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Spaceship Discussion Thread

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Re: Spaceship Discussion Thread

Postby muzik » June 27th, 2016, 12:26 pm

dvgrn wrote:
Gamedziner wrote:Is there any "small" (less than 1000 cells) means by which those two cells could be prevented from appearing, thus allowing a sort of flotilla knightship?

If something like that existed, it would have to move at the same speed as the knightship to keep doing its suppression work, and so it would be a very good candidate knightship on its own.

It might work to start a new search for a "support" ship that suppresses those two cells in the almost-knightship, and see if any solutions happen to come up for the different possible searchable shapes. I would expect that one or more people have already tried something along those lines, but I don't know for sure.

This is what I was essentially trying to suggest to search.
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Re: Spaceship Discussion Thread

Postby Scorbie » June 28th, 2016, 11:01 am

Kinda crazy question: is it possible to make a smaller helix for the too-fast 13,1c/31 to with blinker fuses instead of just xwsss?
Ex) back G + suppressed blinker fuse => another G at the front
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Re: Spaceship Discussion Thread

Postby biggiemac » June 28th, 2016, 5:34 pm

It would be a higher multiplier almost certainly, but could have fewer overall spaceships per cycle. Not sure how easy it would be to synthesize but I don't know, there's already a mountain of synthesis problems with all the HWSS in the current best helix.
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Re: Spaceship Discussion Thread

Postby Sphenocorona » June 28th, 2016, 7:58 pm

Although I'm not experienced with building helices to be specific periods, I think I have to agree with the above: to actually gain over the 11c/24 burn reaction, the amount of time spent burning must be very long relative to the lengths of the fuses.

However, I do believe there is room for improvement in helix design. By starting with a somewhat odd LWSS-on-MWSS flotilla I was able to find a helix edge component in a few different variations (low *WSS options on top, smaller area options below. Left-most is for comparison):
x = 188, y = 60, rule = B3/S23
75bo50bo49bo$5b3o46b3o11b3o3b3o28b3o11b3o3b3o27b3o11b3o3b3o$5bo2bo4bo
40bo2bo4bo5bo2bo2bob2o27bo2bo4bo5bo2bo2bob2o26bo2bo4bo5bo2bo2bob2o$5bo
6b3o39bo6b3o4bo6b3o27bo6b3o4bo6b3o26bo6b3o4bo6b3o$2o3bo5b2obo34b2o3bo
5b2obo4bo3bo2b3o22b2o3bo5b2obo4bo3bo2b3o21b2o3bo5b2obo4bo3bo2b3o$b2o3b
obo2b3o36b2o3bobo2b3o6bo2bo2b2o24b2o3bobo2b3o6bo2bo2b2o23b2o3bobo2b3o
6bo2bo2b2o$o10b3o35bo10b3o19bo17bo10b3o36bo10b3o19bo$11b3o46b3o18b3o
27b3o47b3o18b3o$12b2o10bo36b2o18bob2o27b2o48b2o18bob2o$23b3o56b3o45bo
52b3o$22b2obo56b2o45b3o51b2o$22b3o103b2obo$23b2o103b3o$129b2o54b3o$16b
3o165bo2bo$15bo2bo115b3o50bo$18bo114bo2bo50bo$18bo48b3o48b3o15bo31b3o
13bobo$15bobo48bo2bo47bo2bo11bo3bo30bo2bo$69bo50bo15bo33bo$28b3o38bo
50bo12bobo34bo$27bo2bo35bobo48bobo47bobo$30bo$30bo$27bobo16$75bo50bo$
54b3o11b3o3b3o28b3o11b3o3b3o$54bo2bo4bo5bo2bo2bob2o27bo2bo4bo5bo2bo2bo
b2o$54bo6b3o4bo6b3o27bo6b3o4bo6b3o$49b2o3bo5b2obo4bo3bo2b3o22b2o3bo5b
2obo4bo3bo2b3o$50b2o3bobo2b3o6bo2bo2b2o24b2o3bobo2b3o6bo2bo2b2o$49bo
10b3o19bo17bo10b3o19bo$60b3o18b3o27b3o18b3o$61b2o18bob2o27b2o18bob2o$
73b3o6b3o39b3o6b3o$72bo2bo6b2o39bo2bo6b2o$75bo50bo$75bo50bo$72bobo9b3o
36bobo9b3o$83bo2bo47bo2bo$78b3o5bo3b3o36b3o5bo$77bo2bo5bo2bo2bo35bo2bo
5bo$80bo2bobo6bo38bo2bobo$80bo11bo38bo$77bobo9bobo36bobo!

I don't know if it's known, but I figure there's probably some other useful corner-turn reactions out there we don't know about yet. If it produced the same glider four gens earlier it would allow for a 4x 17c/45 helix, but since it doesn't, the maximum speed for a period 180 helix is only 3c/7...

EDIT: Interestingly, the Coe ship by itself can function as a helix edge. Not only that, but the glider ends up displaced over 20 cells at nearly lightspeed. Unfortunately the big plume created from the reaction prevents it from being all that useful:
x = 22, y = 10, rule = B3/S23
bo11b3o4bo$b2o10bo2bo2b3o$obo10bo4b2obo$13bo3b4o$13bo5b2o$13bo2bo$14b
2o$14bo$15bo$15bo!
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Re: Spaceship Discussion Thread

Postby Scorbie » June 29th, 2016, 1:04 am

Hmm... Maybe using (half-) x66s or suppressed pufferfish or other constructible spaceahips may yield something nice. I am not sure about the specific search details :(
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Re: Spaceship Discussion Thread

Postby Kazyan » June 29th, 2016, 11:31 pm

Here's a partial for a c/6 ship, found fairly quickly with knightt:

x = 34, y = 9, rule = LifeHistory
3.2A$.2A13.3A$6.A6.2A4.2A$A6.A.2A3.A$6.A6.2A5.2A4.C.2A2.A$.2A.2A3.4A
7.2A2.2C2.6A$3.A6.3A5.A3.A8.A$17.A3.A2.2C2.A.A$18.A.A5.C.A.2A!


What's interesting about this one is that the back can likely be completed symmetrically--observe the behavior around the cells in white. I'm not sure how to get any of our existing spaceship searchers to continue it as a symmetrical search while the front remains asymmetric, though.

This would be relevant to complete because of the relatively loose connections in the asymmetric front. It means that the full ship, if it turns out to be smallish, will be a decent candidate for glider synthesis.
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Re: Spaceship Discussion Thread

Postby Sokwe » June 30th, 2016, 2:54 am

Kazyan wrote:Here's a partial for a c/6 ship... What's interesting about this one is that the back can likely be completed symmetrically

I tried extending this partial using zfind at width-15 symmetric, but it didn't find anything. This was the longest partial result:
x = 15, y = 93, rule = B3/S23
8bo3bo$7bob3obo$8bobob2o2$9bo$10b2o$8bobo$8b2o$7b3o3$9bo$8b2obo$9bob2o
$9bo2bo$10bobo2$5b3o3b2o$6bo$5b2o2bobo$5b2ob2o$6bo2bo2$6bobo$7bo2$2b2o
2bobo2b2o$2b2o2bobo2b2o$2bo3bobo3bo$4bobobobo$4bo5bo2$7bo$5bobobo$4b3o
b3o$2b2o7b2o$5bobobo$5bo3bo$2b2ob2ob2ob2o$7bo$b3o7b3o$b2obo5bob2o$5b2o
b2o$5bo3bo$4b2obob2o$2bo9bo$2bo9bo$3bob5obo$3bo7bo$bobob2ob2obobo$bo
11bo$b2ob2obob2ob2o$2bo2b2ob2o2bo$4bo5bo$2b3o5b3o$3bobo3bobo$6bobo$3b
2obobob2o$bo11bo$bob3o3b3obo$bo4bobo4bo$4bobobobo$4bo5bo$5bo3bo$5bo3bo
$5bo3bo$6bobo$4bo5bo$3bo2bobo2bo$2bobo5bobo$2bo2bo3bo2bo$2b2obobobob2o
$3bo3bo3bo$5bobobo$6bobo$bo2bo5bo2bo$bob2o5b2obo2$3b2o5b2o2$3o2b2ob2o
2b3o$b2o9b2o$2o11b2o2$2o11b2o$2ob2o5b2ob2o$5bo3bo$3bobo3bobo$bo4bobo4b
o$3o9b3o$5o5b5o2$bo3bo3bo3bo!

