ConwayLife.com

On February 8, 2022, Dave Greene wrote: NewLifeCA 8 Feb 2022: Conway's Life News Emails, But Only If You Opt In

Hello! This is Dave Greene with a one-time group message related to the old LifeCA mailing list. You were in the database for the LifeCA Yahoo group at the time of its rather sudden demise at the end of 2020 -- so this email is going to you and to all of the eighty-odd other email addresses in that group.

For the past year and change, I haven't had anywhere to send occasional Life news updates -- and recently it has come to my attention that news isn't getting around to all of you ex-LifeCA folks. For example, several people recently turned out to be unaware that a Conway's Life textbook was being written, let alone that it has now been completed.

There's been quite a surge of other news recently, including solutions in January 2022 to the Grand^N Orphan problem and the Unique Father problem -- and the completion of a period-38 oscillator, leaving only two or three missing periods to make Life provably omniperiodic. 2021 saw a wide variety of discoveries, from new spaceship syntheses and new true-gun periods, to SMOSes and RROs (q.v.) and even a new quadratic-growth replicator. Details can be found as usual in the LifeWiki news archive.

Opt-In Needed
A large fraction of these emails from the LifeCA group are probably defunct at this point, and more people may not want to receive further LifeCA email. So... NO FURTHER MESSAGES WILL BE SENT TO THIS EMAIL LIST.

If you don't want to be contacted again at this address, you don't have to do anything. To be added to a new LifeCA replacement mailing list -- let's call it "NewLifeCA" -- please be sure to reply to this email, saying at least "opt in".

It is currently an open question exactly what form the NewLifeCA mailing list will take. Please feel free to make suggestions in your response.

It might be nice to have a system that allowed for discussions between group members, similar to the LifeCA group, without everyone having to know (or being able to see) everyone else's address -- but for that to work I think we'd need some new volunteer moderators.

Meanwhile, the only things that I am volunteering to do for the moment are

1) compile a new list of freshly opted-in NewLifeCA email addresses;
2) send Conway's Life news occasionally to the resulting NewLifeCA group;
3) forward any messages to the NewLifeCA group that are sent to me at b3s23life (at) gmail specifically to be distributed to the list.

... And I'll only do that last job until it becomes tedious. In the (probably unlikely) event that NewLifeCA gets a lot of traffic in the long run, that will be a sign that it's time to find a better communication method.

However, for most discussion topics, there's no need to re-invent the wheel: a very good option is to start a new thread on the forums.

Again, please reply to opt in to be part of the NewLifeCA group, and/or to weigh in on a discussion of what the best options are for a LifeCA successor group going forward.

On February 11, 2022, Dave Greene wrote: NewLifeCA 11 Feb 2022: a new 35P12H6V0 (plus friends-and-relations)

Very recent news: the old Schick engine suddenly has some competition!

Until yesterday, the smallest known period-12 spaceship was the 39-cell LWSS-on-LWSS version of the Schick engine.

On Thursday morning, February 10, a relative newcomer to the ConwayLife Lounge on Discord (handle is "mystical", showed up on the Discord server last April) found a 35-cell period-12 ship using a hacked version of apgsearch.

(Presumably this means that the program was adjusted to create lots of hopeful combinations of c/2 front ends, then run through apgsearch's census code to see if anything came out that wasn't already known.)

The new spaceship can reflect gliders --

Code: Select all

x = 32, y = 13, rule = B3/S23
bo$b2o$obo$24bo$23b3o4bo$18bo3b2obo3b3o$17b3o2b3o3b2obo$7b2o8bob2ob3o
3b3o$8b2o12b3o3b3o$7bo20b3o$25b3ob2o$20bo5bo$20bo4bo!

-- and it can be turned into a period-36 spaceship using known pufferfish technology

Code: Select all

#C see https://conwaylife.com/wiki/Pufferfish_spaceship for
#C   where the high-period c/2 tagalong technology comes from
x = 28, y = 32, rule = B3/S23
5b3o11b3o$4bo2bo10bo2bo3b3o$7bo5b3o5bo2bo2bo$3bo3bo5bo2bo4bo5bo$3bo3bo
4bo3bo4bobo3bo$7bo4bo8bobo3bo$4bobo6bobo4bo6bo$24bobo$17bobo$5b3o10bo$
5bo2bo$4bo2b2o2b2o$3b3o5b2o$3bo$3b2o13bo$4bo12b3o$17bob2o$18b3o$8bo9b
3o$6b3o9b3o$7b2o9b2o7$4bo$2b4o$b2o$o$b2o!

More details along these lines can be found here.

On February 12, 2022, Dave Greene wrote: NewLifeCA 12 Feb 2022: Setup and security options (please pick one)

Out of 90 or so email addresses from the old LifeCA database, I've gotten 23 opt-ins so far, almost but not quite entirely from people who were active LifeCA participants in the 1990s and/or 2000s -- which is about what I expected. Sometimes you just have to get the band back together.

A second round of emails went out a little later, to twenty-five non-respondents who seemed to be the most likely to have just missed the original opt-in announcement due to spam filters, use of separate email for mailing-list subscriptions, etc. So a few more responses may trickle in. Feel free to spread the word around, especially after we sort this next thing out and maybe everyone will know who is already on the list.

Open-Address Model or Slightly-More-Secure Model?
Here's the next question: should I skip the security precautions and send future NewLifeCA emails directly to every email address in this small group? This would enable simple "Reply All" discussions of topics.

A useful data point is that Bill Gosper has fairly regularly broadcast Life-related messages to groups not too much smaller than this, for the last several years, with no apparent problems. And most of you can probably find each other's email addresses already -- y'all just don't know exactly who y'all are yet.

-- Or should I stick with the BCC: method that I'm using here? That would turn the NewLifeCA list into an "news dispatches only" type group -- which is really what it has been for the last decade or so in any case.

With the BCC: model, anyone who wanted to start a discussion would have to email a "for general release" message to me. That's awkward, but it maybe slightly reduces the chance of someone's account eventually getting hacked and everyone seeing an increase in spam or phishing attempts.

I'd Prefer the Open-Address Model
If I hear no objections, I'll switch from BCC: mode to CC: mode for my next message. Please reply to this email if you object to the plan of sharing email addresses among this group.

I can keep individual people on the BCC: list if they prefer that option. They'll only be able to see the occasional news items coming from me, along the lines of the one I just sent. Any "Reply All" discussions that may get started will be invisible to them. If the group gets too big for the CC: method to be workable, I'll be looking for other options -- but just to get the ball rolling I'm inclined to try the simplest method first.

On 14 February 2022, Dave Greene wrote: NewLifeCA 14 Feb 2022: CGoL Pattern of the Year summary, and this morning's p28 glider gun

Nobody has officially objected to the simple open-email CC: model for these emails yet, so my next few messages at least will use that format unless I hear otherwise, fairly soon (the next week or so). We're up to 25 email addresses in the list now.

--------------------------------------

The NewLifeCA group is getting its start at an auspicious moment: the Pattern of the Year vote is coming up soon on the conwaylife.com forums. That's always a good place for an overview of what's new in the past year that people might have missed hearing about. Links to this year's thirty-some entries can be found here/

I won't repeat all the nice short summaries from that link. The list is somewhat of a work in progress, not quite ready for voting yet -- but it's in an "explorable" state, and there's a lot of good stuff in there.

Among other things, there's a steampunk-era universal-constructor based spaceship, the #12 "QuickSilver Demonoid", which could have been assembled in the 1990s. It just uses Silver reflectors and gliders ... plus a few scattered still lifes that add up to some suspiciously 21st-century single-channel and self-destruct techniques, to make it all work.

The new spaceship syntheses in #17 include recipes for any size of "Canada Grey" greyship. The #07 "DOGun SaGaQR" is, among other things, a quadratic-growth replicator. There's another spaceship, #07, that is its own glider synthesis, and #28 is a reflectorless rotating oscillator that Golly can actually run -- you can fit up to eleven copies in a (very big) loop.

#08 is a new scalable programmable computer design, which someone is now thinking about hacking so as to be able to run Lisp. Many dozens of new high-period oscillators include a never-before-seen nontrivial p38 that uses a very simple new catalyst (see #18). #26 is some company for Sir Robin in the knightship department, including various periods of oblique rakes and puffers.

There are more interesting items on the list, but the last but definitely not least item that I'll mention is that Andrew D. Wade, the creator of the Gemini spaceship back in 2010, has built a demonstration of an "ash-clearing" mechanism (#31) that is good enough that it _might_ actually allow a replicator to clear out a replicator-sized region of settled ash and build a copy of itself in it, with a more than 50% success rate.

--------------------------------------

Those were all 2021 discoveries, though. I'd better try to keep up with current 2022 events also:

This morning a new glider-producing period-28 mechanism appeared. Since then, the true-period 28 gun has already been reduced in size by almost a factor of 5, and the pseudo-period 14 gun by over a factor of two. There's quite a bit of accumulated sparking and welding expertise out there these days:

Code: Select all

#C p14 gun by iNoMed, based on new p28 gun mechanism by JP21
#C https://conwaylife.com/forums/viewtopic.php?p=141607#p141607
#C https://conwaylife.com/forums/viewtopic.php?p=141620#p141620
#C https://conwaylife.com/forums/viewtopic.php?p=141640#p141640
#C For current optimized versions of various glider guns, see
#C    https://catagolue.hatsya.com/census/b3s23/synthesis-costs/gun
x = 119, y = 95, rule = B3/S23
21b2o11b2o40b2o2bo2b2o11bo7bo$20bo2bo9bo2bo8bob2o22bo6bobo13bobo7bobo$
20bobo11bobo8b2obo10b2o4b2o3bo2bobo6bo12bobob3obobo$18b2o2bo4b3o4bo2b
2o4b2o14b2o4bo2b2obobo2b2o5b3obo2b2o3bo9bo$19bobob4obob4obobo4bo3b2o
39bo24b2o$18bo2b2ob2o5b2ob2o2bo3bob2obo3b2o13bobo20bo6bo7bo4b2obo$18b
2o5bo5bo5b2o4bo2bo3bobo14bo13bo8b3obo2bo5bo2bo7bo$25bo5bo13bo3bo9b3o
12b2ob2o2b3o10bobob5obobobobo2b2o$23b4o3b4o10b2obo3bo6bo3bo5bo6bobo6bo
24bo$22bo3bobobo3bo9b4o3bo9bo5bobo2bo2bo2bo4b2o$22b2ob7ob2o12bob3o5bo
2bo6b3obob2ob3o9b2obo$27b3o10b2o2bobo3b2o5b2o9b2obobobo9b5o3bo$40bo6bo
b3o6b2obo5bobo3b2obo7bob2o6bo3bob2o$38bobo3b4o3bo5bo3bo5bo4b2o3bo5bobo
6bo3b2o3bo$38b2o4b2obo3bo5bob2o6b2o7b2o5bo8b2o3bobo3b2o3b2o$27b2o2bo3b
o9bo3bo10b2o5b2o13b2o11bo3b2o3b2o2b2o$26b2obob2o3bo6bo2bo3bobo5bo2bo5b
2o7b2o17b2obo3bobo$19b2o2b3o3bobo3b2o5bob2obo3b2o4bo9bo4b2o3bo25bo$19b
2o2bo4b2obob2o7bo3b2o8bo3bo6bobo3b2obo$23b2o4bo2b2o9b2o12b3o8b2obobobo
11bo$25bo19b2obo7b2o9b3obob2ob3o6b2o$45bob2o6b2o10bobo2bo2bo2bo7b2o6b
5o$4b2o11b2o23bo13bo11bo6bobo12b2ob2o3b2ob2o$3bo2bo9bo2bo11b3o9bo9b3o
9bo8b2ob2o10bo13bo$3bobo3b2ob2o3bobo9b7o5b3o9bo12bo23bo2bo2bo2bo2bo$b
2o2bobo7bobo2b2o4bo2b2obob2o2bo25b3o23bo2bo5bo2bo$2bobobo4bo4bobobo4bo
b4o3b4obo40bo10bo9bo$bo2b2o2b7o2b2o2bo3b2o11b2o38b2o10bo3bo3bo3bo$b2o
5bobobobo5b2o4b3o7b3o40b2o9b2o2bo3bo2b2o$10bobo13b2o9b2o10bo38bo5bo3bo
5bob2o$6b3o5b3o9b3obo3bob3o11bo21bo15b3o2b2o3b2o2b3obo2b2o$5bobobo3bob
obo13bobo14b3o22bo17bobobobobobo5bob2o$5b2o2b5o2b2o10bobo3bobo34b3o14b
2obo2b2ob2o2bo2b2obo$23b2o2bo9bo50bob2o9b4ob2o$23bo3b4o3b4o45b2o9b2ob
4o9b2obo$12bo8bobo7bobo4b2o42b2o10bob2o2bo2b2ob2o2bob2o$21b2o4b3o5b2o
2bo16bo27bo6b2obo5bobobobobobo$11bobobo10bobobo3bob3o18bo18bobo12b2o2b
ob3o2b2o3b2o2b3o$12b3o11bo3b5o20b3o17bo18b2obo5bo3bo5bo$2b2o15bo7b3o5b
2o38bo23b2o2bo3bo2b2o$2b2o8b3o5b2o8b5o2bo37bo2bo20bo3bo3bo3bo$11bobobo
3b2o8bo2bo3b2o37b3o12b2o8bo9bo$29b2o58b2o8bo2bo5bo2bo$14bo48bo27bo7bo
2bo2bo2bo2bo$64bo33bo13bo$2b2o58b3o19b2o13b2ob2o3b2ob2o$2b2o9b5o8bo57b
obo16b5o$4b3o2b2ob2o3b2ob2o5b2o52b2obobo$4bo3bo13bo3b2o53bobobo11b2o$
2b3o4bo2bo2bo2bo2bo61bo12b2o8bobo$2b2o5bo2bo5bo2bo48bo12b2o7bo5bo10bo$
2bo7bo9bo50bo11b3o5bobo10bo5bo$3bo5bo3bo3bo3bo47b3o11b3o4bobo2bo7bo3bo
3bo5b2o$9b2o2bo3bo2b2o11bo49b3o4bobob2o7bo2bobo2bo5b2o$2b2o3bo5bo3bo5b
o10b2o7b2o12b2o15bo8b3o3b2obo10bo3bo3bo$7b3o2b2o3b2o2b3o9b2o7b4o10b4o
12bobo8b2o6bo12bo5bo$b3o6bobobobobobo8b2o11b2ob2o9b2ob2o12b2o8bo2bo4b
2ob2o2b2o5bo$3o4b2obo2b2ob2o2bob2o4bobo13b2o12b2o17bo6bo2bob2obobo2bob
o6bobo$7bob2o9b2obo6bo47bo7b3o3bobob2o$2o74b3o13bobo2bo$32b2o55bo2bobo
bo10b5o$bo4b2o24bobo12bob2o9b2obo5b3o9bo8b3obob2o5b2ob2o3b2ob2o$7bo7bo
16bo14b2obo2b2ob2o2bob4o13bobo10b2o8bo13bo$b3o3bobo3b3o6b2o26bobobobob
obo5bobobobo7b2o21bo2bo2bo2bo2bo$2b3o3b3obo8bobo23b3obo7bob3obob2obob
3o9bo18bo2bo5bo2bo$10b2obo9bo23bo2bobo5bobo2bobo4bo4bo9bo18bo9bo$3b2o
5bo2bo36b4o3b4o5b4ob5o7b3o17bo3bo3bo3bo$39b2o8bo3bo3bo3bo7bobobo2b2o
25b2o2bo3bo2b2o$4bo24b2ob2o5bobo8b2o7b2o5b2obo2bo2bo2bo9bo12bo5bo3bo5b
o$9bo2bo10b2o3bobobo6bo26b2obo5bob2o7bobo12b3o2b2o3b2o2b3o$4b3o3b2o3b
2o5bob5obo2bo15b4o5b4o8b4obobo9b2o15bobobobobobo$5b3o6bobo6bob2ob2ob3o
14bob2o2b3o2b2obo8b5o2bo12bo9b2obo2b2ob2o2bob2o$16bo6bobo4bo18b2ob7ob
2o9bo4b3o13bo8bob2o9b2obo$6b2o13b3o4bob2o40b4o14b3o$2bo18b3o4b2o2bo13b
2o19b2o7bo$obo4bo12b2o6b5o13bobo18bobobobob2o18bo$bobo2bo13b3o23bo23b
2ob2o18bobo$bo4b2o5bobobo2b2o6b5o27bo11bo3b3o15b2o$6b2o4b2ob2o4b3o4b2o
2bo27b2o10bob2o2bo19bo$6b3o2bobobo5b3o4bob2o9b2o10bob6obo4b2o4bobo23bo
$b3o2b3o14bobo4bo11bo8b2o2b2ob2o2b2o3b2o28b3o$6b3o14bob2ob2ob3o8bobo7b
ob6obo$6b2o14bob5obo2bo9bobo7b2o47bo$bo4b2o15b2o3bobobo12b2ob2o4bo45bo
bo$bobo2bo22b2ob2o14b2o51b2o$obo4bo34b2o61bo$2bo40bo62bo$6b2o32b3o11bo
9bo2b3o2b2o30b3o$14b2o24bo9bobobob7obobob2o2b2o$7b2o5b2o16b3o14b2o5b7o
6b3o37bo$6bo26b2o12bob2o6b5o9bo35bobo$4b3o24bo2b2o2bo4bobobobo5bo3bo3b
o7bo36b2o$4b2o25b2o3bobobob2o9b2o4bo4b2o46bo$4bo2bo28bo5b2o11b2o2bo2b
2o49bo$6b2o34bo11bo9bo46b3o!

Also, following up on my previous message about the new smallest p12 spaceship, the same search method has turned up an interesting period-112 puffer that could have been discovered any time in the past half-century -- but apparently only just showed up two days ago, February 12:

Code: Select all

#C predecessor of p112 puffer
x = 18, y = 7, rule = B3/S23
8b3o3b3o$2b3o2bo2bo3bo2bo$bo2bo5bo3bo$4bo5bo3bo$o3bo4bo5bobo$4bo3bo$bobo!

For comparison, the only period-112 technology of any kind in the jslife collection, including the more recent moving-objects update, seems to be this much larger period-quadrupled forerake -- making 28 a perfect number to be talking about today:

Code: Select all

x = 63, y = 51, rule = B3/S23
7bo47bo$6b3o45b3o$4b2ob3o20b3o20b3ob2o$5bo2bob2o4bo4bo7bo3bo7bo4bo4b2o
bo2bo$2b2obo4bobob2ob2ob3o5b2o3b2o5b3ob2ob2obobo4bob2o$2b2obobo2bobo7b
4o3b2obobob2o3b4o7bobo2bobob2o$2bo8b3obobob2o2b2ob2ob2ob2ob2ob2o2b2obo
bob3o8bo$b2o7b2o12bobo3bobo3bobo12b2o7b2o2$5b3o15b2ob2ob2ob2ob2ob2o15b
3o$4bo3bo45bo3bo$3b2o4bo11b21o11bo4b2o$2bobob2ob2o3b3o2b2obo4bo7bo4bob
2o2b3o3b2ob2obobo$b2obo4bob2ob3obo25bob3ob2obo4bob2o$o4bo3bo4bobo4bo4b
obob3obobo4bo4bobo4bo3bo4bo$12bo5b2o23b2o5bo$2o7b2o41b2o7b2o$30b3o$21b
3o$20bo2bo$23bo$19bo3bo4b2o$23bo4b2o$20bobo$37b3o$37bo2bo$37bo$37bo3bo
$22bo7b3o4bo3bo3bo4b3o$21b3o5bo7bo6b3o2bo2bo$20b2obo5bo8bobo3bob2o4bo$
20b3o6bo3bo11b4o3bo$20b3o7b3o12b2o5bo$20b3o26bo2bo$21b2o12b2o13b2o$34b
obo15bo$36bo$48b2o3bo$48b2obo$48bo2b2o$49b3o$42b2o$41bobo$43bo5$49b2o$
48bobo$50bo!

On February 15, 2022, Dave Greene wrote: NewLifeCA 15 Feb 2022: where did this new period-30 gun come from?

I'm sending more NewLifeCA emails than I usually would -- please don't expect this to be the normal rate going forward! -- but these are exciting times.

As some of you have already heard, a new period-30 glider gun was discovered today, that needs only one queen-bee shuttle instead of the two colliding shuttles that have been the norm for the past half-century or so:

Code: Select all

x = 28, y = 18, rule = B3/S23
14b2o$14bo2bo3$14bob2o2b2o$9b2o2bobo4bo$9bo4bo6b3ob2o$2b3o8bo9bob2o$2b
3o5bo2bo$2o22b3o$2o13bo8bo2bo$2o12bobo9b2o$12b2o3bo$8b3ob2o3bo$12b2o3b
o$6bo7bobo$6bo8bo$6bo!

There are other options for the sparkers that help with the glider extraction, including the use of a pentadecathlon, which takes a bit more space but allows this gun mechanism to be glider-constructed relatively easily. In a standard p30-gun synthesis, the two queen bees have to be started up by two gliders with precise relative timing, but here there's only one queen bee to start up, so the trigger glider can be delayed by any multiple of fifteen ticks and it will still work fine:

Code: Select all

#C see the following link for a one-glider seed for a
#C standard Gosper glider gun, for comparison purposes --
#C this new one is significantly simpler:
#C   https://conwaylife.com/forums/viewtopic.php?p=71963#p71963
x = 75, y = 83, rule = B3/S23
7bo$6bobo$6b2o9$7bo$6bobo$6b2o4$7bo$7b3o$10bo$9b2o3$b2o$obo$2o2$32b2o$
7b3o5b2o9b2o4bobo$14bobo9b2o4bo$5bo8b2o$5bo5bo$5bo5bo$11bo47$73bo$72b
2o$72bobo!

Alternate sparkers even allow glider streams to be extracted from both ends of one queen-bee shuttle -- though there's not a whole lot of point since only one stream at most can escape without interfering with the other one:

Code: Select all

x = 38, y = 28, rule = B3/S23
6bo2bo3b5o2b5o3bo2bo$3bo2bo2bo7bo2bo7bo2bo2bo$2bob3o2b5o3bo2bo3b5o2b3o
bo$3bo30bo2$bo23bo$o2bo3bo11b2o4b3o7b3o$o2bo2b3o10b2o2b2ob2o6b3o$2bob
2obobo6b2o6bo3bo$4b3ob3o4b3o6b2ob3o$4b2obobo6b2o6bo5bo$2b3ob3o10b2o2b
2obobobo3b2o$bobo3bo11b2o4b2obob2o2bobo$bo34bo$2o12bo21b2o$15bo$13b3o
2$20bo$18b2o$19b2o2$23b2o$19bo3b2o$18bobo$17bobo$17bo$16b2o!

Here's some background on the developments leading up to this discovery.

