Thread for advanced questions

[Gustone]

Is there a thread for advanced questions?

[dvgrn]

There is now! (I just split the above post off of the "Thread for basic questions".)

[confocaloid]

I think this 'rough "hierarchy" of problem types' needs to be crossposted near the beginning:

I wanted to get my thoughts out about what kinds of things things CGOL people work on (note: I usually dislike acronyms, but "life" and even "game of life" are so overloaded that CGOL is growing on me). I hope this is an appropriate thread for such thoughts (and there appears to be a culture of avoiding new threads around here).

The reason this is connected to a "broader audience" is that I feel the CGOL community in general and on this website really likes to keep to the top level of the hierarchy I propose below and becomes dismissive as the discussion moves further down the rungs of the ladder. This is understandable for maintaining focus and quality, but a team working on outreach may need a different approach. This is by no means intended as an exhaustive list. Criticism is welcome. It is just to get the ball rolling.

Rough "hierarchy" of problem types.
Research: Some doubt about whether it is possible at all. New approaches and (usually) expertise needed to solve it.
Engineering: Believed to be possible, but no working example shown. Path may be sketched out, but work and skill are needed to complete it (nagging uncertainties about spacing and phasing may remain but are assumed resolvable).
Cataloging: Finding any one solution is a routine task, but solution space has not been fully explored. Solution takes the form of “list all”, “determine how many”, “find fastest/smallest”. This could be either an automated or manual process.
Known method: Finding the solution is a routine task for at least one member of the CGOL community.
Widely known method: Many experienced CGOL hobbyists can accomplish the task.
Scripted method: There is software that solves the problem and can be used without much CGOL experience (but it may require software engineering skills).
Novice: Simple constructions that require some understand[ing] of what CGOL can do. Pairing up guns or rakes for collisions, adding and removing eaters, etc.
Trivial: Shows up in early exploration “Whoa, that 5-cell pattern is moving.” “This small pattern makes a big explosion.” “When I start with a line, the result is always symmetrical.”

An orthogonal axis is level of interest. This varies from “Obviously interesting to anyone who sees it.” to “Only of interest to its discoverer.” The above categories can fall anywhere on this axis. E.g., completing some obscure oscillator of known period may be research-level difficulty, but still not very interesting. Gliders are trivial and well known, but obviously interesting.

(Actually it’s not completely orthogonal, because a research problem can grow in interest as it is perceived to be more challenging and many people try and fail to solve it, much like the trajectory of FLT in pure mathematics.)

EDIT by dvgrn: side note on the last parenthetical remark -- "FLT" is "Fermat's Last Theorem", not "faster than light [travel]".

This list doesn't give any definite guidance as to what types of questions belong here vs. in the Thread for basic questions. It's possible to ask either basic or advanced questions related to most of the above categories. That's okay -- just pick the thread that seems to fit the question better.

[WhiteHawk]

I hope this counts as an "advanced" question. If not, I will move it elsewhere.

Is it possible to modify the recent H-to-MWSS to work in Pedestrian Life (B38/S23)? At gen 131, B8 is triggered, which damages the conduit supports. However, perhaps some novel support mechanism can eat the new waste, and neither of the catalysts at the end are touched when the evolution changes.

Code: Select all

x = 102, y = 55, rule = B38/S23
41b2o3bo$42bo2bobo41b2o3bo$40bo4bobo42bo2bobo$40b5obo41bo4bobo$44bo43b
5obo$36bo3b2o3bo46bo$35bobo2b2o4bo37bo3b2o3bo$36bo8b2o36bobo2b2o4bo$84b
o8b2o3$13b2o$12b2ob3o28b2o$13b5o28b2o46b2o$14b3o36bo40b2o$51b3o47bo$50b
o48b3o$50b2o46bo$98b2o3$45b3o$45bobo$43b6o$40bo3b2o$39bo4b2o$39bo3bo3b
o27bo$42bo3bobo2b2o22bo$39bob2o3bobo2b2o22b3o21b2o$39bo2bo4b2o28bo21b
2o3$47bobo$47b2obo44bobo$50bo44b2obo$50b2o46bo$98b2o3$43b2o$43bo47b2o
$44b3o44bo$46bo45b3o$94bo9$o$obo$2o!

[confocaloid]

[...] Is it possible to modify the recent H-to-MWSS to work in Pedestrian Life (B38/S23)? At gen 131, B8 is triggered, [...]

Enough of the H-to-MWSS conversion reaction appears to be preserved (an output MWSS does escape if you feed in the input Herschel). That gives hope of completion.
Further, at the time when the MWSS escapes, two catalysts are not yet touched, which also gives hope of finding a replacement for them.

I think this is (more or less) as far as one can get, without/before actually trying various possibilities (manually or by a search program) and hoping for a lucky completion.

