Stable patterns which are not glider-constructible

[400spartans]

Relevant posts:

Infinite stable agar: viewtopic.php?f=7&t=3180&start=100#p139666
Finite still life: viewtopic.php?p=140258#p140258
306-cell still life reduction: viewtopic.php?p=140295#p140295
p2 agar: viewtopic.php?p=144795#p144795
p2 agar reduction: viewtopic.php?p=144849#p144849
278-cell still life: viewtopic.php?f=7&t=3180&start=275#p166441
236-cell still life: viewtopic.php?f=7&t=3180&start=325#p180119
Patch optimization: viewtopic.php?f=7&t=3180&start=325#p180123
184-cell still life: viewtopic.php?f=7&t=3180&start=350#p193366
Patch optimization: viewtopic.php?f=7&t=3180&start=375#p193436
Area 271 self-forcing patch: viewtopic.php?f=7&t=3180&start=375#p193510

Theory posts:

I've been thinking about a "reverse corollary" of this topic for a while -- the idea that there might be some object that can be synthesized by crashing together some number of spaceships, that can not be synthesized by gliders.

Obviously at least some of the spaceships used in the recipe would also have to be provably not constructible by gliders, and it seems likely that we're still a long way from being able to prove that something like a flying spaghetti monster or Sir Robin doesn't have a glider synthesis. On the other hand, now that there are known patterns that don't have a glider synthesis, it no longer seems so impossible that a proof might be found at some point, for some spaceship.

Maybe it's time to try pushing the envelope on this: what's the biggest blobbiest most spacedustful period-4 c/2 orthogonal spaceship that current technology can come up with? Might there be some kind of extensible greyship-like thing that escorts a patch of active agar instead of a stable central region, that might allow an easier proof of non-glider-constructibility? (This idea has come up before, but I can't find a link offhand.)

In principle the method works for any period, but you need a "stroke of luck" to get results. The agars and patches were found by a search program (https://github.com/ilkka-torma/gol-agars). There seem to be much fewer period-3 agars than periods 1 and 2 (there are none of size less than 6×6, and only three of size 6×6). Thus we have fewer candidates to analyze for self-forcing patches.

For all we know, for example, Sir Robin and Sir Sprayer are unsynthesizable spaceships. The more interior spacedust a big blobby spaceship has, the harder it is to find a synthesis for it in practice.

That doesn't prove that no synthesis will ever be found for any particular case, though. Making provably unsynthesizable spaceships seems like quite a tall order at the moment, but I guess you never know what might show up.

We'd just search for self-forcing agars that evolve into translated versions of themselves after n steps, and then search for finite patches of them that force themselves in their nth predecessor but translated. Again the main limiting factor is that there are very few such agars with reasonable parameters -- in fact, we haven't found any self-forcing agars with (1,0) or (1,1) as the translation vector. Of course, even if by some miracle we found such a patch, we'd still have to complete it into a spaceship.

My favorite conjecture is that there's a still life that can only be created by crashing 137 gliders into three colliding flying spaghetti monsters -- and that flying spaghetti monsters are unsynthesizable. That would mean that in spite of an unbounded number of distinct ancestors of this "FSM still life", and (obviously) no self-forcing patch anywhere in it, there still wouldn't be a glider synthesis.

Relevant links:

https://github.com/ilkka-torma/gol-agars
https://conwaylife.com/wiki/Unique_father_problem
https://conwaylife.com/wiki/Unsynthesiz ... cillator_1
https://arxiv.org/abs/2202.07346

162-cell unsynthesizable still life:

Code: Select all

x = 22, y = 22, rule = B3/S23
16bo$b2o12bobo$bo2b2o2bob2o2bo2bo$2bobo2bob2o2bob2ob2o$3bo2b2o4b2o2bo
2bo$4b2o2bob2o2bo2bo$5bo2b2obo2b2ob2o$3bo2b2o4b2o2bo2bo$3b2obo2b2obo2b
o2bobo$b2o2bo2b2obo2b2ob2o2bo$o2bo2b2o4b2o2bo2bobo$o2b2obo2b2obo2bo2bo
bo$b2o2bo2b2obo2b2ob2o$3bo2b2o4b2o2bo2bo$3b2obo2b2obo2bo2bobo$b2o2bo2b
2obo2b2ob2o2bo$o2bo2b2o4b2o2bo2b2o$bob2obo2b2obo2bo2bo$2bo2bo2b2obo2b
2ob2o$3b2o12bo$17bobo$18b2o!

[hotcrystal0]

Is there any P3 self-forcing patch?

[dvgrn]

Is there any P3 self-forcing patch?

I think the latest I've heard about this is this 2022 post by Ilkka Törmä.

There was some similar speculation about a moving self-forcing patch escorted by a spaceship, but that sounded a lot less hopeful to me.

Here's the self-forcing patch that 400spartans posted on Discord for the 162-bit still life. There seem to be 271 specified cells in the patch (124 ON, 147 OFF). A variation on the still-life completion, with the same population (182) but a smaller bounding octagon, is shown below in in context with the patch.

Code: Select all

x = 97, y = 22, rule = LifeHistory
91.A$76.2A12.A.A$2.2C.DCD2C2DCD62.A2.2C.DCD2C2DCD.A$.DC2DCD2C2DCD2C62.
ADC2DCD2C2DCD2C.2A$.C2D2C4D2C2DC63.C2D2C4D2C2DC2.A$.D2C2DCD2C2DC2DCD61.
D2C2DCD2C2DC2DCD$.2DC2D2CDC2D2CD2C61.2DC2D2CDC2D2CD2C$.C2D2C4D2C2DC2D
61.C2D2C4D2C2DC2DA$D2CDC2D2CDC2DC2DC60.D2CDC2D2CDC2DC2DC.A$C2DC2D2CDC
2D2CD2CD58.AC2DC2D2CDC2D2CD2CD.A$DC2D2C4D2C2DC2DC57.A.DC2D2C4D2C2DC2D
C.A$D2CDC2D2CDC2DC2DCD57.A.D2CDC2D2CDC2DC2DCDA$C2DC2D2CDC2D2CD2C59.AC
2DC2D2CDC2D2CD2C$DC2D2C4D2C2DC2DC59.DC2D2C4D2C2DC2DC$D2CDC2D2CDC2DC2D
CD59.D2CDC2D2CDC2DC2DCDA$C2DC2D2CDC2D2CD2C59.AC2DC2D2CDC2D2CD2C2.A$DC
2D2C4D2C2DC2D58.A.DC2D2C4D2C2DC2D2A$.2CDC2D2CDC2DC2D60.A.2CDC2D2CDC2D
C2DA$2.DC2D2CDC3.CD.C60.A.DC2D2CDC2.ACDAC$78.2A10.A$88.A.A$88.2A!

Assuming I've got the pattern right, a count of 271 exactly ties the current record smallest number of specified cells from the previous record low-population unique-father pattern. It seems very likely that a method like the one Sokwe outlined in that link will very easily set a new record starting from this patch.

... Come to think of it, I'd definitely like to try coding up some automation for Logic Life Search, to see if it's possible to find something a cell or two smaller than manual searches can manage. That seems like a doable project.

[confocaloid]

It's tempting to state a "counter-conjecture" that every Life spaceship is glider-constructible (although people might never discover any synthesis).

Indeed, a non-constructible still life forces part of itself in the same region of Life universe, and therefore it is not rewindable to any predecessor that doesn't have the same patch in the same location.
In contrast, every spaceship within a given region R is easily rewindable to a predecessor where the region R is empty. It might be that once there is some way to create an object in empty space, finding a glider synthesis would be "easy" in principle if not in practice.

Is there a convincing way to refute such "counter-conjecture" (of course other than by a counterexample showing a provably non-glider-constructible Life spaceship)?

[dvgrn]

It's tempting to state a "counter-conjecture" that every Life spaceship is glider-constructible (although people might never discover any synthesis).

Yup, agreed -- the counter-conjecture is maybe more intuitively plausible than the idea that provably non-glider-constructible spaceships exist.

On the other hand, provably non-glider-constructible still lifes were also intuitively implausible for a lot of people, only a few years ago. But then it turned out that self-forcing patches really do exist -- and not just self-forcing patches, but patches that force themselves and some cells around their edges.

The jury still seems to be out on whether a self-forcing, slowly moving agar might turn out to exist. It might be something like c/4 or c/5, for example -- not an impossibly high period, but probably a bit beyond our current ability to search for.

Is there a convincing way to refute such "counter-conjecture" (of course other than by a counterexample showing a provably non-glider-constructible Life spaceship)?