Adam P. Goucher's "Catagolue" (not a misspelling) has been gathering "apgsearch" soup-search results for just about seven years now, from anyone willing to contribute CPU-hours to running random soups and contributing the resulting censuses of objects. New objects that have never been seen in a soup before get their own page on Catagolue, like this one that showed up this morning.

The single-engine p30 gun showed up in tetramer form in the 31x31 soup pattern that that page links to:

Code: Select all

x = 31, y = 31, rule = B3/S23
2b2o2bo2b3obo3bob3o2bo2b2o$4obo3b2obob3obob2o3bob4o$obobob3obo2b2ob2o
2bob3obobobo$ob2ob2obo4b5o4bob2ob2obo$obo8b9o8bobo$ob3o3b3ob2obob2ob3o
3b3obo$b4obo4bo2bobo2bo4bob4o$bo2bob2ob6ob6ob2obo2bo$2obo2bob2ob2obobo
b2ob2obo2bob2o$2b2ob2ob4o7b4ob2ob2o$3o2b4o4b2ob2o4b4o2b3o$3bob2obobo2b
5o2bobob2obo$b2o4b3o3bo3bo3b3o4b2o$3obo4b5obob5o4bob3o$2ob2o2b6ob3ob6o
2b2ob2o$2bobobob2o3b5o3b2obobobo$2ob2o2b6ob3ob6o2b2ob2o$3obo4b5obob5o
4bob3o$b2o4b3o3bo3bo3b3o4b2o$3bob2obobo2b5o2bobob2obo$3o2b4o4b2ob2o4b
4o2b3o$2b2ob2ob4o7b4ob2ob2o$2obo2bob2ob2obobob2ob2obo2bob2o$bo2bob2ob
6ob6ob2obo2bo$b4obo4bo2bobo2bo4bob4o$ob3o3b3ob2obob2ob3o3b3obo$obo8b9o
8bobo$ob2ob2obo4b5o4bob2ob2obo$obobob3obo2b2ob2o2bob3obobobo$4obo3b2ob
ob3obob2o3bob4o$2b2o2bo2b3obo3bob3o2bo2b2o!

On the "ConwayLife Lounge" Discord server, this new arrival was quickly noticed, reduced to dimer form and then to the monomer forms shown above.

----------------------------------------

This is not the first gun to show up in a "semi-natural" (symmetric) soup, however. Jason's Summers' p156 gun shows up quite regularly in the D4_x4 symmetry, in various forms, as the large number of soup links shows:
https://catagolue.hatsya.com/object/yl7 ... 035/b3s23/
https://catagolue.hatsya.com/object/xp3 ... yg33/b3s23
https://catagolue.hatsya.com/census/b3s23/D4_x4/yl312
(lots of trivially different ways to suppress some of the glider streams)

And just three days ago a semi-natural period-46 bi-gun showed up in a different symmetry, C2_2. This one is probably less likely to show up naturally any time soon (i.e., in an asymmetric soup), but of course it's not impossible.

Before that, in mid-December, a single-engine period-46 gun showed up, but that wasn't a soup-search result; it was an engineered discovery using a new catalyst -- in fact, the same "traffic stop" mechanism that also completed the period-38 oscillator last month.

--------------------------------------------------

The first gun appearance in C1 (asymmetric 16x16) soups is one of the big events that has yet to happen on Catagolue. Catagolue is approaching the point where it has collected enough soups that a gun might be expected to spontaneously occur -- we seem to be in about the right order of magnitude, anyway.

The reason why so many new things are showing up in symmetric soups all of a sudden is that Charity Engine, https://www.charityengine.com/ , has recently taken an interest in donating a small percentage of its spare capacity to our particular brand of mathematical research... and the people running the scripts have decided to prioritize symmetric soups rather than C1 soups.

This decision was made on the grounds that interesting new oscillators can more commonly be found in symmetric soups. There's been a significant increase in focus on finding new oscillators and oscillator periods in the last year, based largely on the work of a newcomer to the forums named David Raucci, or "hotDogPi".

-- Okay, enough Life news for now. I'm kind of hoping things will maybe quiet down for a little while...!

Keep the cheer,


Dave

On March 1, 2022, Dave Greene wrote: NewLifeCA 1 March 2022: What's That Floating In My Soup?

Period 23 Redux
We already had a p23 oscillator, "David Hilbert" -- but JP21 found a smaller one a couple of weeks ago:

Code: Select all

#N p23 honeyfarm hassler
#O JP21, 16 February 2022
#C https://conwaylife.com/forums/viewtopic.php?p=141729#p141729
x = 19, y = 21, rule = B3/S23
8b2o$2bob2obobo4bo$2b2obobo4b3o$6b2o3bo$11b2o$2o15b2o$bo15bo$bobo11bob
o$2b2o3bo2bo4b2o$9b2o2$8b2o$2b2o4bo2bo3b2o$bobo11bobo$bo15bo$2o15b2o$
6b2o$7bo3b2o$4b3o4bobob2o$4bo4bobob2obo$9b2o!

Kaleidoscopic Diehards
An entertaining diehard showed up on February 21. Catagolue collects these things now, so we have a lot of them to choose from. Impressively, this new one beats the previous record for symmetric "messless methuselahs" by over 400 ticks:

Code: Select all

#N 2474-tick C4_4 diehard
#O Charity Engine, 21 February 2022
#C https://conwaylife.com/forums/viewtopic.php?p=141951#p141951
x = 32, y = 32, rule = B3/S23
7b2o2b3o4b2obobo3b2o$b2o3bob2obo2bobobob2o2b3ob3o$b4ob3obo2bo2b2o2b3ob
ob2ob2o$2obo2b2o3b2ob2ob3obobo4b2o$obo3bob5o2bobob2obo2b2o2bo$b2ob5o3b
o2bob2o2bobo2bo$bo2bo2bo6bo3b4ob2ob5o$b2o3bobob5obob6ob2ob2obo$o2bob3o
bo3b2obo3bobobob2ob3o$2bobo2b2o8b2obo2bo3bo2bo$4ob3o2b2obo2bobob2o2bo
2bobo$b2obob5o3bob3o2bo2bo2b2ob2o$o2b2ob2o5bo2bo7bob3o2bo$2obob3ob3ob
3o2b2obob2o4bobo$2b4o3bobo2bob3obo2b3o2bobo$b2o4b2ob3ob3obo7b3o$3b3o7b
ob3ob3ob2o4b2o$bobo2b3o2bob3obo2bobo3b4o$obo4b2obob2o2b3ob3ob3obob2o$o
2b3obo7bo2bo5b2ob2o2bo$2ob2o2bo2bo2b3obo3b5obob2o$2bobo2bo2b2obobo2bob
2o2b3ob4o$bo2bo3bo2bob2o8b2o2bobo$3ob2obobobo3bob2o3bob3obo2bo$ob2ob2o
b6obob5obobo3b2o$b5ob2ob4o3bo6bo2bo2bo$5bo2bobo2b2obo2bo3b5ob2o$2bo2b
2o2bob2obobo2b5obo3bobo$2b2o4bobob3ob2ob2o3b2o2bob2o$b2ob2obob3o2b2o2b
o2bob3ob4o$b3ob3o2b2obobobo2bob2obo3b2o$3b2o3bobob2o4b3o2b2o!

I mentioned Charity Engine's recent contributions to soup searching in my last email. New symmetric soup hauls are still coming in from that source, though at a somewhat reduced rate compared to the initial surge.

58P8H4V0 and Synthesis
Another very interesting Charity Engine object showed up in a symmetric soup on February 24th: it's a period-8 c/2 spaceship that nobody knew existed!

It's extremely rare that a soup search turns up a spaceship that hasn't been previously found by some other method. New oscillators do show up occasionally in soups, but spaceships not so much.

Code: Select all

#N 58P8H4V0
#O Charity Engine, 24 February 2022
#C https://conwaylife.com/forums/viewtopic.php?p=142084#p142084
#C Several new puffers have been found based on this spaceship:
#C https://conwaylife.com/wiki/58P8H4V0
#C The spaceship and the source soup can be found on Catagolue,
#C along with the cheapest glider construction (currently 53 gliders).
#C http://catagolue.appspot.com/object?apgcode=xq8_ciire2272hm0mh2722eriiczw1x2c8960698c2x1&rule=b3s23
x = 23, y = 12, rule = B3/S23
7b3o3b3o$6bo2bo3bo2bo$6bo3bobo3bo$2bo5bo5bo5bo$b3o5bo3bo5b3o$2o7bo3bo
7b2o$2b3ob4o3b4ob3o$7b3o3b3o3$o21bo$b2o17b2o!

I think the only other new spaceship discovery from a Catagolue/apgsearch soup so far has been the pufferfish spaceship -- and even that showed up in puffer form, and needed some add-on engineering to make it into an actual spaceship.

The record-breaking smallest period-12 c/2 spaceship mentioned recently in a NewLifeCA message -- the "35P12H6V0" that is compatible with pufferfish tagalongs -- was technically also found with a type of soup search. However, that search was seeded with working c/2 front ends, so the starting patterns weren't entirely random.

On the other hand, it's quite common that a new appearance of a known spaceship in a soup will give some good hints about how to construct the spaceship efficiently by colliding gliders. That might partly account for Goldtiger997's and Mark Niemiec's speedy turnaround on a glider synthesis for 58P8H4V0.

... However, I think that most of the explanation for that quick work is that we have a much bigger and deeper pool of glider-synthesis expertise today than we did nineteen years ago this month, when the first non-Cordership and non-*WSS-based spaceship recipe showed up (for 60P5H2V0).

Depending on how you count, there are syntheses known now for around fifty types of spaceships, and more than half of them have been solved in the last three years -- more often than not by the new generation of Lifenthusiasts that do most of their collaborations on the "ConwayLife Lounge" Discord server.

https://conwaylife.com/wiki/Glider_synt ... _syntheses

New Oscillator Engines
Meanwhile, hotDogPi is continuing to turn up more surprising new spark-assisted oscillator engines, like this period-30 double pi factory from this morning:

Code: Select all

#N p30 suppressed double pi factory
#O hotDogPi, 1 March 2022
#C https://conwaylife.com/forums/viewtopic.php?p=142297#p142297
x = 34, y = 34, rule = B3/S23
18bo$16b3o$15bo7b2o$15bo2b3obo2bo$12b2obobo2bob2o2bo$12bo2bob2o2bo2b2o
$14bo3b2ob3o$15b2obo4bo$17b2obobo$13b3o4bob4o$12bo2b5obo4bo$13bo7bob3o
$4b2o4bo3b3o6bo$4bo4bobo4bo4b2o$6bo2bo2bo4b5o$2b4obob2obo$bo3bobo2bob
2o15b2ob2o$bo2bo2b2obo2bo16bobo$2obobo4b2o8b3o7bobo$3bo4b2o2bo6bo2bo6b
2ob2o$3b2o3b2ob2o6bo2bo7bobo$6bo4b2o7b2o8bobo$3b2obob2o19b2ob2o$2bobob
2obob3o$2bo2bo3bobo$3bobo3bobo$4bo5bo3$16bo2bo2bo$16b7o2$16b7o$16bo2bo
2bo!

hotDogPi's oscillator search program isn't soup-based, for a change; it involves starting with various arrangements of common objects, adding sparks in lots of possible positions, and running the result to find the rare cases where the same arrangement reappears after some number of ticks (minus the sparks).

On March 1, 2022, Dean Hickerson wrote:

Dave Greene wrote:NewLifeCA 1 March 2022: What's That Floating In My Soup?

... An entertaining diehard showed up on February 21. Catagolue collects these things now, so we have a lot of them to choose from. Impressively, this new one beats the previous record for symmetric "messless methuselahs" by over 400 ticks:

#N 2474-tick C4_4 diehard
#O Charity Engine, 21 February 2022
#C viewtopic.php?p=141951#p141951
x = 32, y = 32, rule = B3/S23...

As it happens, I've been working on diehards recently, both by random searching and by constructions. I think that random searches are the way to go up to about 18x18, but that constructions, using objects found by specialized searches, are better after that. In particular, the best 16x16 found by Catagolue beats my best construction by 101 generations, but my best 32x32 beats the one above by 6570 gens. Eventually I'll post my findings on the conwaylife.com forum, but for now I'll just show my 32x32. (I doubt that this is anywhere close to maximal for this size.)

Code: Select all

#N 9044-tick diehard
#O Dean Hickerson
x = 32, y = 32, rule = B3/S23
18b2o$14b2obo2bob2ob2o$14bob2o2b2obob2o2$6b2o$obobo2bo$bo13bo$bob2obo
7bobo10b3o$2ob3o8bobo10bo$o3bo11bo11bo$2o5bo$2o4b2o8b2o$3bo10bobo$3bo
11bobo$5bo3b2o4b3o$9bo$3bo7bo2bobo$3b2o5b2o3b2o$15bo9bo$13bobo6b5o$13b
obo5bo4b2o$14bo6bo4bo$24b2o$2b2o4b2o15bo$2bobo2bobo2b2o13b3o$4bo2bo4bo
5b2o5b2obob2o$4b2ob2o5bobo2bo5b2o3b2o$7bo2bo2b2ob2o8bobob2o$7bob2o14b
2ob2o$3b2ob2obo15b3o$3b2obo2bo5b2o$7b2o6b2o!

On March 1, 2022, Dave Greene wrote:

Dean Hickerspn wrote:...for now I'll just show my 32x32. (I doubt that this is anywhere close to maximal for this size.)

I'll have to see if I can hit five digits at least, with a 32x32 diehard -- this example gives me some ideas, for sure.

On March 6, 2022, Dave Greene wrote: NewLifeCA 6 March 2022: Re: Better 32x32 diehard

I did spend a little time looking for a 32x32 diehard with five-digit survival time, investigating collisions between 2c/5 spaceships and *WSSes that could then be cleaned up with a c/10 copperhead. The best I've come up with so far is this, which isn't quite good enough -- the 2c/5 is too big, and having to generate *two* LWSSes at the last moment would leave too little room in 32x32 for any decent delay circuitry.

Code: Select all

x = 104, y = 31, rule = B3/S23
4b3ob2o$bo4b2o2b2o$2o5bo4bo$2o5bo4bo$bo4b2o2b2o26bo52bo$4b3ob2o29bo50b
obo$35bo3bo47b3o3bo$36b4o48b3obo$90b2o2$92bob2o$91bo2bobo$92bo3b2o$92b
obobo$91b2ob2o$92bo2$93bo$97bo$94bo3b2o$71bo23bo2b2o$72bo21bob4o$68bo
3bo$69b4o$99bob2o$98bob2obo$99bo3bo$100b2obo$99bob2o$97bobo$97bobo!

Unfortunately none of the collisions of *WSSes with really small 2c/5s seem to leave an object or constellation behind that can be cleaned up with a single copperhead. I haven't done a really complete survey, but I think I've covered all of the obvious options. Didn't try a fireship, but that's probably too big to fit in the starting pattern.

However, in the meantime Dean has found a way to get several thousand ticks past the five-digit mark, using a c/3 target instead of a 2c/5 one -- see below. 14,011+ is the new target!

On March 6, 2022, Dean Hickerson wrote: NewLifeCA 6 March 2022: Re: Better 32x32 diehard

Dave Greene wrote:I'll have to see if I can hit five digits at least, with a 32x32 diehard -- this example gives me some ideas, for sure.

I've been trying to do that too, and today I succeeded.

The pattern that I sent before used 2 spaceships to delay its death. If the leading one has speed S, the trailing one has speed T, and the LWSS (or other c/2) is formed in generation N, then the pattern dies at about generation SN/((1-2S)T). We want the factor S/((1-2S)T) to be as large as possible. For that we'd like S to be large (but < 1/2) and T to be small.

The 9044-tick pattern used 2c/5 and c/3, giving a factor of 6. Using 2c/5 and c/10 would give a factor of 20, but I never found a combination that works; the c/10 spaceship tends to create a big mess when it hits something. I was able to fix it by adding two c/3 spaceships between the leader and the trailer, but that won't fit in a 32x32 box.

Yesterday I decided to try c/3 and c/10, for a factor of 10. I didn't really expect it to work, but it does. My first attempt lived for about 13000 gens, but adding a couple of one-time glider reflectors, and backing up a few gens with lifesrc increased that to 14010. That could probably be improved with enough searching.

Code: Select all

#N 14010-tick diehard
#O Dean Hickerson, 3/6/2022
x = 32, y = 32, rule = B3/S23
3b2o2b2obobo4bobo3bo$3bo5b2obobo2bo3bobo$2obo2b4o2b2o4bo2bo$bob2ob2o3b
2o4bo4bo$bo2bobobo2bo2bo$2ob2o4bo4bo4b4obo$3b2o2b2obo2bo3b2o5bo3bo$3bo
bo2bo9bobo6bobo$4b2o4bobo6b4o6b2o$3bob2o4bo2bo3b2o2bo6bo$10b2o2bo13bob
o$30bo$31bo$7b2o3b2o15bobo$b2o5bo2bobo6bo7bo2bo$b2o2b3o3b2o6bobo$5bo
13bo2bo6b3o$b2o17bobo7b2o$ob6o13bo7bo$o4bo2bo15b2o4b2o$b3o3b2o14bobo2b
obo$3b2o18b2o4bo2$6b2o$5bobo5b2o4b2o$5b2o6bo2bo3bo$17bo5b3o$14bob3o5b
2o$ob2o2b2o8b2o3b2o$2obo2b2o6bo$15b3ob2o$14bo2b4o!

On March 6, 2022, Dean Hickerson wrote: NewLifeCA 6 March 2022: Re: Better 32x32 diehard

Dave Greene wrote:The best I've come up with so far is this, which isn't quite good enough -- the 2c/5 is too big, and having to generate *two* LWSSes at the last moment would leave too little room in 32x32 for any decent delay circuitry.

For what it's worth, my solution using 2 intermediate c/3 spaceships is shown in this 36x36 diehard:

Code: Select all

# 18477-tick diehard
x = 36, y = 36, rule = B3/S23
13bo4bo$14b2o3b2o$7bo6b2o3b2o$2bob2o2bo4bo4bo$4b3o3bo4bo4bo$o8bo3bobo
3b3o$o4b2o2b2o2bobo5bo$obobo3bobo3bo6b2o$o8bo5b2o3bo5bob2o$2bob3o8bo3b
obo3b3o2bo$4b2o2bobo2b3o3bobo2bob2o2bo$7bo6bo6bo7b2o$12bo6bo7b3o$13b2o
5b2o5b3obo$13b2o5b2o6bob4o$12bo6bo8bo2bo2bo$35bo$31bo2bo$31b3o$28bob2o
$29bo2$2ob2o19b2o3bo2bobo$2obobo6b2o9bobo2bo4b2o$4bo7bo2bo7b2o3bo2b2ob
o$14b2o13b2o4bo$34b2o$3b2o13b2o4b2o$3b2o13bobo2bobo$20bo2bo5bo3bo$12b
2o5b2ob2o4bobobobo$12b2o3bo2bo8bo3bo$17b2obo$18bob2ob2o8bo$18bo2bob2o
7bobo$19b2o11b2o!

I didn't find a way to do it with only 1 intermediate c/3, but I could have missed something.

On March 7, 2022, Dave Greene wrote: NewLifeCA 7 March 2022: Re: Better 32x32 diehard

Intermediate c/3 spaceships! There's no reason those have to be c/3, and in particular they take up more space than a single c/7 loafer would. Not sure the geometry will allow for shrinking to 32x32, but there's a lot of search space to explore.

On March 14, 2022, Dean Hickerson wrote: Re: Better 32x32 diehard

Dave Greene wrote:Intermediate c/3 spaceships! There's no reason those have to be c/3, and in particular they take up more space than a single c/7 loafer would. Not sure the geometry will allow for shrinking to 32x32, but there's a lot of search space to explore.

Yeah, I really ought to automate the process; I didn't find anything during a brief, unautomated search.

An even better thing to find would be a reaction that sends a *WSS back to the starting location; then a diehard could use this trick multiple times.

Meanwhile, I found a way to move part of the 14010-tick diehard farther south, giving more room in the northwest. That allowed me to delay production of the LWSS by 403 gens, giving this better diehard:

Code: Select all

#N 18049-tick diehard
#O Dean Hickerson, 3/14/2022
x = 32, y = 32, rule = B3/S23
ob4o$3o4b3o4bo$4bo10bo2bo$2b2obob2o6bobob2o$2b2ob2o4b2o5b2ob2o$3b2o6b
2o5b2ob2o$7bo7bobob2o7bo$2b2o11bo2bo8bobo$7bo6bo12bobo$5b3o21bo$4bo6bo
17b2o$4bob2o2bobo15bobo$5bobo3b2o$29b3o$20bo8bobo$7b2o3b2o5bobo6bobo$b
2o5bo2bobo5bo2bo7b2o$b2o2b3o3b2o7bobo$5bo15bo8bo$b2o21b2o2bobo$ob6o15b
obo2bobo$o4bo2bo14b2o4bo$b3o3b2o$3b2o$13b2o4b2o$3b2o3bobo2bo2bo3bo$b6o
b2o7bo5b3o$3o2b2o2b2o3bob3o5b2o$2obo4b3o5b2o3b2o$2o4bob2o4bo$3bobo4bo
4b3ob2o$bobobobob2o3bo2b4o!

On March 8, 2022, Dave Greene wrote: NewLifeCA 8 March 2022: new smallest 3c/7 spaceship, semi-natural darts, and an SSGRL

Does anyone object to patterns being referenced in the form of links to LifeViewer-enabled pages? I can make a habit of sending actual RLE in these emails, but for larger patterns especially, links just seem a lot more convenient.

For all of you spaceship aficionados out there, in late February Keith Amling came up with a new lower-population stabilization for the front end of the known "Anura" and "Soba" 3c/7 spaceships.

Use "Show in Viewer" for the next several posts starting from the first link, to see some of the connections now available at 3c/7.

Also, thanks to the recent Charity-Engine-driven surge of symmetric soup searches, a c/3 spaceship -- or rather a pair of them, darts of course -- has appeared "semi-naturally", in a D4_+1 soup.

The exploration of new oscillator engines is still under way: now for the first time there's a true-period p30 gun that doesn't contain any queen-bee shuttles. (There aren't any known ways to split a glider into two gliders with just pentadecathlons, and bounce one of them around into a closed loop -- right?)

Code: Select all

#N queen-bee-less p30 glider gun
#C David Raucci, 1 March 2022
#C https://conwaylife.com/forums/viewtopic.php?p=142297#p142297
x = 40, y = 33, rule = B3/S23
18bo$18bo6b2o$18bo6bo$23bobo$23b2o2$4bo5bo$3bobo3bobo18bo6bo$2bo2bo3bo
bo17b2o6b2o$2bobob2obob2o6bo8b3o6b3o$3b2o3b2o3b2o3b3o8b2o6b2o$6bo3bob
3o2b2o2bo8bo6bo$3b2ob2obobo2b2o2bo2bo$3bo2bo3bo2b3o3b2o$2obo4bob2ob3o
12bo$bo2b2o2bobo3bo11bobo$bo5bo2bob2o13b2o$2b4obob2obo$6bo2bo2bo$4bo4b
obo4b2o2bobo$4b2o4bo3b3ob2obobo$13bo4bo2bob3o9bo$12bo2b4o7bo9bo$13b3o
4bob4o8b3o$17bob2obo$15b4obo2bo$14bo7b2o$12bo2b3o6b2o$12b2obobo2bob2o
2bo$15bo2b3obo2bo$15bo7b2o$16b3o$18bo!