I then tried to extend it at width-17, but I ran into this repeatable component, which zfind can't effectively handle:
x = 15, y = 186, rule = LifeHistory
8.5A$7.A2.A2.A$8.A.A.2A$9.A$10.A$10.2A$8.A.2A$10.A$7.A.A$8.A2$8.3A$8.
2A.2A$9.A.2A$9.A2.2A$11.A$6.A5.A$5.3A$10.3A$8.3A$8.2A$5.5A$7.A$7.A$7.
A$4.2A3.2A$2.A9.A$2.A9.A$.A11.A$2.2A.5A.2A$3.A7.A$3.A.A.A.A.A$3.A7.A$
3.A7.A$.2A9.2A$.2A4.A4.2A$.2A.2A3.2A.2A2$5.2A.2A$4.3A.3A$2A3.2A.2A3.
2A$2A11.2A2$.A.A7.A.A$2.A9.A2$.2A9.2A$A13.A$2A11.2A$.2A9.2A$2.A9.A3$
2.C9.C$.3C7.3C$C3.C5.C3.C$.C3.C3.C3.C$5.C3.C$2.2C7.2C$3.C.C.C.C.C$3.
3C3.3C$3.C3.C3.C$4.3C.3C$6.C.C$5.2C.2C$3.C.2C.2C.C$2.2C.2C.2C.2C2$6.C
.C$7.C$3.4C.4C$4.C.C.C.C3$5.2C.2C$2.C2.C.C.C2.C$2.C2.C3.C2.C$2.2C.C3.
C.2C$5.2C.2C$5.2C.2C$5.2C.2C$5.2C.2C2$.2C.2C3.2C.2C$.2C9.2C2$2.A9.A$.
A.A7.A.A$A13.A$.A3.A3.A3.A$5.A3.A$2.A.A5.A.A$2.3A.A.A.3A$5.2A.2A$2.2A
.A.A.A.2A$2.2A3.A3.2A$3.9A$3.2A5.2A$4.A5.A$2.A2.A3.A2.A$2.2A.2A.2A.2A
$4.2A3.2A$5.5A$3.3A.A.3A2$3.2A5.2A2$6.3A$4.2A.A.2A$4.A2.A2.A$.2A2.A3.
A2.2A$.4A5.4A$3.2A5.2A2$4.A5.A$4.A.A.A.A$2.3A.A.A.3A$.A2.A5.A2.A$A13.
A2$3.A7.A$A2.A7.A2.A$A.A9.A.A$.A11.A$3.3A3.3A$4.A5.A$5.A3.A$2.A.7A.A
2$4.2A3.2A$5.A3.A$4.A5.A$4.A5.A$2.A3.A.A3.A$2.5A.5A$3.2A2.A2.2A$3.A2.
A.A2.A$4.2A3.2A$4.3A.3A2$7.A$4.2A.A.2A$3.A3.A3.A$3.A7.A$2.A2.A3.A2.A$
4.2A3.2A$3.3A3.3A$3.3A3.3A$3.A.A3.A.A$3.3A3.3A$.2A.A5.A.2A$.2A.2A3.2A
.2A3$2.A9.A$.3A7.3A$A3.A5.A3.A$.A3.A3.A3.A$5.A3.A$2.2A7.2A$3.A.A.A.A.
A$3.3A3.3A$3.A3.A3.A$4.3A.3A$6.A.A$5.2A.2A$3.A.2A.2A.A$2.2A.2A.2A.2A
2$6.A.A$7.A$3.4A.4A$4.A.A.A.A3$5.2A.2A$2.A2.A.A.A2.A$2.A2.A3.A2.A$2.
2A.A3.A.2A$5.2A.2A$5.2A.2A$5.2A.2A$5.2A.2A2$.2A.2A3.2A.2A$.2A9.2A!
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Re: Spaceship Discussion Thread

Postby muzik » June 30th, 2016, 4:36 am

Has anyone searched for any elementary c/8 or c/9 orthogonal ships?

BECAUSE THIS IS ANNOYING

Image



Here's a c/8 partial from the other thread:

x = 14, y = 35, rule = B3/S23
o12bo$2o3b4o3b2o$6b2o$3o8b3o$14o$b2o2b4o2b2o$2bo8bo$2b3o4b3o$bo
2bo4bo2bo2$bo3b4o3bo$5bo2bo$b2o3b2o3b2o$obo2bo2bo2bobo$2ob3o2b3o
b2o$b3o6b3o$2bo8bo3$b3o6b3o3$bo2bo4bo2bo$o3bo4bo3bo$bo2bo4bo2bo$
2b4o2b4o$3b8o$4bo4bo$4bo4bo$4b2o2b2o$6b2o$b2o8b2o$o2bo6bo2bo$bob
o6bobo$2bo8bo!


If c/8 is found with this front end, I suggest a (less creative than anything green) name of "Double Loafer".

An interesting thing to note is the copperhead decays into an interchange without the block, as does the center of this partial...
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Re: Spaceship Discussion Thread

Postby Scorbie » June 30th, 2016, 5:01 am

Sokwe wrote:
Kazyan wrote:Here's a partial for a c/6 ship... What's interesting about this one is that the back can likely be completed symmetrically

I tried extending this partial using zfind at width-15 symmetric, but it didn't find anything. This was the longest partial result:
x = 15, y = 93, rule = B3/S23
8bo3bo$7bob3obo$8bobob2o2$9bo$10b2o$8bobo$8b2o$7b3o3$9bo$8b2obo$9bob2o
$9bo2bo$10bobo2$5b3o3b2o$6bo$5b2o2bobo$5b2ob2o$6bo2bo2$6bobo$7bo2$2b2o
2bobo2b2o$2b2o2bobo2b2o$2bo3bobo3bo$4bobobobo$4bo5bo2$7bo$5bobobo$4b3o
b3o$2b2o7b2o$5bobobo$5bo3bo$2b2ob2ob2ob2o$7bo$b3o7b3o$b2obo5bob2o$5b2o
b2o$5bo3bo$4b2obob2o$2bo9bo$2bo9bo$3bob5obo$3bo7bo$bobob2ob2obobo$bo
11bo$b2ob2obob2ob2o$2bo2b2ob2o2bo$4bo5bo$2b3o5b3o$3bobo3bobo$6bobo$3b
2obobob2o$bo11bo$bob3o3b3obo$bo4bobo4bo$4bobobobo$4bo5bo$5bo3bo$5bo3bo
$5bo3bo$6bobo$4bo5bo$3bo2bobo2bo$2bobo5bobo$2bo2bo3bo2bo$2b2obobobob2o
$3bo3bo3bo$5bobobo$6bobo$bo2bo5bo2bo$bob2o5b2obo2$3b2o5b2o2$3o2b2ob2o
2b3o$b2o9b2o$2o11b2o2$2o11b2o$2ob2o5b2ob2o$5bo3bo$3bobo3bobo$bo4bobo4b
o$3o9b3o$5o5b5o2$bo3bo3bo3bo!

