Thread for basic questions

[MathAndCode]

I thought the lifewiki shuttle page implies that the P29 is valid as a shuttle.

Yes. My point is that 49P88 is a shuttle, not that the p29 pre-pulsar hassler isn't.

[pcallahan]

I thought the lifewiki shuttle page implies that the P29 is valid as a shuttle.

Yes. My point is that 49P88 is a shuttle, not that the p29 pre-pulsar hassler isn't.

I'm not going to argue against the definition. It's just an intuitive impression. I don't see it going back and forth. However, I have no objection to its being classified as a shuttle. My biggest disappointment was never finding anything to do with it.

[Entity Valkyrie 2]

Shuttle is usually a subcategory of hassler (unless it's a RRO or RFO or R180°O etc.)

[dvgrn]

Shuttle is usually a subcategory of hassler (unless it's a RRO or RFO or R180°O etc.)

My own mental reference for the word "shuttle" is actually not the analogy with vehicles (which could perfectly well go round in a circle rather than back and forth).

A weaver's shuttle is the piece that holds the weft yard/thread/whatever, and goes back and forth across the loom. Presumably that's where the vehicular version got the name "shuttle" from -- but with those original shuttles there's a definite implication of back and forth, not round and round.

[pcallahan]

A weaver's shuttle is the piece that holds the weft yard/thread/whatever, and goes back and forth across the loom. Presumably that's where the vehicular version got the name "shuttle" from -- but with those original shuttles there's a definite implication of back and forth, not round and round.

I don't think I would have thought of that, but the idea of a shuttlecock in badminton came to mind.

[pzq_alex]

What is the smallest (or least recovery time) lwss reflector that can be built using current technology?

[GUYTU6J]

What is the smallest (or least recovery time) lwss reflector that can be built using current technology?

You mean a stable one? Try connecting a LWSS-to-G/H and a G/H-to-LWSS, both accessible in the thread for stable signal converters.
(Curiously, if you were asking for MWSS the answer would be much simpler, as can be seen at the lower left corner of loafer-mwss-signal-loop.rle.gz in Golly.)

Or if periodic technology is allowed, you can have some lower recovery time, for instance this at p46:

Code: Select all

x = 32, y = 31, rule = B3/S23
22b2o5b2o$22b2o5b2o12$24bo3bo$24bo3bo3$21b2obo3bob2o$22b3o3b3o$23bo5bo
8$o2bo25b2o$4bo24b2o$o3bo$b4o!

[creeperman7002]

I just realized that the abelian sandpile model is a visual example of the laws of thermodynamics in action. Does this mean that the model could have practical applications?

[Entity Valkyrie 2]

What is the smallest (or least recovery time) lwss reflector that can be built using current technology?

These have a recovery time of 78:

Code: Select all

x = 123, y = 79, rule = B3/S23
93b2o$93bobo$95bo4b2o$91b4ob2o2bo2bo$91bo2bobobobob2o$94bobobobo$95b2o
bobo$99bo2$85b2o$15b2o11bo57bo7b2o$15b2o10bobo56bobo5b2o17bo$27bobo2b
2o3bo49b2o22b3o$26b2ob2o2bo2bobo12bo58bo$30bobo3bobo10b3o16bo41b2o$26b
2obo2b4obo10bo18bobo$26b2obobo3bo12b2o17bobo$30bobo3bo28b3ob2o47b2o$
31bobo3bo26bo54bo$32bo3b2o27b3ob2o26b2o20bob2o$57b2o8bob2o26bo13b2o4b
3o2bo$58bo39b3o10b2o3bo3b2o$58bobo39bo15b4o$23b2o34b2o39bob2o15bo$23b
2o73b2obobo12b3o$8b2o88bo2bo13bo$7bo2bo89b2o14b5o$6bob2o110bo$6bo111bo
$5b2o111b2o$20b2o$20bo$21b3o24b2o$23bo11b2o11b2o$2o15b2o17bo$bo15bo3bo
11b3o4bo49bo$bobo11bobo2bobo10bo6b3o45b3o$2b2o11b2o3bobo20bo43bo$9bo9b
2ob3o17b2o43b2o$8bobo14bo$8bobo8b2ob3o43b2o$9bo9b2obo11b2o33bo4b2o$34b
o31b3o5b2o$31b2obo31bo$20b2o9bo2b3o4b2o$20bobo9b2o3bo3b2o$12b3o7bo2bo
8b4o$6b2o4bo2bo5b2obobo7bo15b2o$7bo4bo9bo2bo9b3o12bobo$4b3o5bo7bobo15b
o13bo$4bo8bobo4b2o11b5o14b2o$33bo$35bo35b2o$34b2o36bo24b2o$72bobo23bo$
62bo10b2o17b2ob3o$60b3o29b2obo$59bo$59b2o$44b2o$45bo$45bob2o$46bo2bo$
47b2o45b2o$62b2o30b2o$62b2o5$70bo3b2o$69bobo3bo11b2o$65b2obobo3bo12bo$
65b2obo4bo14b3o$69b5obo14bo$52b2o7b2obob2obo4bobo$53bo7bob2obo2bob3o2b
o$50b3o15b2obo4b2o$50bo!