And last but not least, this morning Goldtiger997 posted an SSGRL -- "self-synthesizing glide-reflecting loopship" -- with a design similar to last year's self-synthesizing oblique loopship and self-constructing reflectorless rotating oscillator (both also by Goldtiger997).

A "loopship" is a type of self-constructing spaceship that travels by repeatedly creating a signal storage loop big enough to hold the construction recipe for that same memory storage loop.

The other distinction here is that "self-constructing" means some kind of stored recipe and universal-constructor technology is at work in moving the spaceship -- but "self-synthesizing" means that the spaceship consists of nothing but gliders rewindable to infinity at some point in its evolution, and therefore it is its own glider synthesis.

Interestingly enough, the default synthesis is nowhere near the minimum cost to construct one of these self-synthesizing spaceships. The total number of gliders could be cut very nearly in half, from 141,617 (for the current SSGRL) to somewhere in the neighborhood of 75,000 gliders. Nobody has tackled that little optimization project yet.

Keep the cheer,


Dave

On March 11, 2022, Dave Greene wrote: NewLifeCA 11 March 2022: smaller p6 pipsquirter, and final printable Life textbook!

Sometime a year or two ago, a p6 pipsquirter with lower population and slightly different clearance was posted to the forums -- but nobody can yet find where it was exactly. It showed up recently because someone had copied it into their own sparker stamp collection. Apparently it didn't get noticed by many people when it was posted, because if it had been, the p42 glider gun would have been updated to use it:

Code: Select all

#C See https://conwaylife.com/forums/viewtopic.php?p=142671#p142671
#C This gun is two rows shorter than yesterday's smallest-known p42 gun.
#C The p21 engine was found by David Raucci (hotDogPi) in 2021;
#C the use of 28P7.3 to extract gliders was by Tanner Jacobi;
#C the 38P7.2 oscillators are by Nicolay Beluchenko in 2009;
#C and a search is going on for the source of the smaller p6 pipsquirters.
x = 43, y = 46, rule = B3/S23
32b2o$32b2o$33bo3bob3o$32bo3b6o$31bo6bo$32b5o$17b2o$18bo8bo4b5o$17bo7b
3o3bo6bo$17b2o5bo7bo3b6o$19bo4b2o7bo3bob3o$17b2o13b2o$16bo4b2o9b2o$11b
o4b4o2bo$2bo7bobo7bobo12b2o$2b3o5bobo5bo12bo5b2o$5bo3b2o2b2o3b2o5b2o2b
o2b6obo$4bo2bo3b2o2bo8b3obo10b2o$4bo3b3o2b3o7b2o10bob3o$5b2o5bo11bob6o
2bo2b2o$9bo3bo11b2o5bo8bo$9b4o5bo8b2o11bobo$11bo5bo23b2o$17b3o10b2o$
30b2o$12bo9b3obo3bo$2o5b2o3b2o8b6o3bo$bo5b2o3b2o11bo6bo$bobo23b5o$2b2o
$6b2o19b5o$5bobo17bo6bo$6bo4bobo8b6o3bo$12b2o8b3obo3bo$12bo17b2o$30b2o
$4b2o$4b2obo$3bo3bo$4bobobo2bo$b3o2b5obo$bo2b2o5b2o$2b2o2b2o3bo10bo$4b
obo5b3o8b2o$4bobo7bo7b2o$5bo!

The smaller pipsquirters only work in one position to help with a p6 "bouncer" glider reflection, though. So Noam's original p6 pipsquirter from nearly 25 years ago (November 1997) is really holding up surprisingly well -- it has better fallback, so it works in two adjacent positions.

The glider gun collection has been through several rounds of reduction since Dieter Leithner and Peter Rott's original late-1990's collection, but it still serves as a very good litmus test for new circuit technology: if a Herschel conduit, period multiplier, reflector, or other mechanism can reduce the size of at least one gun, it's pretty much guaranteed to be an interesting new find rather than a rediscovery.

The minimum bounding box is still the overriding criterion for determining membership in the current collection, which is now kept up-to-date via the "gun" and "guntrue" pages on Catagolue (two separate collections, the second one for true-period guns only).

Links are on the right side of that page, or there's an undocumented "textcensus" option to give the size of each gun:

https://catagolue.hatsya.com/textcensus ... -costs/gun
https://catagolue.hatsya.com/textcensus ... ts/guntrue

Updating an entry in either of these collections is now just a matter of scrolling to the bottom of the above "syntheses" page and pasting in RLE for a working gun. If the gun is a record-breaker, it will show up in the appropriate list(s) on Catagolue within the next eight hours.

If anyone wants to try this out, there are a lot of four-digit prime-period guns at the top of the lists that should be relatively easy to reduce. It's impressively difficult to improve the bounding box of guns with periods below 1024, at this point!

Life Textbook Finally Ready to Print
For the last few months we've been trying out Lulu.com's print-on-demand printing service, and have gotten fairly reliable quality in all of the trial books we've printed so far. The colors look a little nicer in some prints than in others, apparently unpredictably... but it has always been good enough -- the illustrations are clear, and the books are nice and solid, stay open to the page you open them to, and so on.

Due diligence is done, so we've gone ahead and pushed the "submit for global distribution" button. At some point in the next month or two, the book should show up as a print-on-demand option in searches on Amazon and Barnes&Noble and so on. In the meantime, it can already be ordered via Lulu.com. The book website is updated with the details, and there's a Kickstarter running at the moment. I'm heading for G4G14 in less than a month, and figured I should have a box of books to bring along.

Here's Nathaniel's writeup on Reddit, and the Kickstarter link.

Blurbs?
Related to this, here's a rare request for the NewLifeCA group -- or, well, not really a request, more like a hopeful but thoroughly optional suggestion.

A few nice positive tweets have come in about the book so far, from Ned Batchelder and Rudy Rucker.

If anyone happens to feel like saying something good about the book that could be used as a "blurb" on the https://conwaylife.com/book/ page, please feel free to say it soon (and let me know where you said it)!

Keep the cheer,


Dave

On March 14, 2022, Dean Hickerson wrote: Regarding the gun collection, Dave Greene wrote:

Dave Greene wrote:Updating an entry in either of these collections is now just a matter of scrolling to the bottom of the above "syntheses" page and pasting in RLE for a working gun. If the gun is a record-breaker, it will show up in the appropriate list(s) on Catagolue within the next eight hours.

It seems strange that this is done on the "syntheses" page, since a gun isn't a synthesis of anything. But it does work; see below.

Dave Greene wrote:If anyone wants to try this out, there are a lot of four-digit prime-period guns at the top of the lists that should be relatively easy to reduce.

I recently needed a period 1216 gun, and found that adding a quadri-Snark to the p304 gun in the collection gave a smaller p1216 than the one that was there. I submitted it 2 days ago, and the collection has been updated:

https://catagolue.hatsya.com/object/gun_1216/b3s23

There are probably other composite-period guns that could be reduced in this way.

Dean Hickerson

On March 15, 2022, Dave Greene wrote: NewLifeCA 15 March 2022: Re: Gun collection on Catagolue

Dean Hickerson wrote:It seems strange that this is done on the "syntheses" page, since a gun isn't a synthesis of anything.

It is a bit strange at first, no argument there... From Catagolue's point of view, a glider gun is a "synthesis" of a period-N glider stream, and in this special case it knows that the relevant thing to count is not the number of gliders to build the gun, but rather the number of cells in its bounding box. This allows the same basic code to sort and display glider guns and object synthesis recipes, and replace old guns when new record-breakers turn up, even though the metric is different.

An exploration of Catagolue will turn up at least one more instance of casual code re-use that's confusing at first but then comes to seem normal.

It's possible to run soups with various symmetries -- C4_4, D8_1, D2_+1, and so on -- as well as the "standard" random 16x16 C1 soups. There are also quite a few other categories like 2x128 soups, "inflated" soups that start with 2x2, 4x4, etc. blocks of ON cells instead of single cells, randomly generated glider collisions, and even "stdin" symmetries where people can pipe in any set of starting patterns that they want an ash census of -- partial spaceship search results, for example, just to see if Catagolue happens to record a new spaceship emerging from a partial.

Most of these categories generate starting patterns that aren't actually symmetrical in any way, but they're all classified as "symmetries" anyway, because that was the name of the category when Catagolue was first set up. By now everyone has gotten used to it and talks about "stdin symmetry" and so on without blinking an eye.

Keep the cheer,


Dave

On March 16, 2022, Dave Greene wrote: NewLifeCA 3/16/2022: CGoL Pattern of the Year voting time, and new record quadratic growth

I've mentioned the POTY 2021 nominations list before, but now it has been finalized and is a lot easier to look through -- and the voting has officially started.

There are now single links to stamp collections showing the new discoveries in each category, instead of nominations with dozens of unlabeled supporting links each:

Instructions for how to vote are at the bottom of the first post. You do have to have a forum account, though, and to get one of those if you don't have one, you have to answer a question about Life that seems to be beyond the capacity of most spambots / spambot handlers.

Quadratic-Growth New Records
In other news: as some of you already know, dani / danielle -- who is one of the moderators on the Conwaylife Lounge Discord server -- has been running some productive searches in the last few days, producing two successive record-breakers for low-population and small-bounding-box quadratic growth Life patterns.

The initial discovery was in a form like this --

Code: Select all

#C https://conwaylife.com/forums/viewtopic.php?p=142708#p142708
#C https://conwaylife.com/forums/viewtopic.php?f=2&t=5594#p142790
x = 63, y = 53, rule = B3/S23
33b3o$32bo3bo$32bo4bo$32bobo2bo$32bobob2o$29bo2bob2o$29bo2b2o$30b3o10$
58bo$49bo7bobob2o$48b2ob2o2b2ob2o2bo$bobob3o2bobo2bo32bo5bobo5bo$ob3ob
o2b3o2bo33bo8bo2b2o$2obob4ob2obo35bo2b3o2bo$o5bo3bob2o41b3o$o2b4o2b2ob
obo$bo2bobo2b6o$o3bob3o2bo3bo$bo2bo2b4obob2o$3b2obobo2b3o$2bobo3b2o3b
3o$o3bo3b2o3bo$5b2o7b2o$b2ob5obo2bobo$b2o2b4obobob2o$2bo2b3ob3o3bo$2bo
b3obo2b2o2bo2$23bobo2bo2b3obo$23bobo6b4o$24bob2obo2b4ob2o$26b2obob3obo
2bo$23b2ob2o2b2ob3o2bo$25b4o2b5o$23b2ob2o2b2obob3o$23bo2b3o3bo2b2obo$
23b3obob2ob2o4bo$23bob2obob4o2bo$24bo2bo4b2ob2o$28b2ob2o3bo$24bo3bobob
2ob4o$23bo6bobobob3o$24bob9o3bo$23bobo2b3o!]

-- which came from a program that dropped patches of random soup behind a couple of switch engines, and then piped all those experiments through apgsearch to see if any interesting new stuff came out. Quadratic-growth pattern, new 2-engine Cordership... you name it, if it's interesting, then probably apgsearch census code will notice it.

A couple of reduced versions followed, one with a 26x18 bounding box, and one with a population of only 22 cells -- breaking a fairly long-standing record set by switch engine ping-pong.

The version with an R-pentomino+glider was just a population-minimizing substitution to get the two switch engines into the right phases -- you can't just put in two 8-cell switch-engine predecessors, because the relative phases end up being wrong.

The same search program turned up another switch-engine-producing switch engine pair a few days later, which allowed for a 21-cell predecessor.

A few other non-record-breaking quadratic-growth patterns have also turned up, as well as a rediscovery of the 2-engine Cordership (twice so far: see the "xq96" category in Catagolue's sep_stdin symmetry.)

Keep the cheer,


Dave

On March 23, 2022, Dave Greene wrote: NewLifeCA 3/23/2022: Life Day news, NewLifeCA Archive, and Fwd: Better 32x32 diehard

Happy Life Day, all! (3/23, you know -- *not* a Star Wars reference of any kind. Definitely not. Don't even look that up, it's bad for the digestion.)

See below for Dean Hickerson's new-record 32x32 27003-tick diehard. (!)

A few more news items:

1) A week ago, a relatively new user of the conwaylife.com forums assembled a new kind of puffer. I'm not sure if it can properly be called a "gliderless Gosper glider gun puffer", since the glider guns certainly produce authentic gliders -- but it's certainly a "glider-synthesis-less glider gun puffer", the first puffer in that category I believe.

2) Speaking of glider syntheses, last night and this morning Adam P. Goucher posted a set of recipes that allows for a huge simplification of the Reverse Caber Tosser method of constructing anything that's glider-constructible, using exactly 17 gliders in groups separated by super-astronomical distances. Discussion is ongoing on Discord and on the forum thread.

The diameter of the 17-glider pattern needed to build, let's say, Alan Hensel's decimal counter ... is not anywhere near calculable yet. It's many, many orders of magnitude smaller than it would have been if someone had asked yesterday, but an unknown but very large number of orders of magnitude still remain.

3) Nathaniel Johnston and I are just now closing down the Life textbook Kickstarter. It has collected more than double our target amount -- plenty enough to fund the next set of things we want to try doing to reach a wider audience with the book.

Among other things, I'll be passing out a lot of copies of the book PDF and pattern files on USB drives as part of G4G14's Gift Exchange, and spending some time in the G4G Exhibit Room with a laptop, just to see if anyone wants to discuss anything that might need a running copy of Golly as a prop.

We also just finished a Reddit event called an "AMA" -- "Ask Me Anything" -- which turned out very well, topping out at something over 2800 upvotes and attracting a very good number of interesting questions (and, we hope, answers) about Conway's Life and other CAs and CA-like models. Have a look if you're interested in seeing what a "wider audience" might look like:

https://www.reddit.com/r/IAmA/comments/ ... essor_who/
https://www.reddit.com/r/math/comments/ ... t_conways/
https://www.reddit.com/r/cellular_autom ... ok_launch/

It appears that Hacker News also allows AMAs, so after a little research, one of us might give that a try if we can find the time.

NewLifeCA Archive
There are getting to be enough of these NewLifeCA emails that it's getting difficult to send them all out to any late arrivals to the group. I'll be re-posting to some publicly accessible URL everything I've written to this group so far, and (with permission received from Dean already) also everything that Dean Hickerson has sent for redistribution to the group. Naturally I won't make the NewLifeCA email list visible or anything like that.

Most likely I'll make a "NewLifeCA" thread on the conwaylife.com forums, and will lock the thread so that the only thing that gets posted to it is NewLifeCA email "back issues". If anyone has any concerns about this, please let me know.

Final side note: anyone in this group who missed the last link to the Kickstarter but actually wants any of the items from the Kickstarter tiers, can of course feel free to contact me directly also.

Keep the cheer,


Dave

On March 23, 2022, Dean Hickerson wrote: Subject: Re: Better 32x32 diehard

Thanks to Dave Greene for the suggestion to use a c/7 loafer between the 2c/5 and c/10 instead of 2 c/3 spaceships. I finally found a way to make it work, and it's compact enough to be useful here. The pattern below fits more naturally in a 33x33 box, but some backtracking by lifesrc for the west edge and northwest corner squeezes it into 32x32:

Code: Select all

#C 27003-tick diehard
x = 32, y = 32, rule = B3/S23
3obob3o$4b2obob3o$2o2bo5bo$ob2ob2o3b2o$o2b2o2bo$2o3b4obo5b2o4b2o$3bo2b
o3bo5b3ob2o2bo$3b3o15bobo$6bobo13bo$16bo8b3o$16b3o6b2ob2o$o3bobo4bo7bo
6bobob2o$2o2bo5b2o5b2o6b2o3b2o$bo3b2o3bo6bo7b2obob2o$4o6bo16b3o$bob4o
3b2o13bo$3b2o3b4o12b2o$3o4b2o12bo4bo$o3bo2bo3bo2b2o5bo4b2o$o3bo2bob2o
3bobo5b5o$2obobobo2bo4b2o8bo$b3o5bo$2o5bo$bo2bo3b3o3b2o4b2o5b2ob2o$2bo
4b4o3bobo2bobo4bobobo$b5obo2bo5bo2bo6bobo2bo$bo3bo10b2ob2o4b2ob4o$4bo
2bo11bo2bo2bo$4bob2o11bob2o4b2ob2o$2ob2obo8b2ob2obo6bobo$2obo2bo8b2obo
2bo5bo2bo$4b2o13b2o7b2o!

Dean Hickerson

On April 7, 2022, Dave Greene wrote: NewLifeCA 4/7/2022: 20-cell quadratic growth, diereallyhards, Speed Orthogonoid, and more

I'm writing this from G4G14 in Atlanta, so there's not a lot of time for writing summaries at the moment! Here's a quick forward from an email from Adam P. Goucher, who has now joined the NewLifeCA email list:

Adam P. Goucher wrote:The record has been improved to 20 cells (also by Danielle), producing a BLSE every 11136 generations:

Code: Select all

x = 97, y = 33, rule = B3/S23
94bo$92bobo$94b2o6$88b3o11$96bo$95b2o8$3bob2o$2bo3bo$bo$bo$obo!

The upper-right component (11 cells) was one of exactly 400 seeds of the form R+(block or blinker)+(block or blinker) that gives rise to a glider-producing switch-engine, found by a day of searching on my laptop.

The lower-left component (9 cells) evolves into a Herschel and unstable switch-engine, the latter of which is stabilised by interacting with the other switch-engine.

There has been some further development of Dean Hickerson's engineered-diehard experiments on a dedicated conwaylife.com forum thread.

The longest-lasting engineered diehard is quite a bit larger than 32x32; the arbitrary line chosen by the first post was a 10,000-cell bounding box. Inside that limit, the current longest-lasting diehard posted by Pavel Grankovskiy this morning dies out sometime after 2 * 10^870 ticks (!)/

In other news, Goldtiger997 has completed an initial Speed Orthogonoid -- a self-constructing spaceship along the lines of the Speed
Demonoid, that can reach speeds approaching the c/2 orthogonal speed limit.

A pair of 44P5H2V0s recently showed up in a symmetric soup search -- the first c/5 spaceships to do so.

Keith Amling has assembled a c/2 orthogonal stretcher for a stable wick.

Other recent news can be found as usual on the LifeWiki home page, or in the News Archive.

Keep the cheer,


Dave

On April 14, 2022, Dave Greene wrote: NewLifeCA 4/14/2022: diesuperhards

A week ago I wrote:

Dave Greene wrote:... the current longest-lasting diehard posted by Pavel Grankovskiy > this morning dies out sometime after 2 * 10^870 ticks (!)

It turns out that the 10,000-cell bounding box limit is big enough to fit diehards that last unimaginably longer than that. Mechanisms inside 100x100 can actually support tetration.

The initial diesuperhard (not an official term, I just made it up) had a lifespan bigger than the eighth tetration of 121. Posts later in the thread explain the gradual improvements that were worked out to move the lifespan past 121^^12.

Here's a copy of the current best effort in two-state Life format, in case anyone is running a CA editor that doesn't get along well with Golly 4.0+'s LifeSuper:

Code: Select all

#N diesuperhard-12th-tetration
#O Pavel Grankovskiy, 14 April 2022
#C This diehard has a lifespan on the order of the twelfth tetration of 121.
#C https://conwaylife.com/forums/viewtopic.php?p=144204#p144204
x = 108, y = 92, rule = B3/S23
20b2o25bob4obobobo$19bo2bo24bo6bobo$20b2o27bo6bo$49b3o2bobo27b2o15bo$
47bo10bo25b2o8b2o5bo$40b2o13b2o36bo2bo4bo$41bo52b2o8b2o$41bobo6b2o29b
2o21bobo$42b2o6bobo28b2o22bo$53bo7b2o$36b3o11bo2bo7b2o21b2o8bo$27b2o6b
3o15bo30b2o6b3o4b2o$27b2o13bo7bobo38bo7b2o$41bobo6b2o39b2o$42bo$20b2o
17bo5bo50b2o7b3o$20b2o6bo9bobo3bobo18bo30b2o6bobo$28b2o7bobo5bo3b2o13b
obo37bo$28b2o6bobo3bo6b2o14b2o32bo2bobob2o$29bo5bobo3bobo9bo5b2o22bobo
13b2o3b2obo$34bobo5bo9bobo3bo2bo23bo17bobobo$33bobo17bobo3b2o20bobo21b
2o$32bobo19bobo24bo23bo$31bobo21bo24bobo$30bobo6b2o5b2o4bo27b2o$18b2o
3b2o4bobo7b2o5bo4bobo3b2o20bo$19b5o6bo13bobo5bo4bobo20b2o$19b2ob2o20b
2o12b2o13b2o6bo$19b2ob2o10b2o37b2o$20b3o4b2o5b2o$27b2o23b2o22b2o$52bo
23b2o$39bo10bobo13b2o$38bobo9b2o14bobo13b2o$18b2o4b2o5b2o4bob2o26b2o4b
2o6bobo4b3o$19bo4bobo4b2o3b2ob2o22bo9b2o6b2o5b3o$16b3o6b2o10bob2o21bob
o13bo8bo3bo$16bo21bobo22bo6bo6bobo8b5o10bobo$28bo10bo29bobo4bobo10b4o
11b4o$27bobo39bobo3bobo24bob2o$22b2o4bobo39bo5bo6bo18bo4bo$24bo4bobo
25b2o8bo5bo7b3o18b3ob2o$21bo8bo25bobo7bobo3bobo5bo7b2o13b3obo$22b2o31b
o2bobo6bo5bo6b2o6b2o12bo3b2o$40bo14b2o2b2o3bo5bo33bobo$17bo16b2o3bobo
10bo10bobo3bobo12bo17bo2bobo$17b3o8bo5b2o4bo10bobo10bo5bo7bo5bo18bobo$
20bo7b2o22bo8bo5bo9b3o4bo$19b2o7b2o30bobo3bobo7bo3bo8bo$16bo12bo16bo
14bo5bo7bob3obo7bo$15bobo6bo20bobo10bo5bo11b5o8bo$14bo2bo6b2o20bobo8bo
bo3bobo$14bobo7b2o21b2o9bo5bo$15bo3bo5bo35bo$18bobo39bobo$18bo2bo39bo$
2bobo14bobo13bo33bo25b2o$2b2o4bo11bo9bo4b2o6bo25b3o22bo2bo$3bo3bobo6bo
13bobobobo5bobo27bo22bobo$6bo2bo6b2o12b2o10b2o5bo21b2o15b2o6bo$6bobo7b
2o30bobo29b2o6b2o$7bo3bo5bo31bo3b2o25bo$10bobo39bobo26b3o$10bo2bo25bo
12b2o29bo7b2o$3bo7bobo25b2o7bo42b2o9bo2bobo$b2o9bo26b2o6bobo53bobobo$
2b2o4bo31bo7b2o38b2o14bo$8b2o78b2o17bo$8b2o95bo$9bo93b2o2bo$4bo7bob3o
10bo15b2o57b3ob2o$4b2o6bob4o7bobo15b2o4bo7b2o5bo37b2o3bo$bo2b2o6bo5bo
7b2o20bobo5bobo4bobo36bobob2o$5bo7bobobo2b3o26bo6bo6b2o38bo$obo11bobob
4o24bo8b2o45b3o2bo$2o5bo7bo2bob2o23bobo54b2obobo$4b2o2bobobo2bo3b3obo
18bo3bo$2bo2bob2o2bo4b3o2b2obo15b3o8b2ob2o14bo$3o8b2o9bo16bo11bob2o2bo
2b2o3bo4b2o$2bo4bo2bobo10bo2bo12b2o15b2o2b2o2b2o5b2o$o3bobob3o13bo2bo
37b2o4bo26b3o4bo$o3bo5bo14b2o3bo16b2ob2o14bo3bo26bo2bo4b2o$3o2bo3b2obo
13b5o16bob2o2bo43bo2bo2bobobo$2bobo2bob2o16b4o21b2o50b2obo$bob2o2bo2bo
bo14bobo72bobob2o$4bo2b2o2bo14bob2obo11b2ob2o14bo2b2o23bo13bo$9bo2bo
13bo3bobo10bob2o2bo10b3o2b2o2bo16bob5o3b2o5b2obo$8b2o2bo13bo2bo2b2o14b
2o13b2o2b3o18b2ob2o4bo4bob2obo$4bo5bo16b2obob2o29b2o2b3o19b2o2b2o11bo$
5b2o2b2o9bo8bo2b2o5b2ob2o19b2o6bo2bo9b2o2b2obo14bo$2o2bo3b2o11b3obo4bo
8bob2o2bo18bo6b3o10bo3b2ob6o2b2o$2o7bo9b6o6b3o10b2o39bo2bo3b5o2b2o!

