Thread for basic non-CGOL questions

[confocaloid]

[...] Can anyone help fix glider timing?

Code: Select all

x = 35, y = 27, rule = B34c8/S23
11bo$11b3o$14bo$13b2o2$19bo$19bo$8bo11bo4b3o$7bobo8bo$6bo3bo7b2o5bobo
$7bobo16bo$2b2o4bo$bobo$bo26b2o$2o6bo19bo$8b2o13bobo3b3o$10bo13b2o5bo
$8bobo13bo$8b2o3$3b2o$2bobo$2bo30bo$b2o15b2o14bo$18bobo11b3o$18bo!

Evolve for 35 ticks, copy the leading glider, reset, paste back into generation 0 (in the same location):

Code: Select all

x = 44, y = 35, rule = B34c8/S23
11bo$11b3o$14bo$13b2o2$19bo$19bo$8bo11bo4b3o$7bobo8bo$6bo3bo7b2o5bobo$
7bobo16bo$2b2o4bo$bobo$bo26b2o$2o6bo19bo$8b2o13bobo3b3o$10bo13b2o5bo$
8bobo13bo$8b2o3$3b2o$2bobo$2bo30bo$b2o15b2o14bo$18bobo11b3o$18bo6$41bo
$42b2o$41b2o!

Evolve for 35 ticks, copy the leading glider, reset, paste:

Code: Select all

x = 52, y = 44, rule = B34c8/S23
11bo$11b3o$14bo$13b2o2$19bo$19bo$8bo11bo4b3o$7bobo8bo$6bo3bo7b2o5bobo$
7bobo16bo$2b2o4bo$bobo$bo26b2o$2o6bo19bo$8b2o13bobo3b3o$10bo13b2o5bo$
8bobo13bo$8b2o3$3b2o$2bobo$2bo30bo$b2o15b2o14bo$18bobo11b3o$18bo6$41bo
$42b2o$41b2o7$51bo$49bobo$50b2o!

Now the rest should be straightforward:

Code: Select all

x = 70, y = 68, rule = B34c8/S23
11bo$11b3o$14bo$13b2o2$19bo$19bo$8bo11bo4b3o$7bobo8bo$6bo3bo7b2o5bobo$
7bobo16bo$2b2o4bo$bobo$bo26b2o$2o6bo19bo$8b2o13bobo3b3o$10bo13b2o5bo$
8bobo13bo$8b2o3$3b2o$2bobo$2bo30bo$b2o15b2o14bo$18bobo11b3o$18bo6$41bo
$27b2o13b2o$26b2o13b2o$28bo6$51bo$35b3o11bobo$35bo14b2o15b2o$36bo30bo$
65bobo$65b2o3$60b2o$45bo13bobo$38bo5b2o13bo$38b3o3bobo13b2o$41bo19bo6b
2o$40b2o26bo$66bobo$61bo4b2o$43bo16bobo$42bobo5b2o7bo3bo$51bo8bobo$42b
3o4bo11bo$50bo$50bo2$55b2o$55bo$56b3o$58bo!

[WhiteHawk]

Now the rest should be straightforward:

Code: Select all

I did end up finding a more compact solution (EDIT: it's actually not more compact, though perhaps there may be a more compact form)

Code: Select all

x = 77, y = 76, rule = B34c8/S23
7$17bo$17b3o$20bo$19b2o2$24bo$23bobo$23bo2bo4b3o$13bo10b2o$12bobo8b2o
5bo3bo$11bo3bo6b2o6bo3bo$12bobo8b2o$7b2o4bo8bo8bo3bo$6bobo26bo$6bo21b
obo3bo$5b2o6bo15b2o4b3o$13b2o14bo7bo$15bo$13bobo$13b2o3$8b2o28bo$7bob
o29bo$7bo29b3o$6b2o15b2o$23bobo$23bo4$46bo$47b2o$46b2o$32b2o$31b2o$33b
o4$56bo$54bobo$55b2o15b2o$40b3o29bo$40bo29bobo$41bo28b2o3$65b2o$64bob
o$64bo$42bo7bo14b2o$42b3o4b2o15bo6b2o$45bo3bobo21bo$44bo26bobo$44bo3b
o8bo8bo4b2o$55b2o8bobo$45bo3bo6b2o6bo3bo$45bo3bo5b2o8bobo$54b2o10bo$46b
3o4bo2bo$54bobo$55bo2$59b2o$59bo$60b3o$62bo!