Code: Select all

x = 127, y = 99, rule = B3/S23
23bo$23b3o15b2obo4b2o$26bo7bob2obo2bob3o2bo$25b2o7b2obob2obo4bobo13bo$
42b5obo12b3o$38b2obo4bo13bo$38b2obobo3bo12b2o27bo$42bobo3bo38b3o$43bo
3b2o37bo$86b2o$69b2o$70bo$70bobo$3bo31b2o34b2o$2bobo6bo23b2o$3bo6bobo
7b2o$10bobo6bo2bo$b5o3b2ob3o3bob2o$o2bo2bo8bo2bo$2o3b2o2b2ob3obobo$9b
2obo3bob2o12b2o$16bo15bo$14b3o16b3o24b2o$13bo21bo11b2o11b2o$o2bo9b2o
33bo$4bo40b3o59bo$o3bo40bo32b2o5b2o20b3o$b4o74bo5bo24bo$76b3o7b3o20bob
o$10b2o64bo11bo20bobo$9bo2bo97bo$10b2o113b2o$2b2o121bo$bobo119bobo$bo
121b2o$2o$13b2o$13bo$14b3o$16bo$105b2o$104bobo$104bo18b2o$103b2o7b2o9b
o$112b2o10bo$123b2o$120b2o$120b2ob2o$123bo$120b2o3bo$119bo2b4o$48b2o3b
2o17bo45bobobo$48b2o2bob3o13b3o27bo18bo2bob2o$52bo4bo11bo30b3o19bobo$
48b4ob2o2bo11b2o32bo17b2obo$48bo2bobobob2o22b2o19b2o14bobo2bo$51bobobo
bo23bo15bo20b2o2bo$52b2obobo21bobo15b3o23b3o$56bo22b2o19bo24bo$99b2o$
42b2o$16bo26bo7b2o$16b3o24bobo5b2o$19bo24b2o$18b2o$96b2o$96b2o17b2o$
10b2o103b2o$10bo$7b2obo$7bo2b3o4b2o35b2o60b2o$8b2o3bo3b2o35bo61bo$10b
4o41b3o45b2o12b3o$10bo15b2o29bo28b2o16bo14bo$11b3o12bobo2b2o53bo14b3o$
14bo13bo2bo29b2o24b3o11bo$9b5o14b3o2bo26bobo26bo$9bo21b3o26bo$11bo18bo
28b2o$10b2o18b2o7$20b2o$19bobo5b2o$19bo7b2o$18b2o2$32bo$28b2obobo$27bo
bobobo$24bo2bobobobob2o$24b4ob2o2bo2bo$28bo4b2o$26bobo$26b2o!