Code: Select all

x = 27, y = 43, rule = B38/S23
14b2o3bo$15bo2bobo$13bo4bobo$13b5obo$17bo$9bo3b2o3bo$8bobo2b2o4bo$9bo
8b2o5$19b2o$19b2o$26bo$24b3o$23bo$23b2o8$o$obo$3o21b2o$2bo21b2o4$20bo
bo$20b2obo$23bo$23b2o4$16b2o$16bo$17b3o$19bo!
#C [[ GRID THEME Catagolue STOP 100 ]]

[WhiteHawk]

I think this is (more or less) as far as one can get, without/before actually trying various possibilities (manually or by a search program) and hoping for a lucky completion.

Code: Select all

Better result (But not yet complete) with stable ash based on the new reduction

Code: Select all

x = 71, y = 43, rule = B38/S23
14b2o3bo37b2o3bo$15bo2bobo37bo2bobo$13bo4bobo35bo4bobo$13b5obo36b5obo
$17bo42bo$9bo3b2o3bo33bo3b2o3bo$8bobo2b2o4bo31bobo2b2o4bo$9bo8b2o32bo
8b2o5$19b2o41b2o$19b2o41b2o$26bo42bo$24b3o40b3o$23bo42bo$23b2o41b2o3$
63b2o$62bo2bo$63b2o3$o26bo42bo$obo22b3o40b3o$3o21bo42bo$2bo20bobo40bo
bo$24bo42bo3$22b2o41b2o$22b2o41b2o6$16b2o41b2o$16bo25b2o15bo$17b3o23b
2o15b3o$19bo22bo19bo!

Either the preceding conduit would need to produce a glider and herschel, or the FNG could be chained to some stable reflectors and create an H-to-MWSS with an atrocious repeat time.

[dvgrn]

Looks like this works:

Code: Select all

x = 50, y = 43, rule = B38/S23
35b2o3bo$36bo2bobo$34bo4bobo$34b5obo$38bo$30bo3b2o3bo$29bobo2b2o4bo$30b
o8b2o4$5o$o4bo34b2o$o39b2o$bo3bo41bo$3bo41b3o$44bo$44b2o8$21bo24b2o$21b
obo22bobo$21b3o24bo$23bo24b2o2$43b2o$43bo$44b3o$46bo6$37b2o$37bo$38b3o
$40bo!

For comparison, it produces an Annoying Beehive in plain old Life:

Code: Select all

x = 50, y = 43, rule = B3/S23
35b2o3bo$36bo2bobo$34bo4bobo$34b5obo$38bo$30bo3b2o3bo$29bobo2b2o4bo$30b
o8b2o4$5o$o4bo34b2o$o39b2o$bo3bo41bo$3bo41b3o$44bo$44b2o8$21bo24b2o$21b
obo22bobo$21b3o24bo$23bo24b2o2$43b2o$43bo$44b3o$46bo6$37b2o$37bo$38b3o
$40bo!

[WhiteHawk]

For comparison, it produces an Annoying Beehive in plain old Life:

Code: Select all

What is funny is that the most recent reduction of the reflector in life above leaves a beehive in Pedestrian Life but is clean in Life.

Code: Select all

x = 32, y = 47, rule = B38/S23
3$15b2o3bo$16bo2bobo$14bo4bobo$14b5obo$18bo$10bo3b2o3bo$9bobo2b2o4bo$
10bo8b2o5$20b2o$20b2o$27bo$25b3o$24bo$24b2o8$bo26bo$bobo22b3o$b3o21bo
$3bo20bobo$25bo3$23b2o$23b2o6$17b2o$17bo$18b3o$20bo!

EDIT: The Pedestrian Life page should be changed since there is now an H-to-MWSS in the rule.

EDIT 2: any hope for a connection for it's p120 Repeat time? The H-to-R used in Life doesn't work in B38/S23, though the R-to-H does.

EDIT 3: R-R conduit successfully attached below which give significant clearance. Is there an H-to-R conduit which works here?

Code: Select all

x = 48, y = 64, rule = B38/S23
33b2o3bo$34bo2bobo$32bo4bobo$32b5obo$36bo$28bo3b2o3bo$27bobo2b2o4bo$28b
o8b2o5$38b2o$38b2o$45bo$43b3o$42bo$42b2o8$19bo24b2o$19bo24bobo$3b2o3b
2o9b3o24bo$3b2o3b2o11bo24b2o2$41b2o$41bo$42b3o$44bo3$2o$2o5bo7b2o$6bo
bo6b2o$8bo26b2o$35bo$36b3o$b2o35bo$b2o11b2o$14bobo$16bo8b2o3bo$16b2o8b
o2bobo$24bo4bobo$24b5obo$28bo$24b2o3bo$24bobo3bo$25bo3b2o5$7b2o$8b2o$
8bo$38bo$37bobo$37bobo$38bo!