EDIT: There aren't many known odd-period TL hasslers in this rule (see previous discussion in the 2tfl thread). Can anyone find more?

[confocaloid]

Very basic question here, are there any spaceships made out of ships?

I'm looking for a spaceship that, in at least one phase, consists of two or more ships, like this:

Code: Select all

x = 66, y = 6, rule = B3/S23
64b2o$5b2o56bobo$4bobo18b2o36b2o$2o2b2o14b2o2bobo13b2o3b2o13b2o$obo17b
obob2o14bobobobo13bobo$b2o18b2o18b2ob2o15b2o!

... in some two-state isotropic cellular automaton with range-1 Moore neighbourhood, with the additional restriction that by itself the ship must remain a still life as in Life.

[H. H. P. M. P. Cole]

Very basic question here, are there any spaceships made out of ships?

I'm looking for a spaceship that, in at least one phase, consists of two or more ships, like this:

Code: Select all

x = 66, y = 6, rule = B3/S23
64b2o$5b2o56bobo$4bobo18b2o36b2o$2o2b2o14b2o2bobo13b2o3b2o13b2o$obo17b
obob2o14bobobobo13bobo$b2o18b2o18b2ob2o15b2o!

... in some two-state isotropic cellular automaton with range-1 Moore neighbourhood, with the additional restriction that by itself the ship must remain a still life as in Life.

Here are six rules where the first configuration of ships (SL) is a different, unique c/4o spaceship:

Code: Select all

x = 12, y = 3, rule = B3ai4ir5en/S2en3jn4nt5ciq
b2o3b2ob2o$obo2bobobobo$2o3b2o3b2o!

Code: Select all

x = 12, y = 3, rule = B3aiqy4ain5q/S1e2ae3nq4ar
b2o3b2ob2o$obo2bobobobo$2o3b2o3b2o!

Code: Select all

x = 12, y = 3, rule = B3air4ir5en/S2ein3jnq5in6k
b2o3b2ob2o$obo2bobobobo$2o3b2o3b2o!

Code: Select all

x = 12, y = 3, rule = B3ai4ir5en/S1e2en3jn4nt5ciq
b2o3b2ob2o$obo2bobobobo$2o3b2o3b2o!

Code: Select all

x = 12, y = 3, rule = B3ai4ir5n/S1e2aen3n4ajnt5iq
b2o3b2ob2o$obo2bobobobo$2o3b2o3b2o!

Code: Select all

x = 12, y = 3, rule = B3ai4i5c6c/S2e3cnq4aek5ijq
b2o3b2ob2o$obo2bobobobo$2o3b2o3b2o!

This is, of course, not counting higher-period spaceships.

Catagolue census for the first rule

[confocaloid]

[...] with the additional restriction that by itself the ship must remain a still life as in Life.

[...]
This is, of course, not counting higher-period ships.
[...]

My question specifically mentioned that the ship must remain a still life. While the examples you posted indeed count as answers (it might be interesting to find spaceships with a phase consisting of three or more ships, as many as possible), "higher-period ships" are excluded by the question.

edit: well, here are some higher-period ships, for that matter:

Code: Select all

#C p4
x = 3, y = 3, rule = B36n/S23-a4a
2o$obo$b2o!

Code: Select all

#C p2
x = 3, y = 3, rule = B2e3/S2-e3
2o$obo$b2o!