Code: Select all

x = 171, y = 72, rule = B3/S23
71bo$71b3o15b2obo4b2o$74bo7bob2obo2bob3o2bo$73b2o7b2obob2obo4bobo$90b
5obo$86b2obo4bo$86b2obobo3bo$90bobo3bo$91bo3b2o44bo$141b3o$111bo32bo$
109b3o13bo17b2o$108bo16b3o$83b2o23b2o18bo$83b2o42b2o$68b2o$67bo2bo$66b
ob2o$66bo$65b2o$80b2o$80bo36b2o$81b3o33b2o$15b2o11bo54bo10b2o$15b2o10b
obo63bobo$27bobo2b2o3bo55bo$26b2ob2o2bo2bobo53b2o10b2o$30bobo3bobo66bo
$26b2obo2b4obo64b3o9b2o36b2o$26b2obobo3bo66bo11bo19b2o16bobo$30bobo3bo
78b3o15bobo18bo$31bobo3bo79bo15bo20b2o$32bo3b2o58b2o11bo22b2o$51bo44b
2o10bobo$49b3o56bobo2b2o3bo$48bo58b2ob2o2bo2bobo$23b2o23b2o61bobo3bobo
$23b2o82b2obo2b4obo21bo2bob2o$8b2o97b2obobo3bo23b4obo$7bo2bo100bobo3bo
27bobo$6bob2o102bobo3bo23b2o2b2o$6bo106bo3b2o23bo$5b2o125bo10bo$20b2o
38b2o68b3o9b2o2bo$20bo38bo2bo66bo16b3o$21b3o36b2o42b2o23b2o18bo$23bo
11b2o49b2o16b2o42b2o$2o15b2o17bo49bo2b2o$bo15bo3bo11b3o6bob2o17b2o22b
2o2bo$bobo11bobo2bobo10bo6b3ob2o17bo26bo$2b2o11b2o3bobo16bo24b3o20b3o$
9bo9b2ob3o15b3ob2o20bo19bo$8bobo14bo16bobo41b2o13b2o$8bobo8b2ob3o17bob
o4b2o50bo36b2o$9bo9b2obo20bo6bo51b3o33b2o$47b3o54bo10b2o$47bo66bobo52b
2o$20b2o92bo54b2o$20bobo90b2o10b2o$12b3o7bo2bo50b2o48bo$6b2o4bo2bo5b2o
bobo48bobo5b2o38b3o9b2o$7bo4bo9bo2bo49bo7b2o38bo11bo19b2o$4b3o5bo7bobo
51b2o60b3o15bobo$4bo8bobo4b2o116bo15bo$88bo64b2o$84b2obobo$83bobobobo$
80bo2bobobobob2o$80b4ob2o2bo2bo$84bo4b2o$82bobo$82b2o!

These have a bigger recovery time:

Code: Select all

x = 142, y = 62, rule = B3/S23
65bo$65b3o15b2obo4b2o$68bo7bob2obo2bob3o2bo$67b2o7b2obob2obo4bobo8b2o
7b2o$84b5obo9b2o7bobo$80b2obo4bo18bobob3o$80b2obobo3bo17b2o5bo$84bobo
3bo22b2o$85bo3b2o5$77b2o$77b2o$62b2o$61bo2bo$15b2o11bo31bob2o$15b2o10b
obo30bo$27bobo2b2o3bo21b2o69b2o$26b2ob2o2bo2bobo35b2o54b2o$30bobo3bobo
35bo$26b2obo2b4obo37b3o$26b2obobo3bo41bo$30bobo3bo$31bobo3bo86b2o3b2o$
32bo3b2o86b2o3b2o$51bo46b2o8bo$49b3o47bo8b3o$48bo47b3o12bo$23b2o23b2o
46bo13b2o$23b2o$8b2o$7bo2bo$6bob2o$6bo87bo$5b2o87b3o$20b2o38b2o35bo$
20bo38bo2bo21bo11b2o11b2o$21b3o36b2o20b3o24b2o$23bo11b2o44bo$2o15b2o
17bo44b2o$bo15bo3bo11b3o6bob2o17b2o2bo$bobo11bobo2bobo10bo6b3ob2o17bo
3b3o$2b2o11b2o3bobo16bo24b3o3bo$9bo9b2ob3o15b3ob2o21b2o2bo$8bobo14bo
16bobo21bo2b2o$8bobo8b2ob3o17bobo4b2o15b2o16b2o52b2o$9bo9b2obo20bo6bo
3b2o28b2o52bobo$47b3o4bo85bo$47bo7b3o82b2o$20b2o35bo$20bobo$12b3o7bo2b
o66bo3b2o$6b2o4bo2bo5b2obobo64bobo3bo37b2o$7bo4bo9bo2bo61b2obobo3bo12b
2o24bo$4b3o5bo7bobo64b2obo4bo13bo26b3o$4bo8bobo4b2o69b5obo12b3o25bo$
74b2o7b2obob2obo4bobo13bo11b2o$75bo7bob2obo2bob3o2bo24bobo$72b3o15b2ob
o4b2o23bo$72bo49b2o!