I then tried to extend it at width-17, but I ran into this repeatable component, which zfind can't effectively handle:
x = 15, y = 186, rule = LifeHistory
8.5A$7.A2.A2.A$8.A.A.2A$9.A$10.A$10.2A$8.A.2A$10.A$7.A.A$8.A2$8.3A$8.
2A.2A$9.A.2A$9.A2.2A$11.A$6.A5.A$5.3A$10.3A$8.3A$8.2A$5.5A$7.A$7.A$7.
A$4.2A3.2A$2.A9.A$2.A9.A$.A11.A$2.2A.5A.2A$3.A7.A$3.A.A.A.A.A$3.A7.A$
3.A7.A$.2A9.2A$.2A4.A4.2A$.2A.2A3.2A.2A2$5.2A.2A$4.3A.3A$2A3.2A.2A3.
2A$2A11.2A2$.A.A7.A.A$2.A9.A2$.2A9.2A$A13.A$2A11.2A$.2A9.2A$2.A9.A3$
2.C9.C$.3C7.3C$C3.C5.C3.C$.C3.C3.C3.C$5.C3.C$2.2C7.2C$3.C.C.C.C.C$3.
3C3.3C$3.C3.C3.C$4.3C.3C$6.C.C$5.2C.2C$3.C.2C.2C.C$2.2C.2C.2C.2C2$6.C
.C$7.C$3.4C.4C$4.C.C.C.C3$5.2C.2C$2.C2.C.C.C2.C$2.C2.C3.C2.C$2.2C.C3.
C.2C$5.2C.2C$5.2C.2C$5.2C.2C$5.2C.2C2$.2C.2C3.2C.2C$.2C9.2C2$2.A9.A$.
A.A7.A.A$A13.A$.A3.A3.A3.A$5.A3.A$2.A.A5.A.A$2.3A.A.A.3A$5.2A.2A$2.2A
.A.A.A.2A$2.2A3.A3.2A$3.9A$3.2A5.2A$4.A5.A$2.A2.A3.A2.A$2.2A.2A.2A.2A
$4.2A3.2A$5.5A$3.3A.A.3A2$3.2A5.2A2$6.3A$4.2A.A.2A$4.A2.A2.A$.2A2.A3.
A2.2A$.4A5.4A$3.2A5.2A2$4.A5.A$4.A.A.A.A$2.3A.A.A.3A$.A2.A5.A2.A$A13.
A2$3.A7.A$A2.A7.A2.A$A.A9.A.A$.A11.A$3.3A3.3A$4.A5.A$5.A3.A$2.A.7A.A
2$4.2A3.2A$5.A3.A$4.A5.A$4.A5.A$2.A3.A.A3.A$2.5A.5A$3.2A2.A2.2A$3.A2.
A.A2.A$4.2A3.2A$4.3A.3A2$7.A$4.2A.A.2A$3.A3.A3.A$3.A7.A$2.A2.A3.A2.A$
4.2A3.2A$3.3A3.3A$3.3A3.3A$3.A.A3.A.A$3.3A3.3A$.2A.A5.A.2A$.2A.2A3.2A
.2A3$2.A9.A$.3A7.3A$A3.A5.A3.A$.A3.A3.A3.A$5.A3.A$2.2A7.2A$3.A.A.A.A.
A$3.3A3.3A$3.A3.A3.A$4.3A.3A$6.A.A$5.2A.2A$3.A.2A.2A.A$2.2A.2A.2A.2A
2$6.A.A$7.A$3.4A.4A$4.A.A.A.A3$5.2A.2A$2.A2.A.A.A2.A$2.A2.A3.A2.A$2.
2A.A3.A.2A$5.2A.2A$5.2A.2A$5.2A.2A$5.2A.2A2$.2A.2A3.2A.2A$.2A9.2A!

Wow! Seems you are able to feed initial rows on zfind! Any plans on releasing your tweak?
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Re: Spaceship Discussion Thread

Postby Sokwe » June 30th, 2016, 5:45 am

Scorbie wrote:Seems you are able to feed initial rows on zfind! Any plans on releasing your tweak?

It's quite simple, actually. It's similar to what's described here. I'll go post an explanation in the zfind discussion thread.
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Re: Spaceship Discussion Thread

Postby muzik » June 30th, 2016, 6:27 am

Are there any good c/9 partials?
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Re: Spaceship Discussion Thread

Postby Sokwe » June 30th, 2016, 7:37 am

muzik wrote:Are there any good c/9 partials?

The "best" c/9 partials that I'm aware of are the ones posted on page 2 of this thread (even-symmetric partials here and odd-symmetric partials here). It's hard to say if these are "good" partials. None of them are very long, and they generally are all "strongly connected" (only the first even-width partial seems to have a "loosely connected" front end). You could try extending these with zfind as explained here.
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Re: Spaceship Discussion Thread

Postby muzik » June 30th, 2016, 7:48 am

I find it kind of interesting that a lot of high-period ships involve pushing either a loaf or a beehive. We have the dragon that pushes beehives, the loafer which pushes a loaf, and the c/8 partial here and the monotonic even symmetric c/9 both push two loaves...

Maybe some sort of engineerable reaction could be in the making?
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Re: Spaceship Discussion Thread

Postby Sokwe » June 30th, 2016, 7:54 am

muzik wrote:I find it kind of interesting that a lot of high-period ships involve pushing either a loaf or a beehive. We have the dragon that pushes beehives, the loafer which pushes a loaf, and the c/8 partial here and the monotonic even symmetric c/9 both push two loaves...

Maybe some sort of engineerable reaction could be in the making?

People have talked about this a lot over the years, but all of these ships/partials seem to be beehives/loaves followed by "space junk". I haven't seen anyone actually propose how to find the seemingly random back ends (besides using the tools we already have for low-period spaceship searches).
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Re: Spaceship Discussion Thread

Postby muzik » June 30th, 2016, 7:57 am

Are there any search programs that search exclusively for the back ends of spaceships, so that we could potentially link them up to front ends?
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Re: Spaceship Discussion Thread

Postby Sokwe » June 30th, 2016, 8:17 am

muzik wrote:Are there any search programs that search exclusively for the back ends of spaceships, so that we could potentially link them up to front ends?

I think this is essentially what Tim Coe did to find the snail, but I could be misunderstanding the explanation. (Edit: I was wrong)

gfind has a reverse option that searches for spaceships from the back, but in Life it is much slower than the forward search, so I'm not sure if it would help at all. I think you would essentially need to run the forward and reverse searches at the same time, and periodically check to see if any of the reverse partials could complete any of the forward partials. This adds a lot of extra complexity to the program and might not speed it up very much. I think it would be better (and easier) to take the current forward search programs and find ways to distribute them among multiple CPUs and multiple computers.
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Re: Spaceship Discussion Thread

Postby muzik » June 30th, 2016, 8:31 am

Well, what I was mainly thinking of doing is searching for relatively long back partials, and attaching them to the backs of known front ends. Namely the ones that have been posted in this forum
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Re: Spaceship Discussion Thread

Postby Sokwe » June 30th, 2016, 8:39 am

muzik wrote:Well, what I was mainly thinking of doing is searching for relatively long back partials, and attaching them to the backs of known front ends. Namely the ones that have been posted in this forum

The problem is, most of the partials posted on the forums are at widths where no spaceships exist. Thus, to complete the spaceship the back partials would have to be even wider than the front partials. Since reverse searches are so slow, it would actually be faster to start with your front partial result and try to extend it at a larger width.
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Re: Spaceship Discussion Thread

Postby muzik » June 30th, 2016, 8:54 am

I guess that makes sense.


