ConwayLife.com

Posted: **January 29th, 2022, 9:11 pm**

Book wrote: January 29th, 2022, 9:09 pm Is there a technical definition of a pattern "motif" or is this just the common dictionary def? (Used in several articles in the wiki, sometimes as a red link.)

Looks like a dictionary definition to me.

Posted: **January 29th, 2022, 9:18 pm**

Book wrote: January 29th, 2022, 9:09 pm Is there a technical definition of a pattern "motif" or is this just the common dictionary def? (Used in several articles in the wiki, sometimes as a red link.)

All I can say is, "motif" is a term used pretty much exclusively by people who understand more than I do about glider synthesis -- which is to say, people who can recognize various weird rare structural motifs on sight, and therefore need a name for them.

So I won't attempt an official definition, but yes, I think it's more or less straight out of the dictionary -- a commonality between multiple objects, that in the context of glider synthesis hopefully means there's a common method of synthesizing those multiple objects.

EDIT: It's a relatively new term in a Life context, I think; it shows up only once in email archives from 1992 through 2009. It got used a lot in the N-bit still life synthesis projects -- here's a representative sample, and an attempt at a simple definition.

Posted: **January 29th, 2022, 9:27 pm**

dvgrn wrote: January 29th, 2022, 9:18 pm
Book wrote: January 29th, 2022, 9:09 pm Is there a technical definition of a pattern "motif" or is this just the common dictionary def? (Used in several articles in the wiki, sometimes as a red link.)
All I can say is, "motif" is a term used pretty much exclusively by people who understand more than I do about glider synthesis -- which is to say, people who can recognize various weird rare structural motifs on sight, and therefore need a name for them.

So I won't attempt an official definition, but yes, I think it's more or less straight out of the dictionary -- a commonality between multiple objects, that in the context of glider synthesis hopefully means there's a common method of synthesizing those multiple objects.

EDIT: It's a relatively new term in a Life context, I think; it shows up only once in email archives from 1992 through 2009. It got used a lot in the N-bit still life synthesis projects -- here's a representative sample, and an attempt at a simple definition.

Thanks. That gives me an angle of attack...

Posted: **February 3rd, 2022, 5:25 pm**

1. can you point me to a post that describes the Gemini gun?
2. can you point me to a post that describes Chapman-Greene construction arms?

Posted: **February 3rd, 2022, 11:12 pm**

Book wrote: February 3rd, 2022, 5:25 pm 1. can you point me to a post that describes the Gemini gun?

The Gemini gun is easy -- at least, it's easy to find everything that's ever been written about it. It was posted here, and . (Post #3036, wow -- those were early days on the forums). The comments in the Gemini gun patterns say, for example,

#C Period 74820116+8N Geminoid spaceship gun, based on
#C Andrew Wade's Gemini construction from 18 May 2010.
#C
#C This pattern builds a new (5120,1024)c/33785378 spaceship
#C every 74,820,116 generations. This the minimum period
#C for which all higher periods with mod8=4 will also work,
#C unless more changes are made to the construction recipe.
#C
#C The still lifes making up the replicator units in the resulting
#C Geminoid spaceships are identical to the ones in the original
#C Gemini, but the recipe constructing them is slightly different:
#C the destructor elbow block is built in an alternate way, which
#C makes it somewhat easier to repeat the construction.
#C
#C The period can be increased by 8N ticks by moving the north
#C and west reflector columns to the northwest by N cells.
#C
#C Some slightly lower periods are also safe, but destruction
#C gliders from previous spaceships will cross the paths of
#C the first construction gliders for each new spaceship.
#C Dave Greene, 21 July 2010.

The trickiest parts of the design process were

A) creating this structure

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x = 42, y = 57, rule = B3/S23
40b2o$39bobo$39bo$38b2o5$31b2o$31b2o3$30bo$29bobo$30bo$27b3o$27bo10$
18b2o$18b2o3$17bo$16bobo$17bo$14b3o$14bo6$7b2o$3bo3b2o$b3o$o$2o4bo$5bo
bo$6bo$3b3o$3bo2$5bob2o$3b3ob2o$2bo$3b3ob2o$5bobo$5bobo$6bo!

at (3380,-740) in the gemini-gun-p74820116.mc pattern linked in the above post. This is a tricky eater that safely absorbs each new Gemini's attempt to shoot down the (nonexistent) previous copy of its own circuitry, so that it doesn't destroy the gun that built it.

B) using mscibing's existing code, almost completely unmodified, to rebuild the Gemini Gemini's recipe to build a few of the initial construction-arm blocks in a different way. The original Gemini's method of crashing gliders into each other to form the blocks wasn't necessary, and it made it much harder to design a passive suppression mechanism for the destruction arms of newly constructed Geminis.

If more questions come up about the Gemini gun, I'd be happy to answer them here or in a dedicated thread. It was a fun project, much less difficult than some of the later Demonoids and so on -- just because mscibing had already done all the hard work.