Code: Select all

x = 65, y = 112, rule = B3/S23
51b2o$52bo$36bo15bobo$30bo5b3o14b2o$30b3o6bo7b2o$33bo4b2o7b2o$32b2o2$
63b2o$63b2o3$25b2o$25b2o10b2o$37bobo$38bo4$37b2o$37bo$38b3o18b2o$40bo
18bo$60b3o$62bo6$25b2o$26bo28b2o$3b2o21bobo26b2o$4bo22b2o$2bo$2b5o14b
2o$7bo13bo$4b3o12bobo$3bo15b2o$3b4o$b2o3bo3b2o$o2b3o4b2o$2obo25b2o$3bo
24bobo$3b2o23bo$27b2o7b2o$35bobo$11b2o22bo$12bo21b2o$9b3o$9bo2$20bo39b
2o$20b3o37b2o$23bo$14b2o6b2o$14b2o$22b2o$22b2o2$4b2o$5bo55b2o$5bobo53b
obo$6b2o55bo$63b2o9$3b2o26b2o$2bo2bo2b2o22bo6b2o$3b2o2bobo19b3o7bo$5b
2o16b2o4bo7bobo$5bo17bo13b2o$2b2obo2bo15b3o$2bob2obobo16bo$6bobo$3b2o
2bo$b3ob2o$o$b3ob2o$3bob2o30bo$29bo6bobo$13b2o13bobo6bo$13b2o7b2o4bobo
$22bo3b3ob2o3b5o$20bobo2bo8bo2bo2bo$20b2o4b3ob2o2b2o3b2o$28bob2o$24bo$
24b3o$2o25bo$2o24b2o9bo2bo$36bo$36bo3bo$36b4o2$16bo12b2o$15bobo10bo2bo
$15bobo11b2o$16bo20b2o$17b3o17bobo$19bo19bo$39b2o$26b2o$27bo$24b3o$24b
o!

[dvgrn]

What is the smallest (or least recovery time) lwss reflector that can be built using current technology?

These have a recovery time of 78...

Side note mostly to pzq_alex: these do technically work at p74 and p75 as well, as usual for fast syringe-based stuff. It's just that p76 and p77 don't work, so p78 is the lowest "safe" recovery time.

[MathAndCode]

The LifeWiki article about the queen bee shuttle seems to state that the version of the queen bee shuttle where the beehives are eaten by blocks was found in 1970, but the LifeWiki article about the fishhook states that the fishhook was not even discovered as a still life until 1971. Does that mean that using the term eater 1 to refer to a fishhook is incorrect?

[dvgrn]

Does that mean that using the term eater 1 to refer to a fishhook is incorrect?

No, it's correct. The term "eater 1" refers to a fishhook.

I think you're really asking whether "eater 1" was the first eater that was discovered. It definitely wasn't, any more than "eater 5" is unambiguously the fifth eater that was discovered. But that's totally okay. I don't think any of the LifeWiki eater-N pages say that eaters 1 through 5 are numbered in strict chronological order of discovery; in particular, eater 3 was pretty definitely discovered after eater 4.

[MathAndCode]

I think you're really asking whether "eater 1" was the first eater that was discovered.

Yes, that's what I meant.

[bubblegum]

Yes, that's what I meant.

Bad question phrasing, I see.

Besides, it's not like names have to be logical or anything. "Eater 1" doesn't mean "Eater the First", it's just its name.

[blah]

Why does the Macrocell format require the depth of nodes to be specified? They can be deduced by incrementing the depth of the subnodes. Ambiguity between leaf and non-leaf nodes in 3+ state rules can be resolved some other way, like prepending those lines with some specific character. I know .mc isn't supposed to be maximally optimised for size, but this seems particularly useless and wasteful, even after gzip compression.

Also, I haven't tested it on the most recent version of Golly, but on my copy, .mc files with nodes whose subnodes have the wrong depths can have weird behaviour (including crashing when you try to zoom in).

[dvgrn]

Why does the Macrocell format require the depth of nodes to be specified? They can be deduced by incrementing the depth of the subnodes. Ambiguity between leaf and non-leaf nodes in 3+ state rules can be resolved some other way, like prepending those lines with some specific character. I know .mc isn't supposed to be maximally optimised for size, but this seems particularly useless and wasteful, even after gzip compression.