The one smaller intermediate step that I can think of, is that if it turns out to be possible to find an infinite self-forcing agar that can be interpreted as moving at spaceship speeds ... then it might become a bit more plausible that a finite "agarship" might exist, that escorts a patch of immortal agar in the same way that a greyship escorts its patch of zebra stripes.

The argument that a region R is easily rewindable to empty space, isn't really relevant if we know that a patch of moving agar is self-forcing (a big "if", for sure!) A hypothetical patch like that would be indefinitely trackable backwards and forwards through the Life universe: there might be a glider construction that starts from a non-spaceship that includes that patch of agar, and constructs the agar escort mechanism -- but that won't make the entire spaceship glider-constructible.

[Anivec]

Here's the self-forcing patch that 400spartans posted on Discord for the 162-bit still life. There seem to be 271 specified cells in the patch (124 ON, 147 OFF). A variation on the still-life completion, with the same population (182) but a smaller bounding octagon, is shown below in in context with the patch.

Code: Select all

x = 97, y = 22, rule = LifeHistory
91.A$76.2A12.A.A$2.2C.DCD2C2DCD62.A2.2C.DCD2C2DCD.A$.DC2DCD2C2DCD2C62.
ADC2DCD2C2DCD2C.2A$.C2D2C4D2C2DC63.C2D2C4D2C2DC2.A$.D2C2DCD2C2DC2DCD61.
D2C2DCD2C2DC2DCD$.2DC2D2CDC2D2CD2C61.2DC2D2CDC2D2CD2C$.C2D2C4D2C2DC2D
61.C2D2C4D2C2DC2DA$D2CDC2D2CDC2DC2DC60.D2CDC2D2CDC2DC2DC.A$C2DC2D2CDC
2D2CD2CD58.AC2DC2D2CDC2D2CD2CD.A$DC2D2C4D2C2DC2DC57.A.DC2D2C4D2C2DC2D
C.A$D2CDC2D2CDC2DC2DCD57.A.D2CDC2D2CDC2DC2DCDA$C2DC2D2CDC2D2CD2C59.AC
2DC2D2CDC2D2CD2C$DC2D2C4D2C2DC2DC59.DC2D2C4D2C2DC2DC$D2CDC2D2CDC2DC2D
CD59.D2CDC2D2CDC2DC2DCDA$C2DC2D2CDC2D2CD2C59.AC2DC2D2CDC2D2CD2C2.A$DC
2D2C4D2C2DC2D58.A.DC2D2C4D2C2DC2D2A$.2CDC2D2CDC2DC2D60.A.2CDC2D2CDC2D
C2DA$2.DC2D2CDC3.CD.C60.A.DC2D2CDC2.ACDAC$78.2A10.A$88.A.A$88.2A!

Assuming I've got the pattern right, a count of 271 exactly ties the current record smallest number of specified cells from the previous record low-population unique-father pattern. It seems very likely that a method like the one Sokwe outlined in that link will very easily set a new record starting from this patch.

I noticed that a part of the patch resembles the original self forcing agar:

Code: Select all

x = 22, y = 23, rule = LifeHistory
8.D.2D$8.2DBD4.A$.2A3.2D4B2D.A.A$.A2.2ADBEDCED.A2.A$2.A.A2.CB2C2BC.2A
.2A$3.A2.2C4B2C2.A2.A$4.2A2.CB2C2.A2.A$5.A2.2CBC2.2A.2A$3.A2.2C4B2C2.
A2.A$3.2A.C2B2CBC2.A2.A.A$.2A2.A.DECDEBD2A.2A2.A$A2.A2.2C4B2C2.A2.A.A
$A2.2A.E.DECDE2.A2.A.A$.2A2.A2.2CBC2.2A.2A$3.A2.2C4B2C2.A2.A$3.2A.C2B
2CBC2.A2.A.A$.2A2.A.DECDEBD2A.2A2.A$A2.A2.2C4B2C2.A2.2A$.A.2A.E.DECDE
2.A2.A$2.A2.A2.2C.C2.2A.2A$3.2A10.A$13.A.A$13.2A!

[confocaloid]

Edit 2: can you give any details about how you found it?

I'm just using Torma and Salo's program (https://github.com/ilkka-torma/gol-agars) with two minor tweaks to speed things up. First, I exclude patterns which are just a repetition of some smaller tiling. And second, this came up in a search which only looks at p1 agars in which every live cell is adjacent to 3 live cells and every dead cell is adjacent to 4 live cells. There are plenty of infinite self-forcing p1 agars which do not have this property, but the only known finite self-forcing p1 agar patterns all seem to have this property.

Is the last sentence ("the only known finite...") still true today, or solutions without that property are known now?
Does the restriction come from aiming to make it harder to change cells? (Changing an alive cell into a dead cell will lead to some adjacent dead cell having 3 alive neighbours and becoming alive in the next generation. Changing a dead cell into an alive cell will lead to some adjacent alive cell having 4 alive neighbours and becoming dead in the next generation.)

[400spartans]

Is the last sentence ("the only known finite...") still true today, or solutions without that property are known now?
Does the restriction come from aiming to make it harder to change cells? (Changing an alive cell into a dead cell will lead to some adjacent dead cell having 3 alive neighbours and becoming alive in the next generation. Changing a dead cell into an alive cell will lead to some adjacent alive cell having 4 alive neighbours and becoming dead in the next generation.)

Yes, that is still true AFAIK. There's nothing stopping solutions without that property from existing (there are plenty of self-forcing infinite stable agars without that property in https://github.com/ilkka-torma/gol-agar ... main/agars), but there are heuristic reasons to believe that agars with the property are much more likely to have self-forcing subsets that those without it.

I believe the reason why this property seems to be so prevalent is because every 3x3 torus with 4 live cells and 5 dead cells is self-forcing on a 3x3 torus grid. The lack of such convenient and small tiles for periodic agars is probably the biggest roadblock in finding more self-forcing periodic patterns or a self-forcing moving patch.

[hotcrystal0]

Self-forcing P3 agar by 400spartans on the Discord:

Code: Select all

x = 6, y = 12, rule = B3/S23:T6,12
o4bo$obobo$b3o$3bobo$bo3bo$2b2obo$2b2o$bobobo$o3b2o$obo$2bobo$obo2bo!

And a P4 one, by the same person:

Code: Select all

x = 8, y = 8, rule = B3/S23:T8,8
obo2bobo$2b4o$bo4b2o$b2o3bo$bob2obo$2o4b2o$2b2obo$2bo2b2o!

[Timelord Missionary]

Self-forcing P3 agar by 400spartans on the Discord:

Code: Select all

x = 6, y = 12, rule = B3/S23:T6,12
o4bo$obobo$b3o$3bobo$bo3bo$2b2obo$2b2o$bobobo$o3b2o$obo$2bobo$obo2bo!

And a P4 one, by the same person:

Code: Select all

x = 8, y = 8, rule = B3/S23:T8,8
obo2bobo$2b4o$bo4b2o$b2o3bo$bob2obo$2o4b2o$2b2obo$2bo2b2o!

Are either of these able to be stabilized easily to make finite oscillators? That p4 one looks promising, what with the clock 2's. I tried using stable supports on it, but it seems it needs something a bit more sophisticated. I suppose JLS might work with this stuff.

[400spartans]

154-cell unsynthesizable still life:

Code: Select all

x = 23, y = 22, rule = B3/S23
6b2o$5bo2bo3b2o$5bo2bo3bo3b2o$3b2ob2ob2obo2bo2bo$3bo2bo2bo2b2o2bo2bo$b
2o2bo2bo2bo2b2ob2obo$o2b2ob2ob2obo2bo2bobo$bobo2bo2bo2b2o2bo2bo$2o3bo
2bo2bo2b2ob2o$bo2b2ob2ob2o2bo2bo3b2o$bobo2bo2bo2b2o2bo2bo2bo$2bobo2bo
2bo2bob2ob2obo$4b2ob2ob2o2bo2bo2bo$3bo2bo2bo2b2o2bo2bo$3b2o3bo2bo2b2ob
2o$7b2ob2o2bo2bo$6bo2bo2b2o2bo2bo$5bobo2bo2bob2ob2o$5bob2ob2o2bo2bo$6b
o2bo5bobo$7bobo6bo$8bo!