[Did you know ...] that to display the smallest known gun pattern for a Gemini spaceship at 1 cell = 1 pixel, on a standard-density video monitor, a screen over one mile square would be needed?

Book wrote: February 3rd, 2022, 5:25 pm 2. can you point me to a post that describes Chapman-Greene construction arms?

Those are a little harder. Not sure that old prototype has even been dissected and explained thoroughly, since it was really intended to be completely rebuilt and optimized before anyone used it. And then it ended up getting re-used in Gemini (three times) and in Adam P. Goucher's Spartan Universal Computer-Constructor and Paul Tooke's pianola breeders, without anybody ever bothering to do the hard optimization work. I'll find some more links tomorrow.

Posted: **February 4th, 2022, 10:51 am**

dvgrn wrote: February 3rd, 2022, 11:12 pm ... using mscibing's existing code, almost completely unmodified, to rebuild the Gemini Gemini's recipe to build a few of the initial construction-arm blocks in a different way. The original Gemini's method of crashing gliders into each other to form the blocks wasn't necessary, and it made it much harder to design a passive suppression mechanism for the destruction arms of newly constructed Geminis.

Minor memory misfire
The elbow blocks for the Gemini spaceship's two construction arms are still built in a weird way by the Gemini-gun version of the Gemini recipe. You can see the first one happening at (2595, -1630) @ T = 1874400: the right-side constructor arm has built a one-time reflector made of two blocks, then triggered it to produce a 180-degree collision far away from the intersection point of the two construction arms. Something similar happens right after that for the other new construction-arm elbow: run to T = 1914900, find the about-to-collide gliders, then watch from there to see the whole sequence.

I don't think there's any particularly good reason to do things this way; this is mostly just grandstanding to show off an alternate construction method. Maybe there was a reason for it in an early Gemini design stage, but in the final version it would have been just as easy to have the construction arms build those blocks just like any of the other blocks.

The Gemini gun's version of the Gemini builds the destruction elbow block (only) in the standard way with two synchronized 90-degree gliders.
That's the "changed the recipe a little" mentioned here.

Destruction arm elbow
That construction method really caused trouble for the part of the Gemini gun that suppresses the destruction-arm elbow, the first time each Gemini spaceship appears. This is because some of the gliders that construct the two-block one-time turner that eventually make that elbow, pass right through the place where the elbow will be built (of course) -- which makes it difficult to put in passive suppression to keep that destruction elbow from being built when it isn't needed (again, only for the first cycle of Gemini construction on each side). You can see the weird construction method in the original Gemini, at T=7836000 in the northwest corner.

The only change I made to the Gemini was to recompile the recipe so that that one block was built by synchronized gliders coming straight from the construction arms. That enables the passive design I mentioned in the last post -- specifically, it suppresses one of the two synchronized elbow-block-making gliders, and lets the other one through and sends it on a convoluted path that ultimately rebuilds four construction-elbow blocks in the gun.

The idea is that when each Gemini is completed and flies away, it takes its elbow blocks with it (or rather it cleans them up when they aren't needed any more). But the gun needs new elbow blocks to start the construction of the next Gemini -- so the passive mechanism is arranged to produce them at the right times, only when the new Gemini is in its starting location. No separate timing guns are needed to know when the blocks should be built. It all just happens automatically, which allows the gun pattern to be trivially adjusted to build different period Gemini guns, just by adjusting the spacing between the pieces.

Not To Scale
Here's what happens at T = 6923540 in the Gemini gun. Ordinarily two gliders would collide to build the destruction-arm block, but this first time the tricky eater constellation gets in the way, stops one of the two gliders, and sends the other one northeastward on a very long journey through a bunch of Silver reflectors and other Herschel-based signal splitters and reflectors including a Herschel transceiver.

-- Really just one of the eaters in the tricky eater constellation is used at this point. The rest of them are pointed in the opposite direction, and they suppress all the instructions that are later sent to the destruction arm. Those instructions come in on multiple lanes, because this was all built before the time of Snarks and syringes, let alone single-channel construction recipes.

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38.28D38.22D46.24D32.31D34.20D70.22D109.21D68.21D38.26D49.10D33.21D
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28D8.12D21.27D21.37D34.20D71.28D8.12D82.21D68.21D40.32D28.23D33.21D
67.31D28.23D180.34D$8963.85D42.48D21.29D16.40D34.20D71.48D82.21D68.
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3A$12567.3A11.A$12569.A$12548.2A$12548.2A!
#C [[ MAXGRIDSIZE 14 STEP 64 ]]

Posted: **February 4th, 2022, 1:15 pm**

dvgrn wrote: February 3rd, 2022, 11:12 pmNot sure that old prototype has even been dissected and explained thoroughly, since it was really intended to be completely rebuilt and optimized before anyone used it. And then it ended up getting re-used in Gemini (three times) and in the Spartan Universal Computer-Constructor, without anybody ever bothering to do the hard optimization work. I'll find some more links tomorrow.

Here's something I wrote about that prototype construction arm, a while back, for the Life textbook. Some pieces of it made it into the textbook, but this has a little more of the "prototype" part of the story.