I mentioned creating a list of partials of some sort earlier in the thread. How about it?



Earlier I found a c/26 glide-symmetric reaction of sorts. I doubt this would be usable to create a spaceship though.

x = 24, y = 49, rule = B3/S23
20bo$20bobo$20b2o11$9bo$9bobo$9b2o10bobo$21b2o$22bo6$ob2o$3o$bo3$10bob
o$10b2o$11bo$16b2o$15b2o$17bo13$14b3o$14bo$15bo!
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Re: Spaceship Discussion Thread

Postby moebius » June 30th, 2016, 10:17 am

Kazyan and Sokwe,

A while back I posted some of the first ships that came out of a c/6 odd symmetric search started at width 19 and continued at width 17. This search continued and finally completed and found more ships. I looked through the output file and saw a matching several rows with Sokwe's continuation of Kazyan's asymmetric front end.

x = 27, y = 79, rule = B3/S23
2$16bo$14bo3bo$14bo3bo$13bo5bo$14bo4bo$14bo$15bobo$16bo2$14bobo$13b2ob
o$13b2o$13b2o$15bobo$15b3o2$18bo$12bo5bo$11bobo4bo$17bo$11bo2b2obo$12b
ob2o$13bo2$12bobo$12bobo$12bobo2$8bo9bo$7bobo3bo3bobo$7bo2b3ob3o2bo2$
11b5o2$10bo5bo$9b2o5b2o$8bo9bo$6bo2bo7bo2bo$7b3o7b3o$8bobo5bobo$9b2o5b
2o$9b2o5b2o$6b2o3bo3bo3b2o$5bo15bo$6bobo9bobo$8b2o7b2o$8b2o7b2o$7b2o9b
2o$6bo13bo$6bobo9bobo$5b2ob2o7b2ob2o$6bob2o7b2obo$8bo9bo2$5b3o11b3o$5b
4o9b4o$6b2o2bo5bo2b2o2$11b2ob2o$12bobo$9b2obobob2o$9b2obobob2o$9bo2bob
o2bo$11b2ob2o$11b2ob2o$9bobo3bobo2$6b2o11b2o$6b2ob2o5b2ob2o$5b2o13b2o
2$5b3o11b3o!


For general interest here is the full set of c/6 ships the above mentioned search produced:

x = 320, y = 480, rule = B3/S23
6$9bo13bo16bo18bo9bo18bo16bo13bo9bo13bo9bo13bo9bo13bo9bo13bo16bo23bo
23bo23bo$8bobo11bobo8bo13bo11bo9bo11bo13bo8bobo11bobo7bobo11bobo7bobo
11bobo7bobo11bobo7bobo11bobo8bo13bo9bo13bo9bo13bo9bo13bo$8bobo11bobo7b
2o2bo7bo2b2o8b3o9b3o8b2o2bo7bo2b2o7bobo11bobo7bobo11bobo7bobo11bobo7bo
bo11bobo7bobo11bobo7b2o2bo7bo2b2o7b2o2bo7bo2b2o7b2o2bo7bo2b2o7b2o2bo7b
o2b2o$9bo13bo7bo4bo7bo4bo6b2o13b2o6bo4bo7bo4bo7bo13bo9bo13bo9bo13bo9bo
13bo9bo13bo7bo4bo7bo4bo5bo4bo7bo4bo5bo4bo7bo4bo5bo4bo7bo4bo$31b3ob2ob
5ob2ob3o8bo2b3ob3o2bo8b3ob2ob5ob2ob3o125b3ob2ob5ob2ob3o5b3ob2ob5ob2ob
3o5b3ob2ob5ob2ob3o5b3ob2ob5ob2ob3o$8b3o11b3o8bo13bo9bo3b3ob3o3bo9bo13b
o8b3o11b3o7b3o11b3o7b3o11b3o7b3o11b3o7b3o11b3o8bo13bo9bo13bo9bo13bo9bo
13bo$7bob2o3b2ob2o3b2obo9b2obo3bob2o15b3ob3o15b2obo3bob2o9bob2o3b2ob2o
3b2obo5bob2o3b2ob2o3b2obo5bob2o3b2ob2o3b2obo5bob2o3b2ob2o3b2obo5bob2o
3b2ob2o3b2obo9b2obo3bob2o13b2obo3bob2o13b2obo3bob2o13b2obo3bob2o$8bo4b
obobobo4bo11bobo3bobo17b2ob2o17bobo3bobo11bo4bobobobo4bo7bo4bobobobo4b
o7bo4bobobobo4bo7bo4bobobobo4bo7bo4bobobobo4bo11bobo3bobo15bobo3bobo
15bobo3bobo15bobo3bobo$12b2obobob2o15bo3bo3bo18bobo18bo3bo3bo15b2obobo
b2o15b2obobob2o15b2obobob2o15b2obobob2o15b2obobob2o15bo3bo3bo15bo3bo3b
o15bo3bo3bo15bo3bo3bo$13bobobobo18bobobo17bobo3bobo17bobobo18bobobobo
17bobobobo17bobobobo17bobobobo17bobobobo18bobobo19bobobo19bobobo19bobo
bo$15bobo20bo3bo18bo5bo18bo3bo20bobo21bobo21bobo21bobo21bobo20bo3bo19b
o3bo19bo3bo19bo3bo$15bobo21b3o45b3o21bobo21bobo21bobo21bobo21bobo21b3o
21b3o21b3o21b3o$10bo3b2ob2o3bo17bo15b2o13b2o15bo17bo3b2ob2o3bo11bo3b2o
b2o3bo11bo3b2ob2o3bo11bo3b2ob2o3bo11bo3b2ob2o3bo17bo23bo16b3o4bo4b3o9b
3o4bo4b3o$10b3ob2ob2ob3o16b3o13bobo3b7o3bobo13bobo16b3ob2ob2ob3o11b3ob
2ob2ob3o11b3ob2ob2ob3o11b3ob2ob2ob3o11b3ob2ob2ob3o16b3o21b3o15b3o3b3o
3b3o9b3o3b3o3b3o$14b2ob2o19b2ob2o13bo2b2ob5ob2o2bo8bo13bo14b2ob2o19b2o
b2o19b2ob2o19b2ob2o19b2ob2o19b2ob2o19b2ob2o19b2ob2o19b2ob2o$10b3o7b3o
15b2ob2o14bo2bo3bo3bo2bo8b2o2bo7bo2b2o9b3o7b3o11b3o7b3o11b3o7b3o11b3o
7b3o11b3o7b3o15b2ob2o19b2ob2o20bobo21bobo$13b2o3b2o36b4o2bobobo2b4o6bo
4bo7bo4bo11b2o3b2o17b2o3b2o17b2o3b2o17b2o3b2o17b2o3b2o61b2obo2bobo2bob
2o9b2obo2bobo2bob2o$10b2ob2o3b2ob2o14bo5bo14b2ob7ob2o8b3ob2ob5ob2ob3o
8b2ob2o3b2ob2o11b2ob2o3b2ob2o11b2ob2o3b2ob2o11b2ob2o3b2ob2o11b2ob2o3b
2ob2o14bo5bo17bo5bo13b2o2bobobobo2b2o9b2o2bobobobo2b2o$12bobo3bobo15bo
bo3bobo14bobo2bo2bobo11bo13bo12bobo3bobo15bobo3bobo15bobo3bobo15bobo3b
obo15bobo3bobo15bobo3bobo15bobo3bobo15bo7bo15bo7bo$10b2o4bo4b2o13bo2bo
bo2bo38b2obo3bob2o12b2o4bo4b2o11b2o4bo4b2o11b2o4bo4b2o11b2o4bo4b2o11b
2o4bo4b2o13bo2bobo2bo15bo2bobo2bo13b2o2bo3bo2b2o11b2o2bo3bo2b2o$10bo
11bo13b2obobob2o18b3o18bobo3bobo13bo11bo11bo11bo11bo11bo11bo11bo11bo
11bo13b2obobob2o15b2obobob2o14b2obo3bob2o13b2obo3bob2o$9bo13bo8b3o4bob
o4b3o13bo3bo17bo3bo3bo12bo13bo9bo13bo9bo13bo9bo13bo9bo13bo8b3o4bobo4b
3o7b3o4bobo4b3o8bo3bobobobo3bo9bo3bobobobo3bo$11bo9bo17bobo44bobobo16b
o9bo13bo9bo13bo9bo13bo9bo13bo9bo17bobo21bobo16b2o9b2o11b2o9b2o$9b2obo
2b3o2bob2o12bobo3bobo18bobo20bo3bo14b2obo2b3o2bob2o9b2obo2b3o2bob2o9b
2obo2b3o2bob2o9b2obo2b3o2bob2o9b2obo2b3o2bob2o12bobo3bobo15bobo3bobo
13b3o7b3o11b3o7b3o$9bo2b2ob3ob2o2bo38bo3bo20b3o15bo2b2ob3ob2o2bo9bo2b
2ob3ob2o2bo9bo2b2ob3ob2o2bo9bo2b2ob3ob2o2bo9bo2b2ob3ob2o2bo59b2o2b3o2b
2o13b2o2b3o2b2o$9bob11obo11b2o7b2o16b2ob2o21bo16bob11obo9bob11obo9bob
11obo9bob11obo9bob11obo11b2o7b2o13b2o7b2o17b3o21b3o$37bo5bo43b3o139bo
5bo17bo5bo17b2obob2o17b2obob2o$9bo4bo3bo4bo11b2ob2ob2ob2o40b2ob2o14bo
4bo3bo4bo9bo4bo3bo4bo9bo4bo3bo4bo9bo4bo3bo4bo9bo4bo3bo4bo11b2ob2ob2ob
2o13b2ob2ob2ob2o$14bo3bo67b2ob2o19bo3bo19bo3bo19bo3bo19bo3bo19bo3bo66b
3ob3o17b3ob3o$10bo3b2ob2o3bo12b2o7b2o13b2ob2ob2ob2o36bo3b2ob2o3bo11bo
3b2ob2o3bo11bo3b2ob2o3bo11bo3b2ob2o3bo11bo3b2ob2o3bo12b2o7b2o13b2o7b2o
15b2o3b2o17b2o3b2o$10b2o2b2ob2o2b2o35bo2bobobobo2bo14bo5bo14b2o2b2ob2o
2b2o11b2o2b2ob2o2b2o11b2o2b2ob2o2b2o11b2o2b2ob2o2b2o11b2o2b2ob2o2b2o
15b2ob2o19b2ob2o17b3o3b3o15b3o3b3o$10b2o9b2o15bo3bo14b3obobobobob3o12b
obo3bobo13b2o9b2o11b2o9b2o11b2o9b2o11b2o9b2o11b2o9b2o61bo7bo15bo7bo$9b
2o11b2o9b3obobobobob3o12b2obobob2o15bo2bobo2bo12b2o11b2o9b2o11b2o9b2o
