Unproven conjectures

For general discussion about Conway's Game of Life.
User avatar
dvgrn
Moderator
Posts: 10612
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI
Contact:

Re: Unproven conjectures

Post by dvgrn » January 10th, 2020, 7:36 pm

Rhombic wrote:
January 10th, 2020, 6:56 pm
If a still life only has itself as a predecessor, clearly it is its only father, its only grandfather, its only great-grandfather and so on. Does that mean that it would be a Garden of Eden, by induction?
It would be about as close to a Garden of Eden as you could get without being one, but the key quality of "can only exist at T=0" just wouldn't be true. Same for a hypothetical provably non-glider-constructible oscillator, which I have no idea how to go about finding an example of... but I could imagine that a proof-by-search-utility might exist, for some huge low-period object let's say, where every cell is so delicately balanced that the only way to backtrack is to the previous tick of the oscillator.

User avatar
testitemqlstudop
Posts: 1367
Joined: July 21st, 2016, 11:45 am
Location: in catagolue
Contact:

Re: Unproven conjectures

Post by testitemqlstudop » January 13th, 2020, 9:01 am

Rhombic wrote:
January 10th, 2020, 6:56 pm
A philosophical question...

If a still life only has itself as a predecessor, clearly it is its only father, its only grandfather, its only great-grandfather and so on. Does that mean that it would be a Garden of Eden, by induction?
A finite still life inherently has infinite predecessors. Put a dot spark arbitrarily far form the still life's border.

User avatar
pcallahan
Posts: 845
Joined: April 26th, 2013, 1:04 pm

Re: Unproven conjectures

Post by pcallahan » January 20th, 2020, 5:05 pm

pcallahan wrote:
December 29th, 2019, 1:07 am
I made the analysis a lot harder than necessary.

Just start with the two forced empty cells as shown, and head left, filling in the ?s.

Code: Select all

o o . . o o . . . o o . . o o . . . o o . . o o . . . o o . . o o . . . o o . .
. o o . . . o o . . o o . . . o o . . o o . . . o o . . o o . . . o o . . o o .
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? . .
Each ? is either forced to be o to suppress a birth, or . to avoid overcrowding a live cell.
This can also be observed using tiles. Place the bottom row of tiles and then start placing tiles above it in the numbered order shown. At each step, the choice of the next tile is forced in order to avoid 3 live neighbors of a dead cell or more than 3 of a live cell. The final tile (8) is determined by its left and right neighbors.
Screen Shot 2020-01-20 at 1.01.04 PM.png
Screen Shot 2020-01-20 at 1.01.04 PM.png (141.58 KiB) Viewed 10217 times

User avatar
Moosey
Posts: 4306
Joined: January 27th, 2019, 5:54 pm
Location: here
Contact:

Re: Unproven conjectures

Post by Moosey » January 24th, 2020, 3:23 pm

Rhombic wrote:
January 10th, 2020, 6:56 pm
A philosophical question...

If a still life only has itself as a predecessor, clearly it is its only father, its only grandfather, its only great-grandfather and so on. Does that mean that it would be a Garden of Eden, by induction?
No; a still life is its own predecessor and therefore has a predecessor and therefore is not a garden of eden
Though if it is its only predecessor, it is a near GoE.
not active here but active on discord

User avatar
pcallahan
Posts: 845
Joined: April 26th, 2013, 1:04 pm

Re: Unproven conjectures

Post by pcallahan » January 24th, 2020, 3:35 pm

Moosey wrote:
January 24th, 2020, 3:23 pm
Rhombic wrote:
January 10th, 2020, 6:56 pm
A philosophical question...

If a still life only has itself as a predecessor, clearly it is its only father, its only grandfather, its only great-grandfather and so on. Does that mean that it would be a Garden of Eden, by induction?
No; a still life is its own predecessor and therefore has a predecessor and therefore is not a garden of eden
Though if it is its only predecessor, it is a near GoE.
My guess is that every finite still life has a lot of predecessors. Well, trivially, just add any disconnected cells that vanish in one step. So let's stipulate that the still life predecessor must contain at least one dead cell that is live in the still life. Can we identify some cell on the boundary (say the rightmost) that can be replaced with a predecessor pattern in which it is dead?

Infinite still life patterns could not be handled with this approach, and maybe some of them have only themselves as a predecessor. For the periodic case, these can be viewed as finite patterns on a toroidal grid.

User avatar
Entity Valkyrie 2
Posts: 1756
Joined: February 26th, 2019, 7:13 pm
Contact:

Re: Unproven conjectures

Post by Entity Valkyrie 2 » January 26th, 2020, 4:49 pm

Entity Valkyrie 2 wrote:
January 10th, 2020, 4:10 am
Conjecture: is there a Thessalonic glider reflector?
Conjecture: is there a Thessalonic g-to-h?
Conjecture: is there a Thessalonic glider duplicator?

There is almost a Thessalonic glider reflector:

Code: Select all

x = 24, y = 23, rule = B3/S23
5bo$6b2o$5b2o4$22b2o$22bo$20bobo$20b2o$2b2o$bobo$bo$2o$14b2o$14b2o6b2o
$22b2o3$11b2o$12bo$9b3o$9bo!
EDIT: Conjectures solved with this Thessalonic glider reflector:

Code: Select all

x = 393, y = 86, rule = B3/S23
57bo$55b3o$54bo$19bo34b2o196bo$17b3o110bo119b3o$bo14bo111b3o118bo$b3o
12b2o70b2o37bo121b2o$4bo58b2o24bo37b2o108bo$3b2o59bo13b2o6b3o148b3o$
64bobo11b2o6bo153bo$65b2o94b2o76b2o$4b2o130b2o24bo$4b2o17b2o112bo13b2o
6b3o$23b2o112bobo11b2o6bo93b2o11bo15bo9bo53b2o$138b2o113b2o11b3o13b3o
5b3o28b2o24bo$203bo65bo15bo3bo16bo15bo13b2o6b3o42b2o$96b2o103b3o64b2o
14b2o3b2o13b3o15bobo11b2o6bo44bo$96b2o102bo102bo19b2o62bobo$200b2o101b
2o78b2o2b2o$20b2o32b2o327b2o$20bo20b2o11b2o113b2o$21b3o18bo126b2o$23bo
15b3o$17b2o20bo53b2o32b2o129b2o94b2o$17bo75bo20b2o11b2o101b2o26b2o46b
2o46b2o$18b3o37b2o14b2o3b2o13b3o18bo114b2o74b2o$20bo38bo15bo3bo16bo15b
3o94b2o$56b3o13b3o5b3o29bo53b2o41b2o$56bo15bo9bo83bo19b2o$131b2o14b2o
3b2o13b3o15bobo$132bo15bo3bo16bo15bo69b2o94b2o36b2o$129b3o13b3o5b3o28b
2o10b2o57bo19b2o74bo19b2o16bobo$129bo15bo9bo41bo58b3o15bobo11b2o6bo19b
2o14b2o3b2o13b3o15bobo18bo$194b3o9b2o50bo15bo13b2o6b3o18bo15bo3bo16bo
15bo20b2o$194bo11bo66b2o24bo14b3o13b3o5b3o28b2o4b2o$207b3o88b2o14bo15b
o9bo33bobo$209bo164bo$373b2o7b2o$382b2o2$9b2o$9b2o7b2o$18bo$16bobo$16b
2o4b2o$2o20bo$bo18bobo20b2o$bobo16b2o13b2o6bo$2b2o31b2o4bobo16bo49bo
49bo49bo49bo49bo$41b2o17b3o47b3o47b3o47b3o47b3o47b3o$46bo16bo22bo26bo
22bo26bo22bo26bo22bo26bo22bo26bo22bo$44b3o15b2o20b3o25b2o20b3o25b2o20b
3o25b2o20b3o25b2o20b3o25b2o20b3o$43bo39bo49bo49bo49bo49bo49bo38bo$43b
2o38b2o48b2o48b2o48b2o48b2o48b2o37b3o$375bo$103bo49bo49bo49bo49bo49bo
20b2o$31b2o68b3o47b3o47b3o47b3o47b3o47b3o15bo$31b2o18b2o47bo49bo49bo
49bo49bo49bo18b3o$50bobo34b2o11b2o35b2o11b2o35b2o11b2o35b2o11b2o35b2o
11b2o35b2o11b2o20bo$8b2o40bo36b2o48b2o48b2o48b2o48b2o48b2o32b2o$4b2o2b
2o39b2o$3bobo$3bo$2b2o42b2o$46b2o$368b2o$368b2o17b2o$62b2o48b2o48b2o
48b2o48b2o48b2o73b2o$62b2o11b2o35b2o11b2o35b2o11b2o35b2o11b2o35b2o11b
2o35b2o11b2o$75bo49bo49bo49bo49bo49bo$76b3o47b3o47b3o47b3o47b3o47b3o
59b2o$78bo49bo49bo49bo49bo49bo59bo$375b2o12b3o$376bo14bo$373b3o$87b2o
48b2o48b2o48b2o48b2o48b2o34bo$88bo49bo49bo49bo49bo49bo$48b2o35b3o47b3o
47b3o47b3o47b3o47b3o$48bobo34bo49bo49bo49bo49bo49bo$50bo$50b2o$46b2o$
37b2o7bo$22bo14b2o8b3o$22b2o25bo$21bobo!
Bx222 IS MY WORST ENEMY.

Please click here for my own pages.

My recent rules:
StateInvestigator 3.0
B3-kq4ej5i6ckn7e/S2-i34q6a7
B3-kq4ej5y6c/S2-i34q5e
Move the Box

User avatar
Moosey
Posts: 4306
Joined: January 27th, 2019, 5:54 pm
Location: here
Contact:

Re: Unproven conjectures

Post by Moosey » January 26th, 2020, 8:24 pm

What do Thessalonic and Athenic mean in this context?


Unrelated:

Could it be possible to prove that any object can be glider-constructed if it satisfies some other properties (I.e. first of all, property 1) having at least one predecessor satisfying property 1
property 2) for all n, at least one of the predecessors n steps before the object is not the object
<other properties required (?)>)

Basically, I'm curious:
Are those two properties the minimal set, or are there more, and if so, what?
not active here but active on discord

User avatar
Layz Boi
Posts: 264
Joined: October 25th, 2018, 3:57 pm

Re: Unproven conjectures

Post by Layz Boi » February 25th, 2020, 4:50 pm

Image

Every rule that is explosive relative to its background agar, and which leaves ashes of a volatility (relative to its background agar) greater than some constant, is turing complete.

User avatar
Moosey
Posts: 4306
Joined: January 27th, 2019, 5:54 pm
Location: here
Contact:

Re: Unproven conjectures

Post by Moosey » February 27th, 2020, 9:34 am

Layz Boi wrote:
February 25th, 2020, 4:50 pm
Image

Every rule that is explosive relative to its background agar, and which leaves ashes of a volatility (relative to its background agar) greater than some constant, is turing complete.
Has the sierpinski wolfram rule been proven TC?
Just curious, cuz otherwise this could be a counterexample:

Code: Select all

x = 1, y = 1, rule = B15k/S012-i3-a45-kr678
o!
not active here but active on discord

User avatar
Entity Valkyrie 2
Posts: 1756
Joined: February 26th, 2019, 7:13 pm
Contact:

Re: Unproven conjectures

Post by Entity Valkyrie 2 » March 2nd, 2020, 7:06 pm

Moosey wrote:
January 26th, 2020, 8:24 pm
What do Thessalonic and Athenic mean in this context?
Please see my user page for their definitions.
Bx222 IS MY WORST ENEMY.

Please click here for my own pages.