Side note: the one-arm universal constructor ended up getting called a "Chapman-Greene construction arm", because we were working together on developing the underlying ideas at the time. However, it's more appropriate to label the actual prototype pattern as "Paul Chapman's prototype universal constructor". What happened was that I contributed a key working "ladder" mechanism, basically to produce different output gliders for "0", "10", "110", "1110", and "11110" input data -- and literally nothing else that I can recall. Paul assembled the entire rest of the prototype pattern, including the data tape and the shotguns for the different elbow operations, in a marathon working session over the next couple of days.

(You can tell it wasn't me that did the assembly, because I would have painstakingly optimized all of those shotguns before allowing them out the door -- theoretically producing a prototype with about half the number of still lifes, in the end... but in practice probably never getting the project into an operating state at all.)

dvgrn wrote:Conway and Gosper had p30 technology in 1970, so the first logic and construction circuitry was p30. With the primitive parts available -- block, eater, pentadecathlon, Gosper gun, NOT, and and OR gates, glider stream thinners and duplicators, and side tracking guns -- it was theoretically possible to assemble a working replicator, but the resulting pattern would have been far too large to simulate at all, let alone to test in practice through a full replication cycle.

For mathematically-minded Life enthusiasts, it was good enough to complete a proof (or two proofs, Conway's and Gosper's) that Life could support self-replicating patterns. But engineering-minded types felt kind of cheated by this: a theoretical replicator that could never be seen in action was the next worst thing to no replicator at all. To produce a proof by example, a specific Life pattern that could actually self-replicate, quite a bit of new technology would have to be invented.

Logic circuitry was already fairly compact in the 1970s, but it was limited to storing binary information, encoding a 0 or a 1 as the absence or presence of a glider every 30 ticks or 46 ticks. And universal computer-constructors need to be able to build as well as calculate -- but the side-tracking-gun mechanism was hugely inefficient at producing salvos of arbitrarily distant gliders with specific timings and directions. Something better was needed.

The stable Herschel circuitry invented by David Buckingham and extended by Paul Callahan in 1996-98 was, in theory, a huge step forward. It completely removed the painful limitation The "Spartan" subset of Herschel conduits, made out of small well-separated still lifes, was easily versatile enough to build arbitrarily complex computer circuitry.

Progress was very slow on the universal construction front, though. It wasn't until 2004 that Paul Chapman built his prototype stable universal constructor, implementing the key idea of a programmable construction arm: different signals would prompt the U.C. to pull the construction arm's elbow closer, push it farther away, or shoot a glider of either color sideways from the elbow's current position. The choice of operations -- PUSH, PULL, the two FIRE recipes, or a SHUT DOWN signal -- was made by reading a static tape where 1, 2, 3, 4, or 5 "1"s (in the form of boats) were stored in unary, separated by "0"s (blocks). That's an average of three or four bits of static storage to encode two bits' worth of information -- very inefficient, but it was only intended as an initial prototype.

Unfortunately there wasn't much further development of the idea until 2009, when Adam P. Goucher created a very large and complex "universal computer-constructor", where the "constructor" part was Chapman's unaltered prototype construction arm. Data storage for this computer was in proper binary instead of unary, but the general idea remained unchanged: construction data had to be stored on a static tape, and read one bit at a time. The result was a single slow salvo, with no control over the timing of the individual gliders being sent, only their order.

The significance of that limitation is that there's really no reasonable way to use data stored on a classical static binary tape to create recipes that involve pairs of colliding gliders. You'd have to store delay information for each of the two gliders, or at least one relative delay number -- as well as the INCs and DECs that produce the lane numbers for each of two guns.

That's probably eight or ten bits on the tape at a minimum, even with binary encoding, and the stable circuitry required to decode a binary number and turn it into a specific relative delay between two gliders would have had to be absolutely enormous.

Things somewhat like that have actually been done, e.g., in the original p1 megacell. That circuitry only had to decode a binary value and run a slide gun for an appropriate length of time, like k * 2^N where k was the decoded value. That already required a huge sprawling mass of circuitry, and producing exactly timed gliders in increments of a single tick, say -256..255 or some such, would have been a much larger project than that.

So in 2009 it seemed pretty obvious that unidirectional slow salvos were the way to go, because they could be encoded on a static tape relatively efficiently, and could be read from the tape by a manageable amount of stable circuitry, as shown by Paul Chapman's prototype.

The sudden appearance of the Gemini has been described before, so maybe some existing text could be reworked -- for example, in LifeNews, Adam described how it differed from the "Standard Architecture".

The Gemini instantly showed that the Standard Architecture was just plain silly. Obviously (with hindsight) if you want to build some kind of memory storage system for a bunch of spacings between gliders, you just store a bunch of moving gliders at the spacing you want -- no need to bother encoding anything at all!