The lifespan of this diesuperhard is bounded by

121 ^^ 12 < T < 121 ^^ 13

or somewhat more precisely by

21 ^^ 13 < T < 22 ^^ 13

More detailed calculations can be found in this post.

Keep the cheer,


Dave

On April 15, 2022, Dave Greene wrote: NewLifeCA 4/15/2022: Speed Orthogonoid script, single-engine p36 gun, and rare C2_4 collidosocope

Here's a little more recent news that I didn't mention yesterday:

1) Goldtiger997 has completed a Golly script that makes it easy to build an orthogonal spaceship for any sub-c/2 speed.

These are quite a bit bigger than the equivalent Caterloopillars for speeds below c/4, but they do fill in a subset of missing speeds above (edited) c/4 that the current Caterloopillar-building script can't generate. That is to say, Caterloopillars with speeds of the form m/(8k+2) and m/(8k+6) are theoretically possible but no examples have been built yet, whereas Speed Orthogonoids have no such limitations.

2) A single-engine p36 gun has been assembled using the impressively versatile "traffic stop" reaction that has solved several other catalysis problems recently:

Code: Select all

#C p36 glider gun using just one copy of Jason's p36
#C This is the simple minimum-population version from
#C   https://conwaylife.com/forums/viewtopic.php?p=144146#p144146
#C   -- for the smallest bounding box see
#C   https://conwaylife.com/forums/viewtopic.php?p=144164#p144164
#C   or the LifeWiki article at
#C     https://conwaylife.com/wiki/Period-36_glider_gun .
x = 50, y = 30, rule = B3/S23
33bo$28bo3bobo7bo$27bobo2bobo5b3o$27bob3o2b2o3bo$26b2o4b2o3bo2bo$2o23b
o2b4o2b3o3bo$bo21bo2bobo3b3o3b2o9bo$bobo18bo4bo3bo3bo11b3o$2b2o18bo8bo
bobo10bo$13b3o8b3o5b3o11b2o$13bo19bo$13bobo$14b2o$23b2o$23bobo20b3o$
25bo17bo$12b3o8b3o16bobo$16bo28bo$11bo4bo26b2o$15bo$12b2o$12bo$12bo16b
6o$12bo14b2o6b2o$26bobobo2bobobo$24b3obo6bob3o$23bo3b2ob4ob2o3bo$24b2o
3bo4bo3b2o$26b2o2bo2bo2b2o$26bob2o4b2obo!

3) A new record has been set for long-lasting novelty in Catagolue/apsearch's standard-sized random symmetric soups:

Code: Select all

#C A symmetric C2_4  "collidoscope" that stabilizes after 225,593,194 ticks
#C ("yl4608_2_4870_7437a7f8139022277e706736421bde0f" on Catagolue)
#C https://catagolue.hatsya.com/hashsoup/C2_4/c_mnZYdEB3FIdv459965563/b3s23
#C
#C See also https://conwaylife.com/forums/viewtopic.php?p=86214#p86214 for a
#C   collection of stabilization times for the more common D8_4 collidoscopes.
x = 32, y = 32, rule = B3/S23
18bo2bobo$17b7obo2bo$17b3ob2o2b2ob2obo$16b3ob2o3b7o$17bob2ob3ob2o2b2o$
16b2o2bo2bob5obo$20bob4o3b3o$17bobob4ob2o$17b2o4b3ob4o$17b6obob2ob3o$
21b2o3b2o$18b4o3b4o2bo$16b4o2b2o2bo$18b2o2b2o2b4o$16b5ob2o6b2o$17b2obo
3bobo3bo$bo3bobo3bob2o$2o6b2ob5o$2b4o2b2o2b2o$5bo2b2o2b4o$o2b4o3b4o$4b
2o3b2o$3ob2obob6o$b4ob3o4b2o$4b2ob4obobo$3o3b4obo$ob5obo2bo2b2o$2o2b2o
b3ob2obo$7o3b2ob3o$ob2ob2o2b2ob3o$3bo2bob7o$8bobo2bo!

225,593,194 ticks is several times longer than the longest D8_4 collidoscopes that I know about. The above soup is equivalent to a couple of switch engines plus a small constellation:

Code: Select all

x = 46, y = 32, rule = B3/S23
32b2o$32b2o2$41bobo$41bo2bo$41bo2bo$44bo$43b3o2$30bo$29bobo$29bobo$30b
o2$12b2o$12b2o8b2o$22b2o8b2o$32b2o2$15bo$14bobo$14bobo$15bo2$3o$bo$bo
2bo$bo2bo$2bobo2$12b2o$12b2o!

The two streams actually manage to drill past each other occasionally, especially in the first few million ticks. But of course that doesn't last terribly long, since a big explosion at the collision points will instantly interrupt the nearby streams coming from the other direction.

Maybe it would be interesting to investigate if anything like this can make a really long-lasting "true methuselah", actually stopping the switch engines after as long a delay as possible, along the lines of Paul Callahan's proof of concept 1.7-million-tick pattern from 2019.

Keep the cheer,


Dave

On April 24, 2022, Dave Greene wrote: NewLifeCA 24 April 2022: Build Anything Constructible with 16 Gliders, Tetration Revisited, and New Glider Guns

This news item showed up a couple of days ago: the 17-glider upper limit for constructing any glider-constructible pattern has now been reduced to 16 gliders.

The initial discovery was made by dani, who also engineered the20-cell quadratic growth pattern recently. A follow-up search by Oscar Cunningham ("Macbi" on the forums) produced several ways to add a single glider to dani's result and suppress all escaping gliders.

That is the only detail that's needed to complete an arbitrarily large RCT ("reverse caber tosser") synthesis with 16 gliders, because any stationary ash can be cleaned up as part of the construction process, at no additional cost in gliders -- just the usual very large cost in increased bounding box. Some gliders aimed inward at the "epicentre", along with the incoming GPSEs, can also be cleaned up by having the construction arm building expendable structures to catch them, before they actually arrive.

These cleanup mechanisms aren't documented yet, and in some cases aren't entirely invented yet -- but they can be built with the same basic slow-salvo method that constructed the shillelagh, in the pattern shown here.

The RCT's design has actually gotten quite a bit simpler since the 35- and 34-glider fixed cost designs. Written descriptions of the RCT mechanism are all out of date to one degree or another. It seems to be high time to write up a blog post with all of the details... but there are actually a lot of possible options to investigate for cleanup mechanisms, and it's not clear yet (at least to me) which design is the most efficient.

Here's a first effort at what is now looking like a series of three blog posts. These posts will probably all end up getting heavily edited over time as more refinements are made -- but that process may take a while.

Any questions or comments, let me know as usual!

Tetration Too
Also, speaking of blog entries, here's "Biggiemac" / Brett Berger's blog entry about tetration as applied to Conway's Life diehards, and (synchronistically / serendipitously) also to another game that taken up a lot of Brett's time recently:

https://btm.qva.mybluehost.me/telling-t ... etrations/

Glider Gun Progress
For anyone interested in new discoveries that *don't* involve any incomprehensibly large numbers, check out the gun-building threads on the forums. A lot of incremental progress has been made there recently, with some new search results hiding in the p14 and p16 pseudo-period guns and the true-period p28 and p114 guns, among many others.

Keep the cheer,


Dave

On May 2, 2022, Dave Greene wrote: NewLifeCA 2 May 2022: an unconstructible rotor, a new 2c/7 spaceship, quartermax, and more

Here are five Life discoveries from this last week.

1) Andrew J. Wade has found a new 2c/7 spaceship, with an entertaining hole in the middle:

Code: Select all

#N 151P7H2V0, a new 151-cell 2c/7 spaceship
#O Andrew J. Wade, 25 April 2022
#C https://conwaylife.com/forums/viewtopic.php?p=144727#p144727
x = 23, y = 42, rule = B3/S23
11bo$11bo$10bobo$11bo$11bo$5b4o5b4o$4bo3bo5bo3bo$3bo5bo3bo5bo2$7b2o5b
2o$4bo2bo7bo2bo$4bobo9bobo$4b2o11b2o$4b2o11b2o$b2o17b2o$3o17b3o$o2bo
15bo2bo$2ob2o13b2ob2o$3bo15bo3$b3o15b3o$bobo15bobo$bo2bo13bo2bo$b2ob2o
11b2ob2o$2bobo13bobo$3bo15bo2$5b3o7b3o$7bo7bo$3b4o9b4o$3bo15bo$10b3o$
8bo5bo$7bo7bo$4b2obo3bo3bob2o$4bo4bo3bo4bo$5bo5bo5bo$5bo11bo$6b3obobob
3o$9b2ob2o$5b2o9b2o!

2) Another interesting result came in from Ilkka Törmä and Ville Salo on April 27th: it's possible to find "self-forcing" patches of p2 agar. If these patches are present in any Life pattern at time T+2, they must also be present at time T:

Code: Select all

x = 30, y = 19, rule = LifeHistory
.DC2D3C2DCDCDC2D3C2DCD$D.D2C3D2CDCDCD2C3D2CDCDC$D.CDC3DCDC3DCDC3DCDC
3D$DCDCDC2D2CDCDCDCDC2D2CDCDCD$.DCDCD2C2DCDCDCDCD2C2DCDCDCDC$.C3DCDC
3DCDC3DCDC3DCDC3D$.DCDCD2C3D2CDCDCD2C3D2CDCDCD$DCDCDC2D3C2DCDCDC2D3C
2DCDCDC$2DCDC3DCDC3DCDC3DCDC3DCDCD$2D3C3D3C3D3C3D3C3D3CD$2C3D3C3D3C3D
3C3D3C3DC$DC3DCDC3DCDC3DCDC3DCDC3DC$CDC2D3C2DCDCDC2D3C2DCDCDC2DC$DCD
2C3D2CDCDCD2C3D2CDCDCD2CD$2DCDC3DCDC3DCDC3DCDC3DCDCD$DCDCDC2D2CDCDCDC
DC2D2CDCDCDCDC$.DCDCD2C2DCDCDCDCD2C2DCDCDC2.D$2.3DCDC3D3.3DCDC3D3.3D$
2.CDCD2C2D4.CDCD2C2D!

These patches can form part of a period-2 oscillator, and therefore we now know that there exist oscillators with non-glider-constructible rotors.

(We already knew that non-glider-constructible oscillators existed, because oscillators can easily be constructed with stators that include non-glider-constructible still lifes. But until now, the rotor wasn't the thing that made oscillators provably non-constructible.)

The current smallest known oscillator containing the unsynthesizable patch can be found here. Scroll up to the parent post for the two-state version.

3) On April 28th, wwei47 turned up a new record-smallest period-12 backrake:

Code: Select all

#N p12 backrake
#O wwei47, 28 April 2022
#C This is a 34-cell predecessor of the rake,
#C    which has a minimum population of 39 cells.
#C https://conwaylife.com/forums/viewtopic.php?p=144830#p144830
x = 20, y = 6, rule = B3/S23
9bo7bo$b3o4b3o5b3o$o2bo3bo2b2o4bob2o$3bo3bo3bo5b3o$3bo4b2o2bo4b2o$obo
8bo!

4) On May 2, iNoMed completed yet another period-46 gun with a never-before-seen engine mechanism:

Code: Select all

#N "Tamale"
#O iNoMed, 2 May 2022
#C A p46 gun not based on twin-bees shuttles, glider loops, or Kazyan's p46
#C https://conwaylife.com/forums/viewtopic.php?p=144982#p144982
x = 30, y = 31, rule = B3/S23
13b2o$8b2o3bo2bobo$2o5b2o6b2ob3o$bo7bo11bo$bobo11b2ob3o$2b2o11b2obo2$
20b2o$20bo$18bobo$2o5b2o9b2o$2o5bobo$7bobo$8b2o4$20b2o$20bobo$20bobo5b
2o$10b2o9b2o5b2o$9bobo$9bo$8b2o2$11bob2o11b2o$9b3ob2o11bobo$8bo11bo7bo
$9b3ob2o6b2o5b2o$11bobo2bo3b2o$15b2o!

5) Also on May 2, Keith Amling filled in the last piece of the puzzle to complete a "quartermax" spacefiller.

Code: Select all

#N quartermax
#O Keith Amling, 2 May 2022
#C https://conwaylife.com/forums/viewtopic.php?p=144986#p144986
x = 133, y = 112, rule = B3/S23
bo$3o5b3o12bo5bo$ob2o4bo2bo4b3o3b3o3b3o$b3o2bo9bo2bob2obo3bob2o$b3ob2o
bo3bo2bo2b2ob3o5b3o$b2o3bobo2b2o2b5o2b2o5b2o$11b2o9b2o$12bo3bo3bo2bo2b
2o37b3o$17bo2b2obo7b3o24b3o3bo2bo$12b4o3b2o6bo3bo2bo6b3o3b3o8bo2bo5bo$
11bo2b3o4bo2b4o3bo2bo6bo2bo2bo2bo7bo8bo$12b2obobobo2bobo5bo3b2o4bo3bo
2bo10bo3bobobo$10bo4bo3bobob2o2bo3b3o2b2o2b2ob2o3bo2bo3bo2bo$10bo4bo8b
5o3b2ob3ob2o8b3o2b3obo3bo7b3o$14b2o12bo5bo4b2o3b5o2b2obo3bo3b2o6bo2bo$
6bo3bobobo13bo5b2o7bo4b4obobo2b3o2bo6bo$5b3o3b2obo19b3o3b2o2bo4bo3bobo
6bo2bo4bo$4b2obo4bo27b5o5bo2bobo2b4o4b2o3bobo$4b3o3b6o21b2obob2o2b4o6b
o11bo$5b2o3bo3b2o17bo4bobobob2o9bob4obo$15bo16b2ob2obobo3bobo4bo4b2ob
2o3b2ob2o32bo7bo$14bo14bo2b3o3bob3obobo10bo2bo3bobo33b3o5b3o7b3o8b3o$
14b2o12b3obo5bob2o2bobo2b2o7bobo3bo19b3o5b3o5bob2o3b2o2bo6bo2bo7bo2bo$
11bo3bo11b2o2b2o5b3ob6o2b3ob2o2bobobo3b2o3b3o3b3o4bo2bo4bo2bo5b3o3b3ob
o6bo10bo$10b3o14b2ob2o6b3o2bo2b2o2b2obob3obo2bo7bo2bo3bo2bo2bo8bo2bo5b
2obob2obob2o5bo3bo6bo$9b2ob2o13b2o2b2ob3obo12bo9b3o2bo3bo3bobo3bo2b3o
2bo2bobo3bo3bo3bo3bobob2o3bo3bo7bobo$8b2o21bob2o2bo4bo8bob2o6b3o4bo3bo
bobobo2bob2o5b3o5b2o9bobo2b4o4bob4o$7b2o18b2o5bo26b3o3b5obo2bob5o2b3o
2b2obo4b2obo5bobobo2b6ob2ob2o2bo$8bo25bo26b3o2bo25b3obobobob5o2bobo10b
o3bo$7b2o28bo23b2o4b22o7b2o3b2o2b2o7bobo5bobo$5b2obob2o18b6ob2o53bo8b
2o2b2o5bo8b3o$6bobo2b2o16b2obo4b2o28b22o12bo4bo14b2o$3b2obo2bo2bo16bob
2ob4o28bo22bo31b2o2bo$3b2obo5b2o19b4o30b23o35b4o$3bobo22bob2ob3o55bo
35b2o$2b2ob2o20bo2bo36b25o38bo$27bo4b2o32bo26bo33b4o$33bo33b27o37bo$
27bo67bo31bo2b3o$26b2obobo2b2o31b29o33b3o$27bo6b3o29bo30bo32bo$26bo2bo
6bo30b31o27bob3o$27b3o3bo65bo25b2o2bo$27b3o3bo2bo30b33o26b3o$35bo30bo
34bo24bo$67b35o26bo$29bo73bo22bobo$28b2o37b37o25bo$28b6o32bo38bo20bobo
$28b4o2bo32b39o22bo$27bo3bo3bo71bo18bo$28b2o5bo31b41o18b3o$33bo32bo42b
o15b2o2bo$34bobo30b43o15bob3o$30b3obob2o73bo18bo$30bo3bobobo28b45o17b
3o$36bob2o26bo46bo13bo2b3o$29b2o5bo3bo26b47o17bo$115bo11b4o$36b2ob2o
26b49o14bo$35bo5bo24bo50bo9b2o$36bo3bo26b51o5bob4o$119bo2bob2o$67b20ob
32o2b2o$66bo19bobo32b2o$67b19o3b33o$71bo2bo$67b3o6b8o3bo3b33o$67bo2b6o
8bobobobo32b2o$65bobobo5bob3ob4obobob4ob4o2b4o2b4o2b4o2b3o2b2o$64bob2o
2bo3b2o2b2o6bobo6b2o2bob2o2bob2o2bob2o2bob3o2b3o$64bo4bobo5bo5b2obobob
2o5bo5bo5bo5bo7bobo$63b2ob5ob2o11b2ob2o32b3o$63bo2bo2bo6bo5bo4bo4bo28b
2o2bo$64bobo4b5o6bob2obob2obo24bo2b3o$65bo3bobo14bobo28bo2b3o$69b2o3b
2o8bobobobo28bo7b2o$74b2o4b2obo2bobo2bob2o24b2ob5ob2o$80b2o2bobobobo2b
2o22bob3ob6o$86bobo22b2obob3o2bo3b3o$85bo3bo23b2obob2o$110b2o9bo$84b2o
3b2o16b2obo2bob3obo2b2o$83bo7bo15b2ob2obobo2bo4bo$83b4ob4o16bob3o5b2o
3bo$111b2o7b3o$84bobobobo$77bo3b3o2bobo2b3o3bo$76bobobobob2o3b2obobobo
bo$76bobobo3bo5bo3bobobo$77bobo3bo2b3o2bo3bobo$79bobo4b3o4bobo$79b2o6b
o6b2o$86bobo$82bo2bobobo2bo$82b4obob4o$86b3o$84bo5bo$83bob2ob2obo$83bo
7bo$80b2obob2ob2obobo$80bobo3bobo3bobo$83b2o5b2o2bo$85bo3bo2b2o$83b2ob
obobo$82bo2bobobob3o$82b2obo3bo3bo$85bo2bobobo$82b2obo2bob2o$83bobobob
o$83bobobobo$84b2ob2o!

Keep the cheer,


Dave

On June 5, 2022, dvgrn wrote:NewLifeCA 5 June 2022: RCT progress, CatForce improvements, and oscillator discoveries

June already!  Time for another somewhat miscellaneous CGoL news summary.

1) New oscillator discoveries have continued.  Part of them are due to the continuing work of David Raucci / hotdogPi and his script that adds experimental sparks to arrangements of common active objects.  Many, but not all, of the rest come from Charity Engine, which continues to run symmetric soups in impressive numbers (though not quite as impressive as during the initial surge).
 
To see the full collection of new oscillators, follow the links as usual in the LifeWiki news page.

A few of the highlights include

-- a useful small p7 sparker called "meatball".  The gallery in the LifeWiki article shows off some of its uses better than I can in an email.
-- several new SKOPs, including these at p25 and p84:

Code: Select all

x = 64, y = 20, rule = B3/S23
o59bo$3o55b3o$3bo53bo$2bo26b2o26b2o$2bo2bo24bo$30bobo17bo$6b2o23b2o15b
2obo$7bo39bobo$5bobo39bo$4b2o$14b2o$12bobo30bo$12bo30bobo$12b2o27bob2o
15b2o$42bo17bobo$14bo2bo44bo$17bo16b2o26b2o$16bo18bo$17b3o12b3o$19bo
12bo!

"SKOP{n}" is a relatively new term, in common enough use now that it ought to go in the Life Lexicon.  It's short for "Smallest Known Oscillator of Period {n}", and there's a dedicated repository for keeping track of them, maintained by Jeremy Tan.

The Skopje collection is one of the current litmus tests for new discoveries, along with the glider syntheses and gun collections on Catagolue.  If a just-discovered mechanism can be used to set a new record in one of these places, then the odds are good that it's really a new discovery, not a re-discovery or an uninteresting variant of something already known.

2)  The glider-guns thread on the forums is a good place to see some recent applications of new technology along the above lines.  Here for example is a pseudo period-19 gun getting squashed into an almost reasonable bounding box.