[confocaloid]

Crossposting my recent question, which is certainly beyond "basic", but was posted before this thread existed. Unlike earlier questions, it was not yet followed by a discussion in the same thread.

Question: is there a strict still life X with all of the following properties?

1. The bounding box of the still life X is a N-by-N square.
2. Multiple copies of the still life X can be arranged in a two-dimensional lattice, with precisely M empty rows of cells between consecutive rows of copies of X, and with precisely M empty columns of cells between consecutive columns of copies of X.
3. In a two-dimensional arrangement described above, any two "side-by-side adjacent" copies of X can be either left unchanged, or joined together into a single strict still life by a particular "isthmus" connection across the M-cell-thick gap. This way, there are multiple different modifications of any rectangular arrangement of copies of X, where some "isthmuses" are present and other are absent. Every such choice (between adding or not adding an "isthmus") is independent from all other such choices.
4. Every such modified rectangular arrangement has a glider synthesis, for all sizes, and regardless of which "isthmuses" are present and which are absent.

Other things being equal, larger values of N are better.
Other things being equal, smaller values of M are better.
If both N and M are equal in two solutions, then denser still lives are better.

The following would be a solution (with N = 9 and M = 2), if only there was a proof that all possible resulting finite arrangements are glider-constructible. (I don't have either a proof or a disproof of glider-constructibility of these.)

Code: Select all

x = 87, y = 53, rule = B3/S23
36b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$37bobo8bobo8bobo8bobo8bobo$34bo2b
obo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo$2b2ob2o6b2ob2o16b4o
b4o2b4ob4o2b4ob4o2b4ob4o2b4ob4o$3bobo8bobo$o2bobo2bo2bo2bobo2bo14b4ob
4o2b4ob4o2b4ob4o2b4ob4o2b4ob4o$4ob4o2b4ob4o14bo2bobo2bo2bo2bobo2bo2bo
2bobo2bo2bo2bobo2bo2bo2bobo2bo$37bobo8bobo8bobo8bobo8bobo$4ob4o2b4ob4o
16b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$o2bobo2bo2bo2bobo2bo$3bobo8bobo$
2b2ob2o6b2ob2o18b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$37bobo8bobo8bobo8bo
bo8bobo$34bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo$34b4o
b4o2b4ob10ob10ob4o2b4ob4o2$34b4ob4o2b4ob10ob10ob4o2b4ob4o$34bo2bobo2bo
2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo$37bobo8bobo8bobo8bobo8bob
o$36b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$48bobo8bobo8bobo$48bobo8bobo8bo
bo$36b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$2b2ob2o6b2ob2o19bobo8bobo8bobo
8bobo8bobo$3bobo8bobo17bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo
2bobo2bo$o2bobo2bo2bo2bobo2bo14b4ob4o2b4ob10ob10ob4o2b4ob4o$4ob10ob4o$
34b4ob4o2b4ob10ob10ob4o2b4ob4o$4ob10ob4o14bo2bobo2bo2bo2bobo2bo2bo2bob
o2bo2bo2bobo2bo2bo2bobo2bo$o2bobo2bo2bo2bobo2bo17bobo8bobo8bobo8bobo8b
obo$3bobo8bobo19b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$2b2ob2o6b2ob2o30bob
o8bobo8bobo$48bobo8bobo8bobo$36b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o$37bo
bo8bobo8bobo8bobo8bobo$34bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2b
o2bobo2bo$34b4ob4o2b4ob10ob10ob4o2b4ob4o2$34b4ob4o2b4ob10ob10ob4o2b4ob
4o$34bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo$37bobo8bob
o8bobo8bobo8bobo$36b2ob2o6b2ob2o6b2ob2o6b2ob2o6b2ob2o3$36b2ob2o6b2ob2o
6b2ob2o6b2ob2o6b2ob2o$37bobo8bobo8bobo8bobo8bobo$34bo2bobo2bo2bo2bobo
2bo2bo2bobo2bo2bo2bobo2bo2bo2bobo2bo$34b4ob4o2b4ob4o2b4ob4o2b4ob4o2b4o
b4o2$34b4ob4o2b4ob4o2b4ob4o2b4ob4o2b4ob4o$34bo2bobo2bo2bo2bobo2bo2bo2b
obo2bo2bo2bobo2bo2bo2bobo2bo$37bobo8bobo8bobo8bobo8bobo$36b2ob2o6b2ob
2o6b2ob2o6b2ob2o6b2ob2o!

