Thread for advanced questions

[I6_I6]

What is the largest strict still life predecessor that fits in a 16x16 box? Here is a lower bound from D2_x (not yet synthesized):

Code: Select all

x = 16, y = 16, rule = B3/S23
boobbbobobobbooo$
obobbboooboobbbo$
boobooooobooobbo$
oboobboobbbooobb$
bobobbbbbbobooob$
bbobbbboobbobooo$
ooooobooobbbbbbb$
boboobooboobbooo$
booboobbooobooob$
oobboboboobboooo$
bobbobbobbbbbobb$
obbooooooobbbobb$
bbooobbbooboobbb$
bboobbbobooboooo$
bbbbbooooobobobo$
obbbobobbobbobob!

Surely one can fit a tubstretcher predecessor and some delay mechanism to blow it up in a 16x16 box...

But the ash from the tubstretcher wouldn't be part of a strict still life. Muzik's example also contains a non-interacting block (unless separate non-strict SLs are ignored).

[dbell]

Are there any LWSS creating reactions in which the gliders all come from behind the LWSS?

I'm asking this because for c/2 period 10 technology, period 10 forward gliders streams can't work, and period 10 sideways LWSS streams just barely can't work.

However, I think period 10 backward LWSS streams would work, if only they could be made.

A secondary problem is that the reaction has to be repeatable every 10 generations with a shift of 5 cells, so any reaction would probably have to expand into the void in front of the reaction behind it to release its LWSS.

I'm not very hopeful of a solution.

BCNU,
-dbell

[Chris857]

Are there any LWSS creating reactions in which the gliders all come from behind the LWSS?

It's clunky and not fast, but 4 gliders can form an intermediate LWSS that hits another 2 to create a block and LWSS.

Code: Select all

x = 77, y = 83, rule = LifeHistory
9$30.A$31.A$29.3A4$36.A$37.A$35.3A14$11.A.A$12.2A$12.A37.D.D$17.A35.D
$18.A34.D$16.3A31.D2.D$51.3D11$33.2A$32.A.A$34.A3$32.2A$33.2A$32.A11$
47.2D$47.2D3$57.D2.D$61.D$57.D3.D$58.4D!

[parrot]

Is penny lane a billiard table?

[hotdogPi]

Is penny lane a billiard table?

Yes.

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x = 15, y = 12, rule = LifeHistory
6.3B$6.3D$3.2A5.2A$3.A3.A3.A$2A.A.A3.A.A.2A$2A.A.A3.A.A.2A$4.A5.A$5.
5A2$7.A$6.A.A$7.A!

For an outside region to interact with the rotor, two of the red cells must be on. The closest they can get without touching the stator is the dark blue cells, which will only turn on the center one of the three red cells, which is not enough.

[parrot]

So why ain’t it in Category:billiard tables?

[hotdogPi]

Now that I think about it, it's possible to interact with the rotor if you rely on overpopulation. I'm not sure how to handle this case.

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x = 15, y = 13, rule = B3/S23
15o3$3b2o5b2o$3bo7bo$2obo2bobo2bob2o$2obobo3bobob2o$4bo2bo2bo$5b5o2$7b
o$6bobo$7bo!

[muzik]

What would it mean for an object to have a complex period?

[I6_I6]

In the Gemini, there are perpendicular overlapping glider lanes, in the tape reflection mechanism and between the tape and the gliders fired from the left arm of the bottom half. How was it made so that none of those gliders collide with each other?

[Rhombicubocta]

Can an infinite spatially repeating pattern which has repeating units which increase or decrease in bounding boxes in Inner Totalistic rules exist?
More generally is it even possible to construct a rule where such a pattern could exist?

[I6_I6]

Can an infinite spatially repeating pattern which has repeating units which increase or decrease in bounding boxes in Inner Totalistic rules exist?
More generally is it even possible to construct a rule where such a pattern could exist?

Welcome to the Forums!

I might be interpreting your question incorrectly, but here's something I believe matches your description:

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x = 4, y = 4, rule = B3/S2:T6,6
b2o$3bo$o$b2o!

B3/S2 is totalistic. If you have an agar of toads tiling the plane, you could consider the toads as individual units, and they increase and decrease in bounding box throughout their evolution.

[Rhombicubocta]

The toads bounding box does change, but not the bounding boxes repeating unit of the agar does not. The distance between toads in the that agar remains constant.

I am asking can you have pattern where the size of the bounding box in this case the 6 by 6 square would increase.
There is likely an argument that such a “growing agar” can’t exist, but I cannot think why one could not exist.

(Technically agars are oscillators that come back to their original state and so cannot have variable size of repeating units. I just don’t know a better term)

If they do exist I have no clue how you would simulate one since life viewer only can deal with a constant torus size.

