That one is in an INT rule, rather than Life-like, right?

Oops. Forgot my definitions for a minute. However, a lot of known CGoL circuitry works in B38/S23, so it would probably be possible to construct an RRO. I'm not sure about the status of technological advancement in rules farther from Life, such as Morley.

There is only one constructed other than CGoL, but in a B0-rule:

Code: Select all

x = 23, y = 9, rule = B02348/S0123
19bo2bo3$b3o15b3o$bobo15bobo$b3o15b3o3$o2bo!

A B0-less life-like RRO is not constructed at the moment (?):

[Period1GliderGun]

A B0-less life-like RRO is not constructed at the moment (?):

Not unless you count the RRG from Pedestrian Life.

[Haycat2009]

Other than B1 and B4+ rules and S01234 rules, what other rulespaces have no possible ships?
What isotropic transitions must a rule have/not have to have spaceships?

[unname4798]

Other than B1 and B4+ rules and S01234 rules, what other rulespaces have no possible ships?
What isotropic transitions must a rule have/not have to have spaceships?

B1c makes patterns escape from bounding box, but rules off spaceships
With B2c and B2e or B3a and B3i, without B1c, spaceships are possible.

[silversmith]

Other than B1 and B4+ rules and S01234 rules, what other rulespaces have no possible ships?
What isotropic transitions must a rule have/not have to have spaceships?

You can have spaceships in a rule with B1e

2c/31d B1e SMOS (the first?):

Code: Select all

x = 10, y = 10, rule = B1e2ce3ejky4inqt5aj6ack/S1c2-ce3inq4knqt5knqr6k
7b3o$7bobo$8bo5$2o$obo$2o!

5c/28d:

Code: Select all

x = 10, y = 10, rule = B1e2ce3jkqy4iknyz5anr6-en8/S1c2-ce3enqy4jkntz5eqr6ek7e
7b3o$7bobo$8bo5$2o$obo$2o!

To have a rule with space ships in a rule you need at least one of {B0, B1e, B2a}, or you need at least one of {B2c, B3i} and at least one of {B2e, B3a}. You can find more information about the topic using these links:
https://conwaylife.com/wiki/Isotropic_n ... le#Subsets
viewtopic.php?f=11&t=5471

[Haycat2009]

Other than B1 and B4+ rules and S01234 rules, what other rulespaces have no possible ships?
What isotropic transitions must a rule have/not have to have spaceships?

You can have spaceships in a rule with B1e

2c/31d B1e SMOS (the first?):

Code: Select all

x = 10, y = 10, rule = B1e2ce3ejky4inqt5aj6ack/S1c2-ce3inq4knqt5knqr6k
7b3o$7bobo$8bo5$2o$obo$2o!

5c/28d:

Code: Select all

x = 10, y = 10, rule = B1e2ce3jkqy4iknyz5anr6-en8/S1c2-ce3enqy4jkntz5eqr6ek7e
7b3o$7bobo$8bo5$2o$obo$2o!

To have a rule with space ships in a rule you need at least one of {B0, B1e, B2a}, or you need at least one of {B2c, B3i} and at least one of {B2e, B3a}. You can find more information about the topic using these links:
https://conwaylife.com/wiki/Isotropic_n ... le#Subsets
viewtopic.php?f=11&t=5471

So are spaceships in B1c but no B1e rules possible? And can you give me one example each of a spaceship in a B2e+B3a or B2c+B3i rule?

[unname4798]

Other than B1 and B4+ rules and S01234 rules, what other rulespaces have no possible ships?
What isotropic transitions must a rule have/not have to have spaceships?

You can have spaceships in a rule with B1e

2c/31d B1e SMOS (the first?):

Code: Select all

x = 10, y = 10, rule = B1e2ce3ejky4inqt5aj6ack/S1c2-ce3inq4knqt5knqr6k
7b3o$7bobo$8bo5$2o$obo$2o!

5c/28d:

Code: Select all

x = 10, y = 10, rule = B1e2ce3jkqy4iknyz5anr6-en8/S1c2-ce3enqy4jkntz5eqr6ek7e
7b3o$7bobo$8bo5$2o$obo$2o!