[hotdogPi]

I seem to remember a page in LifeWiki userspace that listed the number of times each INT transition occurred in the evolution of the R-pentomino, but I can't find it. Once we find that (or it's recreated from scratch), I suggest this:

This would help determine naturalistic predecessors for "back up 1 generation" searches. For each solution, the "cost" of each cell, whether off or on, would be 1 divided by the number of times it appears in that list. The lowest cost would be the best.

This isn't quite perfect (I somehow have a feeling that a beehive would want to become a 3x2 rather than remain a beehive, and the algorithm also doesn't take into account ranges above 1 such as B8 being most common with traffic lights or the immediate parent of the Herschel having an extra domino), but it should be an improvement on "minimum population no matter what".

[confocaloid]

What is the intended "advanced question" here?

I don't remember any page in the LifeWiki namespace dealing with details of evolution of the R-pentomino. I'm pretty sure that details tied to a particular (non-CGoL) CA type should not go to the LifeWiki namespace. (The wiki is primarily about Conway's Life. The simplest and most obvious extension of the idea is to Life-like cellular automata. All other noteworthy CA types and spaces should really be put on equal footing, neither of them is inherently "better" than another.)

If you want to somehow capture the "degree of being naturalistic" (whatever that would mean), I think it would be better to avoid hardcoding a particular Conway's Life methuselah in the logic.

[hotdogPi]

This has nothing to do with OCA; I'm speaking about Life only. The idea is that we have tools that find predecessors, but we don't currently have any optimized for "is a plausible way to get there from earlier configurations, so that it can easily be backed up further".

[confocaloid]

This has nothing to do with OCA; I'm speaking about Life only. The idea is that we have tools that find predecessors, but we don't currently have any optimized for "is a plausible way to get there from earlier configurations, so that it can easily be backed up further".

Related discussions:

• viewtopic.php?f=2&t=3305&p=57416#p57416 how about a sir robin synthesis?
• viewtopic.php?p=105378#p105378 Re: The Past and Future of CGOL
• viewtopic.php?p=192057#p192057 Re: Incomplete search patterns - try to complete
• viewtopic.php?p=192062#p192062 Re: Incomplete search patterns - try to complete

[hotdogPi]

I might not have been clear enough, especially since the page I thought existed didn't.

Here's an an example from part of what I thought the page looked like, with made up numbers:

S3q — 31415
S3y — 9265
D4a — 35897
D4c — 932
D4e — 3846
D4i — 26433

The R-pentomino that I thought the page had was just to get a representative sample; the exact pattern didn't matter, and I used what I thought already existed.

When searching for a 1-tick predecessor of a pattern, a live cell with "4a" neighbors would have a "cost" of 1/35897, which is low because it's more common, while a live cell with "4c" neighbors would have a much higher cost of 1/932. A predecessor-finding search would therefore try to have fewer of the latter, since it would be more difficult to back it up further.

Dead cells that touch at least one live cell would also contribute to the total. For example, A1e and A1c on the edge of the pattern would contribute to the total, but very little, since they would have high frequency counts.

[confocaloid]

I might be missing the advanced question(s). I can imagine several questions that could be asked here, but neither of them was.

It would help to be more systematic, and (for example) generate, evolve and measure all finite-lifespan patterns in small enough bounding boxes. That should work better than picking a single methuselah.

It would be misleading to merge rotations/reflections of a 3-by-3 configuration into a single condition by adding frequencies together. Misleading, because different 3-by-3 configurations have different symmetries.
Instead of adding frequencies of rotations/reflections together, one would have to measure frequency for each of the 2^9 = 512 possible 3-by-3 configurations separately (even though all rotations/reflections of a single 3-by-3 configuration would have the same measured frequency).

As soon as you have an escaping glider, every 3-by-3 configuration that occurs during evolution of the glider occurs infinitely often.
Likewise, as long as you have a finite-population pattern that never dies out entirely, every 3-by-3 configuration satisfying the condition "the middle cell is currently dead and has precisely one alive neighbour which is a diagonal neighbour" (i.e. the condition "B1c/A1c") will occur infinitely often during evolution of the pattern.

[dvgrn]

I might be missing the advanced question(s). I can imagine several questions that could be asked here, but neither of them was.

Maybe hotdogPi's post is more of a candidate "advanced answer" to the question about the best way to generate a long series of ancestors to any given pattern, while minimizing the odds of backtracking into a dead end.

A question somewhat along these lines showed up as a "basic question" quite recently, and there was another question about how to set a record for backtracking distance not long before that.

