Thread for basic questions

[jmnh]

Congratulations — an omniship that for every slope (p, q) “almost” reaches the maximum speed.
This raises a question for me (is this thread the right place for it? I’m not sure...):
For which slopes (p,q) are there one or more ships that reach exactly the maximum speed? I only know of 3 examples:
(1,0) xWSS
(1,1) glider
(2,1) “Sir Robin”
Are there any other?

[WhiteHawk]

Congratulations — an omniship that for every slope (p, q) “almost” reaches the maximum speed.
This raises a question for me (is this thread the right place for it? I’m not sure...):
For which slopes (p,q) are there one or more ships that reach exactly the maximum speed? I only know of 3 examples:
(1,0) xWSS
(1,1) glider
(2,1) “Sir Robin”
Are there any other?

That's all right now, though a technically better example for (1,0) is 64P2H1V0

[WhiteHawk]

EDIT: p596:

Code: Select all

Does this count as a true hassler? And thus does it surpass the p576 R-pentomino Hassler for highest-period hassler?

(EDIT: Negating LW DYK 184: "...that the p576 R-pentomino hassler is the engine-based non-LCM oscillator with the highest known period?")


(Also not meaning to keep prying, but might an improved 2026 oscillator stamp collection be on the way?)

[g0t0]

This:

Code: Select all

x = 78, y = 48, rule = B3/S23
7$37bo$37bobo$20bo17bobo4b2o$20b2o16bo2bo3b2o$11b2o2b2o4b2o15bobo$11b
2o2b2o4b3o13bobo$15b2o4b2o7bobo4bo$20b2o9b2o$20bo10bo5$38bo$39b2o$38b
2o6$45bobo$46b2o$46bo7b2o$54b2o$52b2o$52b2o!

How many difference object(no derived objects) can do boat-bit?

[g0t0]

Look this!

Code: Select all

x = 320, y = 284, rule = B3/S23
69$111b2o$110bobo2b2o$110bo4bobo$109b2o4bo21$212b2o$211bobo$211bo$210b
2o3$208b3o$210bo$209bo7$171b2o$171b2o5b2o$178b2o3$147b2o27b2o$147b2o27b
2o$182b2o$182b2o$141b2o$141b2o$145b2o$145b2o4$140b2o$140b2o4$174b3o$172b
2o3bo$151bo$150bo26bo$150b3o19bo3bo$173b3o5$187b2o$187b2o4$182b2o$182b
2o$186b2o$186b2o$145b2o$145b2o$151b2o27b2o$151b2o27b2o3$149b2o$149b2o
5b2o$156b2o4$181bo$179bobo$180b2o35$85b2o$84bobo$84bo$83b2o24$245bo$243b
obo$244b2o!

Can we use eater 1s on the same direction to turn the pattern a osc?

[g0t0]

How can I get all census data for one rule and one symmetry in Catagolue?

[I6_I6]

I've noticed that some 23-bit strict SLs don't have a synthesis on catagolue, even though all 23-bitters have been synthesized. Here's an example:

Code: Select all

x = 7, y = 11, rule = B3/S23
3bo$2bobo$3bo2$b5o$bo4bo$4b2o$bo2bo$obobo$obob2o$bo!

Where can I find their syntheses?

[dvgrn]

I've noticed that some 23-bit strict SLs don't have a synthesis on catagolue, even though all 23-bitters have been synthesized...
Where can I find their syntheses?

See the link in the first post of the 23-bit still life syntheses project thread.

[Aleph]

How was the 6G synthesis for https://catagolue.hatsya.com/object/xs1 ... zw11/b3s23 found? I don't see it in any glider stdins, but the synthesis simply looks way too "dense" to have been soup-based.