To have a rule with space ships in a rule you need at least one of {B0, B1e, B2a}, or you need at least one of {B2c, B3i} and at least one of {B2e, B3a}. You can find more information about the topic using these links:
https://conwaylife.com/wiki/Isotropic_n ... le#Subsets
viewtopic.php?f=11&t=5471

So are spaceships in B1c but no B1e rules possible? And can you give me one example each of a spaceship in a B2e+B3a or B2c+B3i rule?

1. No
2. Yes:

Code: Select all

x = 0, y = 0, rule = B2e3/S23
bo$obo$obo!

[Cyclotrons]

I've seen a lot of use of signal loops to prove that all periods exist above the loop mechanism's minimum period. Wouldn't you also need a signal delay mechanism so that some periods aren't skipped?

[toroidalet]

I've seen a lot of use of signal loops to prove that all periods exist above the loop mechanism's minimum period. Wouldn't you also need a signal delay mechanism so that some periods aren't skipped?

If the spaceship or signal is symmetric or glide-reflective, we don't need a separate delay because we can make a delay using reflectors.

Consider this dumb reflector:

Code: Select all

x = 29, y = 21, rule = B3acijn4cjy5cy6an8/S2-n3-ckqy4aw6ci7c8
20b2o$4b2o14b2o$4b2o2$16b2o9b2o$8b2o6b2o9b2o$8b2o2$2o10b2o9b2o$2o10b2o
2bo6b2o$15bo$15b3o$4b2o13b2o$4b2o13b2o4$9b2o$9b2o$11b2o3b2o$11b2o3b2o!

We will pretend that this glider is actually 4c/16, which is what the blocks are for.
We shall use it to make a p47, 48, 49 and 50 as a test.

If we string four copies together like so, you get a p20+32n:

Code: Select all

x = 61, y = 61, rule = B3acijn4cjy5cy6an8/S2-n3-ckqy4aw6ci7c8
25b2o3b2o$25b2o3b2o$32b2o$32b2o4$22b2o13b2o$22b2o13b2o2$19b2o19b2o$19b
2o8b2o9b2o$29b2o$16b2o25b2o$16b2o8b2o5b2o8b2o$26b2o5b2o$13b2o31b2o$13b
2o8b2o11b2o8b2o$23b2o11b2o$10b2o37b2o$10b2o8b2o17b2o8b2o$20b2o17b2o$7b
2o43b2o$7b2o8b2o23b2o8b2o$17b2o23b2o$59b2o$14b2o29b2o12b2o$2b2o10b2o
29b2o$2b2o$2o46b2o$2o9b2o35b2o9b2o$11b2o46b2o$57b2o$14b2o29b2o10b2o$2o
12b2o29b2o$2o$17b2o23b2o$7b2o8b2o23b2o8b2o$7b2o43b2o$20b2o17b2o$10b2o
8b2o17b2o8b2o$10b2o37b2o$23b2o11b2o$13b2o8b2o11b2o8b2o$13b2o31b2o$26b
2o5b2o$16b2o8b2o5b2o8b2o$16b2o25b2o$30b2o$19b2o9b2o2bo5b2o$19b2o12bo6b
2o$33b3o$22b2o13b2o$22b2o13b2o4$27b2o$27b2o$29b2o3b2o$29b2o3b2o!

The 32 comes from the period of the signal, 16. If we lengthen the loop by 1 unit, it has to travel 16 more generations in both directions. 20 comes from the delay of the reflector. If you compare the glider to the block tracks, the reflected glider reaches the same phase in the same position after 13+16n generations. 13*4 mod 32=20.