EDIT by dvgrn: LifeHistory view of 251-cell self-forcing patch for the above still life, cross-posted from a message by DroneBetter on Discord:

Code: Select all

x = 23, y = 22, rule = LifeHistory
6.2A$5.A2.A3.2A$4.DC2DCD2.A3.2A$3.ACD2CD2CDCD.C2.A$3.C2DC2DC2D2C2DC2D
C$.AC2DC2DC2DC2D2CD2CDA$A.D2CD2CD2CDC2DC2DCDA$.A.C2DC2DC2D2C2DC2DC$2A
.2DC2DC2DC2D2CD2CD$.A.D2CD2CD2C2DC2DC2D.2A$.A.C2DC2DC2D2C2DC2DA2.A$2.
ADC2DC2DC2DCD2CDACDA$3.D2CD2CD2C2DC2DC2DC$3.A2DC2DC2D2C2DC2DCD$3.2A.
2DC2DC2D2CD2CD$7.2CD2C2DC2DC2D$6.A2DC2D2C2DC2DC$5.A.C2DC2DCD2C.2A$5.A
.2CD2C2DCD.A$6.A.DCD4.A.A$7.A.A6.A$8.A!

EDIT2 by dvgrn: The patch shown above is missing one cell toward the upper left. One more OFF (red) cell must be specified above the highest ON cell in the first column of the patch region; otherwise the patch is not self-forcing -- see amling's post below.

[Haycat2009]

A question: Are there patterns that are not glider-constructable but are not solutions of the generalised grandfather problem?

And are there any patterns that ONLY have invalid glider synthesises (aka gliders cross), but provably have no valid glider synthesis?

[Anivec]

A question: Are there patterns that are not glider-constructable but are not solutions of the generalised grandfather problem?

Infinite agars count as not glider-constructable (because they’re infinite) but aren’t solutions to the generalised grandfather problem.

[dvgrn]

And are there any patterns that ONLY have invalid glider synthesises (aka gliders cross), but provably have no valid glider synthesis?

It seems somewhat unlikely to me that provably invalid-synthesizable-only objects will ever be found. It's hard to imagine how to prove that a pattern consisting only of gliders has no synthesizable predecessors. For a sufficiently densely packed huge mess of gliders, we might not be able to find a synthesizable predecessor in practice -- but we would only have to do that if we couldn't find any other way to build whatever target object they make.

A densely packed huge mess of gliders will always have an absolutely astounding number of distinct predecessors. It seems wildly unlikely that it would turn out to be possible to prove that none of those predecessors is synthesizable. We already know a lot of tricks resolve glider crossings via one-time turners and so on, and that's just about 0% of all the possible crossing-resolution tricks that are actually out there.

EDIT: I'm not quite sure how to adjust this vague hand-waving analysis to include incremental syntheses where one or more of the stages has a badly tangled set of incoming gliders. Probably no adjustment is needed -- any badly tangled gliders will still be sufficiently isolated from each other that they'll have an astronomical number of predecessors, probably too many to plausibly prove anything about.

[HartmutHolzwart]

I agree with Dave: The only vague idea we have to be able to prove a pattern is not glider constructible is that it has “too few” predecessors. Because glider constructible patterns by definition have “many predecessors”.

However, nobody so far has been able to come up with a concrete computable measure for the number of predecessors.

The idea would be to have an asymptotic upper bound for the number of n- generations predecessors that fit in a certain box with dimensions dependent on n that is still lower than a comparable lower bound for glider constructible patterns.

At least that would be my intuition.

Edit: Most likely we would need some notion of “essential predecessors” and would need a means to count those somehow.

[Anivec]

Here's the self-forcing patch that 400spartans posted on Discord for the 162-bit still life. There seem to be 271 specified cells in the patch (124 ON, 147 OFF). A variation on the still-life completion, with the same population (182) but a smaller bounding octagon, is shown below in in context with the patch.

Code: Select all

x = 97, y = 22, rule = LifeHistory
91.A$76.2A12.A.A$2.2C.DCD2C2DCD62.A2.2C.DCD2C2DCD.A$.DC2DCD2C2DCD2C62.
ADC2DCD2C2DCD2C.2A$.C2D2C4D2C2DC63.C2D2C4D2C2DC2.A$.D2C2DCD2C2DC2DCD61.
D2C2DCD2C2DC2DCD$.2DC2D2CDC2D2CD2C61.2DC2D2CDC2D2CD2C$.C2D2C4D2C2DC2D
61.C2D2C4D2C2DC2DA$D2CDC2D2CDC2DC2DC60.D2CDC2D2CDC2DC2DC.A$C2DC2D2CDC
2D2CD2CD58.AC2DC2D2CDC2D2CD2CD.A$DC2D2C4D2C2DC2DC57.A.DC2D2C4D2C2DC2D
C.A$D2CDC2D2CDC2DC2DCD57.A.D2CDC2D2CDC2DC2DCDA$C2DC2D2CDC2D2CD2C59.AC
2DC2D2CDC2D2CD2C$DC2D2C4D2C2DC2DC59.DC2D2C4D2C2DC2DC$D2CDC2D2CDC2DC2D
CD59.D2CDC2D2CDC2DC2DCDA$C2DC2D2CDC2D2CD2C59.AC2DC2D2CDC2D2CD2C2.A$DC
2D2C4D2C2DC2D58.A.DC2D2C4D2C2DC2D2A$.2CDC2D2CDC2DC2D60.A.2CDC2D2CDC2D
C2DA$2.DC2D2CDC3.CD.C60.A.DC2D2CDC2.ACDAC$78.2A10.A$88.A.A$88.2A!

... Come to think of it, I'd definitely like to try coding up some automation for Logic Life Search, to see if it's possible to find something a cell or two smaller than manual searches can manage. That seems like a doable project.

Here’s a curious modification:

Code: Select all

x = 97, y = 23, rule = LifeHistory
83.2A$76.2A6.A6.A$2.2C.DCD68.A2.2C.DCD5.A.A$.DC2DCD3C2DCD63.ADC2DCD3C
2DCD.A$.C2D2C2DC2DCD2C63.C2D2C2DC2DCD2C.2A$.D2C2DC3D2C2DC63.D2C2DC3D2C
2DC2.A$.2DC2D4C2DC2DCD61.2DC2D4C2DC2DCD$.C2D2C3DC2D2CD2C61.C2D2C3DC2D
2CD2C$D2CDC2DC2D2C2DC2D60.D2CDC2DC2D2C2DC2DA$C2DC2D3CDC2DC2DC59.AC2DC
2D3CDC2DC2DC.A$DC2D2C3DC2D2CD2CD57.A.DC2D2C3DC2D2CD2CD.A$D2CDC2DC2D2C
2DC2DC57.A.D2CDC2DC2D2C2DC2DC.A$C2DC2D3CDC2DC2DCD58.AC2DC2D3CDC2DC2DC
DA$DC2D2C3DC2D2CD2C60.DC2D2C3DC2D2CD2C$D2CDC2DC2D2C2DC2DC59.D2CDC2DC2D
2C2DC2DC$C2DC2D3CDC2DC2DCD58.AC2DC2D3CDC2DC2DCDA$DC2D2C3DC2D2CD2C58.A
.DC2D2C3DC2D2CD2C2.A$.2CDC2DC2D2C2DC2D59.A.2CDC2DC2D2C2DC2D2A$2.DC2D3C
DC2DC2D61.A.DC2D3CDC2DC2DA$8.DC3.CD.C61.2A5.DC2.ACDAC$83.3A4.A$83.A4.
A.A$88.2A!

I’m wondering if it is also self forcing.

154-cell unsynthesizable still life:

Code: Select all

x = 23, y = 22, rule = B3/S23
6b2o$5bo2bo3b2o$5bo2bo3bo3b2o$3b2ob2ob2obo2bo2bo$3bo2bo2bo2b2o2bo2bo$b
2o2bo2bo2bo2b2ob2obo$o2b2ob2ob2obo2bo2bobo$bobo2bo2bo2b2o2bo2bo$2o3bo
2bo2bo2b2ob2o$bo2b2ob2ob2o2bo2bo3b2o$bobo2bo2bo2b2o2bo2bo2bo$2bobo2bo
2bo2bob2ob2obo$4b2ob2ob2o2bo2bo2bo$3bo2bo2bo2b2o2bo2bo$3b2o3bo2bo2b2ob
2o$7b2ob2o2bo2bo$6bo2bo2b2o2bo2bo$5bobo2bo2bob2ob2o$5bob2ob2o2bo2bo$6b
o2bo5bobo$7bobo6bo$8bo!

EDIT by dvgrn: LifeHistory view of 251-cell unsynthesizable patch for the above still life, cross-posted from a message by DroneBetter on Discord:

Code: Select all

x = 23, y = 22, rule = LifeHistory
6.2A$5.A2.A3.2A$4.DC2DCD2.A3.2A$3.ACD2CD2CDCD.C2.A$3.C2DC2DC2D2C2DC2D
C$.AC2DC2DC2DC2D2CD2CDA$A.D2CD2CD2CDC2DC2DCDA$.A.C2DC2DC2D2C2DC2DC$2A
.2DC2DC2DC2D2CD2CD$.A.D2CD2CD2C2DC2DC2D.2A$.A.C2DC2DC2D2C2DC2DA2.A$2.
ADC2DC2DC2DCD2CDACDA$3.D2CD2CD2C2DC2DC2DC$3.A2DC2DC2D2C2DC2DCD$3.2A.
2DC2DC2D2CD2CD$7.2CD2C2DC2DC2D$6.A2DC2D2C2DC2DC$5.A.C2DC2DCD2C.2A$5.A
.2CD2C2DCD.A$6.A.DCD4.A.A$7.A.A6.A$8.A!