The first pseudo-period p19 gun was a 450x281 construction by Karel Suhajda in 2003.  It has been gradually reduced over the years, and now fits inside 169x136, less than a fifth of the original size:

Code: Select all

x = 644, y = 281, rule = B3/S23
223bo35b2obo7bo$221b3o35bob2o7b3o$220bo52bo14bo$220b2o50b2o12b3o$232bo
52bo30b2o$232b3o50b2o28bo2bo$235bo74b2o2bob2obo$190b2o42b2o9bob3o60bo
3bo2bobo$191bo51b2obo3bo33b2o25b3obo3b2o$191bobo50bo4b2o14b2o17b2o27bo
bobo2bo$192b2o2b2o47b4obo14b2o46bo3b3o$196b2o20bo4bo$214b2o2bo4b2o2b3o
47bo26b2o7bo2b4o2b2o$213bo5bo5bo50b3o25bo8bo6bo2bo$212b2o2bobo4b2o50bo
2b2o25bo2bo5b2o3b2obo$213b2o3bo7bo47b4obo27b2o6bo5bob3o$214b3o5b2o3bo
40b2o4bo4bo27bo3b2o8bo4bo$222b2ob2o21b2o19bo5b2o2bo26bo4b2o7b2ob2ob3o$
84b2o162bobo15b3o7b2o28b2o10bo3b2obo3bo$83bo2bo163bo15bo47bo6bo5bo2bo$
82bob2obo2b2o146b2o10b2o19b2o8bo31bobobo3bo4b3obo$82bobo2bo3bo146bo33b
o6bobo27b2o2b2o7bo2bo4bobo$81b2ob3ob3o99b2o36b2o9b3o27b3o8b2o27b2o8bob
3obobobob2o$81bo2bobobo100bobo16b2o19bo11bo27bo53bobo3bo$82b2o105bo18b
obo17bo92b2o2bobobo$87bo100b2o20bo17b2o92bobobobo$78b2o2b3ob2o8b2o99b
3o4b2o4b2o110bobo2bo$78bo2bo3bobo7bobo98b2o2bo3bobo116b2o$79bob2o2b2ob
o7bo98bo3b2o5bo$76b3obo11b3o99bo2b3o6b2o54b2o$75bo4bo9b4o99bo2b2o65bo$
73b3ob2ob2o6bobo2bo2bo76b2o18bo2bo66bobo15b2o58b2o$72bo3bobo3bo11b2o
76bo2bo18bo2bo66b2o15b2o54bo2bobo$71bo2bo7bo4bo79b2o2bob2obo17bo2bo
105b3o30bo4bo$71bob2obobo3bo3bobo78bo3bo2bobo18b3o107bo30bo2bo$69bobo
10bo4b2o2b2o75b3obo3b2o7b2o117bo32b3o$69b2ob2ob2obob3o8b2o13b2o62bobob
o2bo8bo121b2o22b2o4b2o$72bobobobo2bo24bo63bo3b3o9bobo118bobo2bo15bo3b
2o4bo8b2o$72bobobo2b2o26b3o77b2o118bobobobo12bobo8b2o7bobo15b2o$73bobo
bobo24b3o3bo50b2o7bo2b4o2b2o125b2o2bobobo12b2o17bo16bo2bo$74bo2bobo23b
o4bo2bo49bo8bo6bo2bo124bo2bobo3bo18b2o2bo2bo4b2o11b2o2bob2obo$77b2o23b
obobob2obo50bo2bo5b2o3b2obo92b3o19b2o10bobobo2b2ob2o15bobo5b3o3b2o9bo
3bo2bobo$103bo4bo2b2o51b2o6bo5bob3o92bo18b2o2b2o5bo2b3o4bobo16bo5bobo
2b2o2bo9b3o2bo2b2o$104b4o2bo2bo50bo3b2o8bo4bo88bo2bo22bobo5b2o3b3obo
24b2o4bobobo10bobobo2bo$81bo19b3o7bobo49bo4b2o7b2ob2ob3o87b2o7b2o15bo
6bo5bo2bo26bo2b4obo12b2ob2o$79b2o20bo3b2o3b2obob2o46b2o10bo3b2obo3bo
20b2o64b2o7bobo6b2o12bo2bobo3bo27bobo4bo13b2o$80b2o20b3ob2o2bo3bobo54b
o6bo5bo2bo19bo64bo2bo8bo6bo4b2o7b2ob2ob3o18b5o3bobobob3o3b2o9bo2b2o2b
2o$104bobob2ob3o56bobobo3bo4b3obo17bobo64bo11b2o5b3o2b2o8bo4bo19b2o4bo
2b2o3b2o5b2o9bobo2bo2bo$111bo2b2o3b2o31b2o12b2o2b2o7bo2bo4bobo15b2o67b
2o15b3o5b2o5bob3o19bobo4b3o14bobo4bo5b2obo$106bo7bobobob3o30bo12b2o8bo
b3obobobob2o102b2o5b2o3b2obo20b3o9bobo14bo3b3o5bob3o$110bo5bobo4bo26b
3o27bobo3bo102bo8bob3o2bo2bo18bo3b2obob2obob2o10bo2bo2b3o7bo4bo$86b2o
20bo7bob2ob2obo24bo3b3o22b2o2bobobo22bo79b2o11b3o2b2o18b3o7bobo13bo2bo
2b2o7b2ob2ob3o$87bo17b3o8bo5bobo23bo2bobo2bo22bobobobo22bobo90bo28b3ob
obo2bo14b2o12bo2bobo3bo$84b3o17b5o4b2o4b2o2bo24bob2o2b2obo21bobo2bo23b
obo88bob4o24bo2bo4b2o23bo5b2o5bo2bo$83bo3b3o13b2obo2bo4bo6b2o24b2o4bo
2bo23b2o25b2ob3o78b2o5bo3bo2bo22bob2o2b2obo23bobo4b9obo$82bo2bobo2bo
13b5o6b2ob3o25bo2bobob3o57bo77bo4b3obo3b2o23bo2bobo2bo19b2o2b2o5bo2bob
o4bobo$82bob2o3bobo14b2o3b2o7bo25bobo7b3o18bo29b2ob3o59b2o15bobo3bo3bo
2bobo25b3o3bo5b2o13b2o9b2obob2ob2ob2o$81b2o2bo4bo14bo5b2o7bobo20b2obob
2obob2o3bo19bo28b2obo61b2o15b2o4b2o2bob2obo28b3o7bo24bo2bobo3bo$80bo2b
o2b4o16b2o13b2o20bobo9b3o18b3o121bo2bo28bo7b3o26b2o2bobobo$80bobo3bo3b
3o13b2o38b3o4bobo46bo98b2o29b2o5bo3b3o24bobobobo$77b2obob2o2b3o3bo20b
2o24b2o3b2o2bo4b2o39b2o5bobo105bo28bo2bobo2bo23bobo2bo$77bobo5bo3b3o
18bob2o23b3obobobo3b5o39bobo5bo106bo29bob2ob3obo9b2o12b2o$80b3ob2obobo
20b2o24bo4bobo49bo8bo2bo102b3o26b2o2bobo2bo9bobo$73b2o3b2o2b2o2bobo25b
obo18bob4o2bo48b2o12bo129bo2bo2b4o12bo$71b3obobobo35b2o18bobobo4b2o53b
obob3o49bo80bobo7b3o$70bo4bobo58bo2b2o2bobo5bo47bo53b2o78b2obob2o4bo3b
o$69bob2ob2ob2o58b2o3b3o5bobo46b2o12b2o39b2o77bobo3bo2b2ob3o$69bobo3b
2obo60b2o4bo2bo2b2o3b2o55bobo120b3o4bobo$56bo13bo2bo4b3o4bo53bo15b2o
58bo70b2o2b2ob2o34b2o3b2o2bob2o$56bobo12b2o2bo3b2o3bobo50bobo7b2o8bo
57b2o54b2o13bobo2bobo33b3obobobo3b6o$56b2o15b2o3bo6b2o50b2o8bo4b2o116b
obo16b2o3bo31bo4bobo6b3o$73bo7b2o63b2o4b2o49bo23b2o41bo19bob2o31bobob
2ob2o28b2o$71bobo7b2o63b3o53bobo22b2o2b2o36b2o16bo2bobo32bobo5bobo26bo
$71b2o13b2o58bo2bo52bobo24bo3bo46b3o3bobobobo33bo2b2obo2bo5bo21b3o$58b
obo25b2o56bo4bo53bo29bo46bo2bo3b2ob2o35b2o2b3obo4bobo17b3o3bo$57bob2o
18b3o61bobo2bo39b2o17b2o20bob2o46bo49b2o2b2o6b2o16bo4bo2bo$39bo15b3o
16bo4b3obo40bo18b2o42bobo17bobo20bo5b2o44b2o45bo7b2o19bobobob2obo13bo$
37b3o14bo4b2o11b3o5b4o12b3o23b3o62bo21bo11b2o13b2o40bo3b2o43bobo7b2o
20bo4bo2b2o13bo$36bo17b5obo10bo5bo18bo24bo64b2o21b2o10bobo7b2o45bo48b
2o13b2o16b4o2bo2bo10b3o$36b2o20bo12b2o4b2o18bo23b2o100bo7b2o47bo61b2o
13b3o7bobo$26b2o26b2o3bo140bo22b2o4b3o3b2o43b3o52bo2bo18bo3b2o3b2obob
2o$27bo26bobo3bo140b2o9bo8b2o7bo3bobo44b2o52b2o2bo18b3ob2o2bo3bobo$27b
obo25bo3b2o94b2o43b2o8b3o7bo3b5obo4bo46bo51b2o2b2o20bobob2ob3o$17b2o9b
2o4b2o45bo36b2o10b2o24bo52bo9bobobob2o106bobo31bo2b2o3b2o$18bo14bo2bo
44b3o35bobo9bo13b2o6b3o53b2o8bob2obo3bo57bo46b2o27bo7bobobob3o$15b3o
14b2obo48bo35bo10bobo11b2o6bo52bo13bo4bobo56b2o69b3o8bo5bobo4bo$14bo3b
3o12bo12b2o7b3o25b2o11bo35b2o70bobo14b3obobobo55b2o68bo8bo7bob2ob2obo$
13bo2bobo2bo11bobo10b2o7bo40b2o99bo7b2o16b2o3b2o2b7o117bo15bo5bobo$13b
ob2o3bobo10bobo20bo38bo2bo96b3o32b3ob2obobo6bobo21b2o92bo4b2o4b2o2bo$
12b2o2bo4bo12bo31bo29b2o96bo32bobo5bo3b3o5b2o22bo19b2o70bobo4bo6b2o$
11bo2bo2b4o41bobob2o79b2o3b2o40b2o11b4o16b2obob2ob4o3bo4bo23bobo17bo
71b2o6b2ob3o$11bobo3bo3b3o38b3o2b2o78b2o2bo4b2o21b3o24b6o18bobo2bo4b3o
29b2o15bobo75b2o7bo$8b2obob2o2b3o3bo38bobo2bo58bo28bobo5b2o14bo30bo19b
o2bob5o36b2o6bo4b2o76b2o7bobo$8bobo5bo3b3o37b2o3b2o26b2o30b4o23b2o3bo
5b2o15bo3b4o43b2o2bobo2bo34bo2bo4bobo76b2o13b2o$11b3ob2obobo39b2ob3o
26b3o28b5obo23bo2bo30b2o43bob2o3bobo34b2o5bobo76b2o25bobo$4b2o3b2o2b2o
2bobo12b2o3b2o24b2o6b2o19bo2b2o25bo6b2o23bo28bo2bob2o22bo19bo2bobo2bo
31b2o10bo84b2o18b2obo$2b3obobobo22bo3bo20b2o11b2o19b2o2bo11b2o11bo3bob
3o53b2obobo44bo3b3o31bobo92bob2o5bo16b3o15bo$bo4bobo21b3o5b3o18bo33bo
2bo12bo12bobo2b2o55bob2o18bo27b3o34bo51b2ob2o38b2o7b3o11b2o4bo14b3o$ob
2ob2ob2o20bo9bo15b3o34b3o10b3o76b2o19b2o29bo32b2o51b2ob2o42bobo5bo10bo
b5o17bo$obo3b2obo46bo19bo29bo53b2o45bo28b2o47b2o84b2o4b2o12bo20b2o$bo
2bo4b3o4bo59bobo81bo20b2o102bo37b5o62bo3b2o8bo17b2o$2b2o2bo3b2o3bobo
58b2o47b2o14b2o3b2o13bo20bo103b3o33bo4bo61bo3bobo9b2o15bo$4b2o3bo6b2o
108bo15bo3bo13b2o17b3o6bob2o17b2o77bo32bo2bo64b2o3bo9b2o14bobo$4bo7b2o
82b2o25b3o13b3o5b3o29bo6b3ob2o17bo60b2o46bo2bob2o43bo45b2o4b2o9b2o$2bo
bo7b2o82bo26bo15bo9bo35bo24b3o12bo45b2o44bobobo5bo38b3o44bo2bo14bo$2b
2o13b2o78b3o86b3ob2o20bo10bobo44bo5b2o40bo2bo4bobo36bo33b2o4bo8b2o16b
3o$17b2o80bo88bobo33b2o49bobo2bo40b2o2bo2bo23b2o11b2o30b2ob2o2bo24b3o
3bo$10b3o175bobo84bobobobo44b2o24b2o43bo2bo4bo22bo4bo2bo$10b3obo174bo
10b2o9bobo60b2o2bobobo57bobo54bo2bo26bobobob2obo$11b4o185bo9bob2o14bob
o42bo2bobo3bo57bo2bo54b2o28bo4bo2b2o$8bo20b2o170b3o4b3o18b2o31b2o10bob
obo2b2ob2o50b2obo2bo71bo14b4o2bo2bo$8b2o18b2o173bo3bo4b2o15bo12bo19b2o
2b2o5bo2b3o4bobo50bo2bo73bobo10b3o7bobo70b2o3b2o5b2o83b2o5b2o3b2o$30bo
176b5obo26b3o23bobo5b2o3b3obo35b4o14b2o74bobo10bo3b2o3b2obob2o62bo3bob
o4bo5b2o83b2o5bo4bobo3bo$211bo22bo4bo27bo6bo5bo2bo34bob2obo13b2o27bo
47bo12b3ob2o2bo3bobo61bobobo2bob3o99b3obo2bobobo$126bo80b2o3bo22bo3b2o
18b2o12bo2bobo3bo35b2o2b2o41bob2o60bobob2ob3o65b2ob2obobo103bob4ob2o$
126b3o78bobo3bo19b3o23bo4b2o7b2ob2ob3o36b2o2b2o40b2obo9b2o32b2o3b2o18b
o2b2o3b2o60bo73b2o36bo$107bo21bo14bo9bo53bo3b2o45b3o2b2o8bo4bo38bob2ob
o16b2o23bo11b2o11b2o20bo3bo14bo7bobobob3o54b8o2bo32b2ob2obo28bo36bobo
3b4o$106bobo7bo11b2o14b3o5b3o29bo42bo31b3o5b2o5bob3o40b4o17bo49bo18b3o
5b3o15bo5bobo4bo52bo6bo3bo28b3ob4ob2o25b2obo2b2o31b3ob3o4bo$107bo6b3o
30bo3bo13b2o17b3o38b3o32b2o5b2o3b2obo65b3o47b3o15bo9bo6b2o5bo7bob2ob2o
bo50bob2obo2b3o35bo30bob2obobo31bobo2b4obobo$96bo16bo32b2o3b2o13bo20bo
36bo32bo8bob3o2bo2bo58b2ob3o2bo49bo31b2o14bo5bobo50bo3bo2bob2ob2o28b2o
38bob3o28b2o9bobo$96b3o14b2o50bo20b2o11b2o23b2o31b2o11b3o2b2o40bo16bob
obo2bo85bo5bo4b2o4b2o2bo50b2o2bo3bob2o29bo3b5o25b2o2b3ob2o2b3o27bob2o
2bobo3b2o$99bo65b2o32b2o68bo47b3o15bo2bobo91bobo4bo6b2o55bo3bo3bobo28b
2o2b2obo24bo2bo5bo2b3o2bo16b2o5bobob3o4bo$98b2o110bobo23b3o28bob4o47bo
17bob2o90b2o6b2ob3o57b2o5bo2bo7bo14b5o3b2o29b2obo2b2o5b2o2bo15b3o4bo4b
o4bo$52bobo66bo87bo2bo26b3o24bo3bo2bo24b2o19b2o16b2o3bo9b2o82b2o7bo55b
obobo2bo3bo7b3o21b3o2bobo24bo2bo3bo7bo7bo4b2obo2bo3b2o2bobo2bobobo$52b
2o67b2o27bo59bo2bob2o21b4o22b3obo3b2o24bo15bo19bobo2bobo11bo82b2o7bobo
46bo5bobo2b4ob3o2bo3b2o2bo12bo2b2o3b4o3bo22bo2bo3b2ob2obob4o5bo6b2ob2o
4b2o2bob4o2bobo5bo$53bo68b2o26bo62bo2bo23b2o21bo3bo2bobo23bobo15b3o17b
2o2b2ob2o7b3o78b2o13b2o44b3o3b3obobo5b3o2bo3b2ob3o11bo3bobo5b3o23b3o
12b2o7b3obob5o5b2o2bo5bobob3o3b3o$37b2o54b2o27bo27bo63b2o20bo2bo23b2o
2bob2obo18b2o3b2o19bo32bo80b2o58bo5bo3bo2bo2b2o3bo6b5o13bo6b4o29b3ob5o
4b2o7b4ob2o8b2o2bob2o2bo2bo3bo5bo$34bo2bobo54bo22b3obo46b2o16bo27b2o
20bo2bo28bo2bo21b2o21b2o120b2o50bob2obo2b3o3bobobobo2bo7bo8bo8bo2b2o5b
2o23b2o3bobo8bo10bo2bo10bo4bobobo3b3o2bob2obo$33bobobobo54bobo20b3o34b
2o12b2o14b2obo49b2o8bobo19b2o17bo5bo140bob2o48bo2bo5b2o7b2o2bobobo14b
5o6bob3obobobo24bob3o2b3o2b2o2b2o8b2ob4o8bobobo2b2o7b4obobo2bo$32bobob
o2b2o54b2o56bob2o28bob2o59b2o44bo140b2o49bobobobobo4b4o4bobob5o11b3ob
2o3bo2b2o3bo2bobo26bo2bobo2bob2o2b2o5b5obob3o5b2ob2obobo4b4o4b3obobobo
$32bo3bobo2bo110bo2bo31bo23b2o35bo33b6obo149bobo45b2obobo4b2o4bo3bo2bo
5bo11bo2b2o3bo2b2o3bo2bobob2o23bo2bobo2bob2o2b2o4b2ob2o6bo4bo5bo2bo3bo
4b2o6bob2o$29b2ob2ob2obob2o9b2o100b2o57bo69b4o2bobo93bo55b2o49b2obo3bo
2b2o2bobo3b5o13b3o7bob3obobobo2bo21bob3o2b3o2b2o2b2o3bo2bob2o4bo6b5o3b
obo2b2o2bo3b2o2bo$29bobo4bobo2bo5b2o2b2o55b2o99b3o6bob2o17b2o12bo31b2o
bobob2o91b2o100b2o2b2o2bo2bobo2b3ob2o4bo16bo8bo2b2o5b2o23b2o3bobo8bo4b
3o17bo4b2ob3o2bobo3b3o3b2o$31bob9o4bobo59bobo6b2o90bo6b3ob2o17bo14bo
58b2o5b4o60b2o100bobo2bo3b4ob2o35bo6b4o29b3ob5o4b2o4b2o29b2ob2obo4bobo
bo$31bo2bo5b2o5bo53bo8bo6bo19b2o76bo24b3o9b3o32b3o23b2o4b2ob2obo6b2o
151bo2bobo3b2o6b2o32bo3bobo5b3o23b3o12b2o34b2o6b2o3bobo2bo$32bo3bobo2b
o12b2o44b3o7b2o6bo17bobo11b2o6bo57b3ob2o20bo55bo19b2o3b3o6b2o151b5ob2o
bo2b4o3bo31bo2b2o3b4o3bo22bo2bo3b2ob2obob4o31bo2b5o4b2o3b3o$33b3ob2ob
2o7b2o2bo2bo42b2o2bo13b2o17bo13b2o6b3o57bobo78b2o18b2o4b2o163b2o3bo6b
2obo38b3o2bobo24bo2bo3bo7bo31bob3o4b2o3bobo$35bo4bo7b3o2bo2bo42bob4o
30b2o24bo14b2o21b2o17bobo36bo40b2o23bobo161b2o2b4o8bobo30b5o3b2o29b2ob
o2b2o5b2o2bo30bo4bo2bobo2bo3b2o$36b3obo5b3o3bo46bo4bo55b2o15bo21bo19bo
10b2o26b2o64b2o7b2o152bo5bob8o2b2o12b2o21b2o2b2obo24bo2bo5bo2b3o2bo6bo
9b2o12b2obob6obobo4bo$39bob2o5bo4bobo43bo2b2o70b3o23b3o27bo26b2o31bo
33bo8bo151bobo9b4o2bobo14bo19bo3b5o25b2o2b3ob2o2b3o8bo10bo14bobo15bobo
$38bo2bo2bobo9b2o26b2ob2o2b2o8b2o71bo27bo28b3o55b2o29b2o12b3o148b2o16b
obo14bobo19b2o38bob3o12bo6bobo14bobo16b2o$38b2o2b2o2bo9b2o27bobo2bobo
13b2o125bo55bobo29bo14bo71bo95bo16b2o12b2o9bo30bob2obobo7b2o5bo6b2o16b
o$45b2o37bo3b2o7bo8bobo154bo54b3o87b2o125b2o4b3ob4ob2o25b2obo2b2o7b2o$
42b2ob2o38b2obo8bobo8bo152bobo54bo88bobo135b2ob2obo28bo6b2o43bobo$41bo
2bobobo37bobo2bo5b2o9b2o152b2o82b2o147b2o15bo67b2o6bo9b3o15bo14bo$41b
2o2bo2b3o34bo2bobobo252bo2bo145bobo15b3o10b3o60bobo5bo17b3o12bo$42bobo
2bo3bo14bo9b2o5bo2b3ob2o252bob2obo2b2o57b2o72b2o7bo20bo8bo3bo60b2o6bo
2bo12bo15b3o10b2o$42bob2obo2b2o13bobo7bo2bo4b3o19b2o237bo4bo3bo56bobo
2bo69b2o7b3o2bo14b2o8bo3bo5b2o3b2o52b3ob3o13b2o15bo2bo8b2o$43bo2bo19bo
7bo4bo6bo17bo2bo235b2obobob3o57bobobobo80b2obo24b3o6bobo2b2o38bo12bobo
36b2o$44b2o27bo6bo4b2o16bo4bo32b2o200bo2bobobo58b2o2bobobo79b2obo34b2o
40b3o12b2o31bo5b2o$64b5o4bo6bo21bo6bo30bo2bo200b2o3bo58bo2bobo3bo81bo
19bo2bo53bo10bo36b2o2bo2bo$63bo4bo5bo4bo22bo6bo29bob2obo2b2o123bo73bob
2o47b2o10bobobo2b2ob2o82bo14b2o2b2o11b2o3b2o34b2o7b3o2bo32bo2bo2b2o$
59b2obo2bo9bo2bo24bo4bo30bobo2bo3bo124bo66b2o2b4ob2o7b2o37b2o2b2o5bo2b
3o4bobo81bob2o13bo2bo12bo4bo43bo3b3o18b2o11b2o5bo$59b2obob2o10b2o26bo
2bo30b2o3bob3o123b3o66bo2bo6bo6bobo41bobo5b2o3b3obo83bob2o31bo3b3o41b
3o22b2o10b2o$33b2o27bo5bo36b2o31bo2bo3bo195bob2o2b3o5b4o43bo6bo5bo2bo
84bo2b3o27b2o5bo29b3o5b2o4bob2o16bobo11bo2bo$32bo2bo23b2obo4bobo12bo
56b4obo193b3obo13bo37b2o12bo2bobo3bo90bo63bo3bo3bo6bobo2bo5bo24b3o$31b
ob2obo2b2o18b2ob2o2bo2bo12b3o57bo133bo18bo2b2o37bo4bo8b2o41bo4b2o7b2ob
2ob3o89bobo62bo5bo5bo7b2o3b2o27bo$31bobo2bo3bo26b2o13b3o50b2o2b3o11b2o
122b2o15bobo2bo35b3ob2ob2o7b2o2bobo36b3o2b2o8bo4bo91b2o63bo5bo6b2obo9b
2o24bo$30b2o3bob3o41bo3bo13b2o34bo2bo2b3obo8bo121b2o16bobobo35bo3bob2o