I've wondered the same thing from time to time. Seems like the format should either prioritize readability (in which case the nodes should be numbered explicitly so you can see which one is which!) or it should prioritize compressibility (in which case there are all kinds of tricks that would make macrocell files more compact for copying and pasting, without sacrificing machine readability at all).

(Probably we shouldn't talk about that any more, though. Otherwise Chris Rowett will notice that this is an unsolved problem and implement a new UMC format for LifeViewer.)

[mniemiec]

Why does the Macrocell format require the depth of nodes to be specified? They can be deduced by incrementing the depth of the subnodes. ...

Many formats include redundant information that could ultimately be deduced from the pattern context, but that make various operations easier if they are directly available.

RLE "x = <width>, y = <height>" could be deduced by reading the entire pattern; it's useful for old programs that had to pre-allocate fixed-size arrays before filling them.

APG "xs<population>_" could be deduced by counting living cells, but it's a lot easier to sort files by doing simple string comparison.

APG "xp<period>_" and "xq<period>_" could also be deduced even more laboriously by automating the pattern until it repeats.

HRD "p<period> r<rotor cells> <height>x<width>" could all be deduced by counting the number of rows, the number of cells in each row, and the number of non-'.' cells, while the period could be computed by automating the pattern until it repeats; it's easier to search knownrotors if you don't have to do this.

[blah]

Many formats include redundant information that could ultimately be deduced from the pattern context, but that make various operations easier if they are directly available.

[examples]

That's a valid point (the RLE example is even used by some decoders I've written). But it raises another question: What operations are made easier by depth information? As I pointed out, it's pretty simple to calculate. Definitely far easier than RLE bounding boxes (O(N)!).

And there's another thing: Programs that interpret Macrocell files have to be much more 'serious' than programs that interpret RLEs or APGcodes or whatever HRDs are (not to say that there aren't serious programs that interpret those formats, but the barrier to entry is lower). So expecting some extra work, I think, is more reasonable. I believe a good Macrocell interpreter should be able to handle invalid input, and to do that you have to confirm the validity of the provided depths, and to do that you have to calculate them anyway, so you haven't saved time; you've actually cost yourself time.

I've been skimming over Golly's MC reading code. There seem to be two readmacrocell() functions, one in hlifealgo.cpp and the other in ghashbase.cpp. They're clearly copy/pasted (I wonder if there are any optimisations made to one that haven't been put in the other), and neither seem to actually check whether the provided depth is valid. That would explain why it crashed.

Also I think the call to zeronode() should be optimised.

[mniemiec]

Many formats include redundant information that could ultimately be deduced from the pattern context, but that make various operations easier if they are directly available. ...

... whatever HRDs are ...

I had only just become aware of this format a couple of days ago. It's Hickerson Rotor Descriptor format. It's used in the knownrotors file to classify oscillators by their rotors, disregarding their stators.

[wwei47]

How do I synthesize this traffic light predecessor? A synthesis would likely imply a final step for a sparker.

Code: Select all

x = 13, y = 5, rule = LifeHistory
3.7D$3.7D$3.3D.3D$5D3A5D$4D5A4D!

[72c20e]

There are still uncommitted hauls uploaded by apgsearch but not yet included in the census.

What happened?

[dvgrn]

There are still uncommitted hauls uploaded by apgsearch but not yet included in the census.

What happened?

Just very recent ones, right? There are always new hauls trickling in to the C1 census.

If you're looking at some symmetry other than C1, then which one specifically? If only one person is searching a symmetry, then hauls tend to pile up for a while since Catagolue doesn't let people self-verify hauls except maybe sometimes in sort-of-emergencies (I forget the exact rules).

[pcallahan]

Has anyone ever done an enumeration of still lifes with a specific topology? One obvious case consists of loops, or patterns consisting of live cells, connected by adjacency, in which each live cell has exactly 2 live neighbors. These are pretty rare, at least among small patterns, and include tub, beehive, loaf, pond, and mango. Here are two larger examples:

Code: Select all

x = 26, y = 11, rule = B3/S23
20b2o$4bo14bo2bo$3bobo13bo2bo$2bo2bo11b2o4b2o$bo3bobo8bo8bo$o5bobo7bo
8bo$obo5bo8b2o4b2o$bobo3bo11bo2bo$3bo2bo12bo2bo$3bobo14b2o$4bo!