My recent rules:
StateInvestigator 3.0
B3-kq4ej5i6ckn7e/S2-i34q6a7
B3-kq4ej5y6c/S2-i34q5e
Move the Box

User avatar
pcallahan
Posts: 845
Joined: April 26th, 2013, 1:04 pm

Re: Unproven conjectures

Post by pcallahan » March 24th, 2020, 12:18 pm

Moosey wrote:
February 27th, 2020, 9:34 am

Has the sierpinski wolfram rule been proven TC?
Just curious, cuz otherwise this could be a counterexample:

Code: Select all

x = 1, y = 1, rule = B15k/S012-i3-a45-kr678
o!
If you mean an XOR rule that produces Sierpinski-like patterns, each generation is just a linear combination of the previous one, so you can effectively write a closed form solution for the value as far off in the future as you like. I don't see how that could be Turing complete.

User avatar
LaundryPizza03
Posts: 2297
Joined: December 15th, 2017, 12:05 am
Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

Re: Unproven conjectures

Post by LaundryPizza03 » March 26th, 2020, 11:04 am

dvgrn wrote:
December 29th, 2019, 2:10 pm
pcallahan wrote:
December 29th, 2019, 1:07 am
<...>
Segue to another unproven conjecture: if there's a forced stabilization for a patch of this agar, does that mean that a still life like this

Code: Select all

x = 46, y = 35, rule = B3/S23
2o$o2b2o$2b2o2b2o$5b2o2b2o$2b3o3b2o2b2o$3bo2b2o3b2o2b2o$bo3b2o2b2o3b2o
2b2o$b2o5b2o2b2o3b2o2b2o5b2o$5b3o3b2o2b2o3b2o2b2o3bo$6bo2b2o3b2o2b2o3b
2o2bo$4bo3b2o2b2o3b2o2b2o3b3o$4b2o5b2o2b2o3b2o2b2o5b2o$8b3o3b2o2b2o3b
2o2b2o3bo$9bo2b2o3b2o2b2o3b2o2bo$7bo3b2o2b2o3b2o2b2o3b3o$7b2o5b2o2b2o
3b2o2b2o5b2o$11b3o3b2o2b2o3b2o2b2o3bo$12bo2b2o3b2o2b2o3b2o2bo$10bo3b2o
2b2o3b2o2b2o3b3o$10b2o5b2o2b2o3b2o2b2o5b2o$14b3o3b2o2b2o3b2o2b2o3bo$
15bo2b2o3b2o2b2o3b2o2bo$13bo3b2o2b2o3b2o2b2o3b3o$13b2o5b2o2b2o3b2o2b2o
5b2o$17b3o3b2o2b2o3b2o2b2o3bo$18bo2b2o3b2o2b2o3b2o2bo$16bo3b2o2b2o3b2o
2b2o3b3o$16b2o5b2o2b2o3b2o2b2o5b2o$26b2o2b2o3b2o2b2o3bo$29b2o2b2o3b2o
2bo$32b2o2b2o3b3o$35b2o2b2o$38b2o2b2o$41b2o2bo$44b2o!
might not have a glider synthesis recipe? There would be no incremental way to build it one S-tetromino at a time -- it would have to be built up a full row at a time, at best, and if the rows are long enough there might not be room for enough gliders to get in and make the necessary adjustments. Is there a likely angle of attack for one of these things?

I'm not saying this would be a candidate for the Unique Father Problem. At least for small diamonds, there seems to be no shortage of predecessors:

Code: Select all

x = 13, y = 12, rule = B3/S23
2o5b2o$o2bobo2bo$2b2o4bobo$5bob3o2bo$2b3obo2b2obo$bobo2b2obo$5bo2b2obo
$b4o3bo2bo$2bob2o$bobo2b2o2bo$3b2o4b4o$2bobob2o3bo!
Not sure about larger patches -- so far with JLS I'm getting swatches of the agar, but no complete solutions:

Code: Select all

x = 17, y = 18, rule = B3/S23
4bo2bo$3bobob5o2bo$b2o6b4o$2bob2o6bo$bob2o2b2o2bobo$5bob2o2bo3b2o$o2b
2o3bobo5bo$6b2o5bo$3o6b3obo2bo$bo2b2o5bo3bo$o2b2o2bobob3o2bo$o2bo2b2o
2bo$3b2o2b3o3b2obo$2b2o2bo5bo2b2o$b3o7b2obo$2bo2b2o2bobobo$3bob4ob2o$
4bo5bo!
The infinite version of that pattern has no predecessors with the same unit cell. However, there is one whose unit cell is twice as big on each side:

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
o4bobobo4bobo$4b4o5b4o$2bobobo4bobobo$b4o5b4o$bobo4bobobo4bo$2o5b4o5b
2o$o4bobobo4bobo$4b4o5b4o$2bobobo4bobobo$b4o5b4o$bobo4bobobo4bo$2o5b4o
5b2o$o4bobobo4bobo$4b4o5b4o$2bobobo4bobobo$b4o5b4o$bobo4bobobo4bo$2o5b
4o5b2o!
But it is still possible that there is no glider synthesis.

How about this one (or one similar to it)? (You should try LLS; it's faster, at least when solving.)

Code: Select all

x = 21, y = 39, rule = B3/S23
7b2o$8bo$6bo$3bo2b2o$3b3o2bo$6b3o2bo$5bo3b3o2bo$3b3o2bo3b3o2bo$2bo3b3o
2bo3b3o$2bo2bo3b3o2bo3b2o$3b3o2bo3b3o2bo2bo$6b3o2bo3b3o2bo$5bo3b3o2bo
3b2o$3b3o2bo3b3o2bo$2bo3b3o2bo3b3o$2bo2bo3b3o2bo3b2o$3b3o2bo3b3o2bo2bo
$6b3o2bo3b3o2bo$3b3o3b3o2bo3b2o$3bo2b3o3b3o2bo$b2o3bo2b3o3b3o$o2b3o3bo
2b3o$o2bo2b3o3bo2b3o$b2o3bo2b3o3bo2bo$3b3o3bo2b3o3bo$3bo2b3o3bo2b3o$b
2o3bo2b3o3bo$o2b3o3bo2b3o$o2bo2b3o3bo2b3o$b2o3bo2b3o3bo2bo$3b3o3bo2b3o
3bo$3bo2b3o3bo2b3o$6bo2b3o3bo$9bo2b3o$12bo2b3o$13b2o2bo$14bo$12bo$12b
2o!

