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LifeWiki Did-You-Knows

Postby dvgrn » January 4th, 2015, 10:58 pm

I've been plotting to add more did-you-knows to the LifeWiki -- there are a lot more than twenty fascinating factoids about Conway's Life.

A hundred did-you-knows seems like a nice round number. I've quoted my current set of notes below; suggestions for additions are most welcome. I'll update the list in this message as new ideas come in, and clean up some of my rough notes, and eventually copy everything into the LifeWiki.

Should related rules be mentioned occasionally, or should we stick with B3/S23 only for this collection?

Current collection on LifeWiki (for reference): did you know…
  • that the largest interesting pattern constructed, the caterpillar, contains over 11 million cells?
  • that the Gosper glider gun was the first pattern to be discovered that exhibits infinite growth?
  • that the block-laying switch engine and the glider-producing switch engine are the only two infinitely-growing patterns that are known to have ever occurred naturally from a nonsymmetric random starting configuration?
  • that oscillators are known that oscillate at all periods other than 19, 23, 34, 38 and 41?
  • that the pentadecathlon and the blinker are the only known oscillators that are polyominos in more than one phase?
  • that it is impossible for a period 3 oscillator to be a phoenix?
  • that the methuselah with the longest known lifespan, 40514M, lasts for over 40,000 generations before stabilizing? The second-place holder, Fred, runs for over 35,000 ticks.
  • that replicators with quadratic population growth are known to exist in Conway's Game of Life, but none have yet been found?
  • that the first known period 37 and 51 oscillators were found in 2009?
  • that a pattern whose population grows without bound but does not tend to infinity is known as a sawtooth?
  • that there are over 6.5 million distinct strict still lifes with 24 or fewer cells?
  • that infinitely-growing patterns can be constructed with as few as three gliders?
  • that quadratically-growing patterns have been found with as few as 23 initial cells?
  • that the blinker is the only known oscillator that is one cell thick?
  • that the first spaceship found in Conway's Game of Life that travels in an oblique direction was discovered in 2010?
  • that there are still lifes that can be split into four stable islands, but not two or three?
  • that no new spaceships were discovered after 1970 until 1989?
  • that eighteen spaceship velocities have been constructed, including two infinitely adjustable families of ships?
  • that there are 71 distinct ways for two gliders to collide, but it is unknown how many distinct 3-glider collisions there are?
To be added: did you know…
  • that the first odd-period glider gun -- a period 565 p5-spark-assisted B-heptomino loop by [[David Buckingham]] -- was constructed in 1995?
  • that even though the speed limit for spaceships is c/2 in a vacuum, in a medium of [[stripes agar]] there are “spaceships” that can travel at lightspeed along the stripes, or two thirds of lightspeed perpendicular to the stripes?
  • that the smallest known spacefiller pattern consists of 187 cells? (need to fix Max / spacefiller2 articles on wiki)
  • that there are now at least 36 known Herschel conduits, counting stable conduits only, and more than twice that number if oscillator-supported conduits are included?
  • that as of January 2015, because diagonal Geminoids are still theoretical, [[half-bakery knightships]] are the only known spaceships with fixed slope but adjustable speed?
  • that a pattern exists in which no cell in the unbounded Life plane ever becomes periodic?
  • that several candidate universal constructors have been demonstrated in Conway’s Life, but as of the end of 2014 none have been formally proven to be universal?
  • that there are dozens of known Cordership variants, including puffers, rakes and wickstretchers, with periods of any multiple of 96?
  • that [[greyships]] have been constructed with speeds of c/2, c/3, c/4, c/5 and 2c/5?
  • that most [[greyships]] travel parallel to the stripes in their included agars, but some [link?] travel perpendicular to the stripes, or “against the grain”?
  • that a pattern has been constructed that calculates and prints out the digits of pi in decimal, and a similar one prints out the decimal digits of the Golden Ratio?
  • that several different patterns have been constructed to display the sequence of prime numbers, and some have been adapted to display only prime pairs or Fermat primes?
  • that two completely different types of knightships, the [[waterbear]] and the [[HBK]], were constructed in 2014?
  • that no Caterpillar-type spaceships were completed for almost ten years after the original [[Caterpillar]] was constructed in 2004, but that two different designs, the [[waterbear]] and the [[centipede]], were finished in 2014?
  • that the first spiral-growth pattern in Conway's Life was constructed in 2014?
  • that among known glider recipes for irreducible objects, the [[Gemini spaceship]] has the largest known minimal recipe, currently 175,167 gliders -- the runner-up being the [[HBK]] with a 38,380-glider synthesis?
  • ...
  • [simsim314's suggestions]
  • that in 2014 a new natural infinite growth pattern was discovered, starting from a symmetric random starting configuration?
  • that the first self-constructing Conway's Life pattern was built in 2010?
  • that the first stable reflector was found in October 1996, and the first fast stable reflector appeared in 2013, allowing the construction of oscillators of all periods >=43 ticks?
  • that the first c/3 spaceship gun was constructed in 2014?
  • that the first "macro-spaceship" gun (a Gemini spaceship gun) was constructed in 2010, followed by the HBK gun in January 2015?
  • that the [[waterbear]] is the single known high-speed oblique spaceship?
  • that there are no known lightspeed reflectors?
  • that 24 ten-cell patterns exhibit infinite growth, with 17 unique pattern types, but that it has been proven that no nine-cell pattern exhibits infinite growth?
  • that all still lifes up to 18 bits have a known glider synthesis, but it's still not known whether all still lifes are synthesizable.


    Extrementhusiast:
  • ...that the French kiss remained without a glider synthesis until 2013?
  • ...that the soup searches have reduced many glider syntheses?

  • ... [half-finished thoughts, please help complete and extend!]
  • that the smallest (period/size) self constructor is ...
  • that the smallest known Conway's Life universal constructor consists of only X live cells?
  • -- unitcell and metapixel patterns
  • -- Look for other articles along the lines of quad-pseudo-still-life…
  • -- Something about the soup search: power law (add actual power-law formula to Achim Flammenkamp’s LifeWiki page?)

    EDIT: added a few more ideas --
  • that it was shown in 2014 that any salvo of gliders, no matter how tightly packed, can be constructed by crashing together gliders whose initial positions are farther apart than any chosen finite distance?
  • that no spaceships with velocities other than c/4 diagonal (glider), c/2 orthogonal (*WSS variants), and c/12 diagonal (Corderships) had known glider syntheses until 2003, when a 2c/5 spaceship gun was constructed?
  • that after ten years with no new spaceship syntheses, a glider construction was found for the c/7 loafer in 2013?
  • that constructions for X previously inconstructible spaceships were discovered in 2014?
  • that there are N (127?) still lifes known to be constructible with four gliders, but it is not known if this is a complete list?
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Re: LifeWiki Did-You-Knows

Postby simsim314 » January 5th, 2015, 4:03 am

Few comments:

dvgrn wrote:that the block-laying switch engine and the glider-producing switch engine are the only two infinitely-growing patterns that are known to have ever occurred naturally from a random starting configuration?


I would say: that in 2014 new natural infinite growth pattern was discovered. Previously.... were thought to be the only natural occurring infinite growth.

