Thread for basic questions

[Haycat2009]

Are there any known INVALID glider synthesises for solutions of the generalised forms of the Grandfather problem?

[confocaloid]

Are there any known INVALID glider synthesises for solutions of the generalised forms of the Grandfather problem?

Without "known", the question appears to reduce to "Is there any arrangement of (non-interacting at T = 0) gliders, that has an n-tick predecessor but not an (n+1)-tick predecessor, for some n > 0?" There might be a densely packed arrangement of several dozens or hundreds of gliders that cannot be rewound by a SAT solver arbitrarily far back in time.

I have doubts about "known" (it is plausible that nobody thought to search for such patterns).

[confocaloid]

Can anyone prove that stripey.rle does not have any two-glider destruction?

Code: Select all

#C Stripey still life, created by Gabriel Nivasch.
x = 66, y = 65, rule = B3/S23
bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$b64o
2$b64o$o24bo39bo$b23o3b38o$24b3o$b20o2bo3b38o$o20bo2bo2bo37bo$b20ob2o
6b35o$20bo5bo2bo$b19o2b5o2b36o$o19b2o43bo$b17obo2b43o$10bo6bobobo$b8o
3b3o4bob44o$o7bobobo2bo3bo45bo$b7o2b2o2b2o2b2o3b42o$8b2o12bo$b7o2b13o
2b40o$o7b2o15bo39bo$b7o2b15o3b37o$9bo17bo$b7ob2o2b15ob2ob33o$o6bobo2bo
11bo3bobobo32bo$b6o3bobo2b8o3bo3bo2b3o2b2ob24o$7b3o2bobo8b7obobo2bo2bo
bo$b6o3b3ob9o6bobo4b2o4b2o2b19o$o6b2o15bobo2bob2o10bo2bo18bo$b5obob16o
b4o3bo6b3o4b18o$5bobo22b2o2bob2obo2bobo$b4o2b22o3b3ob2ob3o2b21o$o4b2o
22b3o10b2o21bo$b4o2b22o3b10o2bo2b2ob15o$5bo24b2o10bobo3bobo$b5ob23o3b
8obob2o2bo2b14o$o5b2o23b2o6bobobo2bobo16bo$b4o4b22o2b4o4bobo2bob4ob12o
$5b3obo21bo5bo3bob2obo4bobo$b4o2bo2b20o2b5o3b2o2bob3o2bo2b11o$o4bobo
22b2o4bobo3bobo4bobo13bo$b5ob23o2b3obob2ob2o2b2obobob13o$31bo2bobo5bo
3bobo3bo$b30obobob2ob2o4bo2bobo3b3ob7o$o31bobo2bobo4bo3bob4o2bobo6bo$b
32ob3o4bobob3obo4bobo2b6o$40b2obobo3bob2obobo$b22ob11o9bo4b2obobob9o$o
21bobo10bo11b2o4b2o10bo$b21o4b10o2b2o3bo4bo6b10o$22b4o3bo9bo2bobobo4b
3obo$b21o3bobo4b7o3bobob2o2bo2bo2b9o$o21bo2bob2o2bo11b2o4bobobo11bo$b
21o2b2obo3bob2o2b2o6b5obob12o$29bobobobo2bo6bo5bo$b30o2bob2o10b4ob13o$
o32bobo5bob4o3bo14bo$b33o2bo4b2o4bo3b14o$34bobo7b3obo$b34ob2o3b3o4b17o
$o37bobo2bob2o18bo$b38ob2o2bob19o2$b64o$bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo!

[...] At some point later (I don't know when), there should be a still life without any two-glider destruction at all. That is harder to find/verify, because there are many ways how two gliders can hit the target at once.

[dvgrn]

Can anyone prove that stripey.rle does not have any two-glider destruction?

Yikes -- I don't think we quite have the tools for that ready to hand, though maybe it isn't absolutely impossible.