Now, if we put 4 gliders in, it becomes p5+8n. 5 and 8 are coprime, but none of 47, 49 and 25 (50/2) is 5 mod 8. How can we make these odd numbers? 47 is 7 mod 8, and 49 and 25 are 1 mod 8. So we can just multiply 49 and 25 by 5 and add 5 times the gliders. For 47, we can do the same thing with 3 instead of 5 (3*7=21=5+2*8). Since we want a p50 loop rather than a p25, we will then halve the gliders of the p25 loop (p25 doesn't work anyway). 49*5=245=5+8*30, corresponding to a base loop of period 4*245=980:

Code: Select all

x = 156, y = 176, rule = B3acijn4cjy5cy6an8/S2-n3-ckqy4aw6ci7c8
20$120b2o3b2o$120b2o3b2o$127b2o$127b2o4$117b2o13b2o$117b2o13b2o3$113b
2o9b2o10b2o$113b2o9b2o10b2o2$128b2o$109b2o9b2o6b2o10b2o$109b2o9b2o18b
2o2$132b2o13b2o$105b2o9b2o14b2o13b2o$105b2o9b2o2$136b2o$101b2o9b2o22b
2o9b2o$101b2o9b2o33b2o$145b2o$133b2o10b2o$97b2o9b2o23b2o$97b2o9b2o2$
129b2o9b2o$93b2o9b2o23b2o9b2o$93b2o9b2o2$125b2o9b2o$89b2o9b2o23b2o9b2o
$89b2o9b2o2$121b2o9b2o$85b2o9b2o23b2o9b2o$85b2o9b2o2$117b2o9b2o$81b2o
9b2o23b2o9b2o$81b2o9b2o2$113b2o9b2o$77b2o9b2o23b2o9b2o$77b2o9b2o2$109b
2o9b2o$73b2o9b2o23b2o9b2o$73b2o9b2o2$105b2o9b2o$69b2o9b2o23b2o9b2o$69b
2o9b2o2$101b2o9b2o$65b2o9b2o23b2o9b2o$65b2o9b2o2$97b2o9b2o$61b2o9b2o
23b2o9b2o$61b2o9b2o2$93b2o9b2o$57b2o9b2o23b2o9b2o$57b2o9b2o2$89b2o9b2o
$53b2o9b2o23b2o9b2o$53b2o9b2o2$85b2o9b2o$49b2o9b2o23b2o9b2o$49b2o9b2o
2$81b2o9b2o$45b2o9b2o23b2o9b2o$45b2o9b2o2$77b2o9b2o$41b2o9b2o23b2o9b2o
$41b2o9b2o2$73b2o9b2o$37b2o9b2o23b2o9b2o$37b2o9b2o2$69b2o9b2o$33b2o9b
2o23b2o9b2o$33b2o9b2o2$65b2o9b2o$29b2o9b2o23b2o9b2o$29b2o9b2o2$61b2o9b
2o$25b2o9b2o23b2o9b2o$25b2o9b2o2$57b2o9b2o$32b2o23b2o9b2o$20b2o10b2o$
20b2o$18b2o33b2o9b2o$18b2o9b2o22b2o9b2o$29b2o2$49b2o9b2o$18b2o13b2o14b
2o9b2o$18b2o13b2o2$25b2o18b2o9b2o$25b2o10b2o6b2o9b2o$37b2o2$29b2o10b2o
9b2o$29b2o10b2o2bo6b2o$44bo$44b3o$33b2o13b2o$33b2o13b2o4$38b2o$38b2o$
40b2o3b2o$40b2o3b2o!

And a completed p49 (except for the beacons, ugh):