---

that the first self replicating (constructing) pattern was built in 2010, and the smallest (period/size) self constructor...

that Kok's galaxy is the only oscillators known with c4 symmetry.

that first stable reflector was found in 19.. and the first fast was found in 2013 (snark), and allowed creating all oscilator above N generations.

that the first c/3 spaceship gun was constructed in 2014.

that the first "high level" spaceship gun was constructed in 2015 for HBK.

the single known high speed oblique spaceship is the waterbear.

there is no known light speed reflectors.

EDIT It has been proven that no 9 cells pattern exhibit infinite growth, and there is (~20) infinite growth patterns with 10 cells known.
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Re: LifeWiki Did-You-Knows

Postby chris_c » January 5th, 2015, 10:29 am

dvgrn wrote:I've been plotting to add more did-you-knows to the LifeWiki -- there are a lot more than twenty fascinating factoids about Conway's Life.

Looks like a good start. Here are a few things I spotted.
dvgrn wrote:[*] that until 2014 the only Caterpillar-type spaceship was the original 17c/45 [[Caterpillar]] from 2001?

It's from 2004 according to the wiki.
dvgrn wrote:[*] that a pattern exists in which every cell in the unbounded Life plane eventually becomes aperiodic?
[*] that a pattern exists in which every cell in the unbounded Life plane eventually becomes periodic?

Call me a pedant but I don't think a cell can "become" aperiodic: it's either periodic for evermore or it wasn't periodic in the first place. Also, I assume you don't want to count the empty universe as a valid example, so how about:

[*] that a pattern exists in which no cell in the unbounded Life plane ever becomes periodic?
[*] that a pattern exists in which every cell in the unbounded Life plane eventually becomes periodic with period at least 2?

(What do you think are the simplest proofs of the above statements by the way?)
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Re: LifeWiki Did-You-Knows

Postby Scorbie » January 5th, 2015, 10:32 am

chris_c wrote:(What do you think are the simplest proofs of the above statements by the way?)

Yeah, I always wanted to see the proofs of the patterns total periodic and total aperiodic.
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Re: LifeWiki Did-You-Knows

Postby simsim314 » January 6th, 2015, 3:55 am

I've counted 24 different 10 cells infinite growth.

G + R -> 6 options
R + R -> 7
7 + 3 -> 9
6 + 4 -> 1
10 -> 1

But if not counting redundant I think there should be 4 in R + R and 2 in G + R. So it's 17 non redundant (but I'm not sure).

Most of them I've discovered in 2014, until then only 4-5 different 10 cells infinite growth were known.
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Re: LifeWiki Did-You-Knows

Postby codeholic » January 6th, 2015, 12:50 pm

simsim314 wrote:that the first "high level" spaceship gun was constructed in 2015 for HBK.

Hmmm. What about the Gemini gun? Or what do you mean by "high level"?
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Re: LifeWiki Did-You-Knows

Postby codeholic » January 6th, 2015, 12:52 pm

simsim314 wrote:that Kok's galaxy is the only oscillators known with c4 symmetry.

This is not true, e. g. Achim's p16, and there are more.
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Re: LifeWiki Did-You-Knows

Postby simsim314 » January 6th, 2015, 1:17 pm

codeholic wrote:This is not true, e. g. Achim's p16, and there are more.


Woops you're right. But still c4 symmetry is pretty rare. I would say there are only four known irreducible c4 symmetry oscillators. And there are no two different c4 symmetry oscillators with same period.

EDIT about gemini gun. First of all you're right. Gemini gun should be considered high level design gun. But gemini gun is a bit different, in a sense that gemini is also kind of gemini gun itself, you can adress the gemini gun just as not moving gemini. Unlike the HBK gun which is gun dedicated to shoot high level design spaceship. Of couse we should formulate the "high level guns" into same category. Something like:

1. There is gemini gun that was build with similar circuitry as gemini in 2010 (?).
2. The first dedicated high level spaceship gun was built in 2015, shooting 38K gliders synth.
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Re: LifeWiki Did-You-Knows

Postby Extrementhusiast » January 6th, 2015, 6:05 pm

Not to be self-promoting, but
  • ...that the French kiss remained without a glider synthesis until 2013?
  • ...that the soup searches have reduced many glider syntheses?
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Re: LifeWiki Did-You-Knows

Postby simsim314 » January 6th, 2015, 7:09 pm

That all 18 bit SLs have known synthesis but it's still not known whether all SLs have synth or not.
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Re: LifeWiki Did-You-Knows

Postby Scorbie » January 6th, 2015, 8:46 pm

simsim314 wrote:I would say there are only four known irreducible c4 symmetry oscillators. And there are no two different c4 symmetry oscillators with same period.
I also agree that c4 symmetry oscilators are rare, but still, I think they're a little more common than that. There's also Gabriel's p138 and maybe more.
x = 17, y = 8, rule = B3/S23
4bo6b2o2b2o$2bobo6bo2bobo$6bo5bo$2o13bo$6b2o3bobo2bo$bo9b2o2b2o$3bobo$
3bo!
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Re: LifeWiki Did-You-Knows

Postby simsim314 » January 7th, 2015, 3:38 am

Your p2 samples are not exactly c4. If you flip them you get the same oscillator as well.
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Re: LifeWiki Did-You-Knows

Postby Scorbie » January 7th, 2015, 4:16 am

simsim314 wrote:Your p2 samples are not exactly c4. If you flip them you get the same oscillator as well.

My bad... Sorry :roll: (EDIT: Still, there are more not on the wiki, I think...)
(EDIT^2: To be honest, I think I need to know precisely what C4 symmetry is... Exactly how does flipping count?)
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Re: LifeWiki Did-You-Knows

Postby simsim314 » January 7th, 2015, 10:55 am

Your oscillators have c4 symmetry obviously, but they have other symmetries as well. Having "unique" C4 symmetry means that, only rotating the pattern 90 degrees will make the same pattern, but flipping or rotating 180 degree will not. By same I mean will bring to the exact same state, or iterated state of the oscillator.
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Re: LifeWiki Did-You-Knows