11b2o9b2o11b2o9b2o11b2o12b2o5b2o15b2o5b2o13bo11bo11bo11bo$9b2o11b2o8bo
3bo2bobo2bo3bo14bobo18b2obobob2o12b2o11b2o9b2o11b2o9b2o11b2o9b2o11b2o
9b2o11b2o12b2o5b2o15b2o5b2o13bo11bo11bo11bo$12b2o2bo2b2o12bobo9bobo11b
o3bobo3bo10b3o4bobo4b3o11b2o2bo2b2o15b2o2bo2b2o15b2o2bo2b2o15b2o2bo2b
2o15b2o2bo2b2o13b3o7b3o11b3o7b3o11b2ob2o3b2ob2o11b2ob2o3b2ob2o$12b2o2b
o2b2o14bobo5bobo13bo9bo17bobo18b2o2bo2b2o15b2o2bo2b2o15b2o2bo2b2o15b2o
2bo2b2o15b2o2bo2b2o12b3o9b3o9b3o9b3o11bo2bo3bo2bo13bo2bo3bo2bo$12b3obo
b3o17bo3bo16bo2bo3bo2bo14bobo3bobo15b3obob3o15b3obob3o15b3obob3o15b3ob
ob3o15b3obob3o14bo9bo13bo9bo14bobo3bobo15bobo3bobo$39bobo19bo5bo158b4o
bobob4o11b4obobob4o13b2o5b2o15b2o5b2o$36b2obobob2o15bobo3bobo14b2o7b2o
134bo2bobo2bo15bo2bobo2bo15b2o5b2o15b2o5b2o$36b2obobob2o15b2o5b2o16bo
5bo139bobo21bobo17b2o7b2o13b2o7b2o$12b3o3b3o14b3obobob3o15bo5bo15b2ob
2ob2ob2o14b3o3b3o15b3o3b3o15b3o3b3o15b3o3b3o15b3o3b3o18bobo21bobo17b3o
5b3o13b3o5b3o$8b3ob3o3b3ob3o10bo3bobo3bo15bo5bo36b3ob3o3b3ob3o7b3ob3o
3b3ob3o7b3ob3o3b3ob3o7b3ob3o3b3ob3o7b3ob3o3b3ob3o11b2obobob2o15b2obobo
b2o15bo7bo15bo7bo$8b3ob2o5b2ob3o9b2o9b2o10b2ob3o3b3ob2o11b2o7b2o10b3ob
2o5b2ob3o7b3ob2o5b2ob3o7b3ob2o5b2ob3o7b3ob2o5b2ob3o7b3ob2o5b2ob3o12bob
obobo17bobobobo15b4o3b4o13b4o3b4o$33b3o9b3o9b2obo2bobo2bob2o158b2ob2o
19b2ob2o19bo3bo19bo3bo$10bo11bo11b2o2b2ob2o2b2o13bobo3bobo17bo3bo15bo
11bo11bo11bo11bo11bo11bo11bo11bo11bo16bobo21bobo17bob3ob3obo13bob3ob3o
bo$10bo11bo14b2o3b2o13b3obo5bob3o9b3obobobobob3o10bo11bo11bo11bo11bo
11bo11bo11bo11bo11bo60bo9bo13bo9bo$9b3o9b3o8bo3b2o5b2o3bo8b4obo3bob4o
8bo3bo2bobo2bo3bo8b3o9b3o9b3o9b3o9b3o9b3o9b3o9b3o9b3o9b3o13bo5bo17bo5b
o$9b2o11b2o9bob3o5b3obo12b3o3b3o12bobo9bobo9b2o11b2o9b2o11b2o9b2o11b2o
9b2o11b2o9b2o11b2o12b2o5b2o15b2o5b2o12b2o11b2o9b2o11b2o$10b3o7b3o11bo
11bo16bobo17bobo5bobo12b3o7b3o11b3o7b3o11b3o7b3o11b3o7b3o11b3o7b3o13b
2o5b2o15b2o5b2o12b2o11b2o9bobo9bobo$9bo5b3o5bo10bo11bo16bobo20bo3bo14b
o5b3o5bo9bo5b3o5bo9bo5b3o5bo9bo5b3o5bo9bo5b3o5bo13bo5bo17bo5bo15bo9bo$
9bo5b3o5bo10b3o7b3o13b2obobob2o18bobo15bo5b3o5bo9bo5b3o5bo9bo5b3o5bo9b
o5b3o5bo9bo5b3o5bo13bo5bo17bo5bo13bo13bo8b2o13b2o$8bo3b3o3b3o3bo12bo2b
o2bo16bo2bobo2bo15b2obobob2o11bo3b3o3b3o3bo7bo3b3o3b3o3bo7bo3b3o3b3o3b
o7bo3b3o3b3o3bo7bo3b3o3b3o3bo11bob2ob2obo15bob2ob2obo12bo2b2o5b2o2bo8b
2o13b2o$9bob2obobobob2obo9b3o3b3o3b3o12b3o3b3o15b2obobob2o12bob2obobob
ob2obo9bob2obobobob2obo9bob2obobobob2obo9bob2obobobob2obo9bob2obobobob
2obo11b2ob2ob2ob2o13b2ob2ob2ob2o13b3o5b3o11bo13bo$15b3o15b6o3b6o12bo7b
o14b3obobob3o17b3o21b3o21b3o21b3o21b3o18bobo3bobo15bobo3bobo38bo9bo$
33bo4bobobo4bo12bo2bobo2bo14bo3bobo3bo205bo2b2ob2o2bo$39bobo16bo2bobob
obo2bo11b2o9b2o154bo13bo11b3o5b3o12b3o2bobo2b3o$58b2obobobobob2o10b3o
9b3o131b2o7b2o10bobo11bobo10b2o7b2o11b2o3bo3bo3b2o$58bobo7bobo11b2o2b
2ob2o2b2o12bo9bo13bo9bo14bo7bo42bobo17bobo5bobo10bob2obo5bob2obo11bo7b
o12bobo2bo3bo2bobo$85b2o3b2o14bob9obo11bobo3bo3bobo11b2o9b2o12bo9bo18b
o20b2o3b2o15b4o3b4o14b3o3b3o13b4o2bo2b4o$80bo3b2o5b2o3bo10bob7obo12bo
2b3ob3o2bo11bobo2b3o2bobo11bobo3bo3bobo17bo20bobobobo16bo2bobo2bo17b2o
b2o16bo9bo$59b2o7b2o11bob3o5b3obo13bo5bo39b3ob3ob3o12bo2b3ob3o2bo36bo
2bo3bo2bo14b2obobob2o14b2o2bobo2b2o14bo7bo$58b3o3bo3b3o11bo11bo16b3o
20b5o17bobo3bobo38bo9bo12bo11bo14bobobobo15b5ob5o14bo2b3o2bo$56b2o2bo
3bo3bo2b2o9bo11bo15b5o40b2o7b2o16b5o15bob9obo12bo3b3o3bo17bobo17b2obo
3bob2o16bo3bo$61b2o3b2o14b3o7b3o13b2o5b2o16bo5bo15b2o7b2o37bob7obo17b
3o21bobo20bo3bo$56bo5b2ob2o5bo12bo2bo2bo16b2o5b2o15b2o5b2o15bo7bo16bo
5bo17bo5bo17bo2bo2bo16b2obobob2o14bo3bobo3bo15b2o3b2o$57bo2bobobobobo
2bo9b3o3b3o3b3o11bobo5bobo13bo9bo12bobo7bobo13b2o5b2o18b3o45bobo17bo2b
2ob2o2bo$81b6o3b6o12bo7bo12bo2bo7bo2bo9bo13bo11bo9bo16b5o42bobobobo19b
obo20bo3bo$63b3o15bo4bobobo4bo10bo2bo5bo2bo11b3o7b3o11b3o7b3o10bo2bo7b
o2bo12b2o5b2o14bo9bo15bo5bo15b4o3b4o16bo3bo$87bobo16bo2bo5bo2bo12bobo
5bobo15bobobobo14b3o7b3o13b2o5b2o13bob9obo14b3ob3o14b4obobob4o17bo$
107bo2bo3bo2bo14b2o5b2o16bobobobo15bobo5bobo13bobo5bobo13bob7obo16b2ob
2o14b2o3b2ob2o3b2o12bob2ob2obo$107b2obo3bob2o14b2o5b2o16bo5bo16b2o5b2o
15bo7bo16bo5bo17b3ob3o19bobo18bo7bo$105bo3bo5bo3bo9b2o3bo3bo3b2o9b2o2b