[WhiteHawk]

Is there a better way to eat the glider-loaf while leaving clearance for a potential sparker? Note the rule is Pedestrian Life

Code: Select all

x = 54, y = 44, rule = B38/S23
8b2o3b2o$8b2o3b2o$8b2o3b2o$8b2o3b2o$4b2o3b2ob2o3b2o$4bo2bobo3bobo2bo$
5bob2o5b2obo$6bo9bo6bo$7b4ob4o5b3o$9bobobo6bo30b2o$o19b2o12b2o8b3o4b2o
$3o7b3o21b2o4bo6bo$3bo36bo2bobob2o$2b2o37b3o6b3o$45b2obobo2bo$33bob2o
9bo6bo$31b3o7b2o4b3o$b2o6b3o19b2o2bo5b2o$o8bobo18bo3b2o$b2o6b3o16b2ob
obo$15b3o6b2o2b2ob3o$15bobo8bob2o2bo$15b3o6b2o4b3o6bo$31bo3$23b2o$23b
o$14b3o7b3o4bo2bo$26bo8bo$13bobobo12bo5bo$11b4ob4o10b2o4bo$10bo9bo14b
o$9bob2o5b2obo12bo$8bo2bobo3bobo2bo10b4obo$8b2o3b2ob2o3b2o10bo3bo$12b
2o3b2o12bo3bo$12b2o3b2o11bob4o$12b2o3b2o15bo$12b2o3b2o14bo$32bo4b2o$32b
o5bo$33bo$34bo2bo!
[[ PASTET EVERY 35 1 PASTE 2o! 26 17 ]]
[[ PASTET EVERY 35 32 PASTE 2o! 16 11 ]]

[LuveelVoom]

Is there a better way to eat the glider-loaf while leaving clearance for a potential sparker? Note the rule is Pedestrian Life

Code: Select all

x = 54, y = 44, rule = B38/S23
8b2o3b2o$8b2o3b2o$8b2o3b2o$8b2o3b2o$4b2o3b2ob2o3b2o3bo$4bo2bobo3bobo2b
o2bobo$5bob2o5b2obo3bobo$6bo9bo3b2ob3o$7b4ob4o10bo$9bobobo6b2ob3o25b2o
$o19b2obo10b2o8b3o4b2o$3o7b3o21b2o4bo6bo$3bo36bo2bobob2o$2b2o37b3o6b3o
$45b2obobo2bo$33bob2o9bo6bo$31b3o7b2o4b3o$b2o6b3o19b2o2bo5b2o$o8bobo18b
o3b2o$b2o6b3o16b2obobo$15b3o6b2o2b2ob3o$15bobo8bob2o2bo$15b3o6b2o4b3o
6bo$31bo3$23b2o$23bo$14b3o7b3o4bo2bo$26bo8bo$13bobobo12bo5bo$11b4ob4o
10b2o4bo$10bo9bo14bo$9bob2o5b2obo12bo$8bo2bobo3bobo2bo10b4obo$8b2o3b2o
b2o3b2o10bo3bo$12b2o3b2o12bo3bo$12b2o3b2o11bob4o$12b2o3b2o15bo$12b2o3b
2o14bo$32bo4b2o$32bo5bo$33bo$34bo2bo!
[[ PASTET EVERY 35 1 PASTE 2o! 26 17 ]]
[[ PASTET EVERY 35 32 PASTE 2o! 16 11 ]]

An eater one in the proper place works instead of eater two. Every time I try to paste this, the pattern gets weirdly messed up, but it took me around 30 seconds to find, so shouldn’t be hard.

[confocaloid]

"Patterns" is CGoL-only. Since the question involves a combination of a CA other than Conway's Life and PASTET LifeViewer commands, it might be better to move this to "Other Cellular Automata". Probably it's possible to use [R]Investigator instead of "PASTET" for demonstration purposes.