Edit: I expect this type of pattern can’t exist. I don’t have an argument for why the can’t though. Probably some reasoning related to c being the speed limit of information in a cellular automata, but I’m not sure.

[I6_I6]

The toads bounding box does change, but not the bounding boxes repeating unit of the agar does not. The distance between toads in the that agar remains constant.

I am asking can you have pattern where the size of the bounding box in this case the 6 by 6 square would increase.
There is likely an argument that such a “growing agar” can’t exist, but I cannot think why one could not exist.

(Technically agars are oscillators that come back to their original state and so cannot have variable size of repeating units. I just don’t know a better term)

If they do exist I have no clue how you would simulate one since life viewer only can deal with a constant torus size.

Edit: I expect this type of pattern can’t exist. I don’t have an argument for why the can’t though. Probably some reasoning related to c being the speed limit of information in a cellular automata, but I’m not sure.

Ok, now I understand what you were asking, and no, such a pattern can't exist, and it is because of the speed limit.
Suppose there is a theoretical growing agar, where the units' bounding boxes grow every cycle. (The length the cycle and the growth rate don't matter, as long as they're natural numbers and constant.) If we choose one particular unit as the "origin", every cycle, the units adjacent to the origin would move away from it, since the bounding boxes of all the units have grown. The units behind those units would have to move 2x that distance, and the units even further away would have to move 3x that distance, and so on. The further away from the origin you get, the further away from the origin each unit has to move. Since the agar is infinite, there's no upper bound to how for the units need to move, but in an inner-totalistic CA, the speed limit is just 1 cell/gen, which makes growing agars impossible.
Sorry if this proof doesn't make any sense at all.

[b-engine]

Are there Gardens of Eden which their inversions are also Gardens of Eden?

[hotdogPi]

Are there Gardens of Eden which their inversions are also Gardens of Eden?

Yes. Just put a Garden of Eden and its inversion side-by-side.

[NNlk05]

How is backtracking translated into an SAT-able equation?

[hotcrystal0]

(I don’t know if this goes in basic or advanced questions)
Is there any reason why Lenia’s (the continuous CA) behavior most closely resembles LTL bug rules?

[b-engine]

Is there any reason why Lenia’s (the continuous CA) behavior most closely resembles LTL bug rules?

In both types of rules, a singular cell is tiny relative to its neighbors, and high resolution (larger) neighborhood approximates the continuous neighborhood of Lenia.

[aengmore]

Can we use GPU programming to simulate CGoL and other CA? It may be faster than using CPU

[NNlk05]

Can we use GPU programming to simulate CGoL and other CA? It may be faster than using CPU

Believe it or now, I had tried. The main issue is because of the slow data transfer speed between the CPU and the GPU. Every tick you may need to transfer KBs of data. Also, CA isn't easily pallralizable.

[russellsprouts]

Can we use GPU programming to simulate CGoL and other CA? It may be faster than using CPU

GPUs can simulate life very quickly -- including up to trillions of cell updates per second. https://binary-banter.github.io/game-of ... vious-work

Qufince is an example that uses CUDA to simulate a small section in millions of variations very quickly: https://conwaylife.com/forums/viewtopic.php?f=9&t=5997.

However, conventional wisdom says that algorithms like Hashlife are not well suited for a GPU. A GPU could simulate all of the hashtiles quickly, but as NNlk05 said, then the bottleneck is transferring data between the two.

When patterns are friendly to Hashlife, they can simulate even faster than trillions of updates per second -- larger and larger tiles can skip ahead exponentially further, and duplicate tiles are only simulated once.

[pcallahan]

I'm curious if anyone has worked on this. It seems like a natural "puzzle" question about still life patterns though not of deep mathematical interest.

First what is known: take 3x3 neighborhoods. Some can be ruled out as part of a still life, e.g. if the center cell is a violation or if the center-edge cells are live and overcrowded. Of the ones that are not ruled out, I think all can be extended into a finite still life (not 100% sure). You can ask the same question of 4x4 windows and so on.

What is the smallest still life that contains all consistent 3x3 neighborhoods? If not the provably smallest, has anyone constructed a reasonably compact example with relatively few duplicates up to symmetry.

Now consider the same question for 4x4 windows.

It wouldn't surprise me if someone had a construction for the 3x3 case, though I am not aware of it. It would surprise me a little if someone had done it for 4x4 or beyond.

I was working on something else and thought this might be doable along the way, which is why I ask.

[muzik]

Are self-forcing p3 agar patches known?

[vilc]

Are self-forcing p3 agar patches known?

p3 and p4 self-forcing agars were found in January 2025 by 400spartans. The crosspost does not say if a finite self-forcing patch exists for these agars.

[andrewthelifer]

B/S01 has three still-lives: the dot, domino and duoplet.

Out of all INT rules that have only finitely many still-lives of finite population, do any of them have more finite SLs?