For example, we pretty much have to try every single possible collision between the following pattern and one more incoming glider, for 1292 ticks:

Code: Select all

x = 70, y = 65, rule = B3/S23
bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$b64o
2$b64o$o24bo39bo$b23o3b38o$24b3o$b20o2bo3b38o$o20bo2bo2bo37bo$b20ob2o
6b35o$20bo5bo2bo$b19o2b5o2b36o$o19b2o43bo$b17obo2b43o$10bo6bobobo$b8o
3b3o4bob44o$o7bobobo2bo3bo45bo$b7o2b2o2b2o2b2o3b42o$8b2o12bo$b7o2b13o
2b40o$o7b2o15bo39bo$b7o2b15o3b37o$9bo17bo$b7ob2o2b15ob2ob33o$o6bobo2bo
11bo3bobobo32bo$b6o3bobo2b8o3bo3bo2b3o2b2ob24o$7b3o2bobo8b7obobo2bo2bo
bo$b6o3b3ob9o6bobo4b2o4b2o2b19o$o6b2o15bobo2bob2o10bo2bo18bo$b5obob16o
b4o3bo6b3o4b18o$5bobo22b2o2bob2obo2bobo$b4o2b22o3b3ob2ob3o2b21o$o4b2o
22b3o10b2o21bo2b2o$b4o2b22o3b10o2bo2b2ob15o2b2o$5bo24b2o10bobo3bobo18b
o$b5ob23o3b8obob2o2bo2b14o$o5b2o23b2o6bobobo2bobo16bo$b4o4b22o2b4o4bob
o2bob4ob12o$5b3obo21bo5bo3bob2obo4bobo$b4o2bo2b20o2b5o3b2o2bob3o2bo2b
11o$o4bobo22b2o4bobo3bobo4bobo13bo$b5ob23o2b3obob2ob2o2b2obobob13o$31b
o2bobo5bo3bobo3bo$b30obobob2ob2o4bo2bobo3b3ob7o$o31bobo2bobo4bo3bob4o
2bobo6bo$b32ob3o4bobob3obo4bobo2b6o$40b2obobo3bob2obobo$b22ob11o9bo4b
2obobob9o$o21bobo10bo11b2o4b2o10bo$b21o4b10o2b2o3bo4bo6b10o$22b4o3bo9b
o2bobobo4b3obo$b21o3bobo4b7o3bobob2o2bo2bo2b9o$o21bo2bob2o2bo11b2o4bob
obo11bo$b21o2b2obo3bob2o2b2o6b5obob12o$29bobobobo2bo6bo5bo$b30o2bob2o
10b4ob13o$o32bobo5bob4o3bo14bo$b33o2bo4b2o4bo3b14o$34bobo7b3obo$b34ob
2o3b3o4b17o$o37bobo2bob2o18bo$b38ob2o2bob19o2$b64o$bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo!

We can be _reasonably_ sure that no single glider is going to completely clean up all of that ash -- but it isn't a proof until we try all the options.

There's probably a brute-force way to do it that's technically within reach. We can easily enumerate and check all the cases where two gliders strike Stripey simultaneously. Once those are out of the way, we can list all of the possible single-glider crashes.

For each one of those 1G interactions where at least two gliders escape in different directions (which is almost all of them) I think we might be able to define a threshold point where we can prove that adding one more glider can't produce a diehard: we could kick back one of the two gliders and theoretically magically reduce the rest of the ash to nothing, but the other glider is going to escape. I'm not sure where that threshold is exactly, though.

Anyway, at the time when two gliders cross that "you can't catch me" threshold, wherever that is... there's no need to bother checking gliders that collide with the remaining ash after that point. So I think the whole search problem is finite, to prove an answer for any given large still life.