[WhiteHawk]

"Patterns" is CGoL-only. Since the question involves a combination of a CA other than Conway's Life and PASTET LifeViewer commands, it might be better to move this to "Other Cellular Automata". Probably it's possible to use [R]Investigator instead of "PASTET" for demonstration purposes.

There really should be a "Thread For Requesting Help in OCA thread"

[confocaloid]

"Patterns" is CGoL-only. Since the question involves a combination of a CA other than Conway's Life and PASTET LifeViewer commands, it might be better to move this to "Other Cellular Automata". Probably it's possible to use [R]Investigator instead of "PASTET" for demonstration purposes.

There really should be a "Thread For Requesting Help in OCA thread"

I think that's redundant. There is already thread for basic non-CGoL questions, where questions such as this one belong.

[WhiteHawk]

I think that's redundant. There is already thread for basic non-CGoL questions, where questions such as this one belong.

Thread for Basic Questions and Thread For Requesting Help are existing separate threads for life. Why shouldn't there be complementary OCA threads for both topics instead of them being lumped together under the current thread for basic non-CGoL questions?

(Also this kind of went off-topic quickly. Perhaps this discussion could be continued in a different thread)

EDIT: should it be specified in the title that this thread is for life only, so future users don't make the same mistake?

[confocaloid]

[...] Thread for Basic Questions and Thread For Requesting Help are separate threads.

Which makes sense for Conway's Life, because it receives much more attention and there is much more exploration in it. It makes sense to separate "can I fix this CGoL reaction? How to complete this CGoL component?" into a dedicated thread:

Sometimes people creating complex patterns need help with some small component. [...]

In contrast, "Other Cellular Automata" covers a large number of different types of CA, and incredibly many different specific CA, neither of which is comparably popular. Just one "thread for basic non-CGoL questions" is sufficient there.

Also this kind of went off-topic quickly.

I think it was offtopic from the beginning. "Thread For Requesting Help" is CGoL-specific (and also it's generally better to avoid "PASTET" or similar assistance unless necessary).

EDIT: should it be specified in the title that this thread is for life only, so future users don't make the same mistake?

The board "Patterns" is just about Conway's Life, along with all threads in it.

[WhiteHawk]

Is there a good completion for this p72 variant of the period-agnostic beehive/R hassler from EightLife?