That one insight allowed a complete oblique self-constructing spaceship to be created, even using extraordinarily sub-optimal components. The prototype universal constructor was a first proof of concept, not really intended to be used anywhere since it could easily be made so much smaller. But Andrew Wade wasn't any kind of stable-circuitry expert, so he just used what was available: the Gemini spaceship included not just one, but three complete copies of the prototype construction arm, almost completely unmodified. All he did was throw away the hopelessly inefficient static binary storage system and substitute something better. Gemini's storage mechanism was so efficient that it was _still_ possible to create a full self-construction recipe for all that circuitry.

Side note: immediately after Paul's prototype was posted in May 2004, I found I didn't like the static tape very much -- so I threw it away and substituted a memory loop full of recirculating gliders. Both Paul's pattern and mine are in Golly's Signal-Circuitry folder. You'd think storing data as a glider stream would be a step forward, since that's exactly what the Gemini did -- but unfortunately I totally missed the point. My memory loop just held a simulation of the output of Paul's static tape, which then ran through the same complex and inefficient interpretation circuitry. I completely failed to see the opportunity to code the required timings directly... so that had to wait for Andrew Wade to come along a half-decade later.

Posted: **February 4th, 2022, 2:21 pm**

What is the best place to run scripts?

Posted: **February 8th, 2022, 4:17 pm**

Due to the fact that they effectively enclose a p4 agar, would it make sense to call higher-order overweight spaceship flotillae grayships?

Code: Select all

x = 30, y = 83, rule = B3/S23
13bo$12bo$12bo3bo$12b4o4$10b7o$10bo6bo$10bo$11bo2$9bo$8bo$8bo11bo$8b
12o4$6b16o$6bo15bo$6bo$7bo2$5bo$4bo$4bo20bo$4b21o4$2b25o$2bo24bo$2bo$
3bo2$bo$o$o28bo$29o4$29o$o28bo$o$bo2$3bo$2bo$2bo24bo$2b25o4$4b21o$4bo
20bo$4bo$5bo2$7bo$6bo$6bo15bo$6b16o4$8b12o$8bo11bo$8bo$9bo2$11bo$10bo$
10bo6bo$10b7o4$12b4o$12bo3bo$12bo$13bo!

Posted: **February 9th, 2022, 6:14 am**

muzik wrote: February 8th, 2022, 4:17 pm Due to the fact that they effectively enclose a p4 agar, would it make sense to call higher-order overweight spaceship flotillae grayships?
Code: Select all
x = 30, y = 83, rule = B3/S23
13bo$12bo$12bo3bo$12b4o4$10b7o$10bo6bo$10bo$11bo2$9bo$8bo$8bo11bo$8b
12o4$6b16o$6bo15bo$6bo$7bo2$5bo$4bo$4bo20bo$4b21o4$2b25o$2bo24bo$2bo$
3bo2$bo$o$o28bo$29o4$29o$o28bo$o$bo2$3bo$2bo$2bo24bo$2b25o4$4b21o$4bo
20bo$4bo$5bo2$7bo$6bo$6bo15bo$6b16o4$8b12o$8bo11bo$8bo$9bo2$11bo$10bo$
10bo6bo$10b7o4$12b4o$12bo3bo$12bo$13bo!

LifeWiki wrote: A greyship is a spaceship which contains a region of density 1/2 (usually the zebra stripes agar) that can be extended to an arbitrary size both horizontally and vertically.

The p4 agar does not have constant density 1/2, so it does not qualify as a greyship.

Posted: **February 9th, 2022, 8:37 pm**

Is there a Golly script(or something else) that can put multi-staged glider synthesis together into one big single-staged one?

Posted: **February 9th, 2022, 9:37 pm**

Random life lover wrote: February 9th, 2022, 8:37 pm Is there a Golly script(or something else) that can put multi-staged glider synthesis together into one big single-staged one?

Yes. Sort of. It needs a rewrite. But it works most of the time, if you line things up very carefully. Maybe use the Offset Standardi[s|z]er.

Posted: **February 10th, 2022, 2:33 am**

We start with the empty SL, then at each step we modify some n * n region of the plane. We also need to ensure that after each step it remains a SL.

Then is there some n that we can reach any finite SL? What if we restrict ourselves to strict SLs?

For example, with n = 2 we can construct blocks, beehives, loaves and ponds, as well as tubs(boats, ships) of arbitrary length.

Code: Select all

x = 125, y = 58, rule = LifeHistory
113.AC$112.A.A$111.A.A$110.A.A$110.2A6$113.D$112.3D$111.D.D.D$113.D$
113.D$113.D5$113.A$112.A.A$111.A.A$110.A.A$110.CA4$113.D$112.3D$111.D
.D.D$113.D$113.D$113.D5$11.D22.D22.D22.D20.D11.C$12.D22.D22.D22.D9.C
10.D9.A.C$2C6.6D8.2A7.6D8.DA7.6D9.A7.6D7.A.C5.6D7.A.A6.D.D.D$2C10.D9.
ADC10.D9.A.A10.D9.A.A10.D7.A.A10.D7.A.A$11.D11.C10.D11.A10.D11.A10.D
9.A10.D9.A3$23.D$23.D$23.D$21.D.D.D$22.3D$23.D3$34.D22.D$22.2A11.D10.
2A10.D10.2A$21.CD.A6.6D8.A2.A5.6D8.A2.A$22.CA11.D10.ADC9.D9.CD.A$34.D
12.C9.D11.CA!