Code: Select all

x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!
LaundryPizza03 at Wikipedia

User avatar
Layz Boi
Posts: 264
Joined: October 25th, 2018, 3:57 pm

Re: Unproven conjectures

Post by Layz Boi » May 4th, 2020, 11:39 pm

I don't know anything about glider construction. Do either of these agars look particularly impossible to construct?

Code: Select all

x = 74, y = 32, rule = B3/S23
65b2o$65b2o2$6b2o4b2o4b2o4b2o19b2o4b2o4b2o4b4o$5bo2bo2bo2bo2bo2bo2bo2b
o17bo2bo2bo2bo2bo2bo2bo3bo$3bo2bo2bo2bo2bo2bo2bo2bo2bo10bob2obo2bo2bo
2bo2bo2bo2bo2bo$3b2ob2ob2ob2ob2ob2ob2ob2obo10b2obob2ob2ob2ob2ob2ob2ob
2ob2o$2obo2bo2bo2bo2bo2bo2bo2bo2b2o12bobo2bo2bo2bo2bo2bo2bo2bo$obo2bo
2bo2bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo2bo2bo2bo$2bob2ob2ob2ob2ob2ob
2ob2ob2o12b2obob2ob2ob2ob2ob2ob2ob2obo$obo2bo2bo2bo2bo2bo2bo2bo2bob2o
10bobobo2bo2bo2bo2bo2bo2bo2bob2o$2obo2bo2bo2bo2bo2bo2bo2bo2bobo9bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo$3b2ob2ob2ob2ob2ob2ob2ob2obo12b2obob2ob2ob
2ob2ob2ob2ob2obobo$2obo2bo2bo2bo2bo2bo2bo2bo2bobo13bobo2bo2bo2bo2bo2b
o2bo2bob2o$obo2bo2bo2bo2bo2bo2bo2bo2bob2o13bo2bo2bo2bo2bo2bo2bo2bo2bo
$2bob2ob2ob2ob2ob2ob2ob2ob2o14b2obob2ob2ob2ob2ob2ob2ob2obo$obo2bo2bo2b
o2bo2bo2bo2bo2bob2o12bobobo2bo2bo2bo2bo2bo2bo2bob2o$2obo2bo2bo2bo2bo2b
o2bo2bo2bobo11bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$3b2ob2ob2ob2ob2ob2ob2o
b2obo14b2obob2ob2ob2ob2ob2ob2ob2obobo$2obo2bo2bo2bo2bo2bo2bo2bo2bobo15b
obo2bo2bo2bo2bo2bo2bo2bob2o$obo2bo2bo2bo2bo2bo2bo2bo2bob2o15bo2bo2bo2b
o2bo2bo2bo2bo2bo$2bob2ob2ob2ob2ob2ob2ob2ob2o16b2obob2ob2ob2ob2ob2ob2o
b2obo$obo2bo2bo2bo2bo2bo2bo2bo2bo17bobobo2bo2bo2bo2bo2bo2bo2bob2o$2ob
o2bo2bo2bo2bo2bo2bo2bo2b2o14bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$3b2ob2ob
2ob2ob2ob2ob2ob2obo16b2obob2ob2ob2ob2ob2ob2ob2obobo$3bo2bo2bo2bo2bo2b
o2bo2bo2bo19bobo2bo2bo2bo2bo2bo2bo2bob2o$5bo2bo2bo2bo2bo2bo2bo2bo20bo
3bo2bo2bo2bo2bo2bo2bo$6b2o4b2o4b2o4b2o22b3o4b2o4b2o4b2o2$46b3o$45bo2b
o$46b2o!

User avatar
Entity Valkyrie 2
Posts: 1756
Joined: February 26th, 2019, 7:13 pm
Contact:

Re: Unproven conjectures

Post by Entity Valkyrie 2 » June 3rd, 2020, 7:18 am

dvgrn wrote:
December 19th, 2017, 6:51 pm
simsim314 wrote:
Tom Mazanec wrote:How about things where we don't even have a conjecture as to the answer, much less a theorem?
I've demonstrated the concept of constructible ship of any speed and direction - but the period of the constructed speed is extremely high. It's completely unknown and we don't have any clue whether there exists ships with relatively low period and very high speed...
A huge number of existence questions are like this. The answer is "yes" or "no", but there isn't enough information to come up with even an educated guess.

Is there a true period-14 glider gun inside a 50x50 box?
Is there a glider collision that produces a 4x4 array of blocks?
Is there a 16x16 methuselah that takes more than a billion ticks to stabilize?
Is there a stable reflector smaller than a Snark?
Is there a 2c/3 signal elbow with a repeat time less than 20?
Is there a two-engine Cordership using a lucky clean c/12 debris-burning reaction?
EDIT: YES on this last one. Let's change it to "one-engine Cordership".

... I'd guess yes, yes, no, yes, yes, no, but what do I know really? These aren't particularly long-standing or important questions, by the way -- there are hundreds more just like them.
EDIT: GoldTiger997 solved the problem of the 4x4 arroy of blocks:
Goldtiger997 wrote:
May 6th, 2020, 7:55 am
4xN block arrays can now be synthesised:

Code: Select all

x = 1290, y = 91, rule = B3/S23
763bo$764bo$762b3o2$909bo$907bobo25bo$908b2o25bobo$935b2o$762bo167bo$
763bo166bobo$761b3o166b2o2$1278bo$1276b2o$1277b2o2$770bobo$771b2o$771b
o488bo25bo$843bo238bo178bo16bobo3b2o$844bo235b2o177b3o16b2o5b2o$769bo
72b3o236b2o196bo$52bo46bo596bo73b2o6bobo$53b2o42b2o595bobo25bo46b2o7b
2o492bo$52b2o44b2o595b2o3bo21bobo54bo408bo81bobo12bo$220bo65bo414bo20b
2o405bo59b2o6bo73b2o10b2o$218bobo66b2o410b3o425bobo58b2o7bobo58bo25b2o
$51bo48bo118b2o65b2o427bo412b2o67b2o57bobo6b2o$49bobo48bobo191bobo9bo
407bo418bo123b2o5bo2bo19bo$50b2o48b2o192b2o10bobo405b3o416bobo128bo2bo
18bo$295bo10b2o825b2o66b2o62b2o4b2o13b3o$1201b2o68b2o$648bo348bo6bo$
647bo273b2o63bo4b2o4bobo4bobo49bo4b2o3bo59bo4b2o3b2o58bo4b2o3b2o58bo4b
2o3b2o$228bobo416b3o132bo64b2o3bo64b2o2bo64b3o2bo5b2o5b2o50b3o2bo3bobo
58b3o2bo3bo2bo57b3o2bo3bo2bo57b3o2bo3bo2bo$obo58bo28bo137b2o421b2o125b
2obobo63bobobobo63bobobo67bobo9bo57bobo3b2o62bobo3b4o60bobo3b4o60bobo
3b4o$2o57bobo28bobo136bo65bo355bobo124b2ob2o65b2ob2o65b2ob2o65b2ob2o7b
o57b2ob2o65b2ob2o65b2ob2o65b2ob2o$bo58b2o9bo8bo9b2o199b2obobo354bo63b
2o68b2o68b2o68b2o68b2o3b3o62b2o68b2o68b2o68b2o$72b2o4b2o146b3o62b2ob2o
68b2o68b2o68b2o68b2o68b2o68bo2bo66bo2bo66bo2bo8b3o55bo2bo66bo2bo66bo2b
o66bo2bo66bo2bo66bo2bo10bo$71b2o6b2o145bo136bobo67bobo67bobo67bobo67bo
bo67bobobo65bobobo65bobobo8bo56bobobo19b2o44bobobo65bobobo65bobobo65bo
bobo65bobobo9bo$142b2ob2ob2o62b2ob2ob2o7bo54b2ob2ob2o62b2ob2ob2o3bo58b
2ob2ob2o3bo58b2ob2ob2o3bo58b2ob2ob2o3bo58b2ob2ob2o3bo58b2ob2ob2o3bo2bo
55b2ob2ob2o3bo2bo55b2ob2ob2o3bo2bo10bo44b2ob2ob2o3bo2bo19b2o34b2ob2ob
2o3bo2bo55b2ob2ob2o3bo2bo55b2ob2ob2o3bo2bo55b2ob2ob2o3bo2bo55b2ob2ob2o
3bo2bo10b3o$bo140b2ob2ob2o14bo47b2ob2ob2o2b2o58b2ob2ob2o2b2o58b2ob2ob
2o2b2o19bo38b2ob2ob2o2b2o58b2ob2ob2o2b2o58b2ob2ob2o2b2o58b2ob2ob2o2b2o
58b2ob2ob2o2b2o58b2ob2ob2o2b2o58b2ob2ob2o2b2o58b2ob2ob2o2b2o24bo33b2ob
2ob2o2b2o58b2ob2ob2o2b2o58b2ob2ob2o2b2o58b2ob2ob2o2b2o58b2ob2ob2o2b2o$
b2o70b2o2b2o84bo58bo69bo69bo18b2o49bo69bo69bo69bo69bo69bo69bo69bo69bo
69bo21b2o46bo69bo69bo$obo3bo66bo4bo63b2ob2ob2o13b3o46b2ob2ob2o3b3o56b
2ob2ob2o3b3o56b2ob2ob2o3b3o16b2o38b2ob2ob2o3b3o56b2ob2ob2o3b3o13bo42b
2ob2ob2o3b3o56b2ob2ob2o3b3o56b2ob2ob2o3b3o56b2ob2ob2o3b3o56b2ob2ob2o3b
3o56b2ob2ob2o3b3o56b2ob2ob2o3b3o56b2ob2ob2o3b3o18bobo35b2ob2ob2o3b3o
56b2ob2ob2o3b3o56b2ob2ob2o3b3o$5b2o67b4o64b2ob2ob2o11bo50b2ob2ob2o5bo
56b2ob2ob2o5bo56b2ob2ob2o5bo56b2ob2ob2o5bo56b2ob2ob2o5bo13bobo40b2ob2o
b2o5bo56b2ob2ob2o5bo56b2ob2ob2o5bo56b2ob2ob2o5bo56b2ob2ob2o5bo56b2ob2o
b2o5bo56b2ob2ob2o5bo56b2ob2ob2o5bo18bo37b2ob2ob2o5bo56b2ob2ob2o5bo56b
2ob2ob2o5bo$5bobo152b2o147b2o208b2o$74b4o64b2ob2ob2o10bobo49b2ob2ob2o
62b2ob2ob2o19bobo40b2ob2ob2o11bobo48b2ob2ob2o5bo56b2ob2ob2o5bo56b2ob2o
b2o5bo56b2ob2ob2o5bo56b2ob2ob2o5bo56b2ob2ob2o5bo56b2ob2ob2o5bo56b2ob2o
b2o5bo56b2ob2ob2o5bo56b2ob2ob2o5bo56b2ob2ob2o5bo56b2ob2ob2o5bo56b2ob2o
b2o5bo$73bo4bo63b2ob2ob2o62b2ob2ob2o62b2ob2ob2o19bo42b2ob2ob2o11b2o49b
2ob2ob2o3b3o56b2ob2ob2o3b3o56b2ob2ob2o3b3o56b2ob2ob2o3b3o56b2ob2ob2o3b
3o56b2ob2ob2o3b3o56b2ob2ob2o3b3o56b2ob2ob2o3b3o56b2ob2ob2o3b3o56b2ob2o
b2o3b3o56b2ob2ob2o3b3o56b2ob2ob2o3b3o56b2ob2ob2o3b3o$2bo70b2o2b2o293bo
59bo69bo69bo69bo69bo69bo69bo69bo69bo69bo69bo69bo69bo$2b2o138b2ob2ob2o
62b2ob2ob2o62b2ob2ob2o62b2ob2ob2o15b3o44b2ob2ob2o2b2o58b2ob2ob2o2b2o
58b2ob2ob2o2b2o58b2ob2ob2o2b2o58b2ob2ob2o2b2o58b2ob2ob2o2b2o58b2ob2ob
2o2b2o58b2ob2ob2o2b2o58b2ob2ob2o2b2o58b2ob2ob2o2b2o58b2ob2ob2o2b2o58b
2ob2ob2o2b2o58b2ob2ob2o2b2o$bobo138b2ob2ob2o62b2ob2ob2o62b2ob2ob2o62b
2ob2ob2o15bo46b2ob2ob2o7bo54b2ob2ob2o62b2ob2ob2o3bo58b2ob2ob2o3bo2bo
55b2ob2ob2o3bo2bo55b2ob2ob2o3bo2bo55b2ob2ob2o3bo2bo55b2ob2ob2o3bo2bo
55b2ob2ob2o3bo2bo55b2ob2ob2o3bo2bo55b2ob2ob2o3bo2bo55b2ob2ob2o3bo2bo
55b2ob2ob2o3bo2bo8bo$71b2o6b2o295bo59bo136bobo67bobobo65bobobo65bobobo
65bobobo65bobobo65bobobo65bobobo65bobobo65bobobo65bobobo6b2o$72b2o4b2o
356b3o62b2ob2o68b2o68bo2bo66bo2bo66bo2bo66bo2bo66bo2bo66bo2bo66bo2bo
66bo2bo66bo2bo66bo2bo6bobo$60b2o9bo8bo9b2o409b2obobo74bo63b2o68b2o68b
2o68b2o68b2o68b2o3b3o62b2o68b2o68b2o68b2o$59bobo28bobo346bo65bo75bobo
194b2ob2o65b2ob2o65b2ob2o65b2ob2o7bo57b2ob2o65b2ob2o65b2ob2o65b2ob2o$
61bo28bo285bo61b2o141b2o195b2obobo63bobobobo63bobobo67bobo9bo57bobo3b
2o62bobo3b4o60bobo3b4o60bobo3b4o$170b2o203b2o61bobo136b3o202bo64b2o3bo
64b2o2bo64b3o2bo5b2o5b2o50b3o2bo3bobo6bo51b3o2bo3bo2bo57b3o2bo3bo2bo
57b3o2bo3bo2bo$169b2o204bobo199bo343b2o63bo4b2o4bobo4bobo49bo4b2o3bo7b
obo49bo4b2o3b2o58bo4b2o3b2o58bo4b2o3b2o$171bo406bo418bo6bo69b2o$852b3o
83bo132b2o128b2o68b2o$505bo10b2o336bo2bo78b2o132b2o61b2o66b2o62b2o4b2o
13b3o$50b2o48b2o75b2o325b2o10bobo195b3o136bo2bo80b2o133bo60bobo128bo2b
o18bo$49bobo48bobo74bobo324bobo9bo197bo141b3o274bo123b2o5bo2bo19bo$51b
o48bo76bo251b2o65b2o217bo412b2o67b2o57bobo6b2o$428bobo66b2o200b3o425bo
bo58b2o7bobo58bo25b2o$430bo65bo204bo20b2o405bo59b2o6bo73b2o10b2o$52b2o
44b2o595b2o3bo21bobo54bo408bo81bobo12bo$53b2o42b2o595bobo25bo46b2o7b2o
492bo$52bo46bo596bo73b2o6bobo$769bo509bo$920b2o337b3o16b2o5b2o$920bobo
338bo16bobo3b2o$386b3o382bo148bo339bo25bo$386bo384b2o152b2o$387bo382bo
bo145b2o5bobo$917bobo5bo$919bo357b2o$1276b2o$1278bo2$761b3o$763bo$762b
o6$762b3o$764bo$763bo!
For the true period 14 gun, one does exist in StateInvestigator, which could mean that one might exist in life.