A modification for this one:

Code: Select all

x = 32, y = 22, rule = LifeHistory
5.2A5.2A$5.A.A3.A2.A3.2A$7.A2.DC2DCD2.A3.2A$6.2A.ACD2CD2CDCD.C2.A$6.A
2.C2DC2DC2D2C2DC2DC$4.2A2.C2DC2DC2DC2D2CD2CDA$3.A2.2AD2CD2CD2CDC2DC2D
CDA$3.2A.A2.C2DC2DC2D2C2DC2DC.2A$.2A3.A.A2DC2DC2DC2D2CD2CD.A$A2.3A2.2A
D2CD2CD2C2DC2DCDA2.A$2A4.2A2.C2DC2DC2D2C2DC2DA.2A$5.A2.A2.C2DC2DC2DCD
2CDACD.A.A$4.A.A.2A.2CD2CD2C2DC2DC2DC2.2A$4.A2.A2.A.DC2DC2D2C2DC2DCD$
5.A.A.A2.A.DC2DC2D2CD2CD$6.2A.A.2A.2CD2C2DC2DC2D$10.A2.A2DC2D2C2DC2DC
$11.A2.C2DC2DCD2C.2A$9.A.2A.2CD2C2DCD.A$8.A.A2.A.DCD4.A.A$8.A2.A2.A.A
6.A$9.2A4.A!

Another:

Code: Select all

x = 32, y = 24, rule = LifeHistory
13.A$5.2A5.A.A3.2A$5.A.A3.A.DCD2.A3.2A$7.A2.DCDCD2CDCD.C2.A$6.2A.ACDC
2DC2D2C2DC2DC$6.A2.C2DCDC2DC2D2CD2CDA$4.2A2.C2DCDCD2CDC2DC2DCDA$3.A2.
2AD2CDC2DC2D2C2DC2DC.2A$3.2A.A2.C2DCDC2DC2D2CD2CD.A$.2A3.A.A2DC2D2CD2C
2DC2DCDA2.A$A2.3A2.2AD3C2DC2D2C2DC2DA.2A$2A4.2A2.C3DC2DC2DCD2CDACD.A.
A$5.A2.A2.C2D2CD2C2DC2DC2DC2.2A$4.A.A.2A.3C2DC2D2C2DC2DCD$4.A.A3.A.D.
DC2DC2D2CD2CD$5.A.2A2.2A2CD2C2DC2DC2D$3.A.A.A.2A2.2DC2D2C2DC2DC2A$3.2A
3.A2.A.C2DC2DCD2C.2A2.A$9.A.A.2CD2C2DCD.A3.2A$8.2A.A2.DCD4.A.A$12.2A.
A6.A$14.A$14.A.A$15.2A!

One more:

Code: Select all

x = 28, y = 22, rule = LifeHistory
5.A5.2A$4.A.A3.A2.A3.2A$A2.A2.A2.DC2DCD2.A3.2A$4A.2A.ACD2CD2CDCD.C2.A
$5.A2.C2DC2DC2D2C2DC2DC$2.A.A2.C2DC2DC2DC2D2CD2CDA$2.2A.2AD2CD2CD2CDC
2DC2DCDA$5.A2.C2DC2DC2D2C2DC2DC.2A$2.3A2.A2DC2DC2DC2D2CD2CD.A$2.A2.3A
D2CD2CD2C2DC2DCD2.A$4.A3.C2DC2DC2D2C2DC2DA.2A$3.2A.A2.C2DC2DC2DCD2CDA
CD.A$2.A3.2A.2CD2CD2C2DC2DC2DC$.A2.2A2.A.DC2DC2D2C2DC2DCD$2.3A2.A2.A.
DC2DC2D2CD2CD$6.2A.2A.2CD2C2DC2DC2D$4.2A2.A2.A2DC2D2C2DC2DC$3.A2.A2.A
2.C2DC2DCD2C.2A$4.A.2A.2A.2CD2C2DCD.A$5.A2.A2.A.DCD4.A.A$6.A2.A2.A.A6.
A$7.2A4.A!

[vilc]

What is the thinest unconstructible still-life that we can find? This problem is the complementary of the Width-N still-lifes syntheses project. All known small unsynthesisable still-lifes are almost square and have a width of 22, but I found a width-21 stabilisation of the 184 cells unsynthesisable still-life.

Code: Select all

x = 27, y = 21, rule = LifeHistory
11.2A$5.2A3.A2.A.A.A4.2A$4.A2.A2.A2.CDCA.A2.A.A$3.A2.C2D2CD2C2D2.A2.A
$3.2A.2CDC2DC2D2CD2CD2C$4.C2DC2DC2DCD2C2DC2DC$3.A2DC2D2CD2C4DC2DC2D$
4.2CD2C2DC2DCD2CD2CD2CA$4.DC2DC2DC2D2CDC2DC2DC$3.A2DC2D2CD2C4DC2DC2D.
A$2.A.2CD2C2DC2DCD2CD2CD2CA.A$2.A.C2DC2DC2DCD2C2DC2DCD2.A$.2A.2DC2D2C
D2C4DC2DCD.2A$A2.A2CD2C2DC2DCD2CD2CDCA$A.A.DC2DC2DC2D2CDC2DC2DA$.A.A
2DC2D2CD2C4DC2DCD$3.ACD2CDC2DC2D2CD2CD2C$.A2.A2.C.DC.DC.2CD.C2DC$.2A
2.A2.A.A.2A4.A2.A$6.2A2.A2.A5.2A$10.2A!

[amling]

What is the thinest unconstructible still-life that we can find?

I took a crack at modelling the problem myself and using a SAT solver to strip partial patterns down to their largest self-forcing subset. Often this ends up empty meaning there was no (non-empty) self-forcing subset. When run with large patches of certain known agars it finds self-forcing patches and when run with a few known self-forcing patches from the forum it does agree they are self-forcing as-is, which is to say I think it reasonably likely I've got this all right.

I then ran it on a bunch of long, thin strips for a certain known self-forcing agar, ultimately producing this:

Code: Select all

x = 20, y = 48, rule = LifeHistory
6.2A7.2A$5.A.C4D2CD.A$.2A.C2DCD2C2DCDC$.A.2CDC2D2CDC2D2C$2.4D2C4D2C3D
A$2.2CDC2D2CDC2D2CD.A$2.CD2C2DCD2C2DCD2CA$2A4D2C4D2C4D$.AD2C2DCD2C2DC
D2CD$A.D2CDC2D2CDC2D2CD$2A4D2C4D2C4D$2.2CDC2D2CDC2D2CDC$2.CD2C2DCD2C
2DCD2C$2A4D2C4D2C4D2A$.AD2C2DCD2C2DCD2CDA$.AD2CDC2D2CDC2D2CDA$2A4D2C
4D2C4D2A$2.2CDC2D2CDC2D2CDC$2.CD2C2DCD2C2DCD2C$2A4D2C4D2C4D2A$.AD2C2D
CD2C2DCD2CDA$.AD2CDC2D2CDC2D2CDA$2A4D2C4D2C4D2A$2.2CDC2D2CDC2D2CDC$2.
CD2C2DCD2C2DCD2C$2A4D2C4D2C4D2A$.AD2C2DCD2C2DCD2CDA$.AD2CDC2D2CDC2D2C
DA$2A4D2C4D2C4D2A$2.2CDC2D2CDC2D2CDC$2.CD2C2DCD2C2DCD2C$2A4D2C4D2C4D
2A$.AD2C2DCD2C2DCD2CDA$.AD2CDC2D2CDC2D2CDA$2A4D2C4D2C4D2A$2.2CDC2D2CD
C2D2CDC$2.CD2C2DCD2C2DCD2C$2.4D2C4D2C4D2A$2.D2C2DCD2C2DCD2CDA$2.D2CDC
2D2CDC2D2CDA$2.4D2C4D2C4D2A$.A2CDC2D2CDC2D2CDC$.A.D2C2DCD2C2DCD2C$2.A
3D2C4D2C4D$3.2C2DCD2C2DCD2C.A$4.CDC2D2CDC2DC.2A$3.A.D2C4DC.A$3.2A7.2A
!