Code: Select all

x = 145, y = 129, rule = B3/S238
30bo$21bo7bobo$21b3o5bobo$24bo3b2o2b2o$23b2o5b2o2bo$23bob4o3b3o$24bo2b
o2b2o$28bo3bo$28bobobo4bo$35b3o$29b3o2bo$20b2o12b2o$21bo21b2o$21bobo19b
o$22b2o17bobo$14b2o25b2o10b2o$14b2o34bobo2bo$48b3obobobo$47bo5bo2bo$47b
2o8bo$2o13b2o8b3o26bobo$10b2o2bobo7bo2bo9b3o$9bo3b2o8bo3bo9bo2bo$10bo
2b2o8bo13bo3bo9b3o$11b3o9bo3bo13bo8b2o2bo$24bo2bo9bo3bo8b2o3bo54bo$25b
3o9bo2bo7bobo2b2o46bo7bobo$8bobo26b3o8b2o13b2o2bo9bo2b2o19b3o5bobo$7b
o8b2o48bobo7bobo25bo3b2o2b2o$8bo2bo5bo48bobo7bobo24b2o5b2o2bo$8bobobo
b3o50bo9bo25bob4o3b3o$9bo2bobo34b2o53bo2bo2b2o$10b2o10b2o25b2o57bo3bo
$21bobo17b2o65bobobo4bo$21bo19bobo71b3o$20b2o21bo65b3o2bo$29b2o12b2o55b
2o12b2o$30bo2b3o65bo21b2o$27b3o71bobo19bo$27bo4bobobo65b2o17bobo$32bo
3bo57b2o25b2o10b2o$33b2o2bo2bo53b2o34bobo2bo$30b3o3b4obo25bo9bo50b3ob
obobo$30bo2b2o5b2o24bobo7bobo48bo5bo2bo$31b2o2b2o3bo25bobo7bobo48b2o8b
o$33bobo5b3o19b2o2bo9bo2b2o13b2o8b3o26bobo$33bobo7bo46b2o2bobo7bo2bo9b
3o$34bo54bo3b2o8bo3bo9bo2bo$90bo2b2o8bo13bo3bo9b3o$91b3o9bo3bo13bo8b2o
2bo$104bo2bo9bo3bo8b2o3bo$105b3o9bo2bo7bobo2b2o$88bobo26b3o8b2o13b2o$
87bo8b2o$88bo2bo5bo$88bobobob3o$89bo2bobo34b2o$90b2o10b2o25b2o$101bob
o17b2o$101bo19bobo$100b2o21bo$109b2o12b2o$110bo2b3o$107b3o$107bo4bobo
bo$112bo3bo$113b2o2bo2bo$110b3o3b4obo$110bo2b2o5b2o$111b2o2b2o3bo$113b
obo5b3o$113bobo7bo$114bo9$30bo83bo$21bo7bobo81bobo7bo$21b3o5bobo81bob
o5b3o$24bo3b2o2b2o77b2o2b2o3bo$23b2o5b2o2bo75bo2b2o5b2o$23bob4o3b3o75b
3o3b4obo$24bo2bo2b2o81b2o2bo2bo$28bo3bo79bo3bo$28bobobo4bo69bo4bobobo
$35b3o69b3o$29b3o2bo75bo2b3o$20b2o12b2o73b2o12b2o$21bo21b2o55b2o21bo$
21bobo19bo57bo19bobo$22b2o17bobo57bobo17b2o$14b2o25b2o10b2o35b2o10b2o
25b2o$14b2o34bobo2bo33bo2bobo34b2o$48b3obobobo31bobobob3o$47bo5bo2bo31b
o2bo5bo$47b2o8bo29bo8b2o$2o13b2o8b3o26bobo31bobo26b3o8b2o13b2o$10b2o2b
obo7bo2bo9b3o65b3o9bo2bo7bobo2b2o$9bo3b2o8bo3bo9bo2bo63bo2bo9bo3bo8b2o
3bo$10bo2b2o8bo13bo3bo9b3o37b3o9bo3bo13bo8b2o2bo$11b3o9bo3bo13bo8b2o2b
o35bo2b2o8bo13bo3bo9b3o$24bo2bo9bo3bo8b2o3bo33bo3b2o8bo3bo9bo2bo$25b3o
9bo2bo7bobo2b2o35b2o2bobo7bo2bo9b3o$8bobo26b3o8b2o13b2o2bo9bo2b2o13b2o
8b3o26bobo$7bo8b2o48bobo7bobo48b2o8bo$8bo2bo5bo48bobo7bobo48bo5bo2bo$
8bobobob3o50bo9bo50b3obobobo$9bo2bobo34b2o43b2o34bobo2bo$10b2o10b2o25b
2o43b2o25b2o10b2o$21bobo17b2o59b2o17bobo$21bo19bobo57bobo19bo$20b2o21b
o57bo21b2o$29b2o12b2o55b2o12b2o$30bo2b3o73b3o2bo$27b3o85b3o$27bo4bobo
bo71bobobo4bo$32bo3bo71bo3bo$33b2o2bo2bo63bo2bo2b2o$30b3o3b4obo25bo9b
o25bob4o3b3o$30bo2b2o5b2o24bobo7bobo24b2o5b2o2bo$31b2o2b2o3bo25bobo7b
obo25bo3b2o2b2o$33bobo5b3o19b2o2bo9bo2b2o19b3o5bobo$33bobo7bo57bo7bob
o$34bo75bo!

Also, other than p72 and period-multiple p90 (Completed with P45 pi hassler), are there other non-gun completions of the oscillator?