Code: Select all

x = 11, y = 7, rule = StateInvestigator
2.3E$E.2A$.4A3.E$2AI3A$E3A4.A$.E.IA4.2A$2.EAC3.2A!
Bx222 IS MY WORST ENEMY.

Please click here for my own pages.

My recent rules:
StateInvestigator 3.0
B3-kq4ej5i6ckn7e/S2-i34q6a7
B3-kq4ej5y6c/S2-i34q5e
Move the Box

Hunting
Posts: 4395
Joined: September 11th, 2017, 2:54 am

Re: Unproven conjectures

Post by Hunting » June 3rd, 2020, 11:04 am

I'd guess YYYYN for the unsolved ones.
1. Period 14 oscillator that throws a large spark is pretty much imaginable. Egg-using constructions are far from Life, though.
2. Some kind of arks that kills the switch engine.
3. Definitely possible but out of reach currently.
4. Same as 3.
5. The two-engine one was based on two switch engines stabilizing each other, and so did the others.

User avatar
ColorfulGalaxy
Posts: 407
Joined: July 16th, 2020, 3:37 am
Location: Hacked by Trump {Bot}

Re: Unproven conjectures

Post by ColorfulGalaxy » February 11th, 2021, 7:08 am

Hunting wrote:
June 3rd, 2020, 11:04 am
I'd guess YYYYN for the unsolved ones.
1. Period 14 oscillator that throws a large spark is pretty much imaginable. Egg-using constructions are far from Life, though.
2. Some kind of arks that kills the switch engine.
3. Definitely possible but out of reach currently.
4. Same as 3.
5. The two-engine one was based on two switch engines stabilizing each other, and so did the others.
Happy Chinese New Year! Here's another unproven conjecture:

For a non-B0 2-state rule, a one-cell-rotor oscillator exists "ONLY IF but not IF" the rulestring contains Bx/S-x.
For example, HighLife rulestring contains B6i/S6-i and thus this happens:

Code: Select all

x = 0, y  = 0, rule =  B36/S23
2ob2o$o3bo$b3o2$b3o$o3bo$2ob2o!
This doesn't happen in PedestrianLife though, although the rulestring has B8/S-8

GUYTU6J
Posts: 2200
Joined: August 5th, 2016, 10:27 am
Location: 拆哪!I repeat, CHINA! (a.k.a. 种花家)
Contact:

Re: Unproven conjectures

Post by GUYTU6J » February 11th, 2021, 9:26 am

ColorfulGalaxy wrote:
February 11th, 2021, 7:08 am
...
For a non-B0 2-state rule, a one-cell-rotor oscillator exists "ONLY IF but not IF" the rulestring contains Bx/S-x.
...
That the rulestring has Bx/S-x is a necessary but not sufficient condition of the existence of one-cell-rotor p2 oscillators, since you have to consider the stators.