Posted: **February 10th, 2022, 8:52 am**

pzq_alex wrote: February 10th, 2022, 2:33 am We start with the empty SL, then at each step we modify some n * n region of the plane. We also need to ensure that after each step it remains a SL.

Then is there some n that we can reach any finite SL? What if we restrict ourselves to strict SLs?

No, for any finite choice of n there's a still life that can't be constructed by progressively modifying n*n regions (unless I'm thinking about it wrong).

This is a corollary of the counterexample to the still life finitization conjecture that Extrementhusiast found in 2019.

If the target still life includes a patch of Extrementhusiast's agar with a width that's some multiple of n -- let's say 10n to be safe, but there's some much smaller threshold -- then the only intermediate still-life stopping points will be larger and larger stabilized patches of the agar. If you can't fit into n*n all the necessary changes for the last incremental step, along one edge of the stabilized agar, then you can't incrementally step your way up to that size of target still life.

EDIT re: next response: I don't think the question relates to glider synthesis; it's just an abstract question about whether there are chains of still lifes leading to every possible still life starting from empty space, where the difference between successive still lifes in the chain always fits inside an n*n box for some n. The Life evolution rule isn't relevant at all, except as far as ensuring that the still lifes are still lifes. See pzq_alex's example pattern for n=2.

Posted: **February 10th, 2022, 10:42 am**

pzq_alex wrote: February 10th, 2022, 2:33 amWe start with the empty SL, then at each step we modify some n * n region of the plane. We also need to ensure that after each step it remains a SL.

Then is there some n that we can reach any finite SL? What if we restrict ourselves to strict SLs?

It was recently shown that a certain sufficiently large section of chicken wire has no predecessors other than itself, so any still-life that contains a chunk of that shape cannot be synthesized from gliders in any way, even if you allow n to be infinite (and strictness is not an issue here).

Posted: **February 10th, 2022, 10:43 am**

mniemiec wrote: February 10th, 2022, 10:42 am
pzq_alex wrote: February 10th, 2022, 2:33 amWe start with the empty SL, then at each step we modify some n * n region of the plane. We also need to ensure that after each step it remains a SL.

Then is there some n that we can reach any finite SL? What if we restrict ourselves to strict SLs?
It was recently shown that a certain sufficiently large section of chicken wire has no predecessors other than itself, so any still-life that contains a chunk of that shape cannot be synthesized from gliders in any way, even if you allow n to be infinite (and strictness is not an issue here).

The question is about placing cells, not evolving from a predecessor.

Posted: **February 10th, 2022, 10:50 am**

hotdogPi wrote: February 10th, 2022, 10:43 am The question is about placing cells, not evolving from a predecessor.

No possible way of placing cells to convert still-life X into still-life Y can work if still-life Y has no other predecessors than Y - other than placing all cells of Y simultaneously into an empty field.

Posted: **February 10th, 2022, 11:15 am**

mniemiec wrote: February 10th, 2022, 10:50 am
hotdogPi wrote: February 10th, 2022, 10:43 am The question is about placing cells, not evolving from a predecessor.
No possible way of placing cells to convert still-life X into still-life Y can work if still-life Y has no other predecessors than Y - other than placing all cells of Y simultaneously into an empty field.

We don't currently have any examples of still lifes that have no other predecessors than themselves, though -- we just have chunks of agar compatible with completion into still lifes with that property.

Somewhat contrary to the above statement, the recent Unique Father solution can actually be built incrementally with pzq_alex's method, for some n. You could build a stabilized version of the left half of the 26x32 still life with n=26, for example, then complete it with another step:

Code: Select all

x = 132, y = 26, rule = LifeHistory
26B20.11B2ABA11B30.2A.A2B2ABA2B2ABA14B$26B20.11BAB2A3B2A6B30.A.2A2BAB
2A2BAB2A3B2A9B$26B20.9B2A4B2A2BA6B28.2A4.2A4B2A4B2A2BA9B$26B20.4B2ABA
2BAB2A2BABA7B23.2A.A2.A.2A.BAB2A2BAB2A2BABA10B$26B20.4BAB2ABA2B2ABA2B
2A6B23.A.2A.A2.2A.A2B2ABA2B2ABA2B2A9B$26B20.9B2A4B2A9B28.2A4.2A4B2A4B
2A12B$26B20.5B2ABA2B2ABA2B2ABA5B24.2A.A2.2A.A2B2ABA2B2ABA2B2ABA8B$26B
20.5BAB2A2BAB2A2BAB2A5B24.A.2A2.A.2A2BAB2A2BAB2A2BAB2A8B$26B20.3B2A4B
2A4B2A4B2A3B22.2A4.2A4.2A4B2A4B2A4B2A6B$26B20.4BAB2A2BAB2A2BAB2A2BA3B
23.A.2A2.A.2A.BAB2A2BAB2A2BAB2A2BA6B$26B9.D10.3BA2B2ABA2B2ABA2B2ABA4B
11.D10.A2.2A.A2.2A.A2B2ABA2B2ABA2B2ABA7B$26B10.D9.3B2A4B2A4B2A4B2A3B
12.D9.2A4.2A4.2A4B2A4B2A4B2A6B$26B11.D8.5B2ABA2B2ABA2B2ABA5B13.D10.2A
.A2.2A.A2B2ABA2B2ABA2B2ABA8B$26B5.8D7.5BAB2A2BAB2A2BAB2A5B7.8D9.A.2A
2.A.2A2BAB2A2BAB2A2BAB2A8B$26B11.D8.3B2A4B2A4B2A4B2A3B13.D8.2A4.2A4.
2A4B2A4B2A4B2A6B$26B10.D9.4BAB2A2BAB2A2BAB2A2BA3B12.D10.A.2A2.A.2A.BA
B2A2BAB2A2BAB2A2BA6B$26B9.D10.3BA2B2ABA2B2ABA2B2ABA4B11.D10.A2.2A.A2.
2A.A2B2ABA2B2ABA2B2ABA7B$26B20.3B2A4B2A4B2A4B2A3B22.2A4.2A4.2A4B2A4B
2A4B2A6B$26B20.5B2ABA2B2ABA2B2ABA5B24.2A.A2.2A.A2B2ABA2B2ABA2B2ABA8B$
26B20.5BAB2A2BAB2A2BAB2A5B24.A.2A2.A.2A2BAB2A2BAB2A2BAB2A8B$26B20.9B
2A4B2A9B28.2A4.2A4B2A4B2A12B$26B20.6B2A2BAB2A2BAB2ABA4B25.2A2.A.2A.BA
B2A2BAB2A2BAB2ABA7B$26B20.7BABA2B2ABA2BAB2A4B26.A.A2.2A.A2B2ABA2B2ABA
2BAB2A7B$26B20.6BA2B2A4B2A9B25.A2.2A4.2A4B2A4B2A12B$26B20.6B2A3B2ABA
11B25.2A3.2A.A2B2ABA2B2ABA14B$26B20.11BAB2A11B30.A.2A2BAB2A2BAB2A14B!

-- I was thinking that there wasn't a way to stabilize L-shaped patches of this agar, so that it wouldn't be possible to have a value of n for pzq_alex's question smaller than the width or height of the agar patch -- but it looks like that's not true. n=12 might be enough to build arbitrarily large patches, for example:

Code: Select all

x = 32, y = 26, rule = LifeHistory
8.2A.A2.2A.A2.2A.A$8.A.2A2.A.2A2.A.2A3.2A$6.2A4.2A4.2A4.2A2.A$.2A.A2.
A.2A2.A.2A2.A.2A2.A.A$.A.2A.A2.2A.A2.2A.A2.2A.A2.2A$6.2A4.2A4.2A4.2A$
2.2A.A2.2A.A2.2A.A2.2A.A2.2A.A$2.A.2A2.A.2A2.A.2A2.A.2A2.A.2A$2A4.2A
4.2A4.2A4.2A4.2A$.A.2A2.A.2A2.A.2A2.A.2A2.A.2A2.A$A2.2A.A2.2A.A2.2A.A
2.2A.A2.2A.A$2A4.2A4.2A4.2A4.2A4.2A$2.2A.A2.2A.A2.2A.A2.2A.A2.2A.A$2.
A.2A2.A.2A2.A.2A2.A.2A2.A.2A$2A4.2A4.2A4.2A12B$.A.2A2.A.2A2.A.2A2.AB
9A2B$A2.2A.A2.2A.A2.2A.A.BA7BA2B$2A4.2A4.2A4.2ABAB4ABA3B$2.2A.A2.2A.A
2.2A.A2.BABA2BAB2A2B$2.A.2A2.A.2A2.A.2A2.BA10B$6.2A4.2A4.2ABA10B$3.2A
2.A.2A2.A.2A2.ABAB2A7B$4.A.A2.2A.A2.2A.A.BAB2A7B$3.A2.2A4.2A4.2ABA10B
$3.2A3.2A.A2.2A.A2.BA10B$8.A.2A2.A.2A2.B2A9B!

Not sure what the actual lower bound would be here. But the fact that we're not dealing with predecessors of these still lifes at all, really makes a big difference to the analysis.

Posted: **February 10th, 2022, 2:26 pm**

I'm looking for a concise, precise definition of "capped". As it applies to guns and such.

Posted: **February 11th, 2022, 8:03 am**

Book wrote: February 10th, 2022, 2:26 pm I'm looking for a concise, precise definition of "capped". As it applies to guns and such.

A capped gun is a finite pattern consisting of a gun together with a collection of eaters that eat the gun's output spaceship streams. This got me wondering what the equivalent of a cap gun would be. Maybe something like the following pattern by dani?