The above are both extensible in an obvious way, though they leave a lot of empty space. Something closer to a space-filling curve would be more interesting. Note that there are many examples of collections of loops that stabilize each other, the smallest being aircraft carrier (I know this because my simple filter doesn't check connected components so there are a lot of these.)

One way to stabilize a chain of cells is to stretch them out so each adjacent empty cell has 2 or fewer neighbors. If you want to pack them closer, you need to make sure every empty cell in the interior has at least 4 neighbors. It reminds me of what little I know about protein or RNA folding. Clearly, it's much simpler.

There are more examples of still lifes with "snake" topology, i.e. a connected chain of live cells with 2 neighbors that's terminated at each end by a triple of mutually adjacent cells (so exactly 2 cells have 3 neighbors and the rest have 2). You can make them just by stretching all the cells into a diagonal, by packing them densely into hairpin turns, or in more convoluted ways:

Code: Select all

x = 40, y = 16, rule = B3/S23
2o$o21bo$bo19bobo11bob2o$2bo15bo2bobo2bo8b2o2bo$3bo13bobobobobobo10bo$
4bo12bobobobobobo7b3o$5bo10b2obobobobob2o5bo$6bo12bobobobo8bob2o$7bo
11bobobobo9bo2bo$8bo11bo3bo12b2o$9bo$10bo$11bo$12bo$13bo$12b2o!

I can't find any really convoluted examples just by filtering the small still life enumeration. I wonder if anyone has tried counting just loops and snake-like patterns. Also if there are general methods for constructing non-obvious snake packings using a recursive method such as used for space-filling curves.

[mniemiec]

Has anyone ever done an enumeration of still lifes with a specific topology? One obvious case consists of loops, or patterns consisting of live cells, connected by adjacency, in which each live cell has exactly 2 live neighbors. These are pretty rare, at least among small patterns, and include tub, beehive, loaf, pond, and mango. Here are two larger examples: ...

I don't recall anyone having actually done this via computer search, but it is trivial to do by searching for still-lifes in related rule B3/S2. One could similarly restrict survival topologies to searching a non-totalistic rule, replacing S by the list of permitted neighborhoods, and one could similarly restrict birth-suppression topologies by adding additional B neigborhoods. Of course, these only work on a local basis; topologies whose definition is more complicated than just looking at an adjacent neighborhood can't be filtered in this way.

Another way to do all of this (which could work for any topology) is to take an previously-calculated list of still-lifes, and post-process it to filter out any undesired topologies. This is exactly what I used in my still-life searches. E.g. my searcher finds a mixture of still-lifes and pseudo-still-lifes, and I run the result through a filter that separates the two.

[pcallahan]

Another way to do all of this (which could work for any topology) is to take an previously-calculated list of still-lifes, and post-process it to filter out any undesired topologies. This is exactly what I used in my still-life searches.

Yeah, that's what I was doing. However, I will need to make sure there is a single connected component to avoid getting all these results (filtering 24 bit patterns).