I believe that marked patch (with 16x46 bounding box) is self-forcing and I doubt it's possible to stabilize it with less than two columns on either side, but it does get us down to a 20-wide unsynthesizable still life.

I had also run some 15x120 strips (all possible alignments of 15, but only one possible alignment of 120) for this agar, and all failed to produce a self-forcing patch.

[amling]

EDIT by dvgrn: LifeHistory view of 251-cell unsynthesizable patch for the above still life, cross-posted from a message by DroneBetter on Discord:

Code: Select all

x = 23, y = 22, rule = LifeHistory
6.2A$5.A2.A3.2A$4.DC2DCD2.A3.2A$3.ACD2CD2CDCD.C2.A$3.C2DC2DC2D2C2DC2D
C$.AC2DC2DC2DC2D2CD2CDA$A.D2CD2CD2CDC2DC2DCDA$.A.C2DC2DC2D2C2DC2DC$2A
.2DC2DC2DC2D2CD2CD$.A.D2CD2CD2C2DC2DC2D.2A$.A.C2DC2DC2D2C2DC2DA2.A$2.
ADC2DC2DC2DCD2CDACDA$3.D2CD2CD2C2DC2DC2DC$3.A2DC2DC2D2C2DC2DCD$3.2A.
2DC2DC2D2CD2CD$7.2CD2C2DC2DC2D$6.A2DC2D2C2DC2DC$5.A.C2DC2DCD2C.2A$5.A
.2CD2C2DCD.A$6.A.DCD4.A.A$7.A.A6.A$8.A!

I am not able to reproduce this and I'm wondering where the bug is. My implementation agrees that the entire still life does contain a self-forcing patch which (the maximal one) is much bigger than those 251 cells. Manually hacking away at the difference I am able to produce this 252 cell patch which I believe self forces, but it is one bigger than the above (by added first off cell in third row):

Code: Select all

x = 19, y = 18, rule = LifeHistory
2.DC2DCD$2.CD2CD2CDCD.C$DC2DC2DC2D2C2DC2DC$C2DC2DC2DC2D2CD2CD$D2CD2CD
2CDC2DC2DCD$.C2DC2DC2D2C2DC2DC$.2DC2DC2DC2D2CD2CD$.D2CD2CD2C2DC2DC2D$
.C2DC2DC2D2C2DC2D$.DC2DC2DC2DCD2CD.CD$.D2CD2CD2C2DC2DC2DC$2.2DC2DC2D
2C2DC2DCD$4.2DC2DC2D2CD2CD$5.2CD2C2DC2DC2D$5.2DC2D2C2DC2DC$5.C2DC2DCD
2C$5.2CD2C2DCD$6.DCD!

Are we sure this was copied right from the source? Unfortunately "some discord message" isn't something I can trace. I will look into dumping the alleged mismatched predecessor from my code for the 251 cell patch in the mean time.

EDIT: It wasn't so bad to dump. Here is a predecessor which to my eyes (and/or golly ability) does appear to disagree with the 251 patch in one cell, yet produces the 251 patch in the next generation:

Code: Select all

x = 20, y = 20, rule = B3/S23
bo2bo2bo$3bo2bo3bobobo$b2ob2ob2obo2bo2bo$2o2bo2bo2b2o2bo2bo$3bo2bo2bo
2b2ob2obo$b2ob2ob2obo2bo2bo$bo2bo2bo2b2o2bo2bo$o2bo2bo2bo2b2ob2o$ob2ob
2ob2o2bo2bo$bo2bo2bo2b2o2bo2bobo$2bo2bo2bo2bob2ob2o$ob2ob2ob2o2bo2bo2b
o$o3bo2bo2b2o2bo2bobo$b2o3bo2bo2b2ob2obo$5b2ob2o2bo2bo2bo$7bo2b2o2bo2b
o$4b2o2bo2bob2ob2o$5b2ob2o2bo2bo$7bo2b2o2bo$7bo!

Unsurprisingly (in fact, presumably requiredly), it disagrees with the extra cell in the 252 patch.

[Anivec]

Are any of these infinite patches also self forcing? I assume they are all self forcing if my conjecture is true. These are all transformations of known patches, with a few exceptions.
EDIT:
All of these are self forcing. I did a quick check.