There are some tricky cases, like if a collision produces exactly one output glider:

Code: Select all

x = 70, y = 65, rule = B3/S23
bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$b64o
2$b64o$o24bo39bo$b23o3b38o$24b3o$b20o2bo3b38o$o20bo2bo2bo37bo$b20ob2o
6b35o$20bo5bo2bo$b19o2b5o2b36o$o19b2o43bo$b17obo2b43o$10bo6bobobo$b8o
3b3o4bob44o$o7bobobo2bo3bo45bo$b7o2b2o2b2o2b2o3b42o$8b2o12bo$b7o2b13o
2b40o$o7b2o15bo39bo$b7o2b15o3b37o$9bo17bo$b7ob2o2b15ob2ob33o$o6bobo2bo
11bo3bobobo32bo$b6o3bobo2b8o3bo3bo2b3o2b2ob24o$7b3o2bobo8b7obobo2bo2bo
bo$b6o3b3ob9o6bobo4b2o4b2o2b19o$o6b2o15bobo2bob2o10bo2bo18bo$b5obob16o
b4o3bo6b3o4b18o$5bobo22b2o2bob2obo2bobo$b4o2b22o3b3ob2ob3o2b21o$o4b2o
22b3o10b2o21bo$b4o2b22o3b10o2bo2b2ob15o$5bo24b2o10bobo3bobo$b5ob23o3b
8obob2o2bo2b14o$o5b2o23b2o6bobobo2bobo16bo$b4o4b22o2b4o4bobo2bob4ob12o
$5b3obo21bo5bo3bob2obo4bobo$b4o2bo2b20o2b5o3b2o2bob3o2bo2b11o3b2o$o4bo
bo22b2o4bobo3bobo4bobo13bob2o$b5ob23o2b3obob2ob2o2b2obobob13o4bo$31bo
2bobo5bo3bobo3bo$b30obobob2ob2o4bo2bobo3b3ob7o$o31bobo2bobo4bo3bob4o2b
obo6bo$b32ob3o4bobob3obo4bobo2b6o$40b2obobo3bob2obobo$b22ob11o9bo4b2ob
obob9o$o21bobo10bo11b2o4b2o10bo$b21o4b10o2b2o3bo4bo6b10o$22b4o3bo9bo2b
obobo4b3obo$b21o3bobo4b7o3bobob2o2bo2bo2b9o$o21bo2bob2o2bo11b2o4bobobo
11bo$b21o2b2obo3bob2o2b2o6b5obob12o$29bobobobo2bo6bo5bo$b30o2bob2o10b
4ob13o$o32bobo5bob4o3bo14bo$b33o2bo4b2o4bo3b14o$34bobo7b3obo$b34ob2o3b
3o4b17o$o37bobo2bob2o18bo$b38ob2o2bob19o2$b64o$bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo!

But then we only have to check all collisions that happen early enough that that glider hasn't escaped beyond the threshold... plus all kickback reactions that happen at times early enough that the glider bounces back into something other than settled P2 ash -- plus one test of each of the two kickback reactions into settled ash. That's still a finite and enumerable list, and then we're done with that case.

It does seem possible that a still life much smaller than Stripey could be proven to be non-2G-destructible in this way. For Stripey it's a lot of CPU hours, but maybe there's some medium-sized still life that always produces multiple output gliders no matter where you hit it with a single input glider. Might be able to avoid the no-output-gliders and one-output-glider special cases that way, and just brute-force a test for all glider collisions out to T={threshold}.

[allanwindmill]

Hi all! (I am a newbie so I ask beginner questions )

I know there are lots of patterns already discovered and named, but besides going through Life Lexicon or Life Wiki manually and trying to find a pattern, what are the more standard way to find whether a pattern is already cataloged?

For instance, today I found this from an ash:

Code: Select all

x = 4, y = 2, rule = B3/S23
b3o$3o!

It is a period 2 oscillator with the other phase looking like this:

Code: Select all

x = 4, y = 4, rule = B3/S23
2bo$o2bo$o2bo$bo!

And for sure we may see it being rotated 90 degrees:

Code: Select all

x = 2, y = 4, rule = B3/S23
o$2o$2o$bo!

Because it's so simple, I am pretty sure it's already found by others - but how do I confirm? Is there a way to search for patterns, likely with different phases? On the other hand, we have threads like viewtopic.php?f=2&t=279 "Thread For Your Accidental Discoveries" - besides searching the forum, how can I compare and know whether others have found some pattern already?

Cheers!