Code: Select all

x = 120, y = 121, rule = B3/S23
8b2o12bo10b2o10b2o13bo3bo7bo3bo12bo3bo19bo$7bo2bo10bobo10bo9bo2bo8b2ob
obobobo5bobobobo3bo6bobobobo2b2o5bo3bo3bobo$8bo2bo9bobo8bo11bo2bo9bobo
bobo2bo4bobobobo2bobo4bo2bobobo3bo4bobobobobo2bo$9b2o11bo9b2o8b2o4b2o
5bo3bobo2bobo5bo2bobobo2bo4bobo2bobobo6bobobobobobo$41bo8bo4b2o2bobo3b
o9bobobobo6bo3bobob2o6bo2bobo2bo$9b4o7b5o7b4o5bo8bo9bo15bo3bo12bo13bob
o$8bo4bo5bo5bo5bo4bo5b2o4b2o58bo$9b4o7b5o5bo2b3o8bo2bo$31b2o11bo2bo$
11b2o9bo11b2o9b2o$11bo2bo6bobo11bo$13b2o6bobo9bo$22bo10b2o7$4bo9bo9bo
9bo8b2o8b2o10bo3b2o10bo3b2o7bo3bo3bo6b2o3bo3bo$3bobo7bobo7bobo7bobo6bo
2bo6bo2bo4b2o2bobobo2bo5b2obobobo2bo5bobobobobobo4bo2bobobobobo$2bo2bo
6bo2bo6bo2bo6bo2bo6bo2bo6bo2bo4bo3bobobo2bo6bobobobo2bo4bo2bobobobobo
4bo2bobobobobo$3b2o8b2o8b2o8b2o8b2o8b2o7bobobo2b2o5bo3bobo2b2o5bobo2bo
bo2bo6b2o2bobo2bo$61b2obobo9b2o2bobo10bo3bobo13bobo$b4o6b4o6b4o6b4o6b
4o6b4o10bo15bo16bo15bo$o4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo$b3obo4bob3o
6b4o6b4o6b4o6b4o$4bo6bo$b2o10b2o8b2o6b2o8b2o8b2o$bo12bo7bo2bo4bo2bo7bo
8bo2bo$3bo8bo10bobo4bobo10bo7b2o$2b2o8b2o10bo6bo10b2o9$5bo9bo9bo9bo9bo
9bo8b2o11b2o8b2o8b2o8b2o9b2o$4bobo7bobo7bobo7bobo7bobo7bobo6bo2bo11bo
9bo9bo9bo10bo$4bo2bo6bo2bo6bo2bo6bo2bo6bo2bo6bo2bo6bo2bo8bo9bo9bo9bo
10bo$5b2o8b2o8b2o8b2o8b2o8b2o8b2o9b2o8b2o8b2o8b2o9b2o2$3b4o6b4o6b4o6b
4o6b4o6b4o6b4o7b4o6b4o6b4o6b4o7b4o$2bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4b
o4bo4bo5bo4bo4bo4bo4bo4bo4bo4bo5bo4bo$3b3obo4bob3o6b4o6b4o6b4o6b4o6b4o
5bo2b3o6b4o6b4o6b4o7b4o$6bo6bo59b2o$3b2o10b2o8b2o8b2o6b2o8b2o8b2o11b2o
8b2o8b2o6b2o9b2o$3bo12bo7bo2bo6bo2bo4bo2bo6bo2bo7bo13bo7bo2bo6bo2bo4bo
2bo7bo2bo$5bo8bo10bobo6bobo6bobo6bobo10bo9bo9bo2bo5bo2bo5bo2bo6bo2bo$
4b2o8b2o10bo8bo8bo8bo10b2o9b2o9b2o7b2o7b2o8b2o11$9b2o10b2o8b2o9b2o9b2o
9b2o7b2o9b2o11b2o9b2o$7bo2bo8bo2bo7bo2bo7bo2bo7bo2bo7bo2bo6bo2bo7bo2bo
7bo2bo7bo2bo$7b2o10b2o10b2o9b2o7bo2bo7bo2bo9b2o9b2o7b2o9b2o$52b2o9b2o$
5b4o8b4o8b4o7b4o29b4o7b4o7b4o7b4o$4bo4bo6bo4bo6bo4bo5bo4bo5b4o7b4o7bo
4bo5bo4bo5bo4bo5bo4bo$5b3o2bo4bo2b3o6bo2b3o7b4o5bo4bo5bo4bo5bo2b3o7b4o
5bo2b3o7b4o$8b2o6b2o10b2o20b4o7b4o7b2o20b2o$5b2o12b2o10b2o7b2o33b2o7b
2o11b2o7b2o$5bo14bo11bo6bo2bo9b2o9b2o11bo6bo2bo11bo6bo2bo$7bo10bo11bo
7bo2bo11bo9bo2bo7bo7bo2bo10bo7bo2bo$6b2o10b2o10b2o7b2o10bo13b2o7b2o7b
2o11b2o7b2o$51b2o13$6b2o12b2o8b2o8b2o9b2o8b2o8bo3bo10b2o3bo$5bo2bo11bo
9bo9bo10bo9bo8bobobobo8bo2bobobo$6bo2bo12bo9bo9bo10bo9bo5bo2bobobo8bo
2bobobo$3b3o4bo10b2o8b2o8b2o9b2o8b2o5bobo2bobob2o6b2o2bobob2o$2bo8bo
48bo9bo3bobobo11bobobo$3bo8bo6b4o6b4o6b4o7b4o5bob3o11bo4bo10bo4bo$4bo
4b3o6bo4bo4bo4bo4bo4bo5bo4bo4bo4bo14b2o14b2o$5bo2bo8bo2b3o6b4o6b4o7b4o
6b3obo$6bo2bo8b2o43bo$7b2o12b2o8b2o8b2o7b2o8b2o$22bo7bo2bo6bo2bo5bo2bo
7bo$20bo9bo2bo5bo2bo5bo2bo10bo$20b2o9b2o7b2o7b2o10b2o8$6bo10bo10bo9b2o
10b2o9b2o8b2o8b2o9b2o$5bobo8bobo8bobo7bo2bo10bo10bo7bo2bo6bo2bo7bo2bo$
4bo2bo7bo2bo7bo2bo7bo2bo8bo10bo10b2o6bo2bo7bo2bo$4bobo8bobo8bobo9b2o9b
2o9b2o18b2o9b2o$5bo10bo10bo41b4o$36b4o7b4o7b4o6bo4bo6b4o7b4o$3b5o6b5o
6b5o5bo4bo5bo4bo5bo4bo6b3o2bo4bo4bo5bo4bo$2bo5bo4bo5bo4bo5bo5b4o7b3o2b
o5b4o10b2o6b4o7b4o$3b4obo4bob4o6b5o20b2o17b2o$7bo6bo23b2o7b2o11b2o7bo
12b2o7b2o$5bo10bo10bo10bo2bo5bo11bo2bo8bo10bo6bo2bo$5b2o8b2o9bobo11b2o
7bo10bo2bo6b2o12bo4b2o$27bo20b2o11b2o20b2o!