Code: Select all

x = 149, y = 145, rule = B3acijn4cjy5cy6an8/S2-n3-ckqy4aw6ci7c8
12$117b2o3b2o$117b2o3b2o$124b2o$124b2o4$114b2o13b2o$114b2o13b2o$117b3o
$119bo$110b2o6bo2b2o6bo3b2o$110b2o9b2o4bobo3b2o$128b2o$125b2o$106b2o9b
2o6b2o10b2o$106b2o9b2o18b2o2$129b2o13b2o$102b2o9b2o14b2o13b2o$102b2o9b
2o$105b2o$106b2o25b2o4b3o$98b2o5bo3b2o22b2o4bobo2b2o$98b2o9b2o28b2o3b
2o$142b2o$130b2o10b2o$94b2o9b2o23b2o$94b2o9b2o2$126b2o9b2o$90b2o9b2o
23b2o9b2o$90b2o9b2o$93b2o$92bobo27b2o3bobo3b2o$86b2o6bo2b2o23b2o3b2o4b
2o$86b2o9b2o29bo2$118b2o9b2o$82b2o9b2o23b2o9b2o$82b2o9b2o2$114b2o9b2o$
78b2o9b2o23b2o9b2o$78b2o9b2o$81bo$81b2o27b2o3bo5b2o$74b2o4bobo2b2o23b
2o3bobo3b2o$74b2o9b2o28b2o2$106b2o9b2o$70b2o9b2o23b2o9b2o$70b2o9b2o2$
102b2o9b2o$66b2o9b2o23b2o9b2o$66b2o9b2o2$68b3o27b2o4bo4b2o$62b2o6bo2b
2o23b2o2b2o5b2o$62b2o5bo3b2o28b2o2$94b2o9b2o$58b2o9b2o23b2o9b2o$58b2o
9b2o2$90b2o9b2o$54b2o9b2o23b2o9b2o$54b2o9b2o2$56b2o28b2o3bo5b2o$50b2o
5b2o2b2o23b2o2bo6b2o$50b2o4bo4b2o27b3o2$82b2o9b2o$46b2o9b2o23b2o9b2o$
46b2o9b2o2$78b2o9b2o$42b2o9b2o23b2o9b2o$42b2o9b2o2$44b2o28b2o9b2o$38b
2o3bobo3b2o23b2o2bobo4b2o$38b2o5bo3b2o27b2o$79bo$70b2o9b2o$34b2o9b2o
23b2o9b2o$34b2o9b2o2$66b2o9b2o$30b2o9b2o23b2o9b2o$30b2o9b2o2$32bo29b2o
9b2o$26b2o4b2o3b2o23b2o2bo6b2o$26b2o3bobo3b2o27bobo$66b2o$58b2o9b2o$
22b2o9b2o23b2o9b2o$22b2o9b2o2$54b2o9b2o$29b2o23b2o9b2o$17b2o10b2o$17b
2o$15b2o3b2o28b2o9b2o$15b2o2bobo4b2o22b2o3bo5b2o$19b3o4b2o25b2o$54b2o$
46b2o9b2o$15b2o13b2o14b2o9b2o$15b2o13b2o2$22b2o18b2o9b2o$22b2o10b2o6b
2o9b2o$34b2o$31b2o$26b2o3bobo4b2o9b2o$26b2o3bo6b2o2bo6b2o$41bo$41b3o$
30b2o13b2o$30b2o13b2o4$35b2o$35b2o$37b2o3b2o$37b2o3b2o!

Similarly, 25*5=125=5+8*30, with an original period of 500:

Code: Select all

x = 159, y = 76, rule = B3acijn4cjy5cy6an8/S2-n3-ckqy4aw6ci7c8
4$50b2o3b2o61b2o3b2o$50b2o3b2o61b2o3b2o$57b2o66b2o$57b2o66b2o4$47b2o
13b2o51b2o13b2o$47b2o13b2o51b2o13b2o$118b3o$120bo$43b2o9b2o10b2o43b2o
6bo2b2o5bo4b2o$43b2o9b2o10b2o43b2o9b2o6b2o2b2o$129b2o$58b2o66b2o$39b2o
9b2o6b2o10b2o35b2o9b2o6b2o10b2o$39b2o9b2o18b2o35b2o9b2o18b2o2$62b2o13b
2o51b2o13b2o$35b2o9b2o14b2o13b2o24b2o9b2o14b2o13b2o$35b2o9b2o55b2o9b2o
$106b2o33bo$66b2o37bobo26b2o5b2o$31b2o9b2o22b2o9b2o20b2o6bo2b2o22b2o3b
2obo2b2o$31b2o9b2o33b2o20b2o9b2o28b2o3b2o$75b2o66b2o$63b2o10b2o54b2o
10b2o$27b2o9b2o23b2o30b2o9b2o23b2o$27b2o9b2o55b2o9b2o2$59b2o9b2o55b2o
9b2o$23b2o9b2o23b2o9b2o19b2o9b2o23b2o9b2o$23b2o9b2o55b2o9b2o2$55b2o9b
2o25b3o27b2o3bo5b2o$19b2o9b2o23b2o9b2o19b2o6bo2b2o23b2o2bo6b2o$19b2o9b
2o55b2o5bo3b2o27b3o2$51b2o9b2o55b2o9b2o$15b2o9b2o23b2o9b2o19b2o9b2o23b
2o9b2o$15b2o9b2o55b2o9b2o2$47b2o9b2o55b2o9b2o$22b2o23b2o9b2o30b2o23b2o
9b2o$10b2o10b2o54b2o10b2o$10b2o66b2o$8b2o33b2o9b2o20b2o3b2o28b2o9b2o$
8b2o9b2o22b2o9b2o20b2o2bob2o3b2o22b2o2bo6b2o$19b2o59b2o5b2o26bobo$81bo
33b2o$39b2o9b2o55b2o9b2o$8b2o13b2o14b2o9b2o24b2o13b2o14b2o9b2o$8b2o13b
2o51b2o13b2o2$15b2o18b2o9b2o35b2o18b2o9b2o$15b2o10b2o6b2o9b2o35b2o10b
2o6b2o9b2o$27b2o66b2o$92b2o$19b2o10b2o9b2o43b2o2b2o6b2o9b2o$19b2o10b2o
2bo6b2o43b2o4bo5b2o2bo6b2o$34bo67bo$34b3o65b3o$23b2o13b2o51b2o13b2o$
23b2o13b2o51b2o13b2o4$28b2o66b2o$28b2o66b2o$30b2o3b2o61b2o3b2o$30b2o3b
2o61b2o3b2o!