Postby Scorbie » January 7th, 2015, 11:29 am

simsim314 wrote:Your oscillators have c4 symmetry obviously, but they have other symmetries as well. Having "unique" C4 symmetry means that, only rotating the pattern 90 degrees will make the same pattern, but flipping or rotating 180 degree will not. By same I mean will bring to the exact same state, or iterated state of the oscillator.
I see. Maybe these kind of things (oscs with various characteristics) are mainly the realm of billiard table configurations. They're pretty useless but pretty. (Like gems)
x = 117, y = 111, rule = B3/S23
44b2o14b2ob2o$40b2o2bo14bobobobo$2obo35bo2bobo10b2o2bobobobo$ob2o21b2o
bo10b3o2bob2o6bo2bobo2bobo$4b2o19bob2o7bo5bobobobo5b3o2bobo$4bo17b2obo
10b6o2bobobo8bobo2b5o$5bo17bobob4o14bobo6b3obo8bo$4b2o16bo7bo7bobo13bo
8bob3o$2obo18b4obobo7bobobo2b6o5b5o2bobo$ob2o23bob2o6bobobobo5bo10bobo
2b3o$4b2o18b2obo10b2obo2b3o10bobo2bobo2bo$4bo19bob2o13bobo2bo9bobobobo
2b2o$5bo35bo2b2o10bobobobo$4b2o34b2o15b2ob2o$2obo$ob2o18$71b2o16bo$70b
ob3o13bobo14b2o$2o3b2o61b3o4bo12bobo14bobob2obo2b2o$2o3b2o13b2o4bo2bo
2bo29b2o3bo4b2obo10b2obob2o14bobob2o3bo$21bo2b3o2b4o9bob2o15bo2bobob4o
b2o10bobobo3bo13b2o4b3o$2o3b2o14bobo3b2o13b2o2bob2ob2o8bob2obo18bobobo
b3o11b2o2b3obo$obobobo13b2o2bobo3bo14b2ob2obo8b2obo2bobobob3o8b2o9b2o
10bobo3bob2o$2bobo17bobobob2obo10b2obo6bo7bo3bo5bo4bo6bo2b3o3b3o2bo8bo
2bo3bo2bo$b2obo17bo8bo10b2obob4obo8b2obob2o4bobobo6b2o9b2o9b2obo3bobo$
5b2o13b2ob2o3b2ob2o12bo4b2o10bobo9bobo8b3obobobo13bob3o2b2o$6bo14bo8bo
11b2o4bo13bobobo4b2obob2o7bo3bobobo11b3o4b2o$5bo15bob2obobobo10bob4obo
b2o11bo4bo5bo3bo7b2obob2o11bo3b2obobo$5b2o15bo3bobo2b2o8bo6bob2o12b3ob
obobo2bob2o9bobo13b2o2bob2obobo$6bo17b2o3bobo10bob2ob2o23bob2obo10bobo
23b2o$5bo14b4o2b3o2bo9b2ob2obo2b2o12b2ob4obobo2bo11bo$5b2o13bo2bo2bo4b
2o15b2obo11bob2o4bo3b2o$63bo4b3o$64b3obo$66b2o13$3bob2o42b2o$3b2obo13b
2o26bo2bo$b2o17bo2bo6b2o13bo3bobo$2bo18bobo5bobo11b7ob2o$bo40bo8bo$b2o
20bobobob2o11bob2o5bo$3bob2o36bobo5bobo$3b2obo16bo3bo17bo5b2obo$7b2o
36bo8bo$8bo11b2obobobo16b2ob7o$7bo37bobo3bo$7b2o10bobo5bobo15bo2bo$3bo
b2o12b2o6bo2bo15b2o$3b2obo22b2o21$12bo$4b3o5bo$3b2o2b2ob5o$3bo8bo16bo
22bo$3bo8bo5b2o5b3obo22bo$3b4o11b2o6bo13bo11bo2b3ob4obobo$3bo3b2o17bo
13bo11bobo2bo4bobobo$3bo4bo17bo3b5o4b3ob3ob3o2bo3b2o3bo2bobo$3bo4bo9b
2o6bo3bobobo5bo2bobobobo2bo2bobo3bo3b2o$4bo3bo9b2o5b3o2bobobo5bo2b3ob
3o2bobob2o2bo5bo$4b5o43bob2obob4o3bo$66bo$65b2o!



EDIT: No offense, though :cry:
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Re: LifeWiki Did-You-Knows

Postby simsim314 » January 7th, 2015, 11:45 am

Hehe so add 100% volatility to the c4 unique period oscillators :)

There are only 4 knwon C4 100% volatility oscillators. None of them with same period.
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Re: LifeWiki Did-You-Knows

Postby Scorbie » January 7th, 2015, 11:55 am

Settled... phew!
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Re: LifeWiki Did-You-Knows

Postby dvgrn » February 14th, 2015, 10:30 am

simsim314 wrote:Hehe so add 100% volatility to the c4 unique period oscillators :)

There are only 4 knwon C4 100% volatility oscillators. None of them with same period.

Scorbie wrote:Settled... phew!

Not quite! Unless you're talking about C4 patterns other than 132P37 and the P11 pinwheel, anyway.

Due to the eaters and boats, those have volatility of .97 and .91, respectively. I suppose there are C4 infinite-agar versions of both of these with 100% volatility, but allowing infinite agars would probably open another new can of worms (?)

I could replace "100%" with "over 90%", but that's starting to look like a lot of qualifications for a Fascinating Fact. I'm inclined to leave this one out, especially because it's so likely to need to be updated as soon as people run symmetric apgsearch a little more...!

I've started thinking about what can be said about the recent amazing run of glider syntheses for spaceships of various speeds -- see the bottom of the first post for ideas so far. There's definitely something more specific than just "that [recent] soup searches have reduced many glider syntheses"...

Does Bob Shemyakin's thread have a reasonably complete record of 4-glider syntheses? Are any statistics for 5-glider and above syntheses worth quoting at all? What other topics should be explored and turned into nice factoids?
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Re: LifeWiki Did-You-Knows

Postby Extrementhusiast » February 15th, 2015, 5:50 pm

dvgrn wrote:I've started thinking about what can be said about the recent amazing run of glider syntheses for spaceships of various speeds -- see the bottom of the first post for ideas so far. There's definitely something more specific than just "that [recent] soup searches have reduced many glider syntheses"...

Well, why not the pattern with the currently highest clearly-defined number of gliders required to construct it? (This is because a pattern like, say, the Caterpillar is theoretically synthesizable, but an explicit synthesis has not yet been constructed.)
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Re: LifeWiki Did-You-Knows

Postby Kazyan » February 15th, 2015, 8:43 pm

Extrementhusiast wrote:Well, why not the pattern with the currently highest clearly-defined number of gliders required to construct it? (This is because a pattern like, say, the Caterpillar is theoretically synthesizable, but an explicit synthesis has not yet been constructed.)


That would be the Parallel HBK at 38380 gliders. The runner up might be x66, at 166 gliders, but the LifeWiki's bookkeeping is a bit shoddy to know for sure. That gulf, at least, is interesting.
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Re: LifeWiki Did-You-Knows

Postby dvgrn » February 15th, 2015, 9:10 pm

Kazyan wrote:
Extrementhusiast wrote:Well, why not the pattern with the currently highest clearly-defined number of gliders required to construct it? (This is because a pattern like, say, the Caterpillar is theoretically synthesizable, but an explicit synthesis has not yet been constructed.)


That would be the Parallel HBK at 38380 gliders. The runner up might be x66, at 166 gliders, but the LifeWiki's bookkeeping is a bit shoddy to know for sure. That gulf, at least, is interesting.

The HBK gun that chris_c built contains 687432 gliders in two loops, in tandem pairs that produce gliders that collide with each other in groups of six. The result is two perpendicular salvos, totalling 57286 gliders:

ChrisCainHBKrecipe.mc.gz
57286 gliders extracted from Chris Cain's HBK gun
(759.56 KiB) Downloaded 268 times

As the LifeWiki notes, simsim314's recipe is only 38380 gliders, so that's probably the factoid we're looking for here.

However, the Gemini spaceship also has an explicit glider construction, and I do believe it's irreducibly larger than the HBK recipe. Will report back with the exact glider count when I have it...!
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Re: LifeWiki Did-You-Knows

Postby dvgrn » February 16th, 2015, 4:35 am

dvgrn wrote:However, the Gemini spaceship also has an explicit glider construction, and I do believe it's irreducibly larger than the HBK recipe. Will report back with the exact glider count when I have it...!

Looks like the current-best recipe is 192725 gliders in all, over five times bigger than the parallel HBK spaceship synthesis:

gemini-extended-synthesis.mc.gz
192725 gliders construct a Gemini spaceship
(1.35 MiB) Downloaded 250 times

A Gemini spaceship will be completely constructed in about 130 million ticks, but will take a little longer to reach a completely canonical form. The gliders generally have the same spacing as the ones that the actual Gemini replicator units generate, so there's definitely a lot of room to tighten up the slow-salvo glider pairs.