obobobo2b2o12b2o5b2o13bo2bo5bo2bo16b3o42b2obobob2o12bo5bobo5bo$104bo
15bo7bo15bo8b2o11b2o9b2o3bo3bo3b2o10bo2bo5bo2bo15b5o41b3o3b3o12b2ob3ob
ob3ob2o$106b3o7b3o10bobo9bobo9b3o9b3o8bo15bo10bo2bo3bo2bo14b2o5b2o14b
4o3b4o15bo5bo13b2obo2b3o2bob2o$131b2o7b2o13bo9bo11bobo9bobo11b2obo3bob
2o14b2o5b2o14b4o3b4o13b3o5b3o15b2o3b2o$131b2o7b2o13bo9bo13b2o7b2o11bo
3bo5bo3bo11bobo5bobo14bo7bo14b3o5b3o16bo3bo$106b3o7b3o11b2o9b2o11b2o9b
2o12b2o7b2o10bo15bo11bo7bo15bo7bo14bo2bo3bo2bo18bo$105bobo9bobo9bo13bo
10bo11bo11b2o9b2o11b3o7b3o11bo2bo5bo2bo12bob2o3b2obo38bo7bo$105bob2o7b
2obo9bobo9bobo9bobo9bobo9bo13bo34bo2bo5bo2bo12bob2o3b2obo37bobo5bobo$
104b2o13b2o7b2ob2o7b2ob2o8bobo9bobo9bobo9bobo35bo2bo3bo2bo16bo3bo13b3o
11b3o12bo5bo$104b2o13b2o8bob2o7b2obo9b3o9b3o8b2ob2o7b2ob2o9b3o7b3o12b
2obo3bob2o13bo2bo3bo2bo11b2o11b2o10bo11bo$106b3o7b3o12bo9bo13bo9bo11bo
b2o7b2obo9bobo9bobo9bo3bo5bo3bo11bo3bobo3bo14b3o3b3o12b3o9b3o$105b2o
11b2o59bo9bo11bob2o7b2obo8bo15bo11bo7bo15bo2bobo2bo12bo13bo$104bo2bo9b
o2bo7b3o11b3o7b2o13b2o31b2o13b2o9b3o7b3o14bo5bo17bobobobo18bo3bo$107bo
9bo10b4o9b4o8b2obo7bob2o8b3o11b3o7b2o13b2o37bo3bo18bobobobo18b2ob2o$
104bo2bo9bo2bo8b2o2bo5bo2b2o12bo7bo11b4o9b4o9b3o7b3o40b3o18b2obobob2o
16bobobobo$110bo3bo39bo3bo3bo3bo10b2o2bo5bo2b2o9b2o11b2o10b3o7b3o14bo
5bo16b2obobob2o12b3ob2o3b2ob3o$110b2ob2o19b2ob2o20bobo38bo2bo9bo2bo8bo
bo9bobo11bo9bo15bobobobo16bobo3bobo$109bobobobo19bobo21bobo20b2ob2o16b
o9bo11bob2o7b2obo11bo9bo16b2ob2o14b2obo7bob2o$108b2obobob2o15b2obobob
2o16bobobobo19bobo14bo2bo9bo2bo7b2o13b2o9bo11bo14b2o3b2o15b2obo3bob2o$
107bo3bobo3bo14b2obobob2o15b2obobob2o15b2obobob2o17bo3bo13b2o13b2o10b
2ob5ob2o15bo5bo15bobo5bobo$108bo2bobo2bo15bo2bobo2bo18bobo18b2obobob2o
17b2ob2o15b3o7b3o13bo7bo17bo3bo17bo7bo$109bo5bo18b2ob2o16bo3bobo3bo14b
o2bobo2bo16bobobobo13b2o11b2o12bobobobobo17b2ob2o16b2o7b2o$134b2ob2o
20bobo20b2ob2o17b2obobob2o11bo2bo9bo2bo11bo7bo15bobo3bobo$109b3ob3o16b
obo3bobo15bobo3bobo17b2ob2o16bo3bobo3bo13bo9bo14bo7bo14bo9bo13bo2bo3bo
2bo$156b2o5b2o15bobo3bobo15bo2bobo2bo11bo2bo9bo2bo9b2o9b2o36bobo5bobo$
105b3o9b3o9b2o11b2o10b3o7b3o38bo5bo18bo3bo15b2o4bo4b2o11bo3b2ob2o3bo
12b2obo3bob2o$107bo9bo11b2ob2o5b2ob2o8b2o2b2o5b2o2b2o8b2o11b2o38b2ob2o
15b2ob2o3b2ob2o12b3o5b3o14b9o$104b3o11b3o7b2o13b2o32b2ob2o5b2ob2o13b3o
b3o17bobobobo62b2o4bo4b2o$106bo11bo34bo13bo8b2o13b2o35b2obobob2o17b2ob
2o37b2o2b3o3b3o2b2o$105bo13bo8b3o11b3o8bo13bo33b3o9b3o11bo3bobo3bo15b
3ob3o15b3o5b3o13bo9bo$105bo13bo33bo13bo8b3o11b3o10bo9bo14bo2bobo2bo12b
2o3b2ob2o3b2o11bob2o3b2obo10bo3bobo3bobo3bo$200b3o11b3o12bo5bo13b2o11b
2o38b2ob2o$202bo11bo61b2o5b2o15bo7bo$201bo13bo13b3ob3o14bobo7bobo12b4o
3b4o15bo5bo$201bo13bo35bo9bo16b2ob2o15bo11bo$225b3o9b3o38b2ob2o14bo2b
2o5b2o2bo$227bo9bo12b2o9b2o15bo3bo13bo3bo7bo3bo$224b3o11b3o8bo13bo15b
3o15bobobob3obobobo$226bo11bo10b2o11b2o16bo19bo7bo$225bo13bo10b2o9b2o
13b9o14bo9bo$225bo13bo35b11o14bo7bo$248bo3bo7bo3bo9bo2b7o2bo12b2o3bo3b
2o$252bo7bo14b2o7b2o12bobo7bobo$248b2o13b2o11bo7bo15bo7bo$250b3o7b3o
13bobo3bobo$250b3o7b3o14b7o14b3o7b3o$252b4ob4o15bo2b3o2bo13b3o7b3o$
253bobobobo15bob7obo$252bo2bobo2bo13b2ob2o3b2ob2o$254b2ob2o15bo3bo3bo
3bo11b3o7b3o$251bobobobobobo35bo3bo5bo3bo$252b3o3b3o17bo3bo18b2o3b2o$
252b3o3b3o12bo4b2ob2o4bo13b3ob3o$253b2o3b2o14bo3bo3bo3bo11b3o7b3o$273b
o13bo9b2obo7bob2o$249bob2o7b2obo10bo2bo5bo2bo10b2o3b2ob2o3b2o$249bo2bo
7bo2bo$249bo2bo7bo2bo10b3o7b3o10b2obo7bob2o$298b4o5b4o$248bobo11bobo9b
3o7b3o$249bo13bo9bo13bo12b3o3b3o$274bo11bo13bo2bobo2bo$274b3o7b3o12b2o
b2ob2ob2o2$272b5o7b5o11bobo3bobo$272b2ob2o7b2ob2o11b2o5b2o$273bo13bo$
274b3o7b3o13bobo3bobo$275bo9bo14bo2bobo2bo$278b2ob2o18bobobobo$276b2ob
obob2o18bobo$279bobo20b2ob2o$275bo3bobo3bo$275bo3bobo3bo$276b3o3b3o15b
3o3b3o$277bo5bo16b2obobob2o$297bo5bobo5bo$277b2o3b2o13bo3bobobobo3bo$
274b2o9b2o10bo3bobobobo3bo$273b3o9b3o12b3o3b3o$276bo7bo15bo7bo$272bo2b
o9bo2bo10b2o7b2o$272bo15bo$273b2o11b2o11b2obo3bob2o$299b2ob2ob2ob2o$
300bob2ob2obo$301b2o3b2o$302bo3bo$297b2o2bo5bo2b2o$297b2obob2ob2obob2o
$297b3o2b2ob2o2b3o$302b2ob2o$297b2o3bo3bo3b2o$303bobo$301bobobobo$300b
2obobob2o$300bo2bobo2bo$299bo3bobo3bo$298bo3b2ob2o3bo$298bo3b2ob2o3bo$
298bo4bobo4bo$297b2o11b2o$297b2ob3o3b3ob2o$297b3o9b3o3$297b3o9b3o$300b