[synperiplanar]

is there a general guide on how to make dependent reflector loops by hand? i have the following reactions in b2is23-c:

Code: Select all

x = 45, y = 37, rule = B2i3/S23-c
21b2o$20b4o$16bob2ob2obo$15bo2b2o$14b3o2b2o2b2o$14b3o2bob4o$15bo2bo3b
o2bo$16b4obo2b3o$16b2o2b2o2b3o$21b2o2bo$16bob2ob2obo$17b4o$18b2o6$2bo
2bobo$2obob3o$bo6bo11b3o$2o5bo$20bobo15bo2bobo$bo5b2o12bo14b2obob3o$o
6bo29bo6bo$b3obob2o14bo12b2o5bo$bobo2bo15bobo$37bo5b2o$22b3o11bo6bo$37b
3obob2o$27bo9bobo2bo$26bo$26bo2bo$27b3o$23b3o$25bo$24bo!

Code: Select all

x = 20, y = 13, rule = B2i3/S23-c
18b2o$18b2o2$5b4o5b2o$bo4bobo6b2o$obo3b2o6b2o$bo3b3o4b3o$13bo3$13b3o$
15bo$14bo!

but i don't know which can be made into a loop and/or how to do so.

[rabbit]

is there a general guide on how to make dependent reflector loops by hand?

<1st pattern:>

Code: Select all

x = 45, y = 37, rule = B2i3/S23-c
21b2o$20b4o$16bob2ob2obo$15bo2b2o$14b3o2b2o2b2o$14b3o2bob4o$15bo2bo3b
o2bo$16b4obo2b3o$16b2o2b2o2b3o$21b2o2bo$16bob2ob2obo$17b4o$18b2o6$2bo
2bobo$2obob3o$bo6bo11b3o$2o5bo$20bobo15bo2bobo$bo5b2o12bo14b2obob3o$o
6bo29bo6bo$b3obob2o14bo12b2o5bo$bobo2bo15bobo$37bo5b2o$22b3o11bo6bo$37b
3obob2o$27bo9bobo2bo$26bo$26bo2bo$27b3o$23b3o$25bo$24bo!

<2nd pattern:>

Code: Select all

x = 20, y = 13, rule = B2i3/S23-c
18b2o$18b2o2$5b4o5b2o$bo4bobo6b2o$obo3b2o6b2o$bo3b3o4b3o$13bo3$13b3o$
15bo$14bo!

First, paste a second copy of the reflector so that it accepts the output glider of the first to effectively turn it into a dependent 180° reflector:

Code: Select all

x = 31, y = 20, rule = B2i3/S23-c
25bo$24bobo$25bo3$24bo2bo$23bo3b2o$18b2o4bo3bo$4b2o5bo6b2o5b3o$4b2o3b
4o$8b2obobo$bo5bobobob2o$obo3b2obobobo9b2o$bo5bobob2o6bo3bo$8b4o8b2obo
3bo$9bo9b2o3bo2bo$25b3o2$29b2o$29b2o!

Then, run it until the reflector reaches its original state, and paste the original & modified patterns over each other:

Code: Select all

x = 31, y = 20, rule = B2i3/S23-c
25bo$24bobo$24b3o$25bobo$25b2obo$24b3o2bo$22bo2bo2bo$18b2o5bo$18b2o$6b
2o15b2o2bo$5b2obo5b3o$bo6bo7bo8b3o$obo5bo7bo$bo3bobo4bo2bo$6bo5b3o$21b
o$14bo6bo3bo$14b2o8bo$13bobo8b3o2b2o$29b2o!

If the first and last glider in the loop are flipped 180° from each other, you can wrap up the loop right there by pasting a 180°-flipped copy of the pattern onto itself so that the first and last gliders line up between halves. Otherwise, you may have to run the pattern again for a full cycle and paste it over itself again:

Code: Select all

x = 31, y = 25, rule = B2i3/S23-c
25bo$24bobo$24b3o$25bobo$25b2obo$24b3o2bo$22bo2bo2bo$18b2o5bo$18b2o$6b
2o15b2o2bo$5b2obo5b3o$bo6bo7bo8b3o$obo5bo7bo$bo3bobo4bo2bo$6bo5b3o$21b
o$14bo6bo3bo$14b2o8bo$13bobo8b3o2b2o$29b2o3$19bobo$19b2o$20bo!