Code: Select all

x = 3, y = 3, rule = B8/S2e3a4i5i
3o$3o$3o!
Just look at the transitions and figure out how to make a particular oscillator work in some rule. B1c, 2a, 3i transitions are ruled out to prevent birth on the borders, and S4i, 5i are required to keep the border cells alive in the dense phase. So the INT rulespace where the above works is

Code: Select all

|isorulemin       = B8/S2e3a4i5i
|isorulemax       = B1e2-a3-i45678/S01234567
Case closed.

Hunting
Posts: 4395
Joined: September 11th, 2017, 2:54 am

Re: Unproven conjectures

Post by Hunting » February 11th, 2021, 9:52 am

ColorfulGalaxy wrote:
February 11th, 2021, 7:08 am
Hunting wrote:
June 3rd, 2020, 11:04 am
I'd guess YYYYN for the unsolved ones.
1. Period 14 oscillator that throws a large spark is pretty much imaginable. Egg-using constructions are far from Life, though.
2. Some kind of arks that kills the switch engine.
3. Definitely possible but out of reach currently.
4. Same as 3.
5. The two-engine one was based on two switch engines stabilizing each other, and so did the others.
Happy Chinese New Year! Here's another unproven conjecture:

For a non-B0 2-state rule, a one-cell-rotor oscillator exists "ONLY IF but not IF" the rulestring contains Bx/S-x.
For example, HighLife rulestring contains B6i/S6-i and thus this happens:

Code: Select all

x = 0, y  = 0, rule =  B36/S23
2ob2o$o3bo$b3o2$b3o$o3bo$2ob2o!
This doesn't happen in PedestrianLife though, although the rulestring has B8/S-8
I think that only works for non-alternating rules.

User avatar
Macbi
Posts: 903
Joined: March 29th, 2009, 4:58 am

Re: Unproven conjectures

Post by Macbi » March 13th, 2021, 7:41 pm

dvgrn wrote:
December 18th, 2017, 7:14 pm
Conjecture: No glider eater can be constructed with a recovery time of three ticks or less.
Kayzan did the following LLS searches to prove this conjecture:
ThreeTickEater.txt
(8.85 KiB) Downloaded 142 times
ThreeTickEater2.txt
(8.85 KiB) Downloaded 120 times

User avatar
Macbi
Posts: 903
Joined: March 29th, 2009, 4:58 am

Re: Unproven conjectures

Post by Macbi » March 13th, 2021, 7:43 pm

To convince myself I did the following searches with even less clearance. (Double posting to circumvent 3 file limit.)
fast-eater.csv
(2.69 KiB) Downloaded 133 times
fast-eater2.csv
(3.25 KiB) Downloaded 111 times
We can declare this Conjecture a Theorem.

User avatar
Entity Valkyrie 2
Posts: 1756
Joined: February 26th, 2019, 7:13 pm
Contact:

Re: Unproven conjectures

Post by Entity Valkyrie 2 » March 14th, 2021, 6:44 am

Entity Valkyrie 2 wrote:
January 26th, 2020, 4:49 pm
Entity Valkyrie 2 wrote:
January 10th, 2020, 4:10 am
Conjecture: is there a Thessalonic glider reflector?
Conjecture: is there a Thessalonic g-to-h?
Conjecture: is there a Thessalonic glider duplicator?

There is almost a Thessalonic glider reflector:

Code: Select all

x = 24, y = 23, rule = B3/S23
5bo$6b2o$5b2o4$22b2o$22bo$20bobo$20b2o$2b2o$bobo$bo$2o$14b2o$14b2o6b2o
$22b2o3$11b2o$12bo$9b3o$9bo!
EDIT: Conjectures solved with this Thessalonic glider reflector:

Code: Select all

x = 393, y = 86, rule = B3/S23
57bo$55b3o$54bo$19bo34b2o196bo$17b3o110bo119b3o$bo14bo111b3o118bo$b3o
12b2o70b2o37bo121b2o$4bo58b2o24bo37b2o108bo$3b2o59bo13b2o6b3o148b3o$
64bobo11b2o6bo153bo$65b2o94b2o76b2o$4b2o130b2o24bo$4b2o17b2o112bo13b2o
6b3o$23b2o112bobo11b2o6bo93b2o11bo15bo9bo53b2o$138b2o113b2o11b3o13b3o
5b3o28b2o24bo$203bo65bo15bo3bo16bo15bo13b2o6b3o42b2o$96b2o103b3o64b2o
14b2o3b2o13b3o15bobo11b2o6bo44bo$96b2o102bo102bo19b2o62bobo$200b2o101b
2o78b2o2b2o$20b2o32b2o327b2o$20bo20b2o11b2o113b2o$21b3o18bo126b2o$23bo
15b3o$17b2o20bo53b2o32b2o129b2o94b2o$17bo75bo20b2o11b2o101b2o26b2o46b
2o46b2o$18b3o37b2o14b2o3b2o13b3o18bo114b2o74b2o$20bo38bo15bo3bo16bo15b
3o94b2o$56b3o13b3o5b3o29bo53b2o41b2o$56bo15bo9bo83bo19b2o$131b2o14b2o
3b2o13b3o15bobo$132bo15bo3bo16bo15bo69b2o94b2o36b2o$129b3o13b3o5b3o28b
2o10b2o57bo19b2o74bo19b2o16bobo$129bo15bo9bo41bo58b3o15bobo11b2o6bo19b
2o14b2o3b2o13b3o15bobo18bo$194b3o9b2o50bo15bo13b2o6b3o18bo15bo3bo16bo
15bo20b2o$194bo11bo66b2o24bo14b3o13b3o5b3o28b2o4b2o$207b3o88b2o14bo15b
o9bo33bobo$209bo164bo$373b2o7b2o$382b2o2$9b2o$9b2o7b2o$18bo$16bobo$16b
2o4b2o$2o20bo$bo18bobo20b2o$bobo16b2o13b2o6bo$2b2o31b2o4bobo16bo49bo
49bo49bo49bo49bo$41b2o17b3o47b3o47b3o47b3o47b3o47b3o$46bo16bo22bo26bo
22bo26bo22bo26bo22bo26bo22bo26bo22bo$44b3o15b2o20b3o25b2o20b3o25b2o20b
3o25b2o20b3o25b2o20b3o25b2o20b3o$43bo39bo49bo49bo49bo49bo49bo38bo$43b
2o38b2o48b2o48b2o48b2o48b2o48b2o37b3o$375bo$103bo49bo49bo49bo49bo49bo
20b2o$31b2o68b3o47b3o47b3o47b3o47b3o47b3o15bo$31b2o18b2o47bo49bo49bo
49bo49bo49bo18b3o$50bobo34b2o11b2o35b2o11b2o35b2o11b2o35b2o11b2o35b2o
11b2o35b2o11b2o20bo$8b2o40bo36b2o48b2o48b2o48b2o48b2o48b2o32b2o$4b2o2b
2o39b2o$3bobo$3bo$2b2o42b2o$46b2o$368b2o$368b2o17b2o$62b2o48b2o48b2o
48b2o48b2o48b2o73b2o$62b2o11b2o35b2o11b2o35b2o11b2o35b2o11b2o35b2o11b
2o35b2o11b2o$75bo49bo49bo49bo49bo49bo$76b3o47b3o47b3o47b3o47b3o47b3o
59b2o$78bo49bo49bo49bo49bo49bo59bo$375b2o12b3o$376bo14bo$373b3o$87b2o
48b2o48b2o48b2o48b2o48b2o34bo$88bo49bo49bo49bo49bo49bo$48b2o35b3o47b3o
47b3o47b3o47b3o47b3o$48bobo34bo49bo49bo49bo49bo49bo$50bo$50b2o$46b2o$
37b2o7bo$22bo14b2o8b3o$22b2o25bo$21bobo!
Thessalonic (only blocks and eater 1s) solved. Does there exist a purely blockic glider reflector?

EDIT: Also, please reduce the Thessalonic glider reflector if you can.
Bx222 IS MY WORST ENEMY.

Please click here for my own pages.

My recent rules:
StateInvestigator 3.0
B3-kq4ej5i6ckn7e/S2-i34q6a7
B3-kq4ej5y6c/S2-i34q5e
Move the Box

User avatar
dvgrn
Moderator
Posts: 10612
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI
Contact:

Re: Unproven conjectures

Post by dvgrn » March 14th, 2021, 9:35 am

Entity Valkyrie 2 wrote:
March 14th, 2021, 6:44 am
Thessalonic (only blocks and eater 1s) solved. Does there exist a purely blockic glider reflector?
Yes, but the smallest one we know how to build would be huge and impressively slow. This question has been asked a few times before. I could build one if someone gave me a sufficiently large research grant, but it would take more time than I can spare at the moment.
Entity Valkyrie 2 wrote:
March 14th, 2021, 6:44 am
EDIT: Also, please reduce the Thessalonic glider reflector if you can.
Hersrch should be able to dig up a smaller connection without much trouble. It's just a matter of setting up the right search after deleting everything non-Thessalonic out of the data file. Nobody uses Hersrch any more, but here's a link to an old walkthrough in case anyone wants to try it out.

User avatar
wwei47
Posts: 1651
Joined: February 18th, 2021, 11:18 am

Re: Unproven conjectures

Post by wwei47 » March 14th, 2021, 10:52 am

Macbi wrote:
March 13th, 2021, 7:41 pm
Kayzan did the following LLS searches to prove this conjecture:
Macbi wrote:
March 13th, 2021, 7:43 pm
To convince myself I did the following searches with even less clearance.
Here's a periodic 3-tick eater:

Code: Select all

x = 34, y = 27, rule = B3/S23
29b2o$bo27b2o$2bo$3o$30b2o$16b2o14b2o$19b2o6bo5bo$18bob2o4b2o$14bo2bob
3o4b3obo2bo$20b2o4b2obo$14bo5bo6b2o$14b2o14b2o$16b2o3$11bo5b2o$11bo5b
2o$10b3o4$9b5o$8bob3obo$8bobobobo$7b2obobob2o$6bo2b2ob2o2bo$6b2o7b2o!
Help me find high-period c/2 technology!
My guide: https://bit.ly/3uJtzu9
My c/2 tech collection: https://bit.ly/3qUJg0u
Overview of periods: https://bit.ly/3LwE0I5
Most wanted periods: 76,116

User avatar
Entity Valkyrie 2
Posts: 1756
Joined: February 26th, 2019, 7:13 pm
Contact:

Re: Unproven conjectures

Post by Entity Valkyrie 2 » March 20th, 2021, 2:15 am

What is the probability of getting a Garden of Eden from a random soup of size n×n?
Bx222 IS MY WORST ENEMY.

Please click here for my own pages.

My recent rules:
StateInvestigator 3.0
B3-kq4ej5i6ckn7e/S2-i34q6a7
B3-kq4ej5y6c/S2-i34q5e
Move the Box

User avatar
Tom Mazanec
Posts: 32
Joined: December 18th, 2017, 5:22 pm

Re: Unproven conjectures

Post by Tom Mazanec » April 28th, 2021, 10:32 am

Thanks!
Hope for even more progress in this decade, as AI advances...

Post Reply