2bo11b2o36b3o5b2o5bob3o157bo5bo4b2obo34bobo$30bo2bobobo43b4o13bo2bo2b
2o30bob2o3b2o5b2o141b2obob2o23bo9bo2bo6b3o3bo45b2o5b2o3b2obo110b2o49bo
3bo6bobo20b2o$31b3o3bo43bob2o13bobo4bo2bo24b3obo5b2o5b3o138bo3b2o3bo
20bobo9bob3o5b3o2bobo41bo8bob3o2bo2bo103b2o4bobob2o46b3o6bo2b2o13bo4bo
2bo3b2o$99bo5bobobo22bo4bo8b2o2b3o129bo11b2o2b2obo20b2o7bobo4bo2bo2b2o
3b2o2b2o12b2o23b2o11b3o2b2o75bo8bobo10bobo3b2o5b2obo2bo8bo44b2o15bobo
3bo6b2o4bobo8bobo$27b2o2b4o2bo7b2o55b2obo2bo21b3ob2ob2o7b2o4bo127bobo
7bo3bobo2bobo29b2ob5o2b2obo8b2o12bo36bo81bobob4o2b3obob4obob2obo14b2o
9bo60bo2bo3bo2bo6b2o2bo8bo2b2o$27bo2bo6bo8bo35bo3b2o14bo2bo23bo3bobo2b
o12b2o128b2o11b2o2b3o12b2o19bobobobo3bo23b3o31bob4o77bo2bob5obob12o26b
3o70bo6b2o4b6o4b2o$28bob2o3b2o5bo2bo35bobo3bo11bo4bo23bo2bo5bo6bo67b2o
77bo3b2o16bobo18bobobo2b2o22b3o3bo29bo3bo2bo76bobo6bobob2o8b2obo9b2o
77bobo5bo8bob2o2bo2bo2b2obo$25b3obo5bo6b2o37b2o3bo12b5o24bob3o3b2o5bob
o66b2o79b2obob5o10bo21bobobobo22bo2bobo2bo26b3obo3b2o77b2obobobo2bo14b
3o7b2o2b2o49bo20b2o3b2o5b3o4bo2b2obo4bob2o2bo$24bo4bo8b2o3bo41bo40bobo
4b3o2bo5b2o2b2o97b2o36bobo6bobo2bo2bo33bo2bobo21bobo3b2obo25bo3bo2bobo
80b2o3bob2obo3b4o3bo2b2o2bo8bobo47bobo19b2o3b2o7bo3b2o2b5o2b5o2b2o$22b
3ob2ob2o7b2o4bo36b5obo11b2ob2o22b2ob2o2bobobo10b2o96b4o36b2o6bo2bo41b
2o23bo2bobo2b2o24b2o2bob2obo80bob2obobobo4b4o4b3ob3o10bo35bo11bobo20bo
bobo18bo2b2o2bo$21bo3bob2o3bo10b2o36bo4b2o11b2ob2o25bo3bobo2bo107b2ob
2o35bo8b2o68b5obo2bo28bo2bo80b2obo6b2obo6bob2o3bo12b2o34b2o11bo20b2o
14bobo3b2o8b2o3bobo$20bo2bo5bo6bo41b2obob2o44bobobo2b2o110b2o112b3o4bo
2bobo29b2o82bob4obob2obo2b2o2bob2obo4bo44bobo6b2o10bo13bo4bo10bo5bobo
2b2o2bobo5bo$20bob3o4bo3bobobo40bobobobob2o42bobobobo154bo70bo3b4ob2ob
ob2o110bobo4bo4bobo2bobo5bo3bo52bobo9bo15b3o11bo3bo4bo2b2o2bo4bo3bo$
18bobo4bo2bo7b2o2b2o38bo4bobo43bo2bobo155bo70b3o3bo5bobo109b2o2b4ob2o
2bobo2bobo2bo3bobo53bo11b3o5b3o7b2obo9b3obobobobo2bobobobob3o$18b2obob
obob3obo8b2o38b2o52b2o154b3o72bobob2ob3o114bobo2bobo3b8ob4o3bo52b2o16b
3o13b2o12b2ob2obo2bob2ob2o$21bo3bobo187bobo63b4o81b7o2b2o3b2o107b2o6b
3o8bo2b2o3b2o69b4o24b3o14b3o$21bobobo2b2o7b2o175bo4bo59b8o73b2o13bobob
ob3o116b4ob2obob3o4bo61bo7b2o20b2o3bo5b2o2b2o2b2o5bo$22bobobobo7b2o
176bo4bo62b2o11bo41bo22bobo14bobo4bo114bo3b2obobobo6bob2o47bo8b2o10bo
2bo16bo3bobo2bob2obo2bob2obo2bobo$23bo2bobo9bo175b2o11b2o49bobo4bobo2b
o5b2o38bo23bo15bo3bob2obo112bo2bo7b2o5b2ob2o29bobo13b3o9b2o9bo2bo14bob
o2bo2bo5bobo2bobo5bo2bo$26b2o108bo89b2o48b3ob2o2b2ob4o4b2o39b3o39b2obo
bobo111bob2ob4o10bo34b2o12bo24b2o15b2o3b2o2b6ob4ob6o2b2o$134b2o71b2o5b
2o2b2o8bo46bo5bo2bo84bo4bob5o3bo109bo2bo2bo4bo8bobo34bo13b2o55bo4bo$
60bobo24b2o46b2o71bo5b2o2b2o55bob3obo2bob3o32b2o45bobo3bo7b2o109bobobo
2bob3o9b2o48b2o38b2o12b2obo2b2obobobo$60b2o10bo14bo117b3o6b3obo55b2obo
10bo12bo16bo2bobo44b2o3b3o4b2o112b2ob4obo50b2o8b2o39b2o13bob2obobobob
2o$8b2o51bo9bo13bobo117bo9bo57bo4b2o3bo2b2o11bobo15bobobobo48b2o7bo
118bo51bo2bo4bo3bo10bo12b2o7b2o10b2o4b2o2bobo2bo3bo$8bobo2bo56b7o8b2o
72bo56bo57b3obobob2o4b3o9b2o14bobobo2b2o47b2o7bobo108b4o3bobo50bobo3b
3ob3o9bo14bo6bobo11bo4bobobo2bobo2b2o$9bo4bo55bo2b5o80b2o116bo2bob2o2b
3o2bo25bo3bobo2bo19bobo19b2o13b2o107bo4b3ob3o31b2o5b2o10bo9bo10b3o9b3o
9bo9bo4b3obob4ob2o$11bo2bo56b2ob2ob2o79bobo116bobobo2bo2bobo23b2ob2o2b
obobo10b2o9b2o19b2o5bo115bobob4o2bobo31bobo3bobo15b6o4bobo15bo21b2o3b
2o2bo8b3o6b2o$11b3o61bobo198b2obobo2bo3bo15bobo6bobo4b3o2bo5b2o2b2o9bo
25b2obo114bobo9b2o28b3obo2bo8b2o8b2obo6b2o39bo3b4ob8o3bobo2bobo$11b2o
4b2o22b2o32b2o202bobo23b2o8bob3o3b2o5bobo38bo117b2o3bobo2b2obo27b3o2b
2obob2o7bo7b2o10bo39bobo3bo2bobo2bobo2b2ob4o2b2o$2b2o8bo4b2o19bo2bobo
61b2o172bobob2o20bo9bo2bo5bo6bo39bo3bo116bo4b3obobo5b2o16bo2b3o2bo2bo
3bo3b3o59bo3bo5bobo2bobo4bo4bobo$2bobo7b2o23bobobobo27bo33bobo172bo3bo
31bo3bobo2bo12b2o23b2o7b2o2b2o115bo4bo4bo4b3o15bo2b2o5bob2o2bo3bo17bo
13b2o18b2o8bo4bob2obo2b2o2bob2obob4obo$4bo31bobobo2b2o26bo38b2o172b2o
24bo6b3ob2ob2o7b2o4bo22bobo2bo8b2o113bobobo2bobo2b2o3bo2bob2o4bo7bo7bo
2bo3bobobo16bo15bo18bo12bo3b2obo6bob2o6bob2o$4b2o4bo2bo2b2o18bo3bobo2b
o62b2obo172bobo24bo7bo4bo8b2o2b3o22bobobobo115bo5bobo2b4obo2b2o4b2ob2o
6bo5b4obob2ob5obob2o17b3o11bo17b2obo10b3ob3o4b4o4bobobob2obo$2b2o3b3o
5bobo15b2ob2o2bobobo10b2o50b2o175b2obo21b3o8b3obo5b2o5b3o21b2o2bobobo
112b3o3b3obobo5bo2b2o5b5obob3o7b2o7bobo2bo34b5o14bobobo8bo2b2o2bo3b4o
3bob2obo3b2o$bo2b2o2bobo5bo16bobo4b3o2bo5b2o2b2o57b2o80bo80b2o3bobob2o
2bo32bob2o3b2o5b2o20bo3bobobobo111bo5bo3bo2bo2b2obo2b2o8b2ob4o7b2o4b5o
bo2bo39bo13bo2b2o2b2o7b3o14bo2bobobob2o$obobo4b2o24bob3o3b2o5bobo46b2o
13b2o78b3o80bo2b3obo3b3o31bo2bo2b3obo8bo7b2o8bob2o2b5ob2o107bob2obo2b
3o3bobobo4bo10bo2bo10bo9b2o3b2o34b3o12bobo6b2o9bob2o8b2obobo6bobo$ob4o
2bo26bo2bo5bo6bo15b2o30bobo7b2o82bo84b3o4b3o26bo7b2o2b3o11b2o7b2o2b2o
3b2o2bo2bo4bobo104bo2bobob4o7b2o2bobobo8b4ob2o8b2o2b2o2b2o3b3o2bo2bo
29bo10bo4b2o20b12obob5obo2bo$bo4bobo17bo9bo3bobo2bo12b2o6bobo32bo7b2o
82b2o20b2o49b2o14b4o2bo26b2o12bo23bobo2b3o5b3obo105bobobob3o4b4o4bobob
2ob2o5b3obob5o5b2o2b2obo3b2o2bo2b4o29b4o4bob2o23bob2obob4obob3o2b4obob
o$2b3obobobo3b5o8bo9b3ob2ob2o7b2o4bo6bo34b3ob2o6b2o91b2o7b2o49bo13b2o
4b3o25b2o10b4obo22bo3b3o6bo2bo106b2obo6b2o4bo3bo2bo5bo4bo6b2ob2o4b2o2b
2obo3b2o20bobo13b2o3bo3bo4bo6b2obob2o5b2o3bobo10bobo8bo$4b2o3b2o2bo4b
2o5b3o11bo4bo8b2o2b3o5b2o32b2o6bo4bobo92bo59b3o9bo2bob2o3b2o34bo2bo3bo
13b2o11bo2b2obo3bo110bo2b2o3bo2b2o2bobo3b5o6bo4b2obo2bo3b2o2b2o2b2o3b
7o13b2o13bo2b3o4bo11bob2obobo4b2o$11b3o4bobo19b3obo5b2o5b3o38bo2b2o4b
2o4bo93bobo27bo26b3o3bo9bobo4bobo35b2o3bob3o11bobo2b2o7b2ob2ob3o108b2o
3b3o3bobo2b3ob2o4bo17b3o4bo9b2o7bo6bo6bo13b2obo7bo16b2o$8bobo9b3o20bob
2o3b2o5b2o21bo16bobo5bo47bo48b2o4b2o28bo24bo2bobo2bo7b2obo2b2obo2bo28b
o5bobo2bo3bo15b2o8bo4bo109bobobo4bob2ob2o29b2o4b2o4b5obo2b2obobo6bobo
21bo$8b2obob2obob2o3bo18bo2bo2b3obo8bo19b2o14bob2ob2obo7bo13bo9bo15b3o
47bo20b2o10b3o11b3o9bobo3b2obo7bo2b3obobob2o26bobo5bob2obo2b2o11bo13bo
b3o109bo2bobo3b2o6b2o34b2o7bobo2bobobo7b2o22b2o$11bobo7b3o18b2o2b3o11b
2o18b2o16bo4bobo5bo9bobo3b3o5b3o18bo22b2o2b2o18bobo18bo25bo12bo4bo2b2o
7b2o2bo3bo30b2o6bo2bo14b4o5b3o2b2obo112b3o3b2o4b5o2bo31b4obob2ob5obobo
74b2o$11bo2bobob3o28bo49b3obobobo7bo6b2o6bo3bo20b2o11b2o9b2o2b2o19b2o
16bobo26bo12b4o2bo2bo8b2ob4o39b2o14bobo6bo6bo2bo115bobo3b2o4b3obo31bo
7bo2bo3bob2o72b2o$12b2o4bo2bo24b4obo49b2o3b2o2bo11bo6b2o3b2o32b2o7bo6b
2o24b2o10b2o37b3o3bo3bobo8bo2bo58b2o7b2ob4o2b2o113b2o3bo2bobo2bo4bo30b
o2b2o5b3o2bo3bo3bobo34b2o31b2o$13bob2o2b2obo22bo2bo3bo5b2o48b3ob2obobo
58bo7bo22b2ob3o48bo3b3o2b2obob2o6b6o34bobo28b2obo119bo4bobob6obob2o12b
2o9bo6bo2b3o2bo2bo3bobo4b2o36bo16b2o14b3o$13bo2bobo2bo23b2o3bob3o4bo
45bobo3bo2b2ob3o12bo44b2ob2ob2o22b2o3b2o48b3o3bo5bobo11bo35b2o28bo3b2o
115bobo15bobo14bo10bo8b3o2b2o2bob3o6bo33b3o15bo4bo14bo$14bo3b3o25bobo
2bo3bo3bobo15b2o26b2obob2o3b2o3bo10bobo45bo3b2o24bobo2bo49bobob2ob3o
11b3o36bo28bobobo2bo114b2o16bobo14bobo6bo12b3obobo45bo17bo4bo14bo$15b
3o28bob2obo2b2o4b2o15b2o29bobo7b3o10bobo75b3o2b2o49bobo2b2o2b2o3b2o4bo
65b3obobob2o133bo16b2o6bo5b2o7bobo4bo60bo4bo18bo$18bo28bo2bo57bo2bo2b
4o14bo76bobob2o59bobobob3o46bo20bo3bo4bo165b2o7b2obobo49b2o13b2o20bo$
17b2o29b2o59b2o2bo4bo31b3o60bo62bobo4bo46bo19b2o2bob2obo124bobo43b2o5b
obo49bobo34b3o$110bob2obobobo28b4ob2o48bo71b2ob2ob2obo43b3o24bo2bo128b
o14bo15b3o9bo6b2o7bo43b2o6b3o9b2o16b2o9b2o$110bo2bo4bo24bobo4b2o2bo38b
2o7bo72bob2o3bobo71b2o131bo12b3o17bo5bobo15bobo37b2o9bob2o9bo18b2o8b2o
$111bo3b3o25b2o7b3o25b2o11b2o7b3o63bo4b3o4bo2bo191b2o10b3o15bo12bo2bo
6b2o11bo4b2o37bobo9bo2bo10b3o14b2o$72b3o37b3o16b2o6bo7bobo31bo61b2o22b
obo3b2o3bo2b2o50bo141b2o8bo2bo15b2o13b3ob3o13b2o36b2o6bo12bo14bo$72bo
2bo39bo14bo2bo4b2o38b3o35b2o26bo22b2o6bo3b2o53b2o150b2o36bobo13b2o35bo
6b2o$71bo3bo38b2o9b2o4b2o5bobo37bo37b2o2b2o19b3o27b2o7bo52b2o151b2o5bo
31b2o47b2obo2b2o7b2o$71b3o2bo47bobo25bo3b2o62bobo17bo3b3o24b2o7bobo
204bo2bo2b2o79bob2obo9b2o12b2o16bo$72b4o48bo26bobo3bo64bo16bo2bobo2bo
18b2o13b2o205b2o2bo2bo39bo43bobobo19bobo14bobo16b2o$56b2ob2o2b2o58b2o
26b2o3bo65b2o15bob2ob3obo17b2o71bo149bo5b2o11b2o25bobo33b2o2b2ob2o5bo
19bo14bobo2b4o9bobo$49bo7bobo2bobo13b2o53b2o20bo12b2o4b2o62b2o2bobo2bo
24b3o62bobo155b2o10b2o26b2o34bo2bo2bo2bo2bo21b2o12b2o2b8obo5bo$50b2o4b
o3b2o7bobo6bobo52bo17b5obo10bo5bobo60bo2bo2b4o23bob3o63b2o154bo2bo11bo
bo60b2obo3b2o4b5o30bobo8b4o2b2o$49b2o6b2obo8b2o9bo41b2o10b3o14bo4b2o
11b3o7b2o56bobo7b3o20b4o219b3o24bo52bobobo2b2o38bob2o6bo3b2o$58bobo2bo
6bo9b2o36b2o2b2o12bo15b3o16bo5b2obo53b2obob2o4bo3bo10bo15bo216bo27b2o
48bo2bo4b3o3b2o2bo31bo3b4o2bob2ob5o$58bobobobo40bo11bo3bo32bob2o18b2o
56bobo3bo2b2ob3o4b2o6b2o12b2o65bobo150bo24b2o49b3o3bo5bobo3bo32b2o6b2o
3bobo2bo$59b2ob2o39bobo11bo37bobo25b2o52b3o4bobo5bobo5b2o81b2o151bobo
34bo40b3ob4o6bo35b2ob4o3bo2bobo$104b2o12b2obo46b2o13b2o45b2o3b2o2bob2o
11bo88bo167b2o18b2o38b2o3bo5b2o2bo25bo4b2ob3o2bobo2bo2b2o2b2o$113b2o5b
o47bobo7b2o48b3obobobo3b6o38b2o219b2o3bo2bo12bo5b2o37bob4obobob3obo8b
2o13b5o3bobo2b2o2bo3bob2o$113b2o13b2o40bo7b2o47bo4bobo6b3o39bobo62bo
138bobo8bobo4b2o6bo11bo47bo2bobo2bo3b2o2bo5bobo11bo5bo2bo3bo4b2o4bobob
2o$118b2o7bobo40b3ob2o6b2o42bobob2ob2o44b2o2b2o64bo135b2o2bo8bo2b2o6bo
2bo12b3o45bo2bobo2bo3b2o2bo4bo2bo12b5obobo4b4o4bobobobobo$118b2o7bo40b
2o6bo4bobo42bobo5bobo42bo2b2o63b3o135b2o4b6o4b2o6bo61bob4obobob3obo8b
2o15bobobo2b2o7b2o5bo2bo$114b2o3b3o4b2o39bo2b2o4b2o4bo44bo2b2obo2bo5bo
37bo2bo202bob2o2bo2bo2b2obo8bo60b2o3bo5b2o2bo8bo8bo7bo2bobobobo3b3o2bo
b2obo$68b2o44bobo3bo7b2o36bobo5bo53b2o2b3obo4bobo31b2o208bo2b2obo4bob
2o2bo4b3o12bo10b2o39b3ob4o6bo14b2o8bo3b2o2bo2bo3bo5bo$68b2o45bo4bob5o
3bo35bob2ob2obo7bo47b2o2b2o6b2o31b2o13b2o60bo131b2o2b5o2b5o2b2o3bo12b
2o7bo3b2o36b3o3bo5bobo3bo12bo2bo4bo2b3o5bobob3o3b3o$124b2obobobo35bo4b
obo5bo49bo7b2o40b2o7bobo61b2o135bo2b2o2bo23b2o5bobo40bo2bo4b3o3b2o2bo
12bobo5bo2b3ob4o2bobo5bo$122bo3bob2obo36b3obobobo7bo8bo18b2o14bobo7b2o
40b2o7bo62b2o128bobo3b2o8b2o3bobo21bobo43bobobo2b2o21b2o8bo3bo2bobobo$
123bobo4bo39b2o3b2o2bo11bobo17bobo14b2o13b2o31b2o6b2o2b2o192bo5bobo2b
2o2bobo5bo21bo44b2obo3b2o4b5o22bo2bo5b2o$121bobobob3o47b3ob2obobo5b2o
13b2o2b2o30b2o31bobo4bob3o2b2o189bo3bo4bo2b2o2bo4bo3bo9bo9b2o43bo2bo2b
o2bo2bo28bobo3bo3bo$112b7o2b2o3b2o34b2o10bobo3bo2b2ob3o18bo2b2o24bo2bo
37bo5bo2bob2o2bo65bo123b3obobobobo2bobobobob3o10bobo52b2o2b2ob2o5bo29b
2obo3bo2b2o$79b2o30bobob2ob3o41bobo9b2obob2o3b2o3bo18bo2bo24b2o2bo42bo
bo5bobo62bobo120bo4bob3ob2ob2ob2ob3obo4bo7b2o61bobobo28b2ob2obo2bo3bo$
58b2o19bo29b3o3bo5bobo38bo14bobo7b3o13b2o30b2o2b2o44b2ob2obobo63b2o
120b4ob2o3bo8bo3b2ob4o65bob2obo35b3o2bob2obo$59bo17bobo28bo3b4ob2obob
2o53bo2bo2b4o16b2o13b2o14bobo39b3o6bobo4bo189bobo2b4ob4ob4o2bobo68b2ob
o2b2o31bo3bo6bo$59bobo15b2o29b3o4bo2bobo57b2o2bo4bo20b2o7bobo14b2o38b
6o3bobobob3o189bo2bob2o2bo6bo2b2obo2bo4bobo63bo35bo2b8o$60b2o4bo44b5ob
o2bo58bob2obobobo19b2o7bo59b2obo2b2o3b2o71bobo117b2o2bo2bobobo2bobobo
2bo2b2o4b2o64b2o40bo$65bobo42bo2bobo2b2o59bo2bo4bo16b2o6b2o2b2o55bobo
4b3o79b2o122b2obo2b4o2bob2o10bo100bobob2ob2o$65bobo2b2o37bobo3b2obo61b
o3b3o17bobo4bob3o2b2o31b2o18b3ob2o2bo3bobo76bo121bobo2bobo4bobo2bobo
107b3obo2bobobo$66bo3bobo4b2o31bo2bobo2bo62b3o21bo5bo2bob2o2bo27bo2bob
o16bo3bo4b2obob2o198b2o2b2ob2o2b2ob2o2b2o99b2o5bo4bobo3bo$70bo6bobo14b
o16b3o3bo66bo26bobo5bobo25bobobobo7bobo6b3o7bobo320b2o5b2o3b2o$79bo13b
o20b3o66b2o28b2ob2obobo24bobobo2b2o6b2o10b4o2bo2bo$79b2o12b3o17bo90b3o
6bobo4bo25bo3bobo2bo6bo9bo2bobo2b2o$64b2o47b2o87b6o3bobobob3o23b2ob2ob
2obob2o9b2o4bob3ob2obo$65bo139b2obo2b2o3b2o25bobo4bobo2bo5b2o2b2o5bo2b
obo2bo$62b3o136bobo4b3o34bob9o4bobo10b3o3bo$62bo136b3ob2o2bo3bobo31bo
2bo5b2o5bo14b3o$198bo3bo4b2obob2o32bo3bobo2bo12b2o5bo$198b3o7bobo36b3o
b2ob2o7b2o2bo2bo4b2o$73b2o126b4o2bo2bo38bo4bo7b3o2bo2bo$70bo2bobo124bo
2bobo2b2o40b3obo5b3o3bo$69bobobobo98b2o10bo12bob3ob2obo44bob2o5bo4bobo
$68bobobo2b2o94bo2bobo8bo14bo2bobo2bo43bo2bo2bobo9b2o$68bo3bobo2bo92bo
bobobo8b3o13b3o3bo44b2o2b2o2bo9b2o$65b2ob2o2bobobo10b2o80bobobo2b2o26b
3o52b2o$65bobo4b3o2bo5b2o2b2o80bo3bobo2bo24bo52b2ob2o$67bob3o3b2o5bobo
81b2ob2ob2obob2o9b2o13b2o50bo2bobobo$67bo2bo5bo6bo82bobo4bobo2bo5b2o2b
2o65b2o2bo2b3o$68bo3bobo2bo12b2o76bob9o4bobo70bobo2bo3bo$69b3ob2ob2o7b
2o4bo76bo2bo5b2o5bo71bob2obo2b2o$71bo4bo8b2o2b3o77bo3bobo2bo12b2o64bo
2bo$72b3obo5b2o5b3o78b3ob2ob2o7b2o2bo2bo64b2o$75bob2o3b2o5b2o81bo4bo7b
3o2bo2bo$74bo2bo2b3obo8bo79b3obo5b3o3bo$74b2o2b3o11b2o82bob2o5bo4bobo$
81bo93bo2bo2bobo9b2o$78b4obo91b2o2b2o2bo9b2o$77bo2bo3bo97b2o$77b2o3bob
3o92b2ob2o$78bobo2bo3bo90bo2bobobo$78bob2obo2b2o90b2o2bo2b3o$79bo2bo
96bobo2bo3bo$80b2o97bob2obo2b2o$180bo2bo$181b2o!
#C [[ AUTOSTART ]]