P.S. Actually from https://conwaylife.com/ref/mniemiec/p2.htm I found that this particular one is named "Toad". But then again, what if I found something else and don't know which wiki page to look for?

[TYCF]

You can use https://catagolue.hatsya.com/object.

[confocaloid]

Hi all! (I am a newbie so I ask beginner questions :D )

I know there are lots of patterns already discovered and named, but besides going through Life Lexicon or Life Wiki manually and trying to find a pattern, what are the more standard way to find whether a pattern is already cataloged?
[...]

P.S. Actually from https://conwaylife.com/ref/mniemiec/p2.htm I found that this particular one is named "Toad". But then again, what if I found something else and don't know which wiki page to look for?

There are multiple places to look, depending on details. In particular:

• Search For Pattern ("lifesrch") @ Mark D. Niemiec's Life Page
• Identify pattern @ Catagolue
• jslife and other pattern collections @ Jason’s Life Page
• jslife-moving (a collection of moving objects found in Conway's Game of Life. It extends part of Jason Summers' jslife collection)
• LifeWiki
• forum search

[TYCF]

What is the smallest t-pentomino to glider converter?

[b-engine]

What is the smallest t-pentomino to glider converter?

Suppressing 1 cell from birth can turn a T-tetromino into glider, but I have no idea for T-pentomino.

Code: Select all

x = 6, y = 3, rule = B3/S23
3o$bo2bo$3b3o!

[TYCF]

What is the smallest t-pentomino or t-tetromino factory?

[Haycat2009]

Code: Select all

x = 20, y = 20, rule = B3/S23
3b2o3b2o$3b2o3bobo$9bobobo$12bo5b2o$10bo2b2o3b2o$4bo4bobobo$2bob2o4b3o
$3bo2bo4bo$2bo2b3o10b2o$bo2bobo7bo2bobo$obo2bo7bobo2bo$2o10b3o2bo$8bo
4bo2bo$7b3o4b2obo$6bobobo4bo$2o3b2o2bo$2o5bo$6bobobo$9bobo3b2o$10b2o3b
2o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 ZOOM 10 GPS 40 HEIGHT 500 ]]

Is this a charity p16 variant or something else?

[muzik]

Is there a name for this specific spark, in the context of it being a spark?

Code: Select all

x = 3, y = 2, rule = B3/S23
obo$2bo!

[hotcrystal0]

Here is an example of a wick that requires support from one end but not the other:

Code: Select all

x = 56, y = 13, rule = B3/S23
9bo10bo10bo10bo10bo$8bobo8bobo8bobo8bobo8bobo$4b2o3bo10bo8bo2bo4bo3b2o
5b2o3bo$3bo4bo5b4o8b2o9bo3b2o4bo4bo$8bo3bo2b5o4bobo2bo5b3o2b2o10bo$b2o
b2o2b2o2bobo3b2o2bobo4b2o2b3o5bo3b2ob2o2b2o$2o7b3o9bo11bo10b2o7b3o$b2o
b2o2b2o2bobo3b2o2bobo4b2o2b3o5bo3b2ob2o2b2o$8bo3bo2b5o4bobo2bo5b3o2b2o
10bo$3bo4bo5b4o8b2o9bo3b2o4bo4bo$4b2o3bo10bo8bo2bo4bo3b2o5b2o3bo$8bob
o8bobo8bobo8bobo8bobo$9bo10bo10bo10bo10bo!

Are there any other such wicks?

Edit:

Code: Select all

x = 20, y = 20, rule = B3/S23
3b2o3b2o$3b2o3bobo$9bobobo$12bo5b2o$10bo2b2o3b2o$4bo4bobobo$2bob2o4b3o
$3bo2bo4bo$2bo2b3o10b2o$bo2bobo7bo2bobo$obo2bo7bobo2bo$2o10b3o2bo$8bo
4bo2bo$7b3o4b2obo$6bobobo4bo$2o3b2o2bo$2o5bo$6bobobo$9bobo3b2o$10b2o3b
2o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 ZOOM 10 GPS 40 HEIGHT 500 ]]

Is this a charity p16 variant or something else?