EDIT: Is there a way to stabilize AK-94 by eating the 3x3 checkerboards that pop up in this 2tfl rule?

Code: Select all

x = 25, y = 21, rule = B38/S234c
b2o$2bo$2bobo$3b2o2$23b2o$23b2o$2o$bo$bobo$2b2o3b3o$6bo3bo10b2o$5bo5b
o9bobo$6bo3bo12bo$7b3o13b2o$2o$2o$19b2o$19bobo$21bo$21b2o!

[confocaloid]

Is there a good completion for this p72 variant of the period-agnostic beehive/R hassler from EightLife? [...]

Also, other than p72 and period-multiple p90 (Completed with P45 pi hassler), are there other non-gun completions of the oscillator?

EDIT: Is there a way to stabilize AK-94 by eating the 3x3 checkerboards that pop up [...]

While all those questions seem to be valid, each such question amounts to a form of request to do some substantial amount of research (looking up known and/or discovering new catalysts, sparkers, components).

There is a general expectation of "doing it yourself" and asking for help related to some specific problems (as opposed to asking that someone else do the entire thing). That doesn't exactly invalidate such questions, but that makes it less likely that people will provide useful answers, especially when there are many similar questions asked in a short time.

It is often better to focus on some specific topic / specific CA / specific puzzle / specific challenge, and try to go as far as possible to see what are the problems and think about how each of those problems could be resolved. Asking about some specific part(s) of a big "challenge" and providing more details about what you have already tried is more likely to lead to an interesting discussion with reasonably good answers.

How did you find all of those jellyfish guns?

Trying all the possible solutions, as easy and difficult as it is.
The oscillator is found using apgsearch.

[...] If you are interested in exploring your own rules, then the general advice is to explore for a while and then become obsessively interested in one of those rules. If you spread yourself too thinly between different rules, then you're not going to be able to put in the amount of effort required to do more than scratch the surface. [...]

[WhiteHawk]

Is there a way to get a good weld out of these two Eater 2 variants in B34c8/S23? It needs to fit in the traffic jam corner.

Code: Select all

x = 10, y = 9, rule = B34c8/S23
7bo$3b2obobo$2o2bobobo$2obo2bob2o$3b4o$2obo2bob2o$bobobo2b2o$bobob2o$
2bo!

EDIT: Never mind, the traffic wire doesn't work in this rule

[WhiteHawk]

p36; should be easy but it just seem like most Life p4 sparkers fail in EightLife and the ones that do work are too wide

Code: Select all

Would it be beneficial to search for p4 sparkers in EightLife, since effectively all of the smallest and narrowest ones are lost?

(also sorry for the doublepost)

[confocaloid]

Some explored cellular automata have a known stable 90-degree reflector (for some spaceship). In every such case, one can look at fastest known such reflectors (i.e. lowest repeat time).

Question: which previously explored CA have slowest fastest known stable 90-degree reflectors? In other words, at least one stable 90-degree reflector must be known, but the fastest known examples should be really slow (possibly even after substantial efforts to discover a faster reflector).

One can also ask a similar question for stable spaceship duplicators.

Are there any isotropic range-1 two-state rules with small glider reflectors/duplicators with short repeat time? [...]

• https://github.com/yujh-yujh/gliderduplicatordb
• viewtopic.php?f=11&t=4759
• viewtopic.php?f=11&t=5158
• viewtopic.php?f=11&t=5162
• viewtopic.php?f=11&t=5606

[silversmith]

Question: which previously explored CA have slowest fastest known stable 90-degree reflectors? In other words, at least one stable 90-degree reflector must be known, but the fastest known examples should be really slow (possibly even after substantial efforts to discover a faster reflector).