47 works the same, except we multiply by 3 instead of 5. 47*3=141=5+8*17:

Code: Select all

x = 207, y = 91, rule = B3acijn4cjy5cy6an8/S2-n3-ckqy4aw6ci7c8
7$58b2o3b2o$58b2o3b2o106b2o3b2o$65b2o104b2o3b2o$65b2o111b2o$178b2o3$
55b2o13b2o$55b2o13b2o96b2o13b2o$168b2o13b2o$171b3o$51b2o9b2o10b2o97bo
8bo$51b2o9b2o10b2o88b2o6bo2b2o6bo3b2o$164b2o9b2o4b3o3b2o$66b2o$47b2o9b
2o6b2o10b2o99b2o$47b2o9b2o18b2o80b2o9b2o6b2o10b2o$160b2o9b2o18b2o$70b
2o13b2o$43b2o9b2o14b2o13b2o96b2o13b2o$43b2o9b2o100b2o9b2o14b2o13b2o$
156b2o2bo6b2o$74b2o84b2o$39b2o9b2o22b2o9b2o72bobo25b2o4bo$39b2o9b2o33b
2o65b2o9b2o22b2o5b2o2b2o$83b2o67b2o9b2o28b2o3b2o$71b2o10b2o111b2o$35b
2o9b2o23b2o111b2o10b2o$35b2o9b2o100b2o9b2o23b2o$148b2o9b2o$67b2o9b2o$
31b2o9b2o23b2o9b2o100b2o9b2o$31b2o9b2o100b2o9b2o23b2o9b2o$144b2o2b2o5b
2o27bo$63b2o9b2o71bobo32b2o$27b2o9b2o23b2o9b2o73bo26b2o5b2o2b2o$27b2o
9b2o100b2o9b2o23b2o9b2o$140b2o9b2o$59b2o9b2o$23b2o9b2o23b2o9b2o100b2o
9b2o$23b2o9b2o100b2o9b2o23b2o9b2o$136b2o9b2o$55b2o9b2o$19b2o9b2o23b2o
9b2o100b2o9b2o$19b2o9b2o100b2o9b2o23b2o9b2o$132b2o2b2o5b2o26bo$51b2o9b
2o73b2o32bobo$15b2o9b2o23b2o9b2o72bo27b2o5b2o2b2o$15b2o9b2o100b2o9b2o
23b2o9b2o$128b2o9b2o$47b2o9b2o$22b2o23b2o9b2o100b2o9b2o$10b2o10b2o111b
2o23b2o9b2o$10b2o111b2o10b2o$8b2o33b2o9b2o67b2o$8b2o9b2o22b2o9b2o65b2o
3b2o28b2o9b2o$19b2o100b2o2b2o5b2o22b2o9b2o$127bo4b2o25bobo$39b2o9b2o
107b2o$8b2o13b2o14b2o9b2o100b2o6bo2b2o$8b2o13b2o96b2o13b2o14b2o9b2o$
121b2o13b2o$15b2o18b2o9b2o$15b2o10b2o6b2o9b2o80b2o18b2o9b2o$27b2o99b2o
10b2o6b2o9b2o$140b2o$19b2o10b2o9b2o$19b2o10b2o2bo6b2o88b2o3b3o4b2o9b2o
$34bo97b2o3bo6b2o2bo6b2o$34b3o101bo8bo$23b2o13b2o107b3o$23b2o13b2o96b
2o13b2o$136b2o13b2o3$28b2o$28b2o111b2o$30b2o3b2o104b2o$30b2o3b2o106b2o
3b2o$143b2o3b2o!