3) A few days ago (2 June) Hartmut Holzwart, Keith Amling, Matthias Merzenich collaborated to complete a new greyship front edge that allows for the construction of rectangular and trapezoidal greyships that mix different widths of chicken wire with a minimum width of 13.

Code: Select all

x = 435, y = 86, rule = B3/S23
85bo10bo78bo10bo78bo10bo78bo10bo$84b3o8b3o76b3o8b3o76b3o8b3o76b3o8b3o$
84bob2o7bob2o75bob2o7bob2o75bob2o7bob2o75bob2o7bob2o$85b3o8b3o76b3o8b
3o76b3o8b3o76b3o8b3o$85b2obo4bo2b3o76b2obo4bo2b3o76b2obo4bo2b3o76b2obo
4bo2b3o$85bo3b3ob2o2bo77bo3b3ob2o2bo77bo3b3ob2o2bo77bo3b3ob2o2bo$93bo
2bo86bo2bo86bo2bo86bo2bo$86bo2b2o85bo2b2o85bo2b2o85bo2b2o$88bo2bo86bo
2bo86bo2bo86bo2bo$90bo89bo89bo89bo$89bob2o86bob2o86bob2o86bob2o$88b3o
2bo84b3o2bo84b3o2bo84b3o2bo$87bo3b4o82bo3b4o82bo3b4o82bo3b4o$86b5o4bo
80b5o4bo80b5o4bo80b5o4bo$85bo5b6o78bo5b6o78bo5b6o78bo5b6o$84b7o6bo76b
7o6bo76b7o6bo76b7o6bo$83bo7b8o74bo7b8o74bo7b8o74bo7b8o$73bo8b9o8bo8bo
54bo8b9o8bo8bo54bo8b9o8bo8bo54bo8b9o8bo8bo$72b3o6bo9b10o6b3o52b3o6bo9b
10o6b3o52b3o6bo9b10o6b3o52b3o6bo9b10o6b3o$72bob2o4b11o10bo5bob2o19bo
10bo20bob2o4b11o10bo5bob2o19bo10bo20bob2o4b11o10bo5bob2o19bo10bo20bob
2o4b11o10bo5bob2o$73b3o3bo11b12o5b3o18b3o8b3o20b3o3bo11b12o5b3o18b3o8b
3o20b3o3bo11b12o5b3o18b3o8b3o20b3o3bo11b12o5b3o$73b2o3b13o12bo4b2o19bo
b2o7bob2o19b2o3b13o12bo4b2o19bob2o7bob2o19b2o3b13o12bo4b2o19bob2o7bob
2o19b2o3b13o12bo4b2o$77bo13b14o25b3o8b3o23bo13b14o25b3o8b3o23bo13b14o
25b3o8b3o23bo13b14o$77b14o39b2obo4bo2b3o23b14o39b2obo4bo2b3o23b14o39b
2obo4bo2b3o23b14o$75bo15b16o23bo3b3ob2o2bo22bo15b16o23bo3b3ob2o2bo22bo
15b16o23bo3b3ob2o2bo22bo15b16o$74b17o15b2o30bo2bo22b17o15b2o30bo2bo22b
17o15b2o30bo2bo22b17o15b2o$73b2o16b15o2bo22bo2b2o27b2o16b15o2bo22bo2b
2o27b2o16b15o2bo22bo2b2o27b2o16b15o2bo$72bo3b15o15b4o23bo2bo25bo3b15o
15b4o23bo2bo25bo3b15o15b4o23bo2bo25bo3b15o15b4o$71b5o15b15o4bo24bobo
23b5o15b15o4bo24bobo23b5o15b15o4bo24bobo23b5o15b15o4bo$70bo5b15o15b6o
24bo23bo5b15o15b6o24bo23bo5b15o15b6o24bo23bo5b15o15b6o$69b7o15b15o6bo
23b2o21b7o15b15o6bo23b2o21b7o15b15o6bo23b2o21b7o15b15o6bo$68bo7b15o15b
8o22b2o20bo7b15o15b8o22b2o20bo7b15o15b8o22b2o20bo7b15o15b8o$58bo8b9o
15b15o8bo8bo11bo12bo8b9o15b15o8bo8bo11bo12bo8b9o15b15o8bo8bo11bo12bo8b
9o15b15o8bo8bo$57b3o6bo9b15o15b10o6b3o8bo3b2o8b3o6bo9b15o15b10o6b3o8bo
3b2o8b3o6bo9b15o15b10o6b3o8bo3b2o8b3o6bo9b15o15b10o6b3o$57bob2o4b11o
15b15o10bo5bob2o6b2o2b4o7bob2o4b11o15b15o10bo5bob2o6b2o2b4o7bob2o4b11o
15b15o10bo5bob2o6b2o2b4o7bob2o4b11o15b15o10bo5bob2o$58b3o3bo11b15o15b
12o5b3o5b3o3bo2bo7b3o3bo11b15o15b12o5b3o5b3o3bo2bo7b3o3bo11b15o15b12o
5b3o5b3o3bo2bo7b3o3bo11b15o15b12o5b3o$58b2o3b13o15b15o12bo4b2o8b2obo
11b2o3b13o15b15o12bo4b2o8b2obo11b2o3b13o15b15o12bo4b2o8b2obo11b2o3b13o
15b15o12bo4b2o$62bo13b15o15b14o13b2obo15bo13b15o15b14o13b2obo15bo13b
15o15b14o13b2obo15bo13b15o15b14o$62b14o15b15o27bo2bo15b14o15b15o27bo2b
o15b14o15b15o27bo2bo15b14o15b15o$60bo15b15o15b16o11b2o2bob2o9bo15b15o
15b16o11b2o2bob2o9bo15b15o15b16o11b2o2bob2o9bo15b15o15b16o$59b17o15b
15o15b2o7b3o3b3obo8b17o15b15o15b2o7b3o3b3obo8b17o15b15o15b2o7b3o3b3obo
8b17o15b15o15b2o$58b2o16b15o15b15o2bo9b3o5bo6b2o16b15o15b15o2bo9b3o5bo
6b2o16b15o15b15o2bo9b3o5bo6b2o16b15o15b15o2bo$57bo3b15o15b15o15b4o11b
3obo6bo3b15o15b15o15b4o11b3obo6bo3b15o15b15o15b4o11b3obo6bo3b15o15b15o
15b4o$56b5o15b15o15b15o4bo4bo2b3o3bo6b5o15b15o15b15o4bo4bo2b3o3bo6b5o
15b15o15b15o4bo4bo2b3o3bo6b5o15b15o15b15o4bo$55bo5b15o15b15o15b6o4bo5b
o7bo5b15o15b15o15b6o4bo5bo7bo5b15o15b15o15b6o4bo5bo7bo5b15o15b15o15b6o
$54b7o15b15o15b15o6bo9bo6b7o15b15o15b15o6bo9bo6b7o15b15o15b15o6bo9bo6b
7o15b15o15b15o6bo$53bo7b15o15b15o15b8o5bo8bo7b15o15b15o15b8o5bo8bo7b
15o15b15o15b8o5bo8bo7b15o15b15o15b8o$43bo8b9o15b15o15b15o8bo4b3o5b9o
15b15o15b15o8bo4b3o5b9o15b15o15b15o8bo4b3o5b9o15b15o15b15o8bo8bo$42b3o
6bo9b15o15b15o15b10o3b2ob2o2bo9b15o15b15o15b10o3b2ob2o2bo9b15o15b15o
15b10o3b2ob2o2bo9b15o15b15o15b10o6b3o$42bob2o4b11o15b15o15b15o10bo4bo
4b10o15b15o15b15o10bo4bo4b10o15b15o15b15o10bo4bo4b10o15b15o15b15o10bo
5bob2o$43b3o3bo11b15o15b15o15b15o3bo11b15o15b15o15b15o3bo11b15o15b15o
15b15o3bo11b15o15b15o15b12o5b3o$43b2o3b13o15b15o15b15o15b15o15b15o15b
15o15b15o15b15o15b15o15b15o15b15o15b15o12bo4b2o$47bo13b15o15b15o15b15o
15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b14o$47b14o15b15o15b
15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o$45bo15b15o
15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b16o$44b
17o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o
15b2o$43b2o16b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b
15o15b15o15b15o2bo$42bo3b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o
15b15o15b15o15b15o15b15o15b4o$41b5o15b15o15b15o15b15o15b15o15b15o15b
15o15b15o15b15o15b15o15b15o15b15o15b15o4bo$40bo5b15o15b15o15b15o15b15o
15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b6o$39b7o15b15o15b
15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o6bo$38b
o7b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b
15o15b8o$28bo8b9o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b
15o15b15o15b15o15b15o8bo8bo$27b3o6bo9b15o15b15o15b15o15b15o15b15o15b
15o15b15o15b15o15b15o15b15o15b15o15b15o15b10o6b3o$27bob2o4b11o15b15o
15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o10bo
5bob2o$28b3o3bo11b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o
15b15o15b15o15b15o15b12o5b3o$28b2o3b13o15b15o15b15o15b15o15b15o15b15o
15b15o15b15o15b15o15b15o15b15o15b15o15b15o12bo4b2o$32bo13b15o15b15o15b
15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b14o$32b14o
15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b
15o$30bo15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o
15b15o15b15o15b16o$29b17o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b
15o15b15o15b15o15b15o15b15o15b2o$28b2o16b15o15b15o15b15o15b15o15b15o
15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o2bo$15b3o9bo3b15o15b
15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o
15b4o8bo$b3o3b3o5bo2bo7b5o15b15o15b15o15b15o15b15o15b15o15b15o15b15o
15b15o15b15o15b15o15b15o15b15o15b15o4bo6b3o$o2bo2bo2bo5bo9bo5b15o15b
15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o
15b6o4b2obo$3bo6bo4bo3bo4b7o15b15o15b15o15b15o15b15o15b15o15b15o15b15o
15b15o15b15o15b15o15b15o15b15o15b15o6bo3b3o$3bo2bo2b2o4bo3b2o2bo7b15o
15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b
15o15b8o2b3o$3bo8b4o6b9o15b15o15b15o15b15o15b15o15b15o15b15o15b15o15b
15o15b15o15b15o15b15o15b15o15b15o7bo2b3o$obo5bob2o3b3obo10bo2b4obob4o
2bo16b2obo3bob2o16bo2b4obob4o2bo16b2obo3bob2o16bo2b4obob4o2bo16b2obo3b
ob2o16bo2b4obob4o2bo16b2obo3bob2o16bo2b4obob4o2bo16b2obo3bob2o16bo2b4o
bob4o2bo16b2obo3bob2o16bo2b4obob4o2bo16b2o2b2o3b2o$8bo5bob3ob3ob4ob3o
2bobobobobo2b3ob4obob2obob4obo3bob4obob2obob4ob3o2bobobobobo2b3ob4obob
2obob4obo3bob4obob2obob4ob3o2bobobobobo2b3ob4obob2obob4obo3bob4obob2ob
ob4ob3o2bobobobobo2b3ob4obob2obob4obo3bob4obob2obob4ob3o2bobobobobo2b
3ob4obob2obob4obo3bob4obob2obob4ob3o2bobobobobo2b3ob4obob2obob4obo3bob
4obob2obob4ob3o2bobobobobo2b3ob4obob2obob4o2b2o$10bo3bo6b2obobo4bo13bo
4bobobob3o3bo11bo3b3obobobo4bo13bo4bobobob3o3bo11bo3b3obobobo4bo13bo4b
obobob3o3bo11bo3b3obobobo4bo13bo4bobobob3o3bo11bo3b3obobobo4bo13bo4bob
obob3o3bo11bo3b3obobobo4bo13bo4bobobob3o3bo11bo3b3obobobo4bo13bo4bobob
ob3o3bo$29b3o13b3o9bobobo13bobobo9b3o13b3o9bobobo13bobobo9b3o13b3o9bob
obo13bobobo9b3o13b3o9bobobo13bobobo9b3o13b3o9bobobo13bobobo9b3o13b3o9b
obobo13bobobo9b3o13b3o9bobobo$27b3o17b3o6bo23bo6b3o17b3o6bo23bo6b3o17b
3o6bo23bo6b3o17b3o6bo23bo6b3o17b3o6bo23bo6b3o17b3o6bo23bo6b3o17b3o6bo$
26b3o19b3o5bo2bo17bo2bo5b3o19b3o5bo2bo17bo2bo5b3o19b3o5bo2bo17bo2bo5b
3o19b3o5bo2bo17bo2bo5b3o19b3o5bo2bo17bo2bo5b3o19b3o5bo2bo17bo2bo5b3o
19b3o5bo2bo$25bo25bo3bo25bo3bo25bo3bo25bo3bo25bo3bo25bo3bo25bo3bo25bo
3bo25bo3bo25bo3bo25bo3bo25bo3bo25bo3bo$26bo23bo35bo23bo35bo23bo35bo23b
o35bo23bo35bo23bo35bo23bo!

4) There has been quite a bit of progress in sorting out the specifics of a 16-glider RCT construction.  Here's a Part 2 RCT summary article giving some more details.

Long story short, Pavel Grankovskiy constructed an actual recipe for the first "bootstrap" stage of the RCT, and also pointed out that the second bootstrap stage can be accomplished very much less expensively than we thought.  The original plan needed a huge piece of circuitry to do static storage and retrieval of data, but all that was really needed was a big glider loop.

Most of what's left to figure out is some remaining details of the cleanup process.  Many of the parts of RCT design that seemed really difficult in previous versions are already complete in the 16-glider blueprint. (!)

For example, there's now a known set of four cleanup Corderfleets, totalling 72 Corderships, and that number can probably be reduced a bit.  The Corderfleets can clean up all of the long lines of ash from the four incoming glider-producing switch engines.

The Corderships can be built one at a time, with no synchronization needed besides making sure that the ones that clean up blinkers have the right parity (i.e., start on an even tick or on an odd tick, depending on the phase of the blinker).

On June 5, 2022, dvgrn wrote:NewLifeCA #19, 5 June 2022: CatForce improvements, and an almost p19

In the last message, I didn't actually mention the coding improvements to Michael Simkin's CatForce search program as promised in the subject line.  The revised version of CatForce helped to make some of the discoveries that I described.

CatForce was originally written in 2015, as a brute-force catalyst search tool.  Rather than trying known catalysts in likely positions (like catalyst/catfind/catgl or ptbsearch) or trying to invent new catalysts for specific situations (like Bellman, or sometimes JLS/WLS/lifesrc), CatForce just enumerated all possible arrangements of catalysts from its list of stable objects, and ran them all as quickly as possible to see if any of them happened to work.

A large number of discoveries and constructions since 2015 have been made possible or improved by CatForce, starting with the B60 Herschel conduit that makes up the Simkin glider gun.

The p84 oscillator from the previous message was found with an optimized version of CatForce.  The code update was completed recently by forum user mvr, with an added option for symmetric searches -- i.e. adding the same oscillator simultaneously in multiple locations around a symmetrical initial reaction.

One of the first discoveries with the new symmetric-search CatForce was this Spartan H-to-4G converter:

Code: Select all

x = 41, y = 26, rule = B3/S23
14b2o$14b2o23bo$38bobo$39bo3$2o$bo35bo$bobo32bobo$2b2o32bobo$37bo2$37b
o$36bobo$36bobo$37bo$2bo$2bobo$2b3o$4bo34bo$38bobo$14b2o23bo$14b2o2b2o
$18bobo$20bo$20b2o!

We already had a known H-to-4G converter with the same rather unwieldy systemic name of "PNE-6T40_SE-6T40".  It used a 27-cell catalyst to convert a pi heptomino into a symmetrical pair of gliders:

Code: Select all

x = 45, y = 27, rule = B3/S23
$14b2o$14b2o4$40bo$2o37bobo$bo37bobo$bobo34b2ob2o$2b2o33bo2bo2bo$36bob
obobobo$37bobobobo$39bobo$39bo2bo$40b2o2$2bo$2bobo34b2o$2b3o34b2o$4bo
2$14b2o$14b2o2b2o$18bobo$20bo$20b2o!

The new Spartan version is much more usable in self-constructing circuitry.  Pavgran was able to incorporate it into the DBCA ("Decoder and Better Construction Arm") device in his first-stage RCT bootstrap recipe.

A P19 Near-Miss
\One suggested problem for the new symmetric-search CatForce to tackle was this almost period-19 oscillator:

Code: Select all

x = 169, y = 85, rule = B3/S23
54bo39bo38bo9bo$52bobo39bobo36b3o5b3o$53b2o39b2o33b2o5bo3bo$130bo4b2o
3b2o$129bo16b2o$57bobo29bobo37b2o6b3o6bo$58b2o29b2o40bo4bo3bo3bobo$58b
o31bo38b3o3bo5bo2b2o$128bo5bo3bo3bo$63bo21bo42b2o4bo2bobo2bo4b2o$64bo
19bo49bo3bo3bo5bo$62b3o19b3o44b2o2bo5bo3b3o$41bo65bo22bobo3bo3bo4bo$
42bo63bo23bo6b3o6b2o$40b3o24bo13bo24b3o20b2o16bo$68b2o9b2o57bo6bo$12b
2o5b2o46b2o11b2o55bobo5b2o$13bo5bo25bo57bo23b2o8bobo$12bo7bo25b2o53b2o
24b2o9bo$12b2o5b2o24b2o26bobo26b2o$71bobobobo$14bo3bo53b2ob2o83b2o$12b
2obobob2o30bo45bo37b2o3b2o18bo$12bo2bobo2bo28bobo20bo3bo20bobo34bobo3b
obo19bo$14bo3bo31b2o18b2obobob2o18b2o35bo2bobo2bo15b5o$10bob2o5b2obo
47bo2bobo2bo56b2o3b2o16bo$9bo2bo7bo2bo48bo3bo59bo3bo20b2o$54bobo11bob
2o5b2obo11bobo35b2o13b2o13b2obo$ob2o2b2ob2o11b2ob2o2b2obo22b2o10bo2bo
7bo2bo10b2o35bo2bo11bo2bo10b3o2bo$2obo2bo2bo13bo2bo2bob2o22bo37bo35b2o
b2o9b2ob2o9bobo2b2ob2obo$5bo2bo15bo2bo36b2ob2o11b2ob2o34b2o2b2o6bo13bo
6b2o2bo8bob2o$6b2o17b2o33bo3bo2bo13bo2bo3bo31bobo2bo25bo2bobo8bo$61bob
o2bo15bo2bobo31b2o2b2o6bo13bo6b2o2bo3b2o2b2o$6b2o17b2o32b3o2b2o17b2o2b
3o39b2ob2o9b2ob2o9bo2bo$5bo2bo15bo2bo101bo2bo11bo2bo10b3o$2obo2bo2bo
13bo2bo2bob2o26b3o2b2o17b2o2b3o40b2o13b2o$ob2o2b2ob2o11b2ob2o2b2obo28b
obo2bo15bo2bobo48bo3bo12b2o$60bo3bo2bo13bo2bo3bo46b2o3b2o11b2o$9bo2bo
7bo2bo40b2ob2o11b2ob2o49bo2bobo2bo$10bob2o5b2obo32bo37bo40bobo3bobo$
14bo3bo36b2o10bo2bo7bo2bo10b2o41b2o3b2o19bo2bo$12bo2bobo2bo33bobo11bob
2o5b2obo11bobo66b4o$12b2obobob2o51bo3bo81bo$14bo3bo51bo2bobo2bo79b5o$
50b2o18b2obobob2o18b2o40bo22bo$12b2o5b2o28bobo20bo3bo20bobo37b2o21bo$
12bo7bo30bo45bo41bo20b2o$13bo5bo52b2ob2o$12b2o5b2o50bobobobo$45b2o26bo
bo26b2o$46b2o53b2o$45bo57bo$67b2o11b2o$68b2o9b2o$40b3o24bo13bo24b3o$
42bo63bo28b2ob2o$41bo65bo28bobo$62b3o19b3o$64bo19bo50bo3bo$63bo21bo48b
obobobo$133b2obobob2o$58bo31bo42bobo3bobo$58b2o29b2o40b3o7b3o$57bobo
29bobo38bobo9bobo$130b2o11b2o$128b3o13b3o$53b2o39b2o31b2o17b2o$52bobo
39bobo25bo3bo2bo15bo2bo3b2o$54bo39bo25b2ob2o2b2o17b2o2b2obo$120b2ob2o
25b2o$120b2ob2o2b2o17b2o2b2obo$122bo3bo2bo15bo2bo3b2o$127b2o17b2o$128b
3o13b3o$130b2o11b2o$130bobo9bobo$131b3o7b3o$133bobo3bobo$133b2obobob2o
$134bobobobo$135bo3bo2$136b3o$137b2o$138bo!