So ... what is our current collective state of the art, for starting from an arbitrary smallish non-GoE pattern -- fitting inside 16x16, let's say -- and generating ancestors in an unbroken chain reaching as far back as possible? Maybe start fresh with a 16x16 that hasn't been attempted before, like this totally arbitrary 27-tick pure glider generator:

Code: Select all

x = 16, y = 16, rule = B3/S23
o3bo2b2o2b5o$o3bobo2bo3bo$2o2bobo2bo3bo$obobobo2bo3bo$o2b2obo2bo3bo$o
3bobo2bo3bo$o3bo2b2o4bo3$3o2b2o2b3obobo$o3bo2bobo3bobo$o3bo2bobo3bobo
$3obo2bob3o2b2o$o3b4o3bo2bo$o3bo2bo3bo2bo$b2obo2bob3o2bo!

How long would it take for someone to beat AlphaPhoenix's record of 20 ticks, for backtracking this particular pattern, and what techniques should be used?

In case an actual contest might make the question more interesting, I'll send a check for $1.37 on request, to whoever has posted a great^N grandparent of this pattern, with the highest value of N, as of the end of 2024 (everywhere in the world). If a tie break is needed, lower population wins, then smallest minimum covering polyplet area.

[confocaloid]

The main idea behind this question is to reinterpret CGoL patterns as sets of chesspieces on an infinite board. Each alive cell in the pattern is replaced by some chesspiece. Each dead cell in the pattern is left empty. All chesspieces are of the same colour.
Under this reinterpretation, some constant population spaceships and oscillators can be viewed as ensembles of chesspieces, where at every single clock tick, some of those chesspieces move according to the rules of chess (except several pieces can move at the same tick), as cells change their states according to the rules of Conway's Life.

Not counting the glider, are there other constant population spaceships in Conway's Life that can be viewed as ensembles of chesspieces moving according to the rules of chess?
Here are several examples of oscillators with this property. Each can be viewed as an ensemble of queens.

Code: Select all

x = 28, y = 8, rule = B3/S23
9bo$9bobo8bo4bo$o6bo11bobo2bobo$o11b2o5bobo2bobo$o5b2o10b2obo2bob2o$
12bo6bob4obo$8bobo8bobo2bobo$10bo9bo4bo!

[dvgrn]

Not counting the glider, are there other constant population spaceships in Conway's Life that can be viewed as ensembles of chesspieces moving according to the rules of chess?

Here are a few questions, mostly to check if I'm understanding the idea correctly.

1) An ensemble of queens will solve all of the examples, but the blinker could also be modeled by three bishops or three kings -- right? And the phoenix could be modeled either by bishops or by rooks, whereas the oscillator on the right could be modeled either by rooks or knights?

2) There are often going to be multiple solutions for a given chesspiece conversion problem. Is a solution with less powerful pieces preferable, or a solution where fewer pieces have to move? For example, a glider can be emulated by five rooks, where three rooks move on each tick. But it can also be emulated by five bishops, where only two bishops have to move on each tick. Should the solution with bishops be considered an improvement over a solution with rooks or queens?

3) Which rules of chess should be considered to apply? Especially, is each move considered independently of the other piece placements, or can one piece be blocked by the presence of other pieces (unless it's a knight)? If pieces' paths can be blocked, then if several pieces move at the same tick, is it allowable to define a move order within each tick, such that one piece might get out of the way to allow another piece to move to its target square?

4) Should ensembles of pieces all be of one type for a given problem, or is it allowable to have a mix of chess pieces?

5) Can fairy chess pieces be considered?

[confocaloid]

1) An ensemble of queens will solve all of the examples, but the blinker could also be modeled by three bishops or three kings -- right? And the phoenix could be modeled either by bishops or by rooks, whereas the oscillator on the right could be modeled either by rooks or knights?

Yes.

2) There are often going to be multiple solutions for a given chesspiece conversion problem. Is a solution with less powerful pieces preferable, or a solution where fewer pieces have to move? For example, a glider can be emulated by five rooks, where three rooks move on each tick. But it can also be emulated by five bishops, where only two bishops have to move on each tick. Should the solution with bishops be considered an improvement over a solution with rooks or queens?

In the case of the glider, exactly two pieces will move at every tick, and three remaining pieces will stay unmoved:

Code: Select all

x = 13, y = 4, rule = LifeHistory
.C9.DC$A.D7.AC$2AC7.D2A$.D!
#C [[ GRID VIEWONLY ]]

(edited to remove an incomplete solution)

In general, strictly less powerful ensembles are preferable; for example, if one solution can be transformed into another solution by replacing a queen with a rook, or replacing a queen with a bishop, then the resulting solution can be considered "more interesting" (since the possibility of replacement in the other direction is obvious). However, there may be two or more pairwise non-comparable solutions, neither of which beats another in this sense.

3) Which rules of chess should be considered to apply? Especially, is each move considered independently of the other piece placements, or can one piece be blocked by the presence of other pieces (unless it's a knight)? If pieces' paths can be blocked, then if several pieces move at the same tick, is it allowable to define a move order within each tick, such that one piece might get out of the way to allow another piece to move to its target square?