Code: Select all

x = 53, y = 39, rule = B3/S23
13bo$13b3o$16bo18b2o$15b2o18bo$33bobo$18bo14b2o4bo$17b3o10b2o5b3o$16bo
2b2o8bobo4bo$16b2o3bo9bo4b2o$21b2o$21b3o9b3o$21b2o9bo2bo$16b2o3bo10b2o
2bo$8b2o6bo2b2o9b2o3b2o$8b2o7b3o9bo2bo$18bo10bo2bo$29bo2bo$30b2o3b2o$
6b2o24b2o2bo6b2o$6b2o24bo2bo7b2o$33b3o$19b2o$11bo6bobo$8b3obob2o3bo25b
2o$2o6b2o4bo30b2o$2o8bo3bo$5b2o4bobo5b2o11b2o$5b2o12b2o11bobo6b3o$5bob
o25bo3b3ob2obo$4bo3bo29bo2bo2bo6b2o$5bo32b2o2b2o7b2o$8bo23b2o12b2o$5b
3o24b2o11bo2bo$5bo39bob2o$46b3o2$45bobo$45b3o$47bo!

Posted: **February 11th, 2022, 3:21 pm**

on the "Elbow operation" wiki page, it says:

An elbow operation is a recipe, usually a salvo of gliders traveling on one or more construction lanes, that collides with an elbow constellation and performs one of the standard transformations on it: push, pull, or fire for simple construction arms, along with possible construct, duplicate-elbow, or delete-elbow ops for more complicated systems.

"construct", "duplicate-elbow" and "delete-elbow" are red links

I'd like to define them. Help please.

Posted: **February 11th, 2022, 4:32 pm**

Book wrote: February 11th, 2022, 3:21 pm on the "Elbow operation" wiki page, it says:

An elbow operation is a recipe, usually a salvo of gliders traveling on one or more construction lanes, that collides with an elbow constellation and performs one of the standard transformations on it: push, pull, or fire for simple construction arms, along with possible construct, duplicate-elbow, or delete-elbow ops for more complicated systems.

"construct", "duplicate-elbow" and "delete-elbow" are red links

I'd like to define them. Help please.

Section 11.2.3 of the Life textbook describes a "construct-hand" operation in detail. There are many such recipes, so that one is just an example, not necessarily a canonical "construct-hand".

Code: Select all

#C A sequence of 25 gliders on a single lane that collide with a
#C 90-degree elbow block so as to create a hand block.
x = 729, y = 690, rule = LifeHistory
A.A$.2A$.A20$23.A$24.2A$23.2A21$47.A$45.A.A$46.2A20$69.A$70.A$68.3A
28$99.A$97.A.A$98.2A21$121.A$122.2A$121.2A30$152.A.A$153.2A$153.A36$
192.A$193.A$191.3A21$215.A$213.A.A$214.2A38$253.A.A$254.2A$254.A56$
313.A$311.A.A$312.2A38$353.A$354.A$352.3A27$382.A$380.A.A$381.2A20$
404.A$405.A$403.3A22$427.A$428.2A$427.2A21$451.A$449.A.A$450.2A20$
473.A$474.A$472.3A21$495.A$496.2A$495.2A30$528.A$526.A.A$527.2A27$
555.A.A$556.2A$556.A31$588.A.A$589.2A$589.A20$611.A$612.2A$611.2A21$
635.A$636.A$634.3A6$727.2D$727.2D14$657.A$658.2A$657.2A25$685.A$686.A
$684.3A3$685.2C$685.2C!

Duplicating an elbow is actually covered by Section 11.3.3. The discussion talks about creating a "hand" target block, but it's actually right on the single-channel construction lane, so it could be used as an elbow without having to adjust it first (if the closer elbow gets used up or destroyed):

Code: Select all

x = 476, y = 472, rule = LifeHistory
2.A$A.A$.2A34$38.A$36.A.A$37.2A37$77.A$75.A.A$76.2A21$100.A$98.A.A$
99.2A20$122.A$123.A$121.3A21$145.A$143.A.A$144.2A20$167.A$168.A$166.
3A22$191.A$192.A$190.3A35$228.A$226.A.A$227.2A20$250.A$251.A$249.3A
21$273.A$271.A.A$272.2A23$298.A$296.A.A$297.2A20$320.A$321.A$319.3A
21$343.A$341.A.A$342.2A21$364.A.A$365.2A$365.A20$388.A$389.A$387.3A
22$410.A.A$411.2A$411.A20$433.A$434.2A$433.2A24$455.2D$455.2D4.A$462.
A$460.3A3$461.2C$461.2C5$474.2D$474.2D!

An example single-channel recipe for destroying an elbow can be found in Exercise 11.25 of the book:

Code: Select all

x = 166, y = 170, rule = LifeHistory
A$.2A$2A21$22.A.A$23.2A$23.A20$45.A$46.2A$45.2A21$67.A.A$68.2A$68.A
20$91.A$92.A$90.3A22$113.A.A$114.2A$114.A20$136.A$137.2A$136.2A25$
164.A$165.A$163.3A3$164.2C$164.2C!