To the left is the original form.  The glider-supported version in the middle shows what the p19 reaction would look like.  To the right are some increasingly unlikely attempts from the forum thread, to find alternate supports for the reaction.

If CatForce (or Bellman or JLS or some other search program yet to be invented) could find a way to turn one of these supports back into a copy of itself, in exactly 19 ticks, then we'd be another step closer to proving that Life is omniperiodic.

Unfortunately at the moment it looks as if any search program powerful enough to solve this could probably also find other p19 oscillators just as easily!  For example, we already have a known 7-step two-cell traffic light push, so if we had a known way to push a traffic light back two cells in exactly twelve ticks, we would already have built a p19 oscillator.

... Still, at the rate we're going, it does seem like we'll find our way to omniperiodicity someday!

Keep the cheer,


Dave

On July 2, 2022, dvgrn wrote:NewLifeCA #20, 2 July 2022: RCT correction and update, plus many more new oscillators

RCT Update

I wrote in NewLifeCA #18, 5 June 2022:

dvgrn wrote: June 5th, 2022, 9:03 am ... there's now a known set of four cleanup Corderfleets, totalling 72 Corderships, and that number can probably be reduced a bit.

This needs a minor correction.  I had missed one of the timing options in the northwest.  One of the surplus NW-traveling gliders generates a retrograde glider and a moderate-sized cloud of ash, in one of its of its two 0|128 mod 256 timings.

The retrograde glider's effects were already handled correctly by the 50-Cordership fleet, down in the southeast GPSE's ash, but the ash clouds in the northwest weren't accounted for.  It turned out to be possible to use a subset of 34 out of the 50 Corderships to do the cleanup in the NW -- making a total of 50+34+ 2*11 = 106 Corderships in the four Corderfleets (or three Corderfleets, depending on how you count them).

Meanwhile, a lot of progress has been made on other parts of the RCT design.  Adam P. Goucher has completed a secondary "extreme compression" mechanism intended for helping with both construction (in the far northwest) and cleanup (in the center).  This is an optional second level of bootstrapping, but it allows for easy solutions to a couple of things that are otherwise either expensive or awkward, or both.

Long story short, it seems worth including an ECCA (Extreme Compression Construction Arm) in the standard RCT design, because it will reduce the total size of most or all RCT recipes, *and* reduce the amount of effort it takes to complete a working RCT demo.  We're now gradually closing in on a complete working demo of how to build Alan Hensel's decimal counter from 1994, using only 16 gliders.

New Oscillators
The most recent discovery is "Charity's p16" from a couple of days ago, a new p16 oscillator from a Catagolue soup search, with a fairly impressive spark:

Code: Select all

#C https://conwaylife.com/wiki/Charity%27s_p16
x = 12, y = 12, rule = B3/S23
4b3o3b2o$bo2b3o3b2o$obo2b2o$bo3$6b2o$4bob2o$3bo$6bo$2b2obo$2b2o!

Before that, ljkiernan1 used the symmetric-search option in the new version of Michael Simkin's CatForce to find new smallest-population p37 and p58 oscillators. This allowed for the creation of record-breaking p37 and p58 glider guns, as shown in the oscillators' respective LifeWiki articles.

Code: Select all

#N 58P37
#O ljkiernan1, 24 June 2022
#C p37 R-pentomino hassler
x = 27, y = 24, rule = B3/S23
8bo$8b3o14b2o$11bo13bo$10b2o11bobo$23b2o$15b2o$15b3o$14bo2bo$15b2o$2o$
bo$bobo19b2o$2b2o19bobo$25bo$25b2o$10b2o$9bo2bo$9b3o$10b2o$2b2o$bobo
11b2o$bo13bo$2o14b3o$18bo!

Code: Select all

#N p58 pi-heptomino hassler
#O ljkiernan1, 26 June 2022
#C Found using a symmetric CatForce search.
x = 23, y = 30, rule = B3/S23
7bo$5b3o$4bo$4b2o6b2o$12bo$10bobo8b2o$10b2o9b2o3$2b2o$bobo$bo$bobo$2b
2o3$19b2o$19bobo$21bo$19bobo$19b2o3$2o9b2o$2o8bobo$10bo$9b2o6b2o$18bo$
15b3o$15bo!

There have been incremental improvements and occasional big reductions to quite a few glider guns lately, showing that gradualism and saltationism both have their place in gun-collection evolutionary theory.

New Spaceship Syntheses

Goldtiger997 has been gradually working through a series of difficult synthesis problems.  Among the most recent results are a synthesis for 30P3H1V0 in 24 gliders --

Code: Select all

#N 24-glider synthesis of 30P3H1V0
#O Goldtiger997, 16 June 2022
x = 439, y = 95, rule = B3/S23
430bo$418bo9b2o$418bobo8b2o$418b2o7$362bobo$363b2o$363bo51bo$369bo44bo
$370b2o42b3o$369b2o14$432bo$432bobo$432b2o8$283bo$284bo9bo$282b3o7b2o$
293b2o$390b2o$389bo2bo$192bo196bo2bo$2bo86bobo3bo96bobo195b2o$obo87b2o
4bo95b2o$b2o87bo3b3o$104b2o98b2o98b2o98b2o$104bo91b2o6bo91b2o6bo91b2o
6bo$3b2o100b3o89bo7b3o81b2o6bo7b3o81b2o6bo7b3o$4b2o87b2o12bo88bo10bo
80bo2bo4bo10bo80bo2bo4bo10bo$3bo90b2o100b2o90bobo5b2o90bobo5b2o$93bo
195bo99bo$184b3o226bo$186bo226b2o$92b3o90bo226bobo3bo$94bo322b2o$93bo
323bobo5$392b2o$391bobo$393bo12$409b2o$409bobo$409bo5$436b2o$369b3o64b
obo$371bo64bo$370bo52b3o$423bo$424bo2$374b3o$376bo$375bo!

-- and a related synthesis for 29P3H1V0 in 35 gliders, meaning that all known spaceships up to 31 bits now have a glider synthesis:

Code: Select all

#N 35-glider synthesis of 29P3H1V0
#O Goldtiger997, 30 June 2022
#C https://conwaylife.com/forums/viewtopic.php?p=147675#p147675
x = 649, y = 62, rule = B3/S23
639bo$638bo$638b3o10$584bo$582bobo$135bo447b2o6bo31bo$135bobo454bo30bo
bo$135b2o453b3o30b2o$618bobo$618b2o$606bo12bo$604bobo$605b2o39bobo$
586bo59b2o$584bobo60bo$11bo573b2o$9b2o$10b2o5$646bo$3bo299bo341bo$2bo
298b2o342b3o$2b3o291bobo3b2o$297b2o335bo$121bo175bo104b2o98b2o98b2o30b
obo$104b2o14bo83b2o98b2o96bobo97bobo97bobo29b2o$104bo15b3o81bo99bo100b
o99bo84b2o13bo$106bo99bo2b2o95bo2b2o95bo2b2o95bo2b2o80b2o13bo2b2o$105b
2o98b2o2bo2bo92b2o2bo2bo92b2o2bo2bo92b2o2bo2bo77bo6bo7b2o2bo2bo$2bo
101bo95bo3bo6b2o91bo2b2o2b2o91bo2b2o2b2o91bo2b2o2b2o85bo5bo2b2o2b2o$2o
103bobo8bo84bo3bobo96b2o98b2o98b2o90b3o5b2o$b2o103b2o8bobo80b3o4b2o
208bo103bobo$116b2o297bo104b2o$203bo6b2o203b3o103bo95b2o$2b2o199b2o4b
2o299bo99bo5bo2bo$b2o115b3o77b2o2bobo6bo297bobo97bobo4bo2bo$3bo114bo
78bobo308bo2bo96bo2bo5b2o$119bo79bo309b2o98b2o$212b2o370b2o$211b2o193b
2o177b2o$213bo191bobo176bo49bo$407bo113b2o110b2o$521bobo109bobo$521bo$
588b2o$589b2o$588bo$637b2o$636b2o$638bo!

Other recent constructions include an 18-glider recipe for a p32 c/2 orthogonal spaceship, and recipes for various c/4 spaceships, including two or three working together escorting toads. 

Keep the cheer,


Dave

On July 2, 2022, dvgrn wrote:NewLifeCA #21, 2 July 2022: p127 century hassler, plus a 1G decimal-counter seed

Symmetric CatForce Oscillators, Continued
No sooner do I write up a summary of new oscillators than an even newer one comes along. This one seems worth an addendum to the previous message: it's a Mersenne prime period (127) and can possibly be turned into a record-breaking p127 gun.

Code: Select all

#N 74P127
#O ljkiernan1, 2 July 2022
#C Found with a symmetric CatForce search. This is currently the only known
#C prime-period oscillator above p47 that doesn't rely on glider or
#C signal loops.
#C Based on repeatedly catalyzing a symmetric arrangement of two centuries.
#C
#C Above:  minimal form of oscillator
#C Below: predecessor of oscillator chain, showing two possible wick connections
#C
#C https://conwaylife.com/wiki/74P127
#C https://conwaylife.com/forums/viewtopic.php?p=147819#p147819
x = 106, y = 85, rule = B3/S23
47bo$47b3o$50bo$49b2o3$41b2o20bo$41b2o19bobo$62bo2bo$54b2o$52b2obo9bo$
52bo9b2obo$52b3o7b3o$61bo2bo$63bo$45b2o14bobo6b2o$44bo2bo12b2o8b2o$43b
o2bo13b2o$43bob2o14b2o$42bo2bo14bo2bo$43b2o14b2obo$44b2o13bo2bo$34b2o
8b2o12bo2bo$34b2o6bobo14b2o$42bo$41bo2bo$41b3o7b3o$40bob2o9bo$40bo9bob
2o$50b2o$40bo2bo$41bobo19b2o$42bo20b2o3$55b2o$55bo$56b3o$58bo2$47bo44b
o$47b3o40b3o$50bo38bo$49b2o38b2o3$13bo27b2o54b2o$13b3o25b2o54b2o$16bo$
15b2o37b2o28b2o$52b2obo28bob2o$52bo34bo$7b2o43b3o30b3o$7b2o2$20b2o$18b
2obo$18bo$18b3o4$104b2o$104b2o3$51b3o32b3o$53bo32bo$2o48bob2o32b2obo$
2o48b2o36b2o$97bo$63b2o10b2o19bobo$17b3o43b2o10b2o20bo$19bo$16bob2o$
16b2o37b2o26b2o$8bo46bo28bo$7bobo19b2o25b3o22b3o$8bo20b2o27bo22bo3$21b
2o$21bo$22b3o$24bo!

It's pretty amazing how quickly the new symmetrical option in CatForce is turning up interesting oscillators these days.

Final RCT Stage

dvgrn wrote: July 2nd, 2022, 8:21 amWe're now gradually closing in on a complete working demo of how to build Alan Hensel's decimal counter from 1994, using only 16 gliders.

Here's a shameless plug for my somewhat silly but entertaining part of the RCT project. I finished a one-glider seed constellation for a decimal counter today.

This could be what we've been calling the ATBC, the Actual Thing Being Constructed by a reverse caber tosser pattern. It will be what's left over at the end of an RCT cleanup process; the single trigger glider will be produced by the final "Corderabsorber" cleanup circuit. So after the RCT spends untold aeons building a seed like this, and then cleaning up its three stages of construction arms, the seed and its trigger glider will the only things left in the Life universe.

It seems likely that slsparse can find a slow salvo recipe for the constellation, or one very similar to it, but it hasn't made it all the way through the compilation process yet. Might have to separate a few of the boat-longboat chains a little more, or something along those lines.

Keep the cheer,


Dave

On July 3, 2022, dvgrn wrote:NewLifeCA #22, 3 July 2022: 4,764,364-tick methuselah inside a 16x16 bounding box

The newest excitement from yesterday and today came from an intermittent contributor to the forums, yaochen2, posting a small maybe-methuselah based on a pair of switch engines, that takes 71,093 ticks to stabilize. It's the same pair of switch engines that Paul Callahan used in the 1.7-million-tick pattern mentioned in a previous NewLifeCA message, but this new pattern fits in 16x15 instead of 16x30:

Code: Select all

#N 71093M
#O yaochen2, 2 July 2022
x = 15, y = 16, rule = B3/S23
7bobo$6bo$7bo2bo$9b3o7$bo$3o2$3o9b2o$b2ob2o7b2o$3bo9bo!

This got some new searches running, and fairly quickly 16x16 starting points were found that lasted 303,421 and 305,230 ticks before successfully shooting down the switch engine.

A little while later a really big record-breaker showed up that was smaller than Paul's 1.7-million-tick pattern, and also lasted several times longer (4,764,364 ticks):

Code: Select all

#N 4764364M
#O dani, 3 July 2022
x = 16, y = 16, rule = B3/S23
5b4o$9bo$9bo$10b2o5$11bo$o9b2o$o10bo2bo$o10b4o$b2o5bo4b3o$b3o5bob2o2bo
$b2o7bobo2bo$9bobobo!

Ordinarily configurations that produce switch engines are counted as linear-growth patterns rather than methuselahs, because the pattern usually "goes boring" fairly quickly and the switch engine just continues off to infinity, laying blocks or shooting forward gliders as the case may be.

This particular pair of switch engines produces backward-firing gliders, which can produce standard "bihivite" crystals (Paul Chapman's term) and the usual range of chaotic explosions in the source ash cloud. Those interactions can take a long time to settle.

In these cases the usual fate of the pattern is either drill-through (the glider stream knocks out everything opposing it and heads blithely and boringly out into empty space) or the creation of a natural eater or boat-bit catcher that brings the ash production to a sudden end.

Here there's an empty "Hallway of Doom" in the ash from the switch-engine pair, which gliders can easily travel up to crash into and stop the switch engines. Unless drill-through or some kind of glider-catching reaction shows up, it's usually just a matter of time before a glider finds its way into the Hallway of Doom, and turns a previously linear-growth pattern into ... well, if it's not a methuselah, then what is it?

In 4764364M, the time before stabilization is extended by a full one and a half million ticks after the southeast ash blob gets drilled through, by a somewhat improbable series of back-and-forth glider interactions between the southeast ash and the northwest ash. Some of the details are given here.

The search for these "switch-engine methuselahs" was far from exhaustive, of course. Seems like there could easily be a 16x16 pattern that lasts ten million ticks or more.

Keep the cheer,


Dave

On July 9, 2022, dvgrn wrote:NewLifeCA #23, 9 July 2022: spaceships, greyships, and yet more oscillators, including a non-trivial p34

If I don't keep up with the news this week, my next message will either have to be way too long or will leave out a lot of good stuff. Here goes:

Spaceships and Greyships

These ships are a bit too big to quote in one of these emails, so I'll just give links here:

• c/2 width-12 chicken wire greyship partial with back slope of 0 by Hartmut Holzwart, completed by Keith Amling 5 July 2022
• new c/5 orthogonal spaceships by forum user "May13", 7 July 2022
• c/2 width-7 chicken wire triangular greyship by Hartmut Holzwart, 7 July 2022, with a variant by Keith Amling
• relatively small new c/6 diagonal spaceship by May13, 9 July 2022, with one part in common with a known pushalong for another spaceship, 77P6H1V1
• new c/3 greyship with a back slope of 6/13 by Keith Amling, 9 July 2022

Oscillators Including A Non-Trivial P34
The surge in new oscillator discoveries is continuing. We've been seeing a gradual increase in the number of people who can successfully use various recently-developed search tools to find new never-before-seen oscillators. Omniperiodicity is now definitely just two unknown periods away, p19 and p41, since non-trivial oscillators have been found for the two periods (p34 and p38) where only trivial ones were known at the beginning of this year. EDIT -- CORRECTION: p38 didn't have a trivial known oscillator at the beginning of 2022, since no p19 is known. Raucci's p38 was found on January 12.

If you want a good oscillator overview, some of the more impressive LifeWiki article pages these days are the hassler collections. Not all of these patterns are new, but a good percentage of them are, as you can tell by the number of entries with David Raucci's name on them. David Raucci / hotdogPi started his campaign of Python-script-based oscillator searches just about a year and a quarter ago.

https://conwaylife.com/wiki/Honey_farm_hassler
https://conwaylife.com/wiki/Lumps_of_muck_hassler
https://conwaylife.com/wiki/Pi-heptomino_hassler
https://conwaylife.com/wiki/Pre-pulsar_hassler

Here are some of the most recent discoveries:

Code: Select all

#N 84P199
#O Mitchell Riley and ljkiernan1, 6 July 2022
#C p199 R-pentomino hassler found using symmetric CatForce.
#C As the starting phase here shows, this can equally well be called
#C a lumps-of-muck hassler. Centuries and pi-heptominos also make an
#C appearance in the 199-tick cycle, but not as cleanly as the LOMs.
#C https://conwaylife.com/wiki/84P199
x = 52, y = 45, rule = B3/S23
16b2o16b2o$16b2o7b2o7b2o$25b2o4$15b3o16b3o$2o13bobo16bobo13b2o$2o13bo
2bo14bo2bo13b2o$16bobo14bobo$16b3o14b3o9$8b2o32b2o$8b2o32b2o4$8b2o32b
2o$8b2o32b2o9$16b3o14b3o$16bobo14bobo$2o13bo2bo14bo2bo13b2o$2o13bobo16b
obo13b2o$15b3o16b3o4$25b2o$16b2o7b2o7b2o$16b2o16b2o!

Code: Select all

#N 52P146
#O Mitchell Riley and ljkiernan1, 6 July 2022
#C https://conwaylife.com/wiki/P146_pi-heptomino_hassler
x = 30, y = 20, rule = B3/S23
29bo$27b3o$2o24bo$bo24b2o$bobo$2b2o7bobo$11bobo$11b3o4$4b2o$5bo$2b3o$
2bo2$8b2o3bo5bo3bo$8b2o2bobo3b2o3b2o$13b2o3b2o3b2o$18bo5bo!

Code: Select all

#N 74P34 
#O Mitchell Riley, 6 July 2022
#C p34 pi-heptomino hassler, the first non-trivial p34 oscillator.
#C The pattern shown here is a two-tick predecessor of the oscillator.
#C https://conwaylife.com/wiki/74P34
x = 27, y = 31, rule = B3/S23
15bo$13b3o$3b2o7bo$4bo7b2o$4bobo$5b2o2$2o$bo$bobo$2b2o$25b2o$9b3o13bo$
9bobo11bobo$9bobo11b2o2$2b2o11bobo$bobo11bobo$bo13b3o$2o$23b2o$23bobo$
25bo$25b2o2$20b2o$20bobo$13b2o7bo$14bo7b2o$11b3o$11bo!

EDIT -- CORRECTION: in the pattern below, adjusted the RLE to match the described phase.

Code: Select all

#N P74 pi-heptomino hassler
#O Mitchell Riley and Tanner Jacobi, 7 July 2022
#C The oscillator is shown here in its most misleading phase
#C -- one of the apparent catalysts is really not a catalyst at all.
#C https://discord.com/channels/357922255553953794/370571014654001154/994788190143651841
x = 52, y = 52, rule = B3/S23
19bob2o$19b2obo$17b2o18b2o$16bo3b2o9bo5bo2bobo$17b3obo9b3o5b2ob3o$34bo
10bo$5bo5b2o6b2o12b2o4b2ob3o$4bobo5bo6b2o18b2obo$4bobo5bobo8b2o$3b2ob
2o5b2o8bobo$23bo$3b2ob2o29b2o6bo$4bob2o29bo5b3o$2bo8bo23bobo4bo$2b2o7b
3o21b2o5b2o$14bo4bo$13b2o3bobo27bo$5b2o11bo2bo25bobo$4bobo11bobo12b3o
11bobo$4bo14bo12bo3bo7b2obo2b2o$3b2o28bobo8b2o2bobo$34bo12b2o2bo$50b2o
$41b3o$43bo$42bo$9bo$8bo$8b3o$2o$o2b2o12bo$bobo2b2o8bobo28b2o$2o2bob2o
7bo3bo12bo14bo$2bobo11b3o12bobo11bobo$2bobo25bo2bo11b2o$3bo27bobo3b2o$
32bo4bo$8b2o5b2o21b3o7b2o$9bo4bobo23bo8bo$6b3o5bo29b2obo$6bo6b2o29b2ob
2o$28bo$26bobo8b2o5b2ob2o$27b2o8bobo5bobo$9bob2o18b2o6bo5bobo$7b3ob2o
4b2o12b2o6b2o5bo$6bo10bo$7b3ob2o5b3o9bob3o$9bobo2bo5bo9b2o3bo$13b2o18b
2o$29bob2o$29b2obo!

Code: Select all

#N 164P112
#O James Pascua, 9 July 2022
#C Pi-heptomino hassler based on a partial found by David Raucci
x = 43, y = 73, rule = B3/S23
27bo$26bobo$25bo3bo$24bo3bo$23bo3bo$22bo3bo$23bobo$24bo5b2o3bo$30b2ob
2o$12b2o20bobo$13bo21bo$13bobo19b3o2b2o$14b2o24b2o12$39b2o$39b2o$10bo$
9b2o12b3o13bo$9b2o11bo3bo11bobo$9bo28bo2bo$23bo3bo11bo2bo$23bo2b2o4b2o
$10bo13b2o6b2o5bo2bo$10b3o26b2o$13bo$12b2o2$29b2o$29bo$2b2o26b3o$o2bo
5b2o6b2o13bo$9b2o4b2o2bo$o2bo11bo3bo$bo2bo28bo$2bobo11bo3bo11b2o$3bo
13b3o12b2o$32bo$2b2o$2b2o12$b2o24b2o$b2o2b3o19bobo$7bo21bo$6bobo20b2o$
8b2ob2o$7bo3b2o5bo$17bobo$16bo3bo$15bo3bo$14bo3bo$13bo3bo$14bobo$15bo!

For anyone that wants to try their hand at completing oscillators that are currently just promising script search results in a "partial" state, there are plenty of not-yet-completed partials posted on the Oscillator Discussion Thread, along with more recently discovered oscillators that I haven't mentioned, like "Raucci's 18th p16" (!).