4) Should ensembles of pieces all be of one type for a given problem, or is it allowable to have a mix of chess pieces?

5) Can fairy chess pieces be considered?

A piece can only move into an empty square. All pieces that move at the same tick are considered to move simultaneously. A piece can block movement of another piece. Every piece in the ensemble can be "tracked" during evolution of the pattern, every piece stays the same and never changes into any other piece as it moves.

An ensemble can include different pieces.

I did not consider fairy chess pieces because otherwise there are too many possibilities, but that could be a separate problem/a different version of the question.

[confocaloid]

[...] For example, a glider can be emulated by five rooks, where three rooks move on each tick. But it can also be emulated by five bishops, where only two bishops have to move on each tick. [...]

In particular, neither of those two would be a solution. The "tetromino engine" must be made out of four pieces each of which can move diagonally, hence rooks will not work. The "glider tail" piece cannot be either a rook or a bishop, since it needs to alternate between orthogonal and diagonal movements.

[dvgrn]

In particular, neither of those two would be a solution. The "tetromino engine" must be made out of four pieces each of which can move diagonally, hence rooks will not work. The "glider tail" piece cannot be either a rook or a bishop, since it needs to alternate between orthogonal and diagonal movements.

Yup, your answer to the other question clarified that. There are ways to use rooks or bishops if one piece can move out of the way, and then another piece can move into the space vacated by the other piece (even if all pieces are moving simultaneously). But if a piece can only move to an empty square, neither rooks nor bishops will work.

[WhiteHawk]

We have no idea if we have all the 11-16 cell oscillators or not. The database is what's currently known and isn't exhaustive. It was also updated almost a decade ago, so Rob's p16 (21 cells) is missing.

List of oscillators with 3 to 16 cells

Bringing up a follow-up question based on some previous discussion over in Basic Questions before this thread existed:

What would it take to prove that Pentapole is the only possible 11-cell oscillator in B3/S23?

I know that it has been confirmed that we know all of the oscillators in life with fewer than 10 cells, and that it has not been proven that we know all the 11-cell oscillators out there. Proving Pentapole, the only 11-cell oscillator currently known, is truly the only one would prove that 12 cells is the minimum population for any oscillator with a period greater than 2.

[confocaloid]

A polyomino is strange iff both
(a) the polyomino evolves into a strict still life, oscillator or spaceship P,
(b) and there are no lower-population polyominoes evolving into P.

Let f(n) be the number of n-bit polyominoes that are "strange". Then (I think)

Code: Select all

#C f(3) = 2
#C f(4) = 3
#C f(5) = 2
#C f(6) = 5
#C f(7) = 4
#C f(8) = 6
#C f(9) = 6
#C f(10) = 3
#C f(11) = 13
#C f(12) = 7
x = 484, y = 367, rule = B3/S23
o39b2o$o39bo$o38$o39b2o38bo$o39bo39b2o$o39bo40bo$o37$3o37bo$o39b2o
$o40b2o38$2o38b2o38bo39b2o39bo$2o38bo39b2o38b3o37b2o$o39b2o38b2o
39bo39b2o$o40bo39bo79bo37$2o38b2o38b2o38bo$o39bo39bo39bo$2o38bo39b
3o37b2o$o39bo39bo40bo$o39b2o79b2o36$4o36bo39bo39bo39bo39bo$2o38bo
39b2o38b2o38bo2bo36b2o$o39b2o38b3o37b4o36b4o37bo$o39b2o40b2o39bo
38bo38b2o$41bo158b2o$41bo35$o39bo39bo39bo40bo39bo$o39bo39bo39b2o
38b2o38b2o$4o36b2o38b2o39b2o38b2o38bo$bobo37b3o37b3o38b2o37b3o37b
4o$3bo39bo39b2o38b2o37bo40bo$43bo35$o39bo39bo$o39b3o37b3o$o41b2o
38b4o$o39b3o39bo$o39bo41bo$o$o$o$o$o31$o39bo39bo39bo39bo39b2o38bo
39bo39bo39bo39bobobo35bo2b3o35bo$3o37bo39bo39bo39bo39bo2bo36b4o36b
o3bo35b2o38b4o36b7o33b4ob2o33b3o$3o37b2o38bo39bo39bo3bo35b4o36bo2b
o36b5o36b2o38bob2o41bo38bo34bob2o$ob2o36b2o38b5o35b2obo36b6o35bobo
39bo38bo37b4o40b2o115b3o$o40bo39bo2bo36b3o40bo36bo41bo37b2o40b2o
40bo115bo$41bo42bo37b2o119b2o$40b2o$40bo33$o39b2o38bo3bo35bo39bo
39bo40bo$o39bo3bo35bo3bo35bo3b2o34bo39b2o38b3o$2o38b5o35b5o35b5o
35b4o37b2o37bo$4o38bo39bo39bo40bo36b4o36b4o$3b2o36b2o38b2o38b2o40b
3o35bob2o36bo$3bo159bo77b2o$3bo159bo!