Now, this shows how we can get an odd number or an odd number times a factor of gcd(20,32)=4. What about 48, which is 12*4? You can do this by making a more convoluted loop with 32 corners, which would then be p160+32n:

Code: Select all

x = 362, y = 170, rule = B3acijn4cjy5cy6an8/S2-n3-ckqy4aw6ci7c8
16$102b2o3b2o198b2o3b2o$102b2o3b2o198b2o3b2o$109b2o203b2o$109b2o203b2o
4$99b2o13b2o188b2o13b2o$99b2o13b2o188b2o13b2o$307bo$307b2o9bo$95b2o9b
2o10b2o180b2o4bobo2b2o3bobo4b2o$95b2o9b2o10b2o180b2o9b2o4b2o4b2o2$110b
2o203b2o$102b2o6b2o10b2o183b2o6b2o10b2o$90b2o10b2o18b2o171b2o10b2o18b
2o$90b2o203b2o$114b2o203b2o$87b2o25b2o10b2o164b2o25b2o10b2o$87b2o37b2o
164b2o5b2o30b2o$100b2o197bobo3b2o$100b2o16b2o13b2o164bo5b2o16b2o5bo7b
2o$118b2o13b2o188b2o3bobo7b2o$87b2o203b2o35b2o$87b2o4b2o197b2o4b2o$93b
2o10b2o15b2o174b2o10b2o15b2o$105b2o15b2o9b2o175b2o15b2o9b2o$74b2o3b2o
26b2o24b2o144b2o3b2o26b2o24b2o$74b2o3b2o15b2o9b2o22b2o146b2o3b2o15b2o
9b2o22b2o$81b2o13b2o21b2o10b2o153b2o13b2o2bo18b2o10b2o$81b2o30b2o4b2o
165b2o17b2o11b2o4b2o$113b2o169bo19bobo11b2o8bo$92b2o13b2o175b2o11b2o
13b2o12b2o$92b2o13b2o17b2o155bobo11b2o13b2o13b2o2b2o$71b2o13b2o38b2o
148b2o13b2o38b2o$71b2o13b2o12b2o11b2o161b2o13b2o12b2o11b2o$100b2o11b2o
190b2o11b2o2$67b2o9b2o36b2o154b2o9b2o36b2o$67b2o9b2o16b2o18b2o10b2o
142b2o9b2o16b2o18b2o10b2o$96b2o11b2o3b2o12b2o4b2o165b2o11b2o3b2o12b2o
4b2o$82b2o25b2o3b2o18b2o151b2o5bo19b2o3b2o18b2o$74b2o6b2o195b2o6b2o4b
3o36bo$62b2o10b2o30b2o13b2o144b2o3bo6b2o12b2o16b2o13b2o2bobo$62b2o27b
2o13b2o13b2o144b2o3b2o22b2o13b2o13b2o3b2o$91b2o41b2o135bobo22b2o41b2o$
59b2o54b2o17b2o128b2o49b2o3b2o17b2o$59b2o22b2o3b2o25b2o147b2o3bo18b2o
3b2o20bobo2b2o$72b2o9b2o3b2o11b2o28b2o134b2o8b2o9b2o3b2o11b2o7bo20b2o$
72b2o27b2o16b2o10b2o135b2o7b2o27b2o16b2o10b2o$119b2o203b2o$59b2o203b2o
$59b2o4b2o30b2o165b2o4b2o30b2o$65b2o10b2o18b2o12b2o13b2o142b2o10b2o18b
2o12b2o7bobo3b2o$77b2o32b2o13b2o150b2o2b2o32b2o7b2o4b2o$46b2o3b2o26b2o
9b2o13b2o144b2o3b2o20bobo3b2o9b2o7bobo3b2o14bo$46b2o3b2o15b2o9b2o9b2o
13b2o144b2o3b2o15b2o3bo2bo2b2o9b2o7b2o4b2o$53b2o13b2o184bo3b2o13b2o7bo
22bo$53b2o61b2o135b3o2b2o20b3o38b2o$101b2o13b2o135b3o50b2o13b2o$64b2o
13b2o9b2o9b2o15b2o3b2o128b3o13b2o13b2o9b2o9b2o15b2o3b2o$64b2o13b2o9b2o
26b2o3b2o144b2o13b2o9b2o26b2o3b2o$43b2o13b2o32b2o154b2o13b2o32b2o$43b
2o13b2o12b2o18b2o10b2o142b2o10bo2b2o12b2o18b2o10b2o$72b2o30b2o4b2o146b
obo9bo6b2o30b2o4b2o$110b2o147b2o9b2o35bo7b2o$39b2o9b2o192b2o3bo5b2o12b
obo33bobo$39b2o9b2o16b2o27b2o145b2o3b2o4b2o16b2o27b2o2b2o$68b2o11b2o3b