A pretty good example of this is the reflector I found in Speciation:

Repeat time 3477 90° reflector

Code: Select all

x = 149, y = 78, rule = B2cei3-eijr4ceirtw5ciqy6-e7c/S1c2-c3-aiqy4ikntw5nqr6-a
118b2o$119bo$119bo$118b2o33$123b3o19b3o$123bobo19bobo$123bobo19bobo$
122bo2bo19bo2bo$122b4o19b4o$126bo17bo10$144b3o$144bobo$144bobo$30b4o
110bo2bo$30bo2bo110b4o$143bo6$136bo4bo$28b4o60b5o6b2o21bo8b3o2b3o$4o9b
o4b2o2b4obobobo14b4o42bo2b2o6b2o3b2o10bobobo3b2o2b2obob4obo$2bo10b4o2b
o2bob2o2bob2o13b3ob3o40bobo8bob2obobo8bo3bobob2o3b2o2bo3bobo$4o9bo4b2o
2b4obobobo14b4o42bo2b2o6b2o3b2o10bobobo3b2o2b2obob4obo$28b4o60b5o6b2o
21bo8b3o2b3o$136bo4bo7$30bo2bo95b3o$30b4o95bobo$129b3o!

[CARuler]

For the 48 high search note that the 2nd ship has gutter symmetry:

what is gutter symmetry??

[confocaloid]

Question: which previously explored CA have slowest fastest known stable 90-degree reflectors? In other words, at least one stable 90-degree reflector must be known, but the fastest known examples should be really slow (possibly even after substantial efforts to discover a faster reflector).

A pretty good example of this is the reflector I found in Speciation:

Repeat time 3477 90° reflector

Code: Select all

x = 149, y = 78, rule = B2cei3-eijr4ceirtw5ciqy6-e7c/S1c2-c3-aiqy4ikntw5nqr6-a

Looks like a stream of those spaceships cannot be compressed much better to begin with (3025 ticks?), therefore this 3477-tick reflector actually can be considered pretty fast (close to the limit).
Your reflector does indeed provide an example to the question as it was stated. However, the idea was different. What was left unstated behind my question, is the idea that the fastest known reflectors must be really slow relative to the theoretical limit (i.e. relative to the lowest possible period of a periodic stream of spaceships of the same type). (So perhaps people did attempt to discover a faster reflector because there's no obvious impossibility, but even after substantial efforts no such faster reflector was found.)

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x = 115, y = 94, rule = B2cei3-eijr4ceirtw5ciqy6-e7c/S1c2-c3-aiqy4ikntw5nqr6-a
32b4o$32bo2bo8$30b4o$2b4o9bo4b2o2b4obobobo14b4o$4bo10b4o2bo2bob2o2bob
2o13b3ob3o$2b4o9bo4b2o2b4obobobo14b4o$30b4o8$32bo2bo$32b4o49$30b4o66b
4o$30bo2bo66bo2bo3$111bo$110b3o$110b3o$86bo22bobobo$88b3o18b2ob2o$28b
4o54bobobo6b2o10b2ob2o$4o9bo4b2o2b4obobobo14b4o18b3o15b5o4b2obo5b2o3b
5o$2bo10b4o2bo2bob2o2bob2o13b3ob3o15b3o2b4obo10b4ob3ob2ob4o2bob2obob2o
$4o9bo4b2o2b4obobobo14b4o18b3o15b5o4b2obo5b2o3b5o$28b4o54bobobo6b2o10b
2ob2o$88b3o18b2ob2o$86bo22bobobo$110b3o$110b3o$111bo3$30bo2bo66bo2bo$
30b4o66b4o!

[silversmith]

However, the idea was different. What was left unstated behind my question, is the idea that the fastest known reflectors must be really slow relative to the theoretical limit (i.e. relative to the lowest possible period of a periodic stream of spaceships of the same type).

Hmmm, it sounds like you would also exclude reflectors which synthesize a large output spaceship, based on the spirit of the question.

An example of this would be a cordership reflector in CGOL, which one could relatively easily assemble out of known components.

What about something like this?