Code: Select all

x = 35, y = 41, rule = B2i3/S23-c
25bo$24bobo$24b3o$25bobo$25b2obo$24b3o2bo$22bo2bo2bo$18b2o5bo$18b2o$6b
2o15b2o2bo$5b2obo5b3o$bo6bo7bo8b3o$obo5bo7bo$bo3bobo4bo2bo$6bo5b3o$21b
o$14bo6bo3bo$14b2o8bo$13bobo8b3o2b2o$29b2o2$4b2o$4b2o2b3o8bobo$10bo8b
2o$9bo3bo6bo$13bo$20b3o5bo$19bo2bo4bobo3bo$18bo7bo5bobo$7b3o8bo7bo6bo$
18b3o5bob2o$7bo2b2o15b2o$15b2o$9bo5b2o$6bo2bo2bo$5bo2b3o$6bob2o$7bobo$
8b3o$8bobo$9bo!

-

Here's an alternate design that also works for some periods and might sometimes be smaller or lower population but is usually larger:

Run one full period of the dependent reflector, and then paste the result over the original pattern:

Code: Select all

x = 23, y = 13, rule = B2i3/S23-c
18b2o$18b2o2$5b4o5b2o$bo4bobo6b2o$obo3b2o6b2o$bo3b3o4b3o$13bo7bo$22bo$
20b3o$13b3o$15bo$14bo!

Repeat this process (in this case, two more times), until the leading glider is a 45° turn away from the input:

Code: Select all

x = 33, y = 21, rule = B2i3/S23-c
18b2o$18b2o2$5b4o5b2o$bo4bobo6b2o$obo3b2o6b2o$bo3b3o4b3o$13bo7bo$22bo$
20b3o$13b3o$15bo$14bo$25bobo$26b2o$26bo3$32bo$30bobo$31b2o!

Then you can paste it four times forming a diamond to complete the loop:

Code: Select all

x = 48, y = 48, rule = B2i3/S23-c
23b2o$23b2o2$10b4o5b2o$6bo4bobo6b2o$5bobo3b2o6b2o21bo$6bo3b3o4b3o21bob
o$18bo7bo15bo$27bo$25b3o$18b3o20bo2bo$20bo20b4o$19bo21b2obo$30bobo10b
2o$31b2o$13b2o16bo$14b2o$13bo27bo$37bo2b2o$35bobo3b2obo$8b2o26b2o4b3o$
7bobo33bo$9bo$2o44b2o$2o44b2o$38bo$4bo33bobo$3b3o4b2o26b2o$3bob2o3bobo
$6b2o2bo$6bo27bo$32b2o$16bo16b2o$15b2o$3b2o10bobo$3bob2o21bo$3b4o20bo$
3bo2bo20b3o$20b3o$20bo$5bo15bo7bo$4bobo21b3o4b3o3bo$5bo21b2o6b2o3bobo$
26b2o6bobo4bo$27b2o5b4o2$23b2o$23b2o!

I'll leave the first mechanism alone so you can try making a loop from it yourself if you want (hint: the second design won't work due to its period being divisible by 4 and the relative phases of the gliders)

[WhiteHawk]

Note this may not work if the loop is Colour or parity-changing (appears to be the case here)