The elbow blocks (especially) could be constructed much more efficiently. There's also a much more efficient way to catch the first round of destruction-arm gliders from each replicator unit: instead of building a whole extra copy of each R.U. just so that it can be shot down, send instead a single mirror-image glider for each destruction-arm output glider. Or for bonus points, construct the eater constellation used in the Gemini guns, then shoot it down again after it has absorbed all of the destruction-arm elbow ops -- that would save another horribly large number of gliders.

On the other hand, nothing can be done to improve the spacing or the count of the twelve streams of data-tape gliders coming in from the lower right, and that's a fair fraction of the whole construction. So at the moment I'm not inclined to put much more effort into optimizing this particular oversized synthesis...!
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Re: LifeWiki Did-You-Knows

Postby dvgrn » February 27th, 2015, 1:24 pm

dvgrn wrote:There's also a much more efficient way to catch the first round of destruction-arm gliders from each replicator unit: instead of building a whole extra copy of each R.U. just so that it can be shot down, send instead a single mirror-image glider for each destruction-arm output glider...

On the other hand, nothing can be done to improve the spacing or the count of the twelve streams of data-tape gliders coming in from the lower right, and that's a fair fraction of the whole construction.

Yes, indeed: the above idea saves over 10,000 gliders -- but there are still almost 182,000 gliders left in the recipe.

Further improvements are possible, but mostly in the range of dozens or hundreds of gliders, not tens of thousands. The biggest remaining target is the 6808 gliders suppressing the two destruction-arm guns. These could still be replaced by some small number of gliders, under fifty anyway, which would build and then destroy two eater constellations that would catch the destruction-arm output before the elbow instead of after it.

EDIT: Oops, "under fifty" is an under-estimate, probably, because you have to build two copies of something like this:
x = 34, y = 51, rule = B3/S23
32b2o$31bobo$31bo$30b2o3$25b2o$25b2o3$24bo$23bobo$24bo$21b3o$21bo4$18b
2o$18b2o3$17bo$16bobo$17bo$14b3o$14bo4$9b2o$9b2o3$8bo$7bobo$8bo$5b3o$
5bo6$3bob2o$b3ob2o$o$b3ob2o$3bobo$3bobo$4bo!

-- and then destroy it again cleanly, leaving just an elbow block in the right place. Spacing is arbitrary, though, so that's good -- it doesn't have to fit in as tight a space as in the Gemini guns, and it doesn't have to deal with the occasional gliders that come in from other directions.

gemini-reduced-synthesis.mc.gz
181999 gliders build a Gemini spaceship
(1.22 MiB) Downloaded 256 times

Then the V-shaped replicator unit construction recipes could be packed a lot better, of course -- anyone feel like writing a script for that? It would be an impressive crystallization of stable circuitry at the tightest packing. As it stands, about the best you can say is that it's done within ninety million ticks (89719200).
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dvgrn
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Re: LifeWiki Did-You-Knows

Postby chris_c » March 1st, 2015, 11:17 am

dvgrn wrote:Oops, "under fifty" is an under-estimate, probably, because you have to build two copies of something like this


I think it can be done in 12 gliders although I don't plan on proving this claim concretely. The idea is to intercept the gliders for the "FIRE WHITE" and "FIRE BLACK" operations after the final reflectors but before the glider duplicators:

x = 1167, y = 1453, rule = LifeHistory
957.A$957.3A$960.A$959.2A$974.2A$974.A$972.A.A$961.A10.2A$960.A.A$
960.A.A$955.2A4.A$954.A.A15.2A$954.A17.A.A$953.2A19.A$974.2A2$949.2A$
950.A$950.A.A$951.2A$963.2A$963.2A9$975.2A$975.A$973.A.A$973.2A8$986.
2A$986.A$984.A.A$984.2A$955.2A15.2A$954.A.A15.2A$954.A$953.2A2$698.2A
$698.A$696.A.A$696.2A$960.A$960.3A$963.A$941.2A19.2A$941.A15.A$697.2A
240.A.A15.3A$691.2A4.2A240.2A19.A$691.2A108.A157.2A$799.3A11.A$773.2A
23.A14.3A$774.A23.2A16.A14.A86.2A$692.2A80.A.A38.2A12.3A86.2A$692.2A
2.2A77.2A2.2A47.A$696.A.A80.2A47.2A126.2A$684.2A12.A257.2A17.2A$684.A
.A11.2A275.2A$686.A140.2A$686.2A120.2A17.2A$808.2A166.2A$976.A$963.2A
12.3A$964.A14.A$684.2A275.3A$684.A.A274.A$686.A86.2A36.2A$686.2A84.A.
A16.2A19.A115.2A$772.A18.A.A15.3A116.2A$771.2A20.A15.A$787.2A4.2A19.
2A$787.A.A25.A$789.A22.3A$780.2A7.2A21.A$676.2A102.2A$676.2A2$670.A$
668.3A$667.A18.2A117.2A$667.2A17.2A118.A$696.2A72.2A34.A.A15.2A$696.A
74.A35.2A15.2A$694.A.A74.A.A$694.2A76.2A$789.A$787.3A$786.A$786.2A$
770.2A$771.A$758.2A11.A.A$759.A12.2A$690.2A67.A.A$690.A.A67.2A2.2A59.
2A$692.A71.2A59.A.A$692.2A111.2A20.A$730.2A73.A21.2A$730.2A71.A.A$
765.2A36.2A$759.2A4.2A$732.2A25.2A171.A$675.2A55.2A75.2A119.3A$675.2A
68.2A61.A.A118.A$684.2A59.A62.A120.2A$684.A.A56.A.A61.2A60.A$686.A9.A
46.2A122.3A$686.2A6.3A50.2A117.A$693.A53.2A117.2A$693.2A58.2A82.A34.A
25.2A$754.A82.3A32.3A24.A$754.A.A83.A34.A23.A.A$755.2A60.2A20.2A33.2A
24.2A2.2A37.A$817.2A7.2A56.2A18.2A35.3A15.A9.A$826.A57.A55.A18.3A5.3A
$734.2A88.A.A55.A.A42.2A11.2A20.A3.A$703.2A29.2A88.2A4.2A44.2A4.2A43.
2A32.2A3.2A$703.2A103.2A20.A44.A2.A$809.A18.A.A45.2A$809.A.A16.2A34.
2A$715.A94.2A52.2A$666.2A46.A.A$666.2A47.2A$672.2A32.2A$672.2A33.A48.
2A15.2A123.2A52.2A$707.A.A46.2A15.A.A121.A.A16.2A34.2A$708.2A65.A121.
A18.A.A45.2A$670.2A69.2A32.2A119.2A20.A44.A2.A$670.2A5.2A62.2A96.2A
32.2A3.2A32.2A4.2A44.2A4.2A$677.2A160.2A11.2A20.A3.A33.A.A55.A.A$766.
A85.A18.3A5.3A32.A57.A$764.3A49.2A35.3A15.A9.A23.2A7.2A56.2A$763.A48.
2A2.2A37.A49.2A20.2A33.2A$763.2A46.A.A114.A34.A$811.A23.2A88.3A32.3A$
810.2A23.A89.A34.A$836.3A115.2A$605.2A231.A115.A$605.A349.3A$603.A.A
351.A$603.2A3$691.2A39.A$668.A23.A39.3A35.2A$666.3A23.A.A40.A34.2A$
604.2A34.2A23.A27.2A39.2A180.A$598.2A4.2A35.A23.2A247.3A$598.2A41.A.A
269.A$642.2A2.2A37.A79.2A146.2A$646.2A35.3A79.2A$682.A86.2A$599.2A68.
2A11.2A85.2A$599.2A2.2A64.2A$603.A.A119.2A$591.2A12.A119.2A36.2A$591.
A.A11.2A141.2A13.2A$593.A154.A.A$593.2A155.A$738.2A10.2A141.2A$738.A
154.2A$640.2A52.2A32.2A9.3A$639.A.A16.2A34.2A11.2A20.A11.A$591.2A46.A
18.A.A46.A21.A.A$567.A23.A.A44.2A20.A47.3A19.2A$567.3A23.A60.2A4.2A
48.A$570.A22.2A59.A.A$569.2A14.2A69.A33.2A$585.2A60.2A7.2A10.2A20.A$
647.2A18.A.A21.3A214.2A$667.A25.A214.2A$666.2A5$637.2A$638.A$638.A.A
524.A$639.2A523.A$586.2A576.3A$586.A.A$588.A$588.2A$657.2A$657.A$655.
A.A$655.2A$570.2A$569.A.A23.A$569.A23.3A$568.2A22.A$576.2A14.2A$576.
2A6$654.2A$638.2A14.2A$639.A22.2A$636.3A23.A$636.A23.A.A$660.2A$575.
2A$574.A.A29.A$574.A29.3A$573.2A28.A38.A$603.2A37.3A$645.A$623.A20.2A
$621.3A15.A$540.2A78.A18.3A$540.A66.2A11.2A20.A$538.A.A66.2A32.2A$
538.2A5$576.2A21.2A37.2A$539.2A35.2A21.A.A36.2A17.2A$533.2A4.2A41.2A
17.A55.2A$533.2A47.2A17.2A2$658.2A$580.2A76.A$534.2A44.2A5.2A56.2A12.
3A$534.2A2.2A47.2A39.2A16.A14.A$538.A.A65.2A20.A14.3A$526.2A12.A64.A.
A21.3A11.A$526.A.A11.2A63.A25.A$528.A75.2A$528.2A5$526.2A$526.A.A$
528.A$528.2A7$518.2A$518.2A2$512.A$510.3A$509.A$509.2A$529.2A$529.A$
527.A.A$527.2A3$513.2A$512.A.A$512.A$511.2A7$516.2A$517.A$514.3A$514.
A4$532.2A$532.A.A$507.2A25.A$508.A25.2A$469.2A37.A.A15.2A$469.A39.2A
15.2A$467.A.A$467.2A6$468.2A$462.2A4.2A$462.2A2$527.2A$527.A.A$463.2A
64.A$463.2A2.2A60.2A$467.A.A$455.2A12.A$455.A.A11.2A$457.A$457.2A52.
2A$510.A.A$510.A$509.2A2$455.2A$455.A.A$457.A$457.2A2$519.2A$519.2A7.
2A$528.A$526.A.A$526.2A4.2A$447.2A61.2A20.A19.2A$447.2A62.A18.A.A18.A
.A$511.A.A16.2A19.A11.A$441.A70.2A36.2A9.3A$439.3A118.A$438.A17.2A
102.2A10.2A$438.2A16.A115.A$454.A.A113.A.A$454.2A114.2A13.2A$547.2A
36.2A$439.A107.2A$439.3A$430.A11.A148.2A$430.3A8.2A14.A133.2A$433.A
22.A.A59.2A67.2A$416.2A14.2A23.A56.2A2.2A67.2A$416.2A95.A.A$513.A$
512.2A42.2A$410.2A145.A34.2A$410.2A142.3A35.2A$414.2A138.A$414.2A36.
2A$452.A.A$454.A$445.2A7.2A$409.2A34.A$409.2A35.3A$448.A3$585.2A$585.
A$586.3A$588.A$444.A$442.3A118.2A$441.A121.2A32.2A$416.2A23.2A87.2A
65.A$417.A111.A.A46.2A15.A.A$383.2A29.3A44.A67.A48.2A15.2A$383.A30.A
44.3A19.2A45.2A$381.A.A74.A21.A.A54.2A$381.2A62.2A11.2A20.A55.A.A$
445.2A32.2A56.A3$525.2A$525.2A29.2A$382.2A120.2A50.2A$376.2A4.2A30.2A
21.2A37.2A26.2A$376.2A36.2A21.A.A36.2A$420.2A17.A137.2A$420.2A17.2A
135.A.A$576.A$377.2A196.2A$377.2A2.2A35.2A149.2A$381.A.A34.2A5.2A79.
2A61.2A$369.2A12.A41.2A39.2A38.A.A56.2A$369.A.A11.2A59.2A20.A41.A56.A
.A$371.A71.A.A21.3A11.2A25.2A57.A$371.2A70.A25.A11.2A84.2A$442.2A110.
2A$554.2A25.2A$495.2A84.2A4.2A$495.A91.2A$496.3A53.2A$498.A53.2A$344.
2A139.2A$345.A140.A99.2A$345.A.A15.2A118.3A96.2A2.2A$346.2A15.2A118.A
97.A.A$581.A12.2A$580.2A11.A.A$593.A$592.2A$608.2A$608.A$609.3A$611.A
$594.2A$593.A.A$593.A$364.2A226.2A60.A$364.A.A285.3A$366.A284.A$366.
2A283.2A$622.A34.A$622.3A32.3A$625.A34.A$602.2A20.2A33.2A$348.2A252.
2A7.2A56.2A$347.A.A261.A57.A$347.A261.A.A55.A.A$346.2A60.A200.2A4.2A
44.2A4.2A$406.3A184.2A20.A44.A2.A$405.A188.A18.A.A45.2A$405.2A187.A.A
16.2A34.2A$376.A34.A183.2A52.2A$376.3A32.3A$379.A34.A$356.2A20.2A33.
2A$356.2A7.2A56.2A$365.A57.A$363.A.A55.A.A$363.2A4.2A44.2A4.2A$347.2A
20.A44.A2.A206.2A32.2A3.2A$348.A18.A.A45.2A207.2A11.2A20.A3.A$348.A.A
16.2A34.2A232.A18.3A5.3A$349.2A52.2A196.2A35.3A15.A9.A$597.2A2.2A37.A
$596.A.A$596.A23.2A$595.2A23.A$621.3A$623.A2$378.2A32.2A3.2A$378.2A