What can be said about the function f(n) for higher n? In particular, is f(n) = 0 for some n > 2? Is f(n) = 1 for some n?

edit: corrected f(n) and added several missing objects.
edit 2: added f(11) and f(12).
edit 3 (2025-01-02): related: viewtopic.php?f=2&t=336 "Polyomino glider predecessor?"

[confocaloid]

There is a 177-bit still life that can fit inside Karel's p177. I didn't check optimality; can anyone find a bigger still life that fits?

Code: Select all

x = 70, y = 70, rule = B3/S23
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$
obob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obobo
$2o66b2o2$2o66b2o$2o66b2o2$2o66b2o$2o66b2o2$2o66b2o$2o66b2o$27bo14bo$
2o23b2ob2o10b2ob2o23b2o$2o23b2ob2o10b2ob2o23b2o$25b2o2b2o8b2o2b2o$2o
24b2ob2o8b2ob2o24b2o$2o25bobo10bobo25b2o$28bo12bo$2o66b2o$2o66b2o2$2o
66b2o$2o66b2o$34b2o$2o11b3o15bo2bobo2bo14b3o11b2o$2o11b4o13bobobob4o2b
o10b4o11b2o$12bo3b2o10b3obob2o4b3o9b2o3bo$2o11b2o3bo8bo3b2o4bobo11bo3b
2o11b2o$2o11b5o8bo2bo4b4ob4o9b5o11b2o$15b2o9b9o3bo4bo9b2o$2o34b2o2b3ob
o23b2o$2o24b5ob4o2b3o2bo24b2o$25bo4bobo2bobo4bo$2o22bo2b2obobobo2bob2o
b4o22b2o$2o22b3obobobob4obobo3bo22b2o$28bobob2o5bobob2o$2o24b3obo4b5ob
obo24b2o$2o23bo3bob4o6bobo24b2o$15b2o9b2obobo3b7ob2o8b2o$2o11b5o9bobo
2b3o7bo9b5o11b2o$2o11b2o3bo8bob3o3b6obo8bo3b2o11b2o$12bo3b2o10bo3b3o5b
ob2o8b2o3bo$2o11b4o12b3o3b5o13b4o11b2o$2o11b3o15bo2bo2bo16b3o11b2o$34b
2o$2o66b2o$2o66b2o2$2o66b2o$2o66b2o$28bo12bo$2o25bobo10bobo25b2o$2o24b
2ob2o8b2ob2o24b2o$25b2o2b2o8b2o2b2o$2o23b2ob2o10b2ob2o23b2o$2o23b2ob2o
10b2ob2o23b2o$27bo14bo$2o66b2o$2o66b2o2$2o66b2o$2o66b2o2$2o66b2o$2o66b
2o2$2o66b2o$obob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2obobo$b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2o!
#C [[ THEME Catagolue GRID ]]

I used Logic Life Search with the following template (state 2 = unspecified, state 3 = specified alive, state 4 = specified dead):

Code: Select all

x = 32, y = 32, rule = LifeHistory
9D2C10D2C9D$10DC10DC10D$8DC6D2C6DC8D$7DCD4C2D2C2D4CDC7D$7DCDC2DC6DC2D
CDC7D$8DC6D2B6DC8D$11D10B11D$3D2C3D16B3D2C3D$2DC2DCD18BDC2DC2D$C2D2C
2D18B2D2C2DC$2CDC3D18B3DCD2C$3DC2D20B2DC3D$3D2CD20BD2C3D$6D20B6D$6D
20B6D$2D2CD22BD2C2D$2D2CD22BD2C2D$6D20B6D$6D20B6D$3D2CD20BD2C3D$3DC2D
20B2DC3D$2CDC3D18B3DCD2C$C2D2C2D18B2D2C2DC$2DC2DCD18BDC2DC2D$3D2C3D
16B3D2C3D$11D10B11D$8DC6D2B6DC8D$7DCDC2DC6DC2DCDC7D$7DCD4C2D2C2D4CDC
7D$8DC6D2C6DC8D$10DC10DC10D$9D2C10D2C9D!
#C [[ GRID ]]