In those instances, 2 extra reflectors may be necessary - see this p48 from life

Code: Select all

x = 135, y = 83, rule = B3/S23
99bo$97b3o$96bo$96b2o$83b2o$84bo$41bo42bobo$39b3o43b2o$38bo54b2o$38b2o
52bo2b2o$25b2o65b2ob2o$26bo65b2ob2o$26bobo65bo$27b2o$35b2o$35b2o53bo5b
2o$35b2o53bo5bo$97b3o7bo$93b2o4bo8b2o$31bo12bobo5b2o32b2o5bobo11b2o$25b
3o3b2o12b2o6bo9b2o20bobo7bo$27bo3b3o4b2o5bo7bobo7bo12b2o7bo9b2o$26bo4b
ob2o3bo15b2o5bobo11bobo6b2o$31b4o4b3o19b2o4bo9bo$32bob3o4bo23b3o$28b2o
5bobo26bo$27bobo7bo26b2o$27bo9b2o$26b2o33b3o$60bo3bo54bo10bo$59bo5bo46b
o7b2o6b3o$59bo5bo46b3o4b2o6bo$13b3o43bo5bo49bo11b2o$15bo44bo3bo49b2o$
14bo38b2o6b3o54b3o$52bobo61b2o3bo$52bo63bo4bo$2o15b2o32b2o15b2o50bo$b
o15bo46b2o2bo46bo3bo5bo$bobo11bobo46bo4bo45bo8bobo$2b2o11b2o4bo43b5o46b
o7bobo$9bo9b3o91b3o9bo$8bobo7bo46b5o43bo4b2o11b2o$8bobo8bo45bo4bo46bo
bo11bobo$9bo5bo3bo46bo2b2o46bo15bo$14bo50b2o15b2o32b2o15b2o$13bo4bo63b
o$13bo3b2o61bobo$14b3o54b3o6b2o38bo$19b2o49bo3bo44bo$6b2o11bo49bo5bo43b
3o$7bo6b2o4b3o46bo5bo$4b3o6b2o7bo46bo5bo$4bo10bo54bo3bo$71b3o33b2o$96b
2o9bo$69b2o26bo7bobo$70bo26bobo5b2o$67b3o23bo4b3obo$57bo9bo4b2o19b3o4b
4o$49b2o6bobo11bobo5b2o15bo3b2obo4bo$38b2o9bo7b2o12bo7bobo7bo5b2o4b3o
3bo$39bo7bobo20b2o9bo6b2o12b2o3b3o$26b2o11bobo5b2o32b2o5bobo12bo$25b2o
8bo4b2o$27bo7b3o$38bo5bo53b2o$37b2o5bo53b2o$98b2o$106b2o$40bo65bobo$38b
2ob2o65bo$38b2ob2o65b2o$38b2o2bo52b2o$40b2o54bo$48b2o43b3o$48bobo42bo
$50bo$50b2o$37b2o$38bo$35b3o$35bo!

[synperiplanar]

I'll leave the first mechanism alone so you can try making a loop from it yourself if you want (hint: the second design won't work due to its period being divisible by 4 and the relative phases of the gliders)