11.2A20.A3.A$391.A18.3A5.3A$355.2A35.3A15.A9.A$351.2A2.2A37.A$350.A.A
$350.A23.2A$349.2A23.A$375.3A$377.A23$282.2A$282.A$280.A.A$280.2A6$
281.2A$275.2A4.2A$275.2A4$276.2A$276.2A2.2A$280.A.A521.A$268.2A12.A
519.3A$268.A.A11.2A517.A$270.A530.2A$270.2A4$770.2A$268.2A501.A$268.A
.A500.A.A$270.A501.2A2.2A37.A$270.2A504.2A35.3A15.A9.A$812.A18.3A5.3A
$799.2A11.2A20.A3.A$799.2A32.2A3.2A2$746.2D$747.D$260.2A485.D.D$260.
2A486.2D$744.2E$254.A490.2E$252.3A489.E7.2E16.2A52.2A$251.A500.E.E14.
A.A16.2A34.2A$251.2A499.E16.A18.A.A45.2A$271.2A495.2A20.A44.A2.A$271.
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56.2A$777.2A20.2A33.2A$255.2A543.A34.A$254.A.A540.3A32.3A$254.A542.A
34.A$253.2A571.2A$826.A$827.3A$829.A4$258.2A$259.A$256.3A$256.A531.A$
786.3A$785.A$785.2A$274.2A$274.A.A$249.2A25.A$250.A25.2A$250.A.A15.2A
$251.2A15.2A4$765.2A$765.2A7$269.2A$269.A.A$271.A508.2A$271.2A507.2A
5$253.2A$252.A.A$252.A$251.2A7$261.2A$261.2A7.2A$270.A$268.A.A$268.2A
4.2A$252.2A20.A19.2A$253.A18.A.A18.A.A$253.A.A16.2A19.A11.A$254.2A36.
2A9.3A$302.A$302.2A10.2A$314.A$312.A.A$312.2A13.2A$289.2A36.2A$289.2A
2$333.2A$333.2A$260.2A67.2A$158.2A96.2A2.2A67.2A$158.A96.A.A$156.A.A
96.A$156.2A96.2A42.2A$299.A34.2A$296.3A35.2A$296.A3$157.2A$151.2A4.2A
$151.2A4$152.2A$152.2A2.2A50.2A117.2A$156.A.A26.A23.A25.A91.A$144.2A
12.A24.3A23.A.A21.3A92.3A$144.A.A11.2A22.A27.2A20.A97.A$146.A35.2A48.
2A$146.2A157.2A$159.A42.A49.A52.2A32.2A$159.3A38.3A47.3A19.2A65.A$
162.A36.A49.A21.A.A46.2A15.A.A$152.2A7.2A23.2A11.2A35.2A11.2A20.A48.
2A15.2A$144.2A7.A32.2A48.2A32.2A$120.A23.A.A6.A.A123.2A$120.3A23.A7.
2A122.A.A$123.A22.2A131.A$122.2A14.2A$138.2A$267.2A$267.2A29.2A$211.
2A85.2A$150.A23.2A35.2A11.2A$149.A.A22.A49.A$150.A14.2A8.3A47.3A91.2A
$165.A11.A49.A90.A.A$166.3A149.A$168.A38.2A48.2A58.2A$185.2A20.A27.2A
20.A53.2A$152.2A30.A.A21.3A23.A.A21.3A50.2A$139.2A10.A.A30.A25.A23.A
25.A46.2A$139.A.A9.A16.2A13.2A48.2A72.A.A$141.A8.2A17.A139.A$141.2A
23.3A140.2A$166.A129.2A$296.2A25.2A$159.2A162.2A4.2A$159.2A168.2A$
123.2A169.2A$122.A.A23.A145.2A$122.A23.3A$121.2A22.A182.2A$129.2A14.
2A177.2A2.2A$129.2A192.A.A$149.2A172.A12.2A$150.A171.2A11.A.A$150.A.A
182.A$151.2A181.2A$167.A182.2A$165.3A182.A$164.A186.3A$164.2A187.A$
336.2A$335.A.A$335.A$128.2A204.2A60.A$127.A.A264.3A$127.A265.A$126.2A
265.2A$364.A34.A$364.3A32.3A$367.A34.A$171.2A171.2A20.2A33.2A$171.2A
171.2A7.2A56.2A$353.A57.A$351.A.A55.A.A$351.2A4.2A44.2A4.2A$166.2A
167.2A20.A44.A2.A$166.2A168.A18.A.A45.2A$170.2A164.A.A16.2A34.2A$170.
2A165.2A52.2A$129.2A21.2A$129.2A21.A.A$135.2A17.A9.2A$135.2A17.2A8.2A
3$133.2A$133.2A5.2A224.2A32.2A3.2A$140.2A224.2A11.2A20.A3.A$379.A18.
3A5.3A$343.2A35.3A15.A9.A$339.2A2.2A37.A$338.A.A$338.A23.2A$337.2A23.
A$363.3A$365.A70$490.2D$491.D$491.D.D$492.2D$488.2E$489.2E$488.E7.2E$
496.E.E$496.E20$798.A$798.3A$801.A$800.2A$815.2A$815.A$813.A.A$802.A
10.2A$801.A.A$365.A435.A.A$363.3A430.2A4.A$337.2A23.A432.A.A15.2A$
338.A23.2A431.A17.A.A$338.A.A453.2A19.A$339.2A2.2A37.A432.2A$343.2A
35.3A15.A9.A$379.A18.3A5.3A$140.2A224.2A11.2A20.A3.A$133.2A5.2A224.2A
32.2A3.2A$133.2A$804.2A$804.2A$135.2A17.2A8.2A$135.2A17.A9.2A$129.2A
21.A.A$129.2A21.2A$170.2A165.2A52.2A$170.2A164.A.A16.2A34.2A$166.2A
168.A18.A.A45.2A$166.2A167.2A20.A44.A2.A$351.2A4.2A44.2A4.2A405.2A$
351.A.A55.A.A404.A$353.A57.A402.A.A$171.2A171.2A7.2A56.2A401.2A$171.
2A171.2A20.2A33.2A$367.A34.A$364.3A32.3A$364.A34.A$126.2A265.2A$127.A
265.A$127.A.A264.3A$128.2A204.2A60.A430.2A$335.A491.A$335.A.A487.A.A$
336.2A487.2A$164.2A187.A442.2A15.2A$164.A186.3A441.A.A15.2A$165.3A
182.A444.A$167.A182.2A442.2A$151.2A181.2A$150.A.A182.A$150.A171.2A11.
A.A$149.2A172.A12.2A$129.2A192.A.A$129.2A14.2A177.2A2.2A471.A$121.2A
22.A182.2A471.3A$122.A23.3A655.A$122.A.A23.A145.2A486.2A19.2A$123.2A
169.2A486.A15.A$159.2A168.2A449.A.A15.3A$159.2A162.2A4.2A449.2A19.A$
296.2A25.2A475.2A$166.A129.2A$141.2A23.3A140.2A$141.A8.2A17.A139.A
449.2A$139.A.A9.A16.2A13.2A48.2A72.A.A449.2A$139.2A10.A.A30.A25.A23.A
25.A46.2A$152.2A30.A.A21.3A23.A.A21.3A50.2A484.2A$185.2A20.A27.2A20.A
53.2A484.2A17.2A$168.A38.2A48.2A58.2A497.2A$166.3A149.A$165.A11.A49.A
90.A.A$150.A14.2A8.3A47.3A91.2A496.2A$149.A.A22.A49.A592.A$150.A23.2A
35.2A11.2A578.2A12.3A$211.2A85.2A487.2A16.A14.A$267.2A29.2A487.A14.3A
$267.2A519.3A11.A$138.2A650.A$122.2A14.2A629.2A$123.A22.2A131.A489.2A
$120.3A23.A7.2A122.A.A$120.A23.A.A6.A.A123.2A$144.2A7.A32.2A48.2A32.
2A$152.2A7.2A23.2A11.2A35.2A11.2A20.A48.2A15.2A$162.A36.A49.A21.A.A
46.2A15.A.A$159.3A38.3A47.3A19.2A65.A$159.A42.A49.A52.2A32.2A$146.2A
157.2A$146.A35.2A48.2A$144.A.A11.2A22.A27.2A20.A97.A$144.2A12.A24.3A
23.A.A21.3A92.3A$156.A.A26.A23.A25.A91.A$152.2A2.2A50.2A117.2A$152.2A
4$151.2A$151.2A4.2A$157.2A3$296.A$296.3A35.2A$299.A34.2A$156.2A96.2A
42.2A$156.A.A96.A$158.A96.A.A$158.2A96.2A2.2A67.2A$260.2A67.2A$333.2A
$333.2A2$289.2A$289.2A36.2A$312.2A13.2A$312.A.A$314.A$302.2A10.2A$
302.A$254.2A36.2A9.3A$253.A.A16.2A19.A11.A$253.A18.A.A18.A.A$252.2A
20.A19.2A$268.2A4.2A$268.A.A$270.A$261.2A7.2A$261.2A7$251.2A$252.A$
252.A.A$253.2A5$271.2A$271.A$269.A.A$269.2A12$251.2A15.2A$250.A.A15.
2A$250.A25.2A743.A$249.2A25.A744.3A$274.A.A747.A$274.2A747.2A$1038.2A
$1038.A$1036.A.A$256.A768.A10.2A$256.3A765.A.A$259.A764.A.A$258.2A
759.2A4.A$896.A121.A.A15.2A$896.A.A119.A17.A.A$896.2A119.2A19.A$1038.
2A2$1013.2A$253.2A759.A$254.A759.A.A$254.A.A758.2A$255.2A770.2A$1027.
2A2$269.2A$269.A.A$271.A$271.2A$251.2A$251.A$252.3A$254.A784.2A$1039.
A$260.2A775.A.A$260.2A775.2A7$270.2A$270.A779.2A$268.A.A779.A$268.2A
778.A.A$1048.2A$1019.2A15.2A$1018.A.A15.2A$1018.A$270.2A745.2A$270.A$
268.A.A11.2A$268.2A12.A$280.A.A$276.2A2.2A$276.2A746.A$1024.3A$1027.A
$1005.2A19.2A$275.2A728.A15.A$275.2A4.2A720.A.A15.3A$281.2A720.2A19.A
$1023.2A3$982.2A$982.2A$280.2A$280.A.A737.2A$282.A737.2A17.2A$282.2A