180 and 90 degree ship reflectors

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x = 50, y = 40, rule = 1e2-a3-cij4aijkrtz5cnqr/2ce3aejnr4aj5y6a/3
14.12A$14.A10.A$14.A10.A$14.A8.3A$14.A$14.A11.4A$14.A11.A2.A$14.A11.A
2.A$14.A14.A9.4A$14.A.14A$14.A.A22.2A$14.A.A$14.A.5A9.3A$14.A5.A9.A4.
10A$14.A5.A9.A4.A8.A$14.A5.A7.A.A4.8A.A$14.A5.5A3.A13.A.A$14.A13.A13.
A.A$14.A3.5A19.A.A$14.A7.A19.A.A$9.A4.7A.A7.8A4.A.A$9.A10.A.A7.A6.A4.
A.A$7.A.A10.A.A7.A6.A4.A.A$7.A.A10.A.A7.6A.A4.A.A$20.A.A12.A.A4.A.A$
20.A.A12.A.6A.6A$2.4A14.A.A12.A13.A$2.A2.A14.A.A12.5A.4A4.A$2.A2.A14.A
.A16.A.A2.A4.A$2.A2.A14.A.A16.A.A2.A4.A$2.A2.A14.A.6A4.8A.A2.A4.A$2.
4A14.A6.A4.A8.A2.A4.A$A4.A14.A6.A4.A8.A2.A4.A$A4.A14.A6.A4.7A2.A2.A4.A
$5.A14.A6.A10.A2.A2.6A$5.A.2A11.A6.A10.A2.A$5.A4.A9.8A2.9A2.A$5.A4.A
19.A10.A$30.A10.A$30.12A!

As for the slowest stable duplicator, one could probably make what you are looking for in Mirrorlife. The rule doesn't have a fast splitter, nor many conduits. However, one could:

• Crash a glider into a constellation to produce 3 or more gliders.
• Make arbitraily many gliders using the known 3 glider to 4 glider converter.
• Release 2 or more gliders.
• Clean up the area of the original collision.
• Rebuild the original constellation.

[WhiteHawk]

Nostalgia - if I had rlifesrc in 2000 AD:

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This is a C/4 orthogonal spaceship, is it not?

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x = 8, y = 12, rule = B2/S
3bobo$4bo2bo$3b2o2bo$3bobo$3o2bo$o5bo$o5bo$3o2bo$3bobo$3b2o2bo$4bo2bo
$3bobo!

EDIT: Never mind, it's 4c/4

[Citation needed]

Are there any other three-cell "Garden of Eden" patterns in "Life Without Death" besides the nine known patterns?

[hotdogPi]

Are there any other three-cell "Garden of Eden" patterns in "Life Without Death" besides the nine known patterns?

Any three-cell pattern that causes a birth is a Garden of Eden, while any three-cell pattern that doesn't has itself as a predecessor. It should be easy enough to figure out manually.

[confocaloid]

What are known examples of "misleading symmetry" appearing in common evolutionary sequences?

What I mean by "misleading symmetry" here: one can imagine a common asymmetric predecessor that eventually evolves into a highly symmetric constellation (like traffic light or honey farm in Conway's Life), except the symmetric constellation forms in an asymmetric way (for example, the honey farm constellation might form by leaving first two beehives oriented differently, then leaving a third beehive, and only later leaving the fourth beehive, resulting in an entirely asymmetric formation of a highly symmetric pattern).

One can expect a "simple" way of engineering a solution with more than two states, so this question is probably limited to two-state cellular automata.
Also the CA must be isotropic (rotations/reflections that preserve the grid lines must also preserve the reactions).
Other than that, any tilings (square/hexagonal/triangular) and any neighbourhoods/ranges are accepted.

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x = 13, y = 13, rule = B3/S23
6bo$5bobo$5bobo$6bo2$b2o7b2o$o2bo5bo2bo$b2o7b2o2$6bo$5bobo$5bobo$6bo!