done! thx

Code: Select all

x = 120, y = 122, rule = B2i3/S23-c
63bo2bo$62bo$60b2o$57bo6b2obo$60bo3bo2bo$60b3obo3bo$57bo11bo$58bo3bob
3o$59bo2bo3bo$59bob2o6bo$65b2o$64bo$60bo2bo6$44b2ob2obo$43b2o2b2ob2o$
51bo$43b2o$43b2o5b2o8b2o18b2ob2obo12b2o$50b2o7bo2bo6bob2o6b2o2b2ob2o8b
o$43bo15b2ob2o3b2ob2o15bo7bobo2b2o$43b2ob2o2b2o6b2obo6bo2bo7b2o12bobo
b3o2bo$44bob2ob2o18b2o8b2o5b2o5bo2b2ob3o$86b2o8bo3bo$79bo15b3ob2o2bo$
79b2ob2o2b2o6bo2b3obobo$80bob2ob2o8b2o2bobo$100bo$96b2o6$114b4o$110b2o
bo4bo$109bo3bo4bo$101bo7bo4b2o$99b2obo6bo2bo4b2o$99bo2bo6bo2bo3bo2bo$
100b2o8b2o4bo2bo$113b2o4bo$91b2o17bo4bo3bo$90bo2bo16bo4bob2o$90bob2o17b
4o$91bo2$49bo$49b2o$26b2o20bobo$23bo$22bobo2b2o$20bobob3o2bo$20bo2b2o
b3o$23bo3bo67b2o$22b3ob2o2bo61bo$21bo2b3obobo60bobo2b2o$22b2o2bobo60b
obob3o2bo$27bo61bo2b2ob3o$23b2o67bo3bo$91b3ob2o2bo$90bo2b3obobo$91b2o
2bobo$96bo$69bobo20b2o$69b2o$70bo2$28bo$5b4o17b2obo$b2obo4bo16bo2bo$o
3bo4bo17b2o$o4b2o$o2bo4b2o8b2o$o2bo3bo2bo6bo2bo$b2o4bo2bo6bob2o$4b2o4b
o7bo$bo4bo3bo$bo4bob2o$2b4o6$22b2o$19bo$18bobo2b2o8b2ob2obo$16bobob3o
2bo6b2o2b2ob2o$16bo2b2ob3o15bo$19bo3bo8b2o$18b3ob2o2bo5b2o5b2o8b2o18b
2ob2obo$17bo2b3obobo12b2o7bo2bo6bob2o6b2o2b2ob2o$18b2o2bobo7bo15b2ob2o
3b2ob2o15bo$23bo8b2ob2o2b2o6b2obo6bo2bo7b2o$19b2o12bob2ob2o18b2o8b2o5b
2o$75b2o$68bo$68b2ob2o2b2o$69bob2ob2o6$56bo2bo$55bo$53b2o$50bo6b2obo$
53bo3bo2bo$53b3obo3bo$50bo11bo$51bo3bob3o$52bo2bo3bo$52bob2o6bo$58b2o
$57bo$53bo2bo!

[TheWayOfTheCon]

This is probably something that has been asked before, but
Why do spaceships tend to be orthogonal or diagonal, rather than obliques of all kinds of slopes?

Is it the symmetry? Are they just easier to find/occur?

[LuveelVoom]

This is probably something that has been asked before, but
Why do spaceships tend to be orthogonal or diagonal, rather than obliques of all kinds of slopes?

Is it the symmetry? Are they just easier to find/occur?

There are a lot of questions like this that nobody's ever really looked into in more detail, e.x. why are higher-displacement spaceships both faster to look for but also require higher width? Why does the hardest part of a search tend to be the frontend, but backends are difficult to find? Most interestingly, why do searches slow down when entering sections of a search that humans typically consider interesting?

I suspect with a few hours of pondering by people who understand spaceship algorithms (APG, sokwe, amling, et cetera...) we could obtain fairly good reasons as to why these heuristics exist.

[TheWayOfTheCon]

I suspect with a few hours of pondering by people who understand spaceship algorithms (APG, sokwe, amling, et cetera...) we could obtain fairly good reasons as to why these heuristics exist.

I do think it has something to do with symmetry. There is no symmetry for the oblique directions, only orthogonal and diagonal, and asymmetric spaceships are just harder to find because you can't just shortcut by looking at only one half and mirroring it, you have to account for the entire spaceship.

That doesn't really explain why orthogonal and diagonals are so dominant in the natural field. Sure, many sequences start with or evolve into something symmetric, but take for example, the switch engine. It is entirely asymetrical and has pretty chaotic evolution, but it manages to copy itself exactly along the diagonal?

EDIT: Ok, the sentence prior doesn't make much sense. What I meant to say was the switch engine manages to copy itself in such a way that it allows for diagonal movement. But now I realize that, regardless of where the pattern translates a copy of itself, if it reflects itself the same way it will move diagonally, because on its first reflection it will be translating itself on the inverse direction.

Of course, I'm not an expert in this stuff nor am I trying to be, and this is mostly unproductive rambling, but I think it's good to at least put an idea out there as long as it's something with structure.