0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 * * 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 * * * * * * * * * * 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 1 0 0 0 * * * * * * * * * * * * * * * * 0 0 0 1 1 0 0 0
0 0 1 0 0 1 0 * * * * * * * * * * * * * * * * * * 0 1 0 0 1 0 0
1 0 0 1 1 0 0 * * * * * * * * * * * * * * * * * * 0 0 1 1 0 0 1
1 1 0 1 0 0 0 * * * * * * * * * * * * * * * * * * 0 0 0 1 0 1 1
0 0 0 1 0 0 * * * * * * * * * * * * * * * * * * * * 0 0 1 0 0 0
0 0 0 1 1 0 * * * * * * * * * * * * * * * * * * * * 0 1 1 0 0 0
0 0 0 0 0 0 * * * * * * * * * * * * * * * * * * * * 0 0 0 0 0 0
0 0 0 0 0 0 * * * * * * * * * * * * * * * * * * * * 0 0 0 0 0 0
0 0 1 1 0 * * * * * * * * * * * * * * * * * * * * * * 0 1 1 0 0
0 0 1 1 0 * * * * * * * * * * * * * * * * * * * * * * 0 1 1 0 0
0 0 0 0 0 0 * * * * * * * * * * * * * * * * * * * * 0 0 0 0 0 0
0 0 0 0 0 0 * * * * * * * * * * * * * * * * * * * * 0 0 0 0 0 0
0 0 0 1 1 0 * * * * * * * * * * * * * * * * * * * * 0 1 1 0 0 0
0 0 0 1 0 0 * * * * * * * * * * * * * * * * * * * * 0 0 1 0 0 0
1 1 0 1 0 0 0 * * * * * * * * * * * * * * * * * * 0 0 0 1 0 1 1
1 0 0 1 1 0 0 * * * * * * * * * * * * * * * * * * 0 0 1 1 0 0 1
0 0 1 0 0 1 0 * * * * * * * * * * * * * * * * * * 0 1 0 0 1 0 0
0 0 0 1 1 0 0 0 * * * * * * * * * * * * * * * * 0 0 0 1 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 * * * * * * * * * * 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 * * 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0

A <=64-cell still life can fit inside Karel's p28. Here is one (symmetric!) example:

Code: Select all

x = 36, y = 36, rule = B3/S23
10b2o12b2o$10b2o12b2o5$12b2o8b2o$11bo2bo6bo2bo$11bo12bo$11bo12bo$2o10b
o10bo10b2o$2o5b3o16b3o5b2o$6bo3bo5bo2bo5bo3bo$6bo7b8o7bo$7bo5bo8bo5bo$
13bob6obo$12b2obo4bob2o$13bobob2obobo$13bobob2obobo$12b2obo4bob2o$13bo
b6obo$7bo5bo8bo5bo$6bo7b8o7bo$6bo3bo5bo2bo5bo3bo$2o5b3o16b3o5b2o$2o10b
o10bo10b2o$11bo12bo$11bo12bo$11bo2bo6bo2bo$12b2o8b2o5$10b2o12b2o$10b2o
12b2o!

I bet this can be synthesized.

EDIT: I'm looking for the biggest still Life that fits in Karel's p177, but that seems to be a rather bad idea considering how large the hole is (368 cells). If someone can recommend a better way to do this than throwing it into LLS I'm all ears

[tommyaweosme]

here is my "maximal result" as well as around 8k of my rlifesrc results

Code: Select all

x = 32, y = 32, rule = B3/S23
.........oo..........oo.........$
..........o..........o..........$
........o......oo......o........$
.......o.oooo..oo..oooo.o.......$
.......o.o..o......o..o.o.......$
........o......oo......o........$
..............o.o...o...........$
...oo.....oo.o.o...o.o.....oo...$
..o..o.oo..o.o.o.o..o.o...o..o..$
o..oo...o.o..o.o.oo.o.o....oo..o$
oo.o....o.oooo.o.o..o.oo....o.oo$
...o..oo.o....o.o..o.o..o...o...$
...oo..o.o..oo..o.oo..o..o.oo...$
.......o.oo..o.o.o..o.ooo.......$
......oo..o.o..o.o.oo...........$
..oo.o..o.o.oooo.oo..o.oooo.oo..$
..oo.oooo..o....o...oo.o..o.oo..$
.........o.o.oo.o....o..oo......$
.......ooo.oo.o.oo.o..o.o.......$
...oo.o...o...o..o.oo.o.o..oo...$
...o...oo.o...oo.o..o.o.oo..o...$
oo.o....o.oo...o.oo.o..o....o.oo$
o..oo..o..o..o....o.oo.o...oo..o$
..o..o..oo..ooo...o..o.oo.o..o..$
...oo..........o...oo......oo...$
..............oo................$
........o..............o........$
.......o.o..o......o..o.o.......$
.......o.oooo..oo..oooo.o.......$
........o......oo......o........$
..........o..........o..........$
.........oo..........oo.........!

downloads:
SIZE WARNING (9 mb)!!!

12-26-results1.txt

(8.83 MiB) Downloaded 452 times