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
obo3b2obobo3b2o$3b2obobo3b2obobo$2obobo3b2obobo$obo3b2obobo3b2o$3b2ob
obo3b2obobo$2obobo3b2obobo$obo3b2obobo3b2o$3b2obobo3b2obobo$2obobo3b2o
bobo$obo3b2obobo3b2o$3b2obobo3b2obobo$2obobo3b2obobo$obo3b2obobo3b2o$
3b2obobo3b2obobo$2obobo3b2obobo$obo3b2obobo3b2o$3b2obobo3b2obobo$2obo
bo3b2obobo!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
bobo3bobo3bobo$b2ob2ob2ob2ob2ob2o$o3bobo3bobo3bo$bobo3bobo3bobo$b2ob2o
b2ob2ob2ob2o$o3bobo3bobo3bo$bobo3bobo3bobo$b2ob2ob2ob2ob2ob2o$o3bobo3b
obo3bo$bobo3bobo3bobo$b2ob2ob2ob2ob2ob2o$o3bobo3bobo3bo$bobo3bobo3bob
o$b2ob2ob2ob2ob2ob2o$o3bobo3bobo3bo$bobo3bobo3bobo$b2ob2ob2ob2ob2ob2o
$o3bobo3bobo3bo!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
o2b3o3bo2b3o$3bo2b3o3bo2b3o$3o3bo2b3o3bo$o2b3o3bo2b3o$3bo2b3o3bo2b3o$
3o3bo2b3o3bo$o2b3o3bo2b3o$3bo2b3o3bo2b3o$3o3bo2b3o3bo$o2b3o3bo2b3o$3b
o2b3o3bo2b3o$3o3bo2b3o3bo$o2b3o3bo2b3o$3bo2b3o3bo2b3o$3o3bo2b3o3bo$o2b
3o3bo2b3o$3bo2b3o3bo2b3o$3o3bo2b3o3bo!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
o2bo2bo2bo2bo2bo$3o3b3o3b3o$3b3o3b3o3b3o$o2bo2bo2bo2bo2bo$3o3b3o3b3o$
3b3o3b3o3b3o$o2bo2bo2bo2bo2bo$3o3b3o3b3o$3b3o3b3o3b3o$o2bo2bo2bo2bo2b
o$3o3b3o3b3o$3b3o3b3o3b3o$o2bo2bo2bo2bo2bo$3o3b3o3b3o$3b3o3b3o3b3o$o2b
o2bo2bo2bo2bo$3o3b3o3b3o$3b3o3b3o3b3o!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
3bo2b4o2bo3b2o$4o2bo3b2o3bo$o3b2o3bo2b4o$3bo2b4o2bo3b2o$4o2bo3b2o3bo$
o3b2o3bo2b4o$3bo2b4o2bo3b2o$4o2bo3b2o3bo$o3b2o3bo2b4o$3bo2b4o2bo3b2o$
4o2bo3b2o3bo$o3b2o3bo2b4o$3bo2b4o2bo3b2o$4o2bo3b2o3bo$o3b2o3bo2b4o$3b
o2b4o2bo3b2o$4o2bo3b2o3bo$o3b2o3bo2b4o!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
3bo2bo3bob4obo$4obo3bo2bo3bo$o3bob4obo3bo$3bo2bo3bob4obo$4obo3bo2bo3b
o$o3bob4obo3bo$3bo2bo3bob4obo$4obo3bo2bo3bo$o3bob4obo3bo$3bo2bo3bob4o
bo$4obo3bo2bo3bo$o3bob4obo3bo$3bo2bo3bob4obo$4obo3bo2bo3bo$o3bob4obo3b
o$3bo2bo3bob4obo$4obo3bo2bo3bo$o3bob4obo3bo!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
2obo2bob2obo4bo$ob2obo4bob2obo$4bob2obo2bob2obo$2obo2bob2obo4bo$ob2ob
o4bob2obo$4bob2obo2bob2obo$2obo2bob2obo4bo$ob2obo4bob2obo$4bob2obo2bo
b2obo$2obo2bob2obo4bo$ob2obo4bob2obo$4bob2obo2bob2obo$2obo2bob2obo4bo
$ob2obo4bob2obo$4bob2obo2bob2obo$2obo2bob2obo4bo$ob2obo4bob2obo$4bob2o
bo2bob2obo!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
3b2o4b2o4b2o$2o2bob2o2bob2o2bo$2obo2b2obo2b2obo$3b2o4b2o4b2o$2o2bob2o
2bob2o2bo$2obo2b2obo2b2obo$3b2o4b2o4b2o$2o2bob2o2bob2o2bo$2obo2b2obo2b
2obo$3b2o4b2o4b2o$2o2bob2o2bob2o2bo$2obo2b2obo2b2obo$3b2o4b2o4b2o$2o2b
ob2o2bob2o2bo$2obo2b2obo2b2obo$3b2o4b2o4b2o$2o2bob2o2bob2o2bo$2obo2b2o
bo2b2obo!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
2obo2b2obo2b2obo$2ob2ob2ob2ob2ob2o$4bo5bo5bo$2obo2b2obo2b2obo$2ob2ob2o
b2ob2ob2o$4bo5bo5bo$2obo2b2obo2b2obo$2ob2ob2ob2ob2ob2o$4bo5bo5bo$2obo
2b2obo2b2obo$2ob2ob2ob2ob2ob2o$4bo5bo5bo$2obo2b2obo2b2obo$2ob2ob2ob2o
b2ob2o$4bo5bo5bo$2obo2b2obo2b2obo$2ob2ob2ob2ob2ob2o$4bo5bo5bo!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
o2bo2b2o2bo2bob2o$2o2bo2bob2obo2bo$bob2obo2bo2b2o2bo$o2bo2b2o2bo2bob2o
$2o2bo2bob2obo2bo$bob2obo2bo2b2o2bo$o2bo2b2o2bo2bob2o$2o2bo2bob2obo2b
o$bob2obo2bo2b2o2bo$o2bo2b2o2bo2bob2o$2o2bo2bob2obo2bo$bob2obo2bo2b2o
2bo$o2bo2b2o2bo2bob2o$2o2bo2bob2obo2bo$bob2obo2bo2b2o2bo$o2bo2b2o2bo2b
ob2o$2o2bo2bob2obo2bo$bob2obo2bo2b2o2bo!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
o3bob2obo3bob2o$2obo3bob2obo3bo$bob2obo3bob2obo$o3bob2obo3bob2o$2obo3b
ob2obo3bo$bob2obo3bob2obo$o3bob2obo3bob2o$2obo3bob2obo3bo$bob2obo3bob
2obo$o3bob2obo3bob2o$2obo3bob2obo3bo$bob2obo3bob2obo$o3bob2obo3bob2o$
2obo3bob2obo3bo$bob2obo3bob2obo$o3bob2obo3bob2o$2obo3bob2obo3bo$bob2o
bo3bob2obo!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
2bo2bo2bo2bo2bo2bo$2bo2bo2bo2bo2bo2bo$2ob2ob2ob2ob2ob2o$o2bo2bo2bo2bo
2bo$2bo2bo2bo2bo2bo2bo$b2ob2ob2ob2ob2ob2o$o2bo2bo2bo2bo2bo$o2bo2bo2bo
2bo2bo$b2ob2ob2ob2ob2ob2o$bo2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$ob2ob2ob
2ob2ob2obo$bo2bo2bo2bo2bo2bo$bo2bo2bo2bo2bo2bo$ob2ob2ob2ob2ob2obo$2bo
2bo2bo2bo2bo2bo$bo2bo2bo2bo2bo2bo$2ob2ob2ob2ob2ob2o!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$b2ob2ob2ob2ob2ob2o$bo2bo2bo2bo2bo2b
o$bo2bo2bo2bo2bo2bo$b2ob2ob2ob2ob2ob2o$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo
2bo$b2ob2ob2ob2ob2ob2o$bo2bo2bo2bo2bo2bo$bo2bo2bo2bo2bo2bo$b2ob2ob2ob
2ob2ob2o$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$b2ob2ob2ob2ob2ob2o$bo2bo2b
o2bo2bo2bo$bo2bo2bo2bo2bo2bo$b2ob2ob2ob2ob2ob2o!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
b2ob2ob2ob2ob2ob2o$2bo2bo2bo2bo2bo2bo$bo2bo2bo2bo2bo2bo$2ob2ob2ob2ob2o
b2o$2bo2bo2bo2bo2bo2bo$bo2bo2bo2bo2bo2bo$ob2ob2ob2ob2ob2obo$o2bo2bo2b
o2bo2bo$2bo2bo2bo2bo2bo2bo$b2ob2ob2ob2ob2ob2o$o2bo2bo2bo2bo2bo$2bo2bo
2bo2bo2bo2bo$2ob2ob2ob2ob2ob2o$bo2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$ob2o
b2ob2ob2ob2obo$bo2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
bo2bo2bo2bo2bo2bo$bo2bo2bo2bo2bo2bo$ob2ob2ob2ob2ob2obo$o2bo2bo2bo2bo2b
o$2bo2bo2bo2bo2bo2bo$b2ob2ob2ob2ob2ob2o$o2bo2bo2bo2bo2bo$o2bo2bo2bo2b
o2bo$b2ob2ob2ob2ob2ob2o$2bo2bo2bo2bo2bo2bo$bo2bo2bo2bo2bo2bo$2ob2ob2o
b2ob2ob2o$2bo2bo2bo2bo2bo2bo$2bo2bo2bo2bo2bo2bo$2ob2ob2ob2ob2ob2o$bo2b
o2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$ob2ob2ob2ob2ob2obo!

Code: Select all

x = 18, y = 18, rule = B3/S23:T18,18
b2ob2ob2ob2ob2ob2o$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$b2ob2ob2ob2ob2ob
2o$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$b2ob2ob2ob2ob2ob2o$o2bo2bo2bo2bo
2bo$o2bo2bo2bo2bo2bo$b2ob2ob2ob2ob2ob2o$o2bo2bo2bo2bo2bo$o2bo2bo2bo2b
o2bo$b2ob2ob2ob2ob2ob2o$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo$b2ob2ob2ob2o
b2ob2o$o2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo!

EDIT2:
Here is an overlay of all the self forcing infinite patches:

Code: Select all

x = 338, y = 158, rule = B3/S23
3b2o4b2o4b2o13bo2bo2b2o2bo2bob2o$2o2bob2o2bob2o2bo13b2o2bo2bob2obo2bo
$2obo2b2obo2b2obo15bob2obo2bo2b2o2bo$3b2o4b2o4b2o13bo2bo2b2o2bo2bob2o
$2o2bob2o2bob2o2bo13b2o2bo2bob2obo2bo$2obo2b2obo2b2obo15bob2obo2bo2b2o
2bo$3b2o4b2o4b2o13bo2bo2b2o2bo2bob2o$2o2bob2o2bob2o2bo13b2o2bo2bob2ob
o2bo$2obo2b2obo2b2obo15bob2obo2bo2b2o2bo$3b2o4b2o4b2o13bo2bo2b2o2bo2b
ob2o$2o2bob2o2bob2o2bo13b2o2bo2bob2obo2bo$2obo2b2obo2b2obo15bob2obo2b
o2b2o2bo$3b2o4b2o4b2o13bo2bo2b2o2bo2bob2o$2o2bob2o2bob2o2bo13b2o2bo2b
ob2obo2bo$2obo2b2obo2b2obo15bob2obo2bo2b2o2bo$3b2o4b2o4b2o13bo2bo2b2o
2bo2bob2o$2o2bob2o2bob2o2bo13b2o2bo2bob2obo2bo$2obo2b2obo2b2obo15bob2o
bo2bo2b2o2bo13$2obo2b2obo2b2obo14bo3bob2obo3bob2o$2ob2ob2ob2ob2ob2o13b
2obo3bob2obo3bo$4bo5bo5bo14bob2obo3bob2obo$2obo2b2obo2b2obo14bo3bob2o
bo3bob2o$2ob2ob2ob2ob2ob2o13b2obo3bob2obo3bo$4bo5bo5bo14bob2obo3bob2o
bo$2obo2b2obo2b2obo14bo3bob2obo3bob2o$2ob2ob2ob2ob2ob2o13b2obo3bob2ob
o3bo$4bo5bo5bo14bob2obo3bob2obo$2obo2b2obo2b2obo14bo3bob2obo3bob2o$2o
b2ob2ob2ob2ob2o13b2obo3bob2obo3bo$4bo5bo5bo14bob2obo3bob2obo$2obo2b2o
bo2b2obo14bo3bob2obo3bob2o$2ob2ob2ob2ob2ob2o13b2obo3bob2obo3bo$4bo5bo
5bo14bob2obo3bob2obo$2obo2b2obo2b2obo14bo3bob2obo3bob2o$2ob2ob2ob2ob2o
b2o13b2obo3bob2obo3bo$4bo5bo5bo14bob2obo3bob2obo23$obo3b2obobo3b2o13b
o2b3o3bo2b3o15bo2bo2bo2bo2bo2bo14bobobobo2bobobobo15b2ob2ob2ob2ob2ob2o
22bo2bo2bo2bo2bo2bo16bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo13bo2bo2bo2b
o2bo2bo13bo2bo2bo2bo2bo2bo27b3obo4b3obo$3b2obobo3b2obobo15bo2b3o3bo2b
3o14bo2bo2bo2bo2bo2bo13bobo2bobobobo2bobo12bo2bo2bo2bo2bo2bo24bo2bo2b
o2bo2bo2bo16bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo13bo2bo2bo2bo2bo2bo13b
o2bo2bo2bo2bo2bo25bo4b3obo4b3o$2obobo3b2obobo15b3o3bo2b3o3bo14b2ob2ob
2ob2ob2ob2o13bo2bobobobo2bobobo13bo2bo2bo2bo2bo2bo25b2ob2ob2ob2ob2ob2o
12b2ob2ob2ob2ob2ob2o13b2ob2ob2ob2ob2ob2o13bob2ob2ob2ob2ob2obo13b2ob2o
b2ob2ob2ob2o22b3obo4b3obo$obo3b2obobo3b2o13bo2b3o3bo2b3o15bo2bo2bo2bo
2bo2bo14bobobobo2bobobobo15b2ob2ob2ob2ob2ob2o24bo2bo2bo2bo2bo2bo13bo2b
o2bo2bo2bo2bo13bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo2b
o26b3obo4b3obo$3b2obobo3b2obobo15bo2b3o3bo2b3o14bo2bo2bo2bo2bo2bo13bo
bo2bobobobo2bobo12bo2bo2bo2bo2bo2bo26bo2bo2bo2bo2bo2bo12bo2bo2bo2bo2b
o2bo16bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo13bo2bo2bo2bo2bo2bo24bo4b3o
bo4b3o$2obobo3b2obobo15b3o3bo2b3o3bo14b2ob2ob2ob2ob2ob2o13bo2bobobobo
2bobobo13bo2bo2bo2bo2bo2bo24bob2ob2ob2ob2ob2obo12b2ob2ob2ob2ob2ob2o14b
2ob2ob2ob2ob2ob2o13b2ob2ob2ob2ob2ob2o13b2ob2ob2ob2ob2ob2o22b3obo4b3ob
o$obo3b2obobo3b2o13bo2b3o3bo2b3o15bo2bo2bo2bo2bo2bo14bobobobo2bobobob
o15b2ob2ob2ob2ob2ob2o23bo2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo2bo12bo2bo2bo
2bo2bo2bo14bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo27b3obo4b3obo$3b2obobo
3b2obobo15bo2b3o3bo2b3o14bo2bo2bo2bo2bo2bo13bobo2bobobobo2bobo12bo2bo
2bo2bo2bo2bo25bo2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo2bo12bo2bo2bo2bo2bo2bo
14bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo25bo4b3obo4b3o$2obobo3b2obobo15b
3o3bo2b3o3bo14b2ob2ob2ob2ob2ob2o13bo2bobobobo2bobobo13bo2bo2bo2bo2bo2b
o24bob2ob2ob2ob2ob2obo12b2ob2ob2ob2ob2ob2o14b2ob2ob2ob2ob2ob2o13b2ob2o
b2ob2ob2ob2o13b2ob2ob2ob2ob2ob2o22b3obo4b3obo$obo3b2obobo3b2o13bo2b3o
3bo2b3o15bo2bo2bo2bo2bo2bo14bobobobo2bobobobo15b2ob2ob2ob2ob2ob2o22bo
2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo
2bo13bo2bo2bo2bo2bo2bo26b3obo4b3obo$3b2obobo3b2obobo15bo2b3o3bo2b3o14b
o2bo2bo2bo2bo2bo13bobo2bobobobo2bobo12bo2bo2bo2bo2bo2bo24bo2bo2bo2bo2b
o2bo14bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo2bo14bo2bo2b
o2bo2bo2bo24bo4b3obo4b3o$2obobo3b2obobo15b3o3bo2b3o3bo14b2ob2ob2ob2ob
2ob2o13bo2bobobobo2bobobo13bo2bo2bo2bo2bo2bo24b2ob2ob2ob2ob2ob2o13b2o
b2ob2ob2ob2ob2o13bob2ob2ob2ob2ob2obo12b2ob2ob2ob2ob2ob2o14b2ob2ob2ob2o
b2ob2o22b3obo4b3obo$obo3b2obobo3b2o13bo2b3o3bo2b3o15bo2bo2bo2bo2bo2bo
14bobobobo2bobobobo15b2ob2ob2ob2ob2ob2o24bo2bo2bo2bo2bo2bo14bo2bo2bo2b
o2bo2bo13bo2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo2bo12bo2bo2bo2bo2bo2bo27b3o
bo4b3obo$3b2obobo3b2obobo15bo2b3o3bo2b3o14bo2bo2bo2bo2bo2bo13bobo2bob
obobo2bobo12bo2bo2bo2bo2bo2bo26bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo13b
o2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo2bo12bo2bo2bo2bo2bo2bo25bo4b3obo4b3o$
2obobo3b2obobo15b3o3bo2b3o3bo14b2ob2ob2ob2ob2ob2o13bo2bobobobo2bobobo
13bo2bo2bo2bo2bo2bo24b2ob2ob2ob2ob2ob2o13b2ob2ob2ob2ob2ob2o13bob2ob2o
b2ob2ob2obo12b2ob2ob2ob2ob2ob2o14b2ob2ob2ob2ob2ob2o22b3obo4b3obo$obo3b
2obobo3b2o13bo2b3o3bo2b3o15bo2bo2bo2bo2bo2bo14bobobobo2bobobobo15b2ob
2ob2ob2ob2ob2o23bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo2b
o13bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo26b3obo4b3obo$3b2obobo3b2obobo
15bo2b3o3bo2b3o14bo2bo2bo2bo2bo2bo13bobo2bobobobo2bobo12bo2bo2bo2bo2b
o2bo25bo2bo2bo2bo2bo2bo13bo2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo2bo13bo2bo2b
o2bo2bo2bo15bo2bo2bo2bo2bo2bo24bo4b3obo4b3o$2obobo3b2obobo15b3o3bo2b3o
3bo14b2ob2ob2ob2ob2ob2o13bo2bobobobo2bobobo13bo2bo2bo2bo2bo2bo25b2ob2o
b2ob2ob2ob2o12b2ob2ob2ob2ob2ob2o13b2ob2ob2ob2ob2ob2o13bob2ob2ob2ob2ob
2obo13b2ob2ob2ob2ob2ob2o22b3obo4b3obo13$bobo3bobo3bobo14bo2bo2bo2bo2b
o2bo14b2obo2b2obo2b2obo14bo2bo2bobobobobobo53bo2bo2bo2bo2bo2bo16bo2bo
2bo2bo2bo2bo13bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo
24bob3obob3obob3o$b2ob2ob2ob2ob2ob2o12b3o3b3o3b3o17bo2bo2bo2bo2bo2bo12b
obobobo2bo2bo2bo55bo2bo2bo2bo2bo2bo13bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2b
o2bo14bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo24b3o3b3o3b3o$o3bobo3bobo3b
o16b3o3b3o3b3o12bo2b2obo2b2obo2b2o14bobobobobobobobobo52bob2ob2ob2ob2o
b2obo13b2ob2ob2ob2ob2ob2o13b2ob2ob2ob2ob2ob2o13b2ob2ob2ob2ob2ob2o13b2o
b2ob2ob2ob2ob2o26bo5bo5bo$bobo3bobo3bobo14bo2bo2bo2bo2bo2bo14b2obo2b2o
bo2b2obo14bo2bo2bobobobobobo53bo2bo2bo2bo2bo2bo16bo2bo2bo2bo2bo2bo13b
o2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo2bo13bo2bo2bo2bo2bo2bo24bob3obob3obob
3o$b2ob2ob2ob2ob2ob2o12b3o3b3o3b3o17bo2bo2bo2bo2bo2bo12bobobobo2bo2bo
2bo54bo2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo2bo13bo2bo2bo2bo2bo2bo15bo2bo2b
o2bo2bo2bo14bo2bo2bo2bo2bo2bo23b3o3b3o3b3o$o3bobo3bobo3bo16b3o3b3o3b3o
12bo2b2obo2b2obo2b2o14bobobobobobobobobo52b2ob2ob2ob2ob2ob2o14b2ob2ob
2ob2ob2ob2o12bob2ob2ob2ob2ob2obo12b2ob2ob2ob2ob2ob2o14b2ob2ob2ob2ob2o
b2o26bo5bo5bo$bobo3bobo3bobo14bo2bo2bo2bo2bo2bo14b2obo2b2obo2b2obo14b
o2bo2bobobobobobo55bo2bo2bo2bo2bo2bo12bo2bo2bo2bo2bo2bo15bo2bo2bo2bo2b
o2bo15bo2bo2bo2bo2bo2bo12bo2bo2bo2bo2bo2bo25bob3obob3obob3o$b2ob2ob2o
b2ob2ob2o12b3o3b3o3b3o17bo2bo2bo2bo2bo2bo12bobobobo2bo2bo2bo54bo2bo2b
o2bo2bo2bo15bo2bo2bo2bo2bo2bo13bo2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo2bo15b
o2bo2bo2bo2bo2bo22b3o3b3o3b3o$o3bobo3bobo3bo16b3o3b3o3b3o12bo2b2obo2b
2obo2b2o14bobobobobobobobobo53b2ob2ob2ob2ob2ob2o12bob2ob2ob2ob2ob2obo
13b2ob2ob2ob2ob2ob2o12bob2ob2ob2ob2ob2obo12b2ob2ob2ob2ob2ob2o27bo5bo5b
o$bobo3bobo3bobo14bo2bo2bo2bo2bo2bo14b2obo2b2obo2b2obo14bo2bo2bobobob
obobo55bo2bo2bo2bo2bo2bo12bo2bo2bo2bo2bo2bo15bo2bo2bo2bo2bo2bo13bo2bo
2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo25bob3obob3obob3o$b2ob2ob2ob2ob2ob2o12b
3o3b3o3b3o17bo2bo2bo2bo2bo2bo12bobobobo2bo2bo2bo56bo2bo2bo2bo2bo2bo14b
o2bo2bo2bo2bo2bo12bo2bo2bo2bo2bo2bo16bo2bo2bo2bo2bo2bo12bo2bo2bo2bo2b
o2bo24b3o3b3o3b3o$o3bobo3bobo3bo16b3o3b3o3b3o12bo2b2obo2b2obo2b2o14bo
bobobobobobobobo52bob2ob2ob2ob2ob2obo12bob2ob2ob2ob2ob2obo12bob2ob2ob
2ob2ob2obo13b2ob2ob2ob2ob2ob2o12b2ob2ob2ob2ob2ob2o27bo5bo5bo$bobo3bob
o3bobo14bo2bo2bo2bo2bo2bo14b2obo2b2obo2b2obo14bo2bo2bobobobobobo54bo2b
o2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo13bo2bo2bo2bo2bo2b
o16bo2bo2bo2bo2bo2bo23bob3obob3obob3o$b2ob2ob2ob2ob2ob2o12b3o3b3o3b3o
17bo2bo2bo2bo2bo2bo12bobobobo2bo2bo2bo56bo2bo2bo2bo2bo2bo14bo2bo2bo2b
o2bo2bo12bo2bo2bo2bo2bo2bo16bo2bo2bo2bo2bo2bo13bo2bo2bo2bo2bo2bo23b3o
3b3o3b3o$o3bobo3bobo3bo16b3o3b3o3b3o12bo2b2obo2b2obo2b2o14bobobobobob
obobobo52b2ob2ob2ob2ob2ob2o13b2ob2ob2ob2ob2ob2o14b2ob2ob2ob2ob2ob2o12b
2ob2ob2ob2ob2ob2o13bob2ob2ob2ob2ob2obo26bo5bo5bo$bobo3bobo3bobo14bo2b
o2bo2bo2bo2bo14b2obo2b2obo2b2obo14bo2bo2bobobobobobo54bo2bo2bo2bo2bo2b
o14bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo15bo2bo2bo2b
o2bo2bo23bob3obob3obob3o$b2ob2ob2ob2ob2ob2o12b3o3b3o3b3o17bo2bo2bo2bo
2bo2bo12bobobobo2bo2bo2bo55bo2bo2bo2bo2bo2bo13bo2bo2bo2bo2bo2bo14bo2b
o2bo2bo2bo2bo14bo2bo2bo2bo2bo2bo16bo2bo2bo2bo2bo2bo22b3o3b3o3b3o$o3bo
bo3bobo3bo16b3o3b3o3b3o12bo2b2obo2b2obo2b2o14bobobobobobobobobo53b2ob
2ob2ob2ob2ob2o12b2ob2ob2ob2ob2ob2o13bob2ob2ob2ob2ob2obo12bob2ob2ob2ob
2ob2obo12bob2ob2ob2ob2ob2obo26bo5bo5bo23$2b2obo2b2obo2b2obo$2bob2o2bo
b2o2bob2o$2o4b2o4b2o$bob2o2bob2o2bob2o$o2b2obo2b2obo2b2o$2o4b2o4b2o$2b
2obo2b2obo2b2obo$2bob2o2bob2o2bob2o$2o4b2o4b2o$bob2o2bob2o2bob2o$o2b2o
bo2b2obo2b2o$2o4b2o4b2o$2b2obo2b2obo2b2obo$2bob2o2bob2o2bob2o$2o4b2o4b
2o$bob2o2bob2o2bob2o$o2b2obo2b2obo2b2o$2o4b2o4b2o!