[Msculenny]

An interesting thought experiment:
Does there or can there exist a pattern, which consists of a finite amount of cells, and given infinite time will make EVERY cell alive at least once? In other words, is there a pattern such that given any cell, that cell will become alive in a finite amount of generations when starting from that pattern?
Spacefiller doesn't fulfill this requirement, as it only fills half the cells.
An idea I have is a pattern which moves in a square spiral, which would eventually visit every cell, but is such a pattern even possible?

[hotcrystal0]

Space nonfiller

[Sokwe]

This is probably something that has been asked before, but
Why do spaceships tend to be orthogonal or diagonal, rather than obliques of all kinds of slopes?

Is it the symmetry? Are they just easier to find/occur?

Obviously we don't know generally whether orthogonal and diagonal spaceships are more common than oblique ships in some sense. Still, at least at small scales this seems empirically to be true. I think it most likely comes down to symmetry, period, and to a lesser extent speed and search bias.

• Symmetry: this doesn't just mean symmetry of the whole ship. A symmetric component might instead help maintain a ship's forward momentum. For example, consider the B-heptomino in Life, which is asymmetric, but appears to travel orthogonally at c/2 for a while. That seems to be influenced by the front two rows, which remain symmetric during this forward movement, forcing it to be orthogonal:

  Code: Select all

  x = 4, y = 3, rule = LifeHistory
  2.E$.3E$2A.A!

  A pattern whose movement is sustained by such a reaction would need to break this symmetry and then reform with some horizontal offset. This does happen sometimes, and I think we see it a lot more in non-totalistic rules, but it still seems less likely than just maintaining the forward momentum in my experience. There are also a lot of spaceships that have glide symmetry, which also necessitates orthogonal or diagonal movement.
• Period: generally, lower-period spaceships seem to be more common than higher-period ships (at similar sizes and speeds). There are some exceptions, but I've found that this generally holds. The lowest periods generally cannot sustain an oblique ship, which requires a move of at least 3 in the taxicab metric. Even if a spaceship is higher-period, it might have a lower-period reaction sustaining the movement. Consider again the B-heptomino in Life, where the forward movement is maintained by the first two rows having period 2. Since oblique ships can't have low-period components, I imagine they must be more chaotic, which seems like it would reduce the likelihood of a component returning to its original shape.
• Speed: generally, slower spaceships seem to be more common than faster spaceships (at similar sizes and periods). Relatively low-period oblique ships often travel at or near the speed limit, making them less common than slower orthogonal and diagonal ships at the same period.
• Search bias: obviously, our tools for finding elementary spaceships are limited to periods below about 10 and to relatively small sizes (with some exceptions like LLSSS's ability to disprove ships at any width in some cases). For all we know, at very large sizes and high periods the difference in frequency between orthogonal, diagonal, and oblique spaceships might go down. I still think asymptotically by area that orthogonal and diagonal spaceships made of low-period components will dominate the overall count.

[WhiteHawk]

[*]Speed: generally, slower spaceships seem to be more common than faster spaceships (at similar sizes and periods). Relatively low-period oblique ships often travel at or near the speed limit, making them less common than slower orthogonal and diagonal ships at the same period.
[/list]

Do you mean faster spaceships are more common than slower ships at similar sizes and periods - there are a lot of c/2s in life (& C ships in something like Seeds - B2/S ) - while I guess circuitry-based ships may provide more examples for slow speeds due to construction timing constraints, elementary ships seem to me to be the opposite, right?

[Sokwe]

Do you mean faster spaceships are more common than slower ships at similar sizes and periods

No, I've found that slower ships seem to be more common at similar periods. c/2 ships are common generally because they can be low-period and typically have forward movement sustained in a similar way to the B-Heptomino in life, but start looking at higher periods like 5 to 15 and you typically find that slower spaceships seem to be more common than faster spaceships. However, Life belongs to a smallish collection of rules where 2c/5 ships are more common than c/5 ships.

[Msculenny]

Space nonfiller

Damn, and I thought I came up with a brilliant question . But thanks for showing this!