755.2A$655.A$653.3A$627.2A23.A387.2A$628.A23.2A386.A$628.A.A396.2A12.
3A$629.2A2.2A37.A355.A14.A$633.2A35.3A15.A9.A326.3A$669.A18.3A5.3A
326.A$656.2A11.2A20.A3.A$656.2A32.2A3.2A295.2A$992.2A7$627.2A52.2A$
626.A.A16.2A34.2A$626.A18.A.A45.2A$625.2A20.A44.A2.A$641.2A4.2A44.2A
4.2A$377.A263.A.A55.A.A$375.3A265.A57.A$349.2A23.A259.2A7.2A56.2A$
350.A23.2A258.2A20.2A33.2A105.A$350.A.A304.A34.A105.3A$351.2A2.2A37.A
259.3A32.3A109.A$355.2A35.3A15.A9.A233.A34.A110.2A$391.A18.3A5.3A262.
2A130.2A$378.2A11.2A20.A3.A265.A131.A$378.2A32.2A3.2A265.3A126.A.A$
624.2A60.A115.A10.2A$625.A175.A.A$625.A.A173.A.A$626.2A168.2A4.A$643.
A151.A.A15.2A$641.3A151.A17.A.A$640.A153.2A19.A$349.2A52.2A235.2A173.
2A$348.A.A16.2A34.2A219.2A$348.A18.A.A45.2A208.A$347.2A20.A44.A2.A
194.2A11.A.A$363.2A4.2A44.2A4.2A190.A12.2A$363.A.A55.A.A189.A.A$365.A
57.A190.2A2.2A184.2A$356.2A7.2A56.2A193.2A184.2A$356.2A20.2A33.2A$
379.A34.A$376.3A32.3A$376.A34.A207.2A$405.2A206.2A4.2A$405.A207.2A$
406.3A$346.2A60.A$347.A468.2A$347.A.A466.A$348.2A464.A.A$814.2A$607.A
$577.2A28.3A$570.2A5.2A31.A$366.2A202.2A37.2A$366.A237.A$364.A.A237.
3A$364.2A105.A100.2A17.2A14.A$471.3A98.2A17.A14.2A219.2A$474.A91.2A
21.A.A235.A$473.2A91.2A21.2A234.A.A$486.A53.2A283.2A$484.3A53.2A254.
2A15.2A$483.A311.A.A15.2A$483.2A118.2A190.A$542.2A59.2A17.2A170.2A$
430.2A110.2A78.2A$431.A25.A11.2A84.2A$431.A.A21.3A11.2A25.2A57.A$346.
2A15.2A67.2A20.A41.A56.A.A67.2A$345.A.A15.2A48.2A39.2A38.A.A56.2A68.A
$345.A60.2A5.2A79.2A61.2A51.2A12.3A174.A$344.2A60.2A149.2A52.A14.A
174.3A$563.2A43.3A193.A$564.A43.A173.2A19.2A$408.2A17.2A135.A.A29.2A
184.A15.A$408.2A17.A137.2A29.A183.A.A15.3A$402.2A21.A.A36.2A131.3A
180.2A19.A$402.2A21.2A37.2A26.2A105.A200.2A$371.2A119.2A50.2A$371.A
141.2A29.2A$369.A.A11.2A128.2A244.2A$369.2A12.A375.2A$381.A.A$377.2A
2.2A50.2A32.2A56.A271.2A$377.2A54.2A11.2A20.A55.A.A270.2A17.2A$446.A
21.A.A54.2A289.2A$402.A44.3A19.2A45.2A$402.3A44.A67.A48.2A15.2A$376.
2A27.A111.A.A46.2A15.A.A231.2A$376.2A4.2A20.2A23.2A87.2A65.A231.A$
382.2A45.A121.2A32.2A217.2A12.3A$430.3A118.2A234.2A16.A14.A$432.A354.
A14.3A$576.A211.3A11.A$574.3A213.A$573.A195.2A$381.2A190.2A194.2A$
381.A.A$383.A$383.2A51.A$397.2A35.3A$397.2A34.A$433.2A7.2A$442.A$440.
A.A$402.2A36.2A$402.2A138.A$398.2A142.3A35.2A$398.2A145.A34.2A$500.2A
42.2A$501.A$404.2A95.A.A$404.2A14.2A23.A56.2A2.2A67.2A$421.A22.A.A59.
2A67.2A$418.3A8.2A14.A133.2A$418.A11.A148.2A$427.3A$427.A107.2A$535.
2A36.2A$442.2A114.2A13.2A$442.A.A113.A.A$426.2A16.A115.A$426.A17.2A
102.2A10.2A$427.3A118.A$429.A70.2A36.2A9.3A$499.A.A16.2A19.A11.A$435.
2A62.A18.A.A18.A.A$435.2A61.2A20.A19.2A$514.2A4.2A$514.A.A$516.A$507.
2A7.2A$507.2A2$445.2A$445.A$443.A.A$443.2A2$497.2A$498.A$498.A.A$445.
2A52.2A$445.A$443.A.A11.2A$443.2A12.A$455.A.A$451.2A2.2A60.2A$451.2A
64.A$515.A.A$515.2A2$450.2A$450.2A4.2A$456.2A6$455.2A$455.A.A$457.A
39.2A15.2A$457.2A37.A.A15.2A$496.A25.2A$495.2A25.A$520.A.A$520.2A4$
502.A$502.3A$505.A$504.2A7$499.2A$500.A$500.A.A$501.2A3$515.2A$515.A.
A$517.A$517.2A$497.2A$497.A$498.3A$500.A2$506.2A$506.2A7$516.2A$516.A
$514.A.A$514.2A5$516.2A$10.3E503.A$12.E501.A.A11.2A$11.E502.2A12.A$
526.A.A$522.2A2.2A$522.2A73.2A$598.A25.A$598.A.A21.3A11.A$599.2A20.A
14.3A$521.2A57.2A39.2A16.A14.A$3E518.2A4.2A44.2A5.2A56.2A12.3A$2.E
524.2A44.2A76.A$.E649.2A2$575.2A17.2A$575.2A17.A55.2A$569.2A21.A.A36.
2A17.2A$526.2A41.2A21.2A37.2A$526.A.A$528.A$528.2A3$600.2A32.2A$600.
2A11.2A20.A$613.A18.3A$614.3A15.A$616.A20.2A$638.A$596.2A37.3A$566.2A
28.A38.A$567.A29.3A$567.A.A29.A$568.2A$653.2A$629.A23.A.A$629.3A23.A$
632.A22.2A$631.2A14.2A$647.2A6$569.2A$569.2A14.2A$561.2A22.A$562.A23.
3A$562.A.A23.A$563.2A$648.2A$648.A.A$650.A$650.2A$581.2A$581.A$579.A.
A$579.2A$632.2A$631.A.A$631.A$630.2A5$659.2A$660.A25.A$640.2A18.A.A
21.3A$578.2A60.2A7.2A10.2A20.A$562.2A14.2A69.A33.2A$563.A22.2A59.A.A$
560.3A23.A60.2A4.2A48.A$560.A23.A.A44.2A20.A47.3A19.2A$584.2A46.A18.A
.A46.A21.A.A$632.A.A16.2A34.2A11.2A20.A11.A$633.2A52.2A32.2A9.3A$731.
A$731.2A10.2A$586.2A155.A$586.A154.A.A$584.A.A11.2A141.2A13.2A$584.2A
12.A119.2A36.2A$596.A.A119.2A$592.2A2.2A64.2A$592.2A68.2A11.2A85.2A$
675.A86.2A$639.2A35.3A79.2A$635.2A2.2A37.A79.2A$591.2A41.A.A$591.2A4.
2A35.A23.2A$597.2A34.2A23.A27.2A39.2A$659.3A23.A.A40.A34.2A$661.A23.A
39.3A35.2A$684.2A39.A3$596.2A$596.A.A$598.A$598.2A4$756.2A$756.A$757.
3A$759.A$670.2A164.A$663.2A5.2A62.2A98.3A$663.2A69.2A32.2A38.2A23.A$
701.2A65.A40.A23.2A$700.A.A46.2A15.A.A40.A.A$665.2A33.A48.2A15.2A42.
2A2.2A37.A$665.2A32.2A113.2A35.3A15.A9.A$659.2A47.2A140.A18.3A5.3A$
659.2A46.A.A127.2A11.2A20.A3.A$708.A128.2A32.2A3.2A3$696.2A$696.2A29.
2A$727.2A3$748.2A58.2A52.2A$747.A.A57.A.A16.2A34.2A$747.A59.A18.A.A
45.2A$686.2A58.2A58.2A20.A44.A2.A$686.A53.2A80.2A4.2A44.2A4.2A$679.2A
6.3A50.2A80.A.A55.A.A$679.A9.A46.2A86.A57.A$677.A.A56.A.A76.2A7.2A56.
2A$677.2A59.A76.2A20.2A33.2A$668.2A68.2A98.A34.A$668.2A55.2A108.3A32.
3A$725.2A25.2A81.A34.A$752.2A4.2A104.2A$758.2A104.A$723.2A140.3A$723.
2A80.2A60.A$685.2A119.A$685.A71.2A41.2A4.A.A$683.A.A67.2A2.2A41.A.A4.
2A$683.2A67.A.A47.A$752.A12.2A35.2A$751.2A11.A.A$764.A$763.2A60.2A$
779.2A44.A$779.A43.A.A$780.3A40.2A$782.A$687.2A76.2A$687.A.A74.A.A$
689.A74.A$689.2A72.2A$660.2A17.2A$660.A18.2A$661.3A$663.A2$669.2A$
669.2A102.2A30.2A15.2A$773.2A7.2A20.A.A15.2A$782.A21.A$780.A.A20.2A$
780.2A$764.2A$765.A$679.2A84.A.A$679.A86.2A$677.A.A130.A$677.2A103.A
27.3A$780.3A30.A$779.A11.A20.2A$764.A14.2A8.3A15.A$763.A.A22.A18.3A$
679.2A83.A23.2A20.A$679.A129.2A$677.A.A11.2A$677.2A12.A$689.A.A$685.
2A2.2A$685.2A$768.2A36.2A$767.A.A36.2A17.2A$767.A57.2A$684.2A80.2A7.
2A$684.2A4.2A84.A$690.2A81.3A50.2A$773.A52.A$813.2A12.3A$796.2A16.A
14.A$796.A14.3A$797.3A11.A$689.2A108.A$689.A.A$691.A$691.2A!