2o9b2o149bobo22b2o11b2o3b2o9b2o$54b2o25b2o3b2o22b2o147b2o25b2o3b2o22b
2o$46b2o6b2o54b2o139b2o6b2o28bo25b2o$34b2o10b2o30b2o159b2o10b2o10bo19b
2o3b3o$34b2o27b2o13b2o27b2o130b2o21b3o3b2o13b2o3b3o21b2o$63b2o30b2o10b
2o153b3o3b2o19bo10b2o10b2o$31b2o54b2o6b2o139b2o25bo28b2o6b2o$31b2o22b
2o3b2o25b2o147b2o22b2o3b2o25b2o$44b2o9b2o3b2o11b2o174b2o9b2o3b2o11b2o
22bobo$44b2o27b2o16b2o9b2o141b2o2b2o27b2o16b2o4b2o3b2o$91b2o9b2o141bob
o33bobo12b2o5bo3b2o$31b2o203b2o7bo35b2o9b2o$31b2o4b2o30b2o165b2o4b2o
30b2o6bo9bobo$37b2o10b2o18b2o12b2o13b2o142b2o10b2o18b2o12b2o2bo10b2o$
49b2o32b2o13b2o154b2o32b2o13b2o$18b2o3b2o26b2o9b2o13b2o144b2o3b2o26b2o
9b2o13b2o$18b2o3b2o15b2o9b2o9b2o13b2o144b2o3b2o15b2o9b2o9b2o13b2o13b3o
$25b2o13b2o188b2o13b2o50b3o$25b2o61b2o140b2o38b3o20b2o2b3o$73b2o13b2o
157bo22bo7b2o13b2o3bo$36b2o13b2o9b2o9b2o15b2o3b2o144b2o4b2o7b2o9b2o2bo
2bo3b2o15b2o3b2o$36b2o13b2o9b2o26b2o3b2o129bo14b2o3bobo7b2o9b2o3bobo
20b2o3b2o$15b2o13b2o32b2o154b2o4b2o7b2o32b2o2b2o$15b2o13b2o12b2o18b2o
10b2o142b2o3bobo7b2o12b2o18b2o10b2o$44b2o30b2o4b2o165b2o30b2o4b2o$82b
2o203b2o$22b2o203b2o$10b2o10b2o16b2o27b2o144b2o10b2o16b2o27b2o7b2o$10b
2o28b2o11b2o3b2o9b2o144b2o20bo7b2o11b2o3b2o9b2o8b2o$26b2o25b2o3b2o22b
2o147b2o2bobo20b2o3b2o18bo3b2o$7b2o17b2o54b2o128b2o17b2o3b2o49b2o$7b2o
41b2o160b2o41b2o22bobo$20b2o13b2o13b2o27b2o139b2o3b2o13b2o13b2o22b2o3b
2o$20b2o13b2o30b2o10b2o139bobo2b2o13b2o16b2o12b2o6bo3b2o$59b2o6b2o151b
o36b3o4b2o6b2o$7b2o18b2o3b2o25b2o151b2o18b2o3b2o19bo5b2o$7b2o4b2o12b2o
3b2o11b2o165b2o4b2o12b2o3b2o11b2o$13b2o10b2o18b2o16b2o9b2o142b2o10b2o
18b2o16b2o9b2o$25b2o36b2o9b2o154b2o36b2o9b2o2$28b2o11b2o190b2o11b2o$
28b2o11b2o12b2o13b2o161b2o11b2o12b2o13b2o$15b2o38b2o13b2o148b2o38b2o
13b2o$15b2o17b2o13b2o169b2o2b2o13b2o13b2o11bobo$34b2o13b2o174b2o12b2o
13b2o11b2o$28b2o194bo8b2o11bobo19bo$22b2o4b2o30b2o165b2o4b2o11b2o17b2o
$10b2o10b2o21b2o13b2o153b2o10b2o18bo2b2o13b2o$10b2o22b2o9b2o15b2o3b2o
146b2o22b2o9b2o15b2o3b2o$8b2o24b2o26b2o3b2o144b2o24b2o26b2o3b2o$8b2o9b
2o15b2o175b2o9b2o15b2o$19b2o15b2o10b2o174b2o15b2o10b2o$48b2o4b2o197b2o
4b2o$17b2o35b2o166b2o35b2o$8b2o7bobo3b2o188b2o7bobo3b2o$8b2o7bo5b2o16b
2o170b2o7bo5b2o16b2o5bo$41b2o203b2o3bobo$15b2o37b2o164b2o30b2o5b2o$15b
2o10b2o25b2o164b2o10b2o25b2o$27b2o203b2o$51b2o203b2o$19b2o18b2o10b2o
171b2o18b2o10b2o$19b2o10b2o6b2o183b2o10b2o6b2o$31b2o203b2o2$23b2o10b2o
9b2o180b2o4b2o4b2o9b2o$23b2o10b2o9b2o180b2o4bobo3b2o2bobo4b2o$234bo9b
2o$245bo$27b2o13b2o188b2o13b2o$27b2o13b2o188b2o13b2o4$32b2o203b2o$32b
2o203b2o$34b2o3b2o198b2o3b2o$34b2o3b2o198b2o3b2o!