It's not a very interesting or well-motivated question, but I still wonder if there are dense solutions that are more random looking than hairpin loops. Like this one:

Code: Select all

x = 109, y = 57, rule = B3/S23
52bo3bo$51bobobobo$48bo2bobobobo2bo$47bobobobobobobobo$44bo2bobobobobo
bobobo2bo$43bobobobobobobobobobobobo$40bo2bobobobobobobobobobobobo2bo$
39bobobobobobobobobobobobobobobobo$36bo2bobobobobobobobobobobobobobobo
bo2bo$35bobobobobobobobobobobobobobobobobobobobo$32bo2bobobobobobobobo
bobobobobobobobobobobobo2bo$31bobobobobobobobobobobobobobobobobobobobo
bobobobo$28bo2bobobobobobobobobobobobobobobobobobobobobobobobo2bo$27bo
bobobobobobobobobobobobobobobobobobobobobobobobobobobo$24bo2bobobobobo
bobobobobobobobobobobobobobobobobobobobobobobo2bo$23bobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobo$20bo2bobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobo2bo$19bobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobo$16bo2bobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo2bo$15bo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobo$12bo2bobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobo2bo$11bobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobo$8bo2bobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
o2bo$7bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobo$4bo2bobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo2bo$3bo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobo$3bobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$b
2o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3b
o3bo3bo3b2o$o107bo$b2o3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo3bo
3bo3bo3bo3bo3bo3bo3bo3bo3bo3b2o$3bobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo$3b
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobo$4bo2bobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo2bo$7b
obobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobo$8bo2bobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobo2bo$11bobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bo$12bo2bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobo2bo$15bobobobobobobobobobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobo$16bo2bobobobobobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobo2bo$19bobobobobobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobo$20bo2bobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobo2bo$23bobobobobobobo
bobobobobobobobobobobobobobobobobobobobobobobobobo$24bo2bobobobobobobo
bobobobobobobobobobobobobobobobobobobobobo2bo$27bobobobobobobobobobobo
bobobobobobobobobobobobobobobobobo$28bo2bobobobobobobobobobobobobobobo
bobobobobobobobobo2bo$31bobobobobobobobobobobobobobobobobobobobobobobo
bo$32bo2bobobobobobobobobobobobobobobobobobobobo2bo$35bobobobobobobobo
bobobobobobobobobobobobo$36bo2bobobobobobobobobobobobobobobobo2bo$39bo
bobobobobobobobobobobobobobobo$40bo2bobobobobobobobobobobobo2bo$43bobo
bobobobobobobobobobo$44bo2bobobobobobobobo2bo$47bobobobobobobobo$48bo
2bobobobo2bo$51bobobobo$52bo3bo!