A nice point is that removing those gliders downgrades the "FIRE" operations to "DEC" operations but that this has absolutely no effect on the elbow block:

x = 421, y = 177, rule = B3/S23
184bo$183bo$183b3o2$169bo249bo$168bo249bo$168b3o247b3o2$179bo$178bo$
178b3o2$167bobo247bobo$167b2o248b2o$168bo249bo30$129bo249bo$128bo5bo
243bo5bo$128b3o2bo244b3o2bo$133b3o247b3o5$127bobo247bobo$127b2o248b2o$
128bo249bo28$91bobo247bobo$91b2o248b2o$92bo249bo5$90bo249bo$90bobo247b
obo$90b2o248b2o27$71bo$70bo$70b3o12$42bo249bo$40b2o248b2o$41b2o248b2o
5$40bo249bo$39bo249bo$39b3o7bo239b3o$48bo$48b3o32$2o248b2o$2o248b2o!


P.S. It was nice to finally understand how Gemini works in more detail: two groups of reflectors in each construction unit so that it is perfectly happy in accepting gliders from the NW or the SE.... genius!
chris_c
 
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Re: LifeWiki Did-You-Knows

Postby dvgrn » March 1st, 2015, 12:17 pm

chris_c wrote:
dvgrn wrote:Oops, "under fifty" is an under-estimate, probably, because you have to build two copies of something like this


I think it can be done in 12 gliders although I don't plan on proving this claim concretely.

Ah, nice! Sure, there's nothing stopping that from working. That brings the recipe down within spitting distance of 175K gliders -- 175172 to be precise (if not necessarily exact). You still need two gliders to shoot down the destructor elbows, plus the six for each replicator unit.

As noted above, the recipe can be reduced to well below 175000 gliders, by building the initial Gemini R.U.s with more efficient non-slow-pair recipes that the actual Gemini can't use. But I don't plan on proving that claim concretely, either!
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