I also made a bit of a mistake here, since a 4c/n diagonal spaceship cannot be glide-symmetric. However, we can pretend that in this example it is really a symmetric spaceship since the Glitter^2 reflector is a symmetric splitter. To keep the block tracks aligned, we have an alternative beaconless reflector.

In general, if the gcd of 2*(signal's period) and (reflector delay mod period)*4 is (p_1^a_1)*(p_2^a_2)*...(p_n^a_n), a rectangular loop can make any oscillator period such that no power of p_k is greater than a_k. By the way, this is why the problem doesn't really arise for low-period spaceships such as gliders and c/2 ships.

If this is not the case, the remaining periods can be taken care of with an awful radiator-shaped loop (provided the signal is symmetric or glide-symmetric, or you have 90° reflectors in both directions).

[Chai]

When running a single dot in the rule B1/S012345678, at generations (2^n)-1, as n approaches infinity, the pattern's density *appears* to approach 1/3. Does it actually approach 1/3? If so, why? (if there's a meaningful answer to the second question)

[hotdogPi]

I'm getting 4/9, not 1/3.

[Chai]

After running it for 16777215 generations in golly, it has a bounding box of 33554431 x 33554431 and a population of 375299968947541. 375299968947541/(33554431^2) ≈ 0.333333353 (?)

[confocaloid]

After 16,777,215 generations I get population 500,399,958,596,785 and bounding box 33,554,431-by-33,554,431; population/area ~ 0.4444439411168167

Code: Select all

x = 1, y = 1, rule = B1/S012345678
o!

[hotdogPi]

I am getting 1/3 for B1c rather than B1. Is that what you meant?