[HartmutHolzwart]

Nice! Do any of these lead to a smaller non-glider-constructible still life?

[I6_I6]

What's the smallest possible patch for each agar for them to be self-forcing?
Example stabilizations done by hand:

Code: Select all

x = 25, y = 15, rule = LifeHistory
8.2A$8.A2.2A.2A$5.2A.A3.A.A2.A$5.A.A.3A3.3A2.A$2.2A.A3.A2.3A3.3A2.A$
2.A.A.3A3.A2.3A3.3A$A.A3.A2.3A3.A2.3A$2A.3A3.A2.3A3.A2.3A$3.A2.3A3.A
2.3A3.A2.A$3A3.A2.3A3.A2.3A2.2A$A2.3A3.A2.3A3.A$3.A2.3A3.A2.3A$6.A2.
3A3.A$9.A2.3A$12.A!

Code: Select all

x = 19, y = 22, rule = LifeHistory
8.2A4.2A$5.A2.A2.A2.A2.A$3.3A3.3A3.3A$2.A3.3A3.3A$.A.3A3.3A3.3A$A2.A
2.A2.A2.A2.A2.A$.2A3.3A3.3A3.A$3.3A3.3A3.3A$3.A2.A2.A2.A2.A$.2A3.3A3.
3A$A2.3A3.3A3.3A$A2.A2.A2.A2.A2.A2.A$.2A3.3A3.3A3.A$3.3A3.3A3.3A$3.A
2.A2.A2.A2.A$.2A3.3A3.3A$A2.3A3.3A3.3A$A2.A2.A2.A2.A2.A2.A$.2A3.3A3.
3A3.A$3.3A3.3A3.3A$3.A2.A2.A2.A2.A$5.2A4.2A!

[Anivec]

What's the smallest possible patch for each agar for them to be self-forcing?
Example stabilizations done by hand:

Code: Select all

x = 25, y = 15, rule = LifeHistory
8.2A$8.A2.2A.2A$5.2A.A3.A.A2.A$5.A.A.3A3.3A2.A$2.2A.A3.A2.3A3.3A2.A$
2.A.A.3A3.A2.3A3.3A$A.A3.A2.3A3.A2.3A$2A.3A3.A2.3A3.A2.3A$3.A2.3A3.A
2.3A3.A2.A$3A3.A2.3A3.A2.3A2.2A$A2.3A3.A2.3A3.A$3.A2.3A3.A2.3A$6.A2.
3A3.A$9.A2.3A$12.A!

Code: Select all

x = 19, y = 22, rule = LifeHistory
8.2A4.2A$5.A2.A2.A2.A2.A$3.3A3.3A3.3A$2.A3.3A3.3A$.A.3A3.3A3.3A$A2.A
2.A2.A2.A2.A2.A$.2A3.3A3.3A3.A$3.3A3.3A3.3A$3.A2.A2.A2.A2.A$.2A3.3A3.
3A$A2.3A3.3A3.3A$A2.A2.A2.A2.A2.A2.A$.2A3.3A3.3A3.A$3.3A3.3A3.3A$3.A
2.A2.A2.A2.A$.2A3.3A3.3A$A2.3A3.3A3.3A$A2.A2.A2.A2.A2.A2.A$.2A3.3A3.
3A3.A$3.3A3.3A3.3A$3.A2.A2.A2.A2.A$5.2A4.2A!

Not so fast now, certain agars must reach a certain size before becoming unsynthesizable. The ones I provided become unsynthesizable for very large continuations of the specified type.

I am not sure if proving by hand is sufficient.

[HartmutHolzwart]

… at least one could try to find parents with WLS or JLS or LSS? If ther are none except the pattern itself, we‘re done.

[Anivec]

… at least one could try to find parents with WLS or JLS or LSS? If ther are none except the pattern itself, we‘re done.

Or you could do the other way around and have the search program build one that has all the properties all other unsynthesizable objects have.