It's 68P16, and I don't think it's considered a Charity's P16 variant.

[Mathemagician314]

What’s the oscillator with the highest ratio of the period compared to the minimum number of isotropic birth and survival conditions?

I know that’s long-winded; for example, the duoplet in Seeds would have a ratio of 2, with a period of 2 and only requiring one birth condition (B2e) and no survival conditions. Does anyone know any other good examples?

[confocaloid]

Here is an example of a wick that requires support from one end but not the other:
[...]
Are there any other such wicks?

Code: Select all

x = 69, y = 39, rule = B3/S23
2o$obo$2bo$2bob2o$obobobo$2o4bo$6bob2o$4bobobobo$4b2o4bo$10bob2o$8bobo
bobo$8b2o4bo$14bob2o$12bobobobo$12b2o4bo$18bob2o$16bobobobo$16b2o4bo$
22bob2o$20bobobobo$20b2o4bo$26bob2o$24bobobobo$24b2o4bo$30bob2o$28bobo
bobo$28b2o4bo$34bob2o29bo$32bobobobo20bo6bo$32b2o4bo19bo7b3o$38bob2o
16b3o$36bobobobo$36b2o4bo$42bob2o$40bobobobo$40b2o4bo$46bob2o$44bobob
2o$44b2o!

[confocaloid]

What’s the oscillator with the highest ratio of the period compared to the minimum number of isotropic birth and survival conditions?

I know that’s long-winded; for example, the duoplet in Seeds would have a ratio of 2, with a period of 2 and only requiring one birth condition (B2e) and no survival conditions. Does anyone know any other good examples?

Here is a p65532 oscillator in a rule with one isotropic birth condition and no isotropic survival conditions (ratio 65532/(1+0) = 65532):

Code: Select all

x = 60, y = 60, rule = B2a/S
40bo$40bo18$58b2o21$2o18$19bo$19bo!

However, in addition to requiring presence of B2a in the ruleset, the above oscillator also requires absence of conditions { B0, B1c, B1e, B2c, B2e, B2n, B3n, B3r, B4i, B4w, S1c, S1e, S2k }. It works the same way in 1/2^14 of all rules.

What is the most versatile way of getting high-period oscillators, measuring "versatile" by the number of rules in the rulespace where the oscillator works the same way?

[confocaloid]

deleted

[Sokwe]

Would it be possible to give a reasonably detailed summary/outline (aimed towards beginners) of what kinds of searches are feasible with current software tools, as a function of available computing resources and willingness to wait for the result?

This is getting a little beyond "basic" questions. Is the answer meant to serve some purpose?

[confocaloid]

Yes that might be beyond basic questions. Looking through forum threads, there are posts mentioning/briefly discussing feasibility of specific kinds of searches. I wondered if that could be made into a summary oriented towards beginners.

[Gamerninja]

Is there an oscillator with a rotor size of 1?

[hotdogPi]

Is there an oscillator with a rotor size of 1?

No. A rotor size of 1 must a a p2 because there are only 2^1=2 possible states. Because the birth conditions are a subset of the survival conditions, a cell that turns on will stay on the next generation.

[dvgrn]

Is there an oscillator with a rotor size of 1?

No. A rotor size of 1 must a a p2 because there are only 2^1=2 possible states. Because the birth conditions are a subset of the survival conditions, a cell that turns on will stay on the next generation.

Yup, that's the implication of the summary in the Rotor article --

In summary, rotor cells must be adjacent to one another; possibly occurring only in isolated pairs.

You can easily invent rules that have a birth condition with no matching survival condition, where the result is that a single cell with a certain neighborhood will just flicker on and off.

[Haycat2009]

What is the repeat time of Snark64 as a catalyst? It is obviously less than 64 (p56 gun with phi sparkler is not impossible)

[b-engine]

Should we consider new p2 oscillators (especially on-off and pole 2) as uninteresting, along with new still lifes?

[TYCF]

What is the smallest t-pentomino or t-tetromino factory?

Does anybody know?