Posted: **February 11th, 2022, 5:20 pm**

dvgrn wrote: February 11th, 2022, 4:32 pm
Book wrote: February 11th, 2022, 3:21 pm on the "Elbow operation" wiki page, it says:

An elbow operation is a recipe, usually a salvo of gliders traveling on one or more construction lanes, that collides with an elbow constellation and performs one of the standard transformations on it: push, pull, or fire for simple construction arms, along with possible construct, duplicate-elbow, or delete-elbow ops for more complicated systems.

"construct", "duplicate-elbow" and "delete-elbow" are red links

I'd like to define them. Help please.
Section 11.2.3 of the Life textbook describes a "construct-hand" operation in detail. There are many such recipes, so that one is just an example, not necessarily a canonical "construct-hand".
Code: Select all
#C A sequence of 25 gliders on a single lane that collide with a
#C 90-degree elbow block so as to create a hand block.
x = 729, y = 690, rule = LifeHistory
A.A$.2A$.A20$23.A$24.2A$23.2A21$47.A$45.A.A$46.2A20$69.A$70.A$68.3A
28$99.A$97.A.A$98.2A21$121.A$122.2A$121.2A30$152.A.A$153.2A$153.A36$
192.A$193.A$191.3A21$215.A$213.A.A$214.2A38$253.A.A$254.2A$254.A56$
313.A$311.A.A$312.2A38$353.A$354.A$352.3A27$382.A$380.A.A$381.2A20$
404.A$405.A$403.3A22$427.A$428.2A$427.2A21$451.A$449.A.A$450.2A20$
473.A$474.A$472.3A21$495.A$496.2A$495.2A30$528.A$526.A.A$527.2A27$
555.A.A$556.2A$556.A31$588.A.A$589.2A$589.A20$611.A$612.2A$611.2A21$
635.A$636.A$634.3A6$727.2D$727.2D14$657.A$658.2A$657.2A25$685.A$686.A
$684.3A3$685.2C$685.2C!
Duplicating an elbow is actually covered by Section 11.3.3. The discussion talks about creating a "hand" target block, but it's actually right on the single-channel construction lane, so it could be used as an elbow without having to adjust it first (if the closer elbow gets used up or destroyed):
Code: Select all
x = 476, y = 472, rule = LifeHistory
2.A$A.A$.2A34$38.A$36.A.A$37.2A37$77.A$75.A.A$76.2A21$100.A$98.A.A$
99.2A20$122.A$123.A$121.3A21$145.A$143.A.A$144.2A20$167.A$168.A$166.
3A22$191.A$192.A$190.3A35$228.A$226.A.A$227.2A20$250.A$251.A$249.3A
21$273.A$271.A.A$272.2A23$298.A$296.A.A$297.2A20$320.A$321.A$319.3A
21$343.A$341.A.A$342.2A21$364.A.A$365.2A$365.A20$388.A$389.A$387.3A
22$410.A.A$411.2A$411.A20$433.A$434.2A$433.2A24$455.2D$455.2D4.A$462.
A$460.3A3$461.2C$461.2C5$474.2D$474.2D!
An example single-channel recipe for destroying an elbow can be found in Exercise 11.25 of the book:
Code: Select all
x = 166, y = 170, rule = LifeHistory
A$.2A$2A21$22.A.A$23.2A$23.A20$45.A$46.2A$45.2A21$67.A.A$68.2A$68.A
20$91.A$92.A$90.3A22$113.A.A$114.2A$114.A20$136.A$137.2A$136.2A25$
164.A$165.A$163.3A3$164.2C$164.2C!

Thanks.

More pragmatically, should these terms be defined in the wiki? With examples (I'm a bit leery of trying that, even with your great examples). Or should they simply not be (red) links.

Posted: **February 11th, 2022, 5:31 pm**

Book wrote: February 11th, 2022, 5:20 pm More pragmatically, should these terms be defined in the wiki? With examples (I'm a bit leery of trying that, even with your great examples). Or should they simply not be (red) links.

I could go either way on this. "Elbow duplicator" and "elbow destroyer", or maybe more commonly just "elbow-duplicate" and "elbow-destroy", are names for types of single-channel recipes that are routinely used in self-constructing circuitry. But it's kind of specialized terminology, more like a useful label than a term that needs a wiki definition. By analogy: "R1L0" is a very useful label for a particular rake in the Silverfish chapter of the Life textbook, but it's not really the name of an independent object, it's just a functional piece of a complicated thing that needs a label.

A creative solution might be to redirect "hand constructor", "elbow duplicator" and "elbow destroyer" (or all three of them in one big link?) to the Snarkmaker recipe, which also contains all three of those recipes as sub-recipes -- and the text even says exactly where they are in the full Snarkmaker recipe.

Posted: **February 12th, 2022, 8:07 am**

This question sounds more like one from Book rather than GUYTU6J (as the latter has many previously unanswered questions), but what patterns can be demonstrated as examples for the quadratic filter, exponential filter and recursive filter?

ConwayLife.com

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