2o5b2o$299b2o2b3o2b2o$296b3o2b2obob2o2b3o$304bo$303bobo$303bobo12$16bo
23bo$9bo13bo9bo13bo$8b2o2bo7bo2b2o7b2o2bo7bo2b2o$7bo4bo7bo4bo5bo4bo7bo
4bo$7b3ob2ob5ob2ob3o5b3ob2ob5ob2ob3o$9bo13bo9bo13bo$11b2obo3bob2o13b2o
bo3bob2o$12bobo3bobo15bobo3bobo$12bo3bo3bo15bo3bo3bo$14bobobo19bobobo$
14bo3bo19bo3bo$15b3o21b3o$16bo23bo$15b3o21b3o$14b2ob2o19b2ob2o$14b2ob
2o19b2ob2o2$13bo5bo17bo5bo$12bobo3bobo15bobo3bobo$12bo2bobo2bo15bo2bob
o2bo$12b2obobob2o15b2obobob2o$8b3o4bobo4b3o7b3o4bobo4b3o$15bobo21bobo$
12bobo3bobo15bobo3bobo2$11b2o7b2o13b2o7b2o$13bo5bo17bo5bo$11b2ob2ob2ob
2o13b2ob2ob2ob2o2$11b2o7b2o13b2o7b2o$14b2ob2o19b2ob2o2$12b2o5b2o15b2o
5b2o$12b2o5b2o15b2o5b2o$10b3o7b3o11b3o7b3o$9b3o9b3o9b3o9b3o$11bo9bo13b
o9bo$10b4obobob4o11b4obobob4o$12bo2bobo2bo15bo2bobo2bo$15bobo21bobo$
15bobo21bobo$12b2obobob2o15b2obobob2o$13bobobobo17bobobobo$14b2ob2o19b
2ob2o$15bobo21bobo2$13bo5bo17bo5bo$12b2o5b2o15b2o5b2o$12b2o5b2o15b2o5b
2o$13bo5bo17bo5bo$13bo5bo17bo5bo$12bob2ob2obo15bob2ob2obo$11b2ob2ob2ob
2o13b2ob2ob2ob2o$12bobo3bobo15bobo3bobo3$11b2o7b2o13b2o7b2o$11bobo5bob
o13bobo5bobo$13b2o3b2o17b2o3b2o$13bobobobo17bobobobo$11bo2bo3bo2bo13bo
2bo3bo2bo$10bo11bo11bo11bo$11bo3b3o3bo13bo3b3o3bo$15b3o21b3o$13bo2bo2b
o17bo2bo2bo4$10b13o11b13o$9bob11obo9bob11obo$9b3obo5bob3o9b3obo5bob3o$
12b2ob3ob2o15b2ob3ob2o$11bo2b5o2bo13bo2b5o2bo$14bo3bo19bo3bo$11b3ob3ob
3o13b3ob3ob3o$13b2o3b2o17b2o3b2o$14b2ob2o19b2ob2o$15b3o21b3o2$12b2o5b
2o15b2o5b2o$11bo2bo3bo2bo13bo2bo3bo2bo$12b9o15b9o$12b9o15b9o$8b3o5bo5b
3o7b3o5bo5b3o$8b3o11b3o7b3o11b3o$9b3o9b3o9b3o9b3o$11bob7obo13bob7obo$
12bo7bo15bo7bo$15bobo21bobo$14bo3bo19bo3bo$16bo23bo2$12b2obobob2o15b2o
bobob2o$11bo3bobo3bo13bo3bobo3bo$11bo9bo13bo9bo$12b2o5b2o15b2o5b2o$11b
2o7b2o13b2o7b2o$11bo9bo13bo9bo3$12bo7bo15bo7bo$10b3o7b3o11b3o7b3o$13bo
5bo17bo5bo$9bo2bo7bo2bo9bo2bo7bo2bo$13bo5bo17bo5bo$13bo5bo17bo5bo$10bo
11bo11bo11bo$9b2o3bo3bo3b2o9b2o3bo3bo3b2o$8bo2bob2o3b2obo2bo7bo2bob2o
3b2obo2bo$11bobobobobobo13bobobobobobo$9bobo2bo3bo2bobo9bobo2bo3bo2bob
o$10b3o7b3o11b3o7b3o$12b2o5b2o15b2o5b2o$13bo5bo17bo5bo$10b2o9b2o11b2o
9b2o$9b2o2bo5bo2b2o9b2o2bo5bo2b2o$9b2o11b2o9b2o11b2o$13bo5bo17bo5bo$
14bo3bo19bo3bo$11b2o2bobo2b2o13b2o2bobo2b2o$12b3o3b3o15b3o3b3o$11b3o5b
3o13b3o5b3o$10bobo7bobo11bobo7bobo$10bob2o5b2obo11bob2o5b2obo$10bo11bo
11bo11bo$13bo5bo17bo5bo$13b2obob2o17b2obob2o$11bo3b3o3bo13bo3b3o3bo$
16bo23bo$14b2ob2o19b2ob2o4$13b3ob3o17b3ob3o$14bobobo19bobobo$15b3o21b
3o$11b2ob5ob2o13b2ob5ob2o$9bo4bo3bo4bo9bo4bo3bo4bo$13bo5bo17bo5bo$8bo
5bo3bo5bo7bo5bo3bo5bo$12bo7bo15bo7bo$9bo4b2ob2o4bo9bo4b2ob2o4bo$10bobo
b2ob2obobo11bobob2ob2obobo$15bobo21bobo$11bo3bobo3bo13bo3bobo3bo$11bo
2bo3bo2bo13bo2bo3bo2bo$11b2obo3bob2o13b2obo3bob2o$10b2o2bo3bo2b2o11b2o
2bo3bo2b2o$10b2ob2o3b2ob2o11b2ob2o3b2ob2o$12b3o3b3o15b3o3b3o3$11b3o5b
3o13b3o5b3o$11b2o7b2o13b2o7b2o$9b2o11b2o9b2o11b2o$9b4o7b4o9b4o7b4o$9bo
3bo5bo3bo9bo3bo5bo3bo$10bo11bo11bo11bo$10bobo7bobo11bobo7bobo$11bo9bo
13bo9bo$14bo3bo19bo3bo$12b2obobob2o15b2obobob2o$15bobo21bobo2$12b3o3b
3o15b3o3b3o2$11bo4bo4bo13bo4bo4bo$10bob2ob3ob2obo11bob2ob3ob2obo$9bo2b
3o3b3o2bo9bo2b3o3b3o2bo$8bo3b4ob4o3bo7bo3b4ob4o3bo$14b2ob2o19b2ob2o$
10b2o2b2ob2o2b2o11b2o2b2ob2o2b2o$9b2o11b2o9b2o11b2o$9b2o5bo5b2o9b2o5bo
5b2o3$12b2o5b2o15b2o5b2o$11bo2bo3bo2bo13bo2bo3bo2bo$10b2o2bo3bo2b2o11b
2o2bo3bo2b2o$11bobo5bobo13bobo5bobo$10bo2bo5bo2bo11bo2bo5bo2bo$10bobo
2b3o2bobo11bobo2b3o2bobo$10bobo7bobo11bobo7bobo$13b3ob3o17b3ob3o$12b2o
b3ob2o15b2ob3ob2o$10bobobobobobobo11bobobobobobobo$10b2obobobobob2o11b
2obobobobob2o$9bo2bo7bo2bo9bo2bo7bo2bo$10b4o5b4o11b4o5b4o$12bo7bo15bo
7bo3$37b2o3b2o$34b5o3b5o3$33bo13bo$32bob2o9b2obo$34bo2b2o3b2o2bo$34bo
3bo3bo3bo$39bobo$36b2obobob2o$36b2obobob2o$39bobo$39bobo$39bobo$36b2ob
obob2o2$36b2obobob2o$37bobobobo2$37bobobobo$38bo3bo$36b2o5b2o$35bo2bo
3bo2bo$38bo3bo2$35b2o7b2o$35bo2bo3bo2bo$39bobo$36bob2ob2obo$38b2ob2o$
35b2o7b2o$36bo7bo$37bo5bo$38b5o$38b5o$40bo$36bo7bo$34b2o9b2o$34bobo2b
3o2bobo$35b3ob3ob3o$36bobo3bobo$35b2o7b2o$35b2o7b2o$36bo7bo$34bobo7bob
o$33bo13bo$34b3o7b3o$37bobobobo$37bobobobo$37bo5bo$33b2o2bobobobo2b2o$
33b2o11b2o$33b3o9b3o$35bo9bo$35bo9bo$34b2o9b2o$34bo11bo$33bobo9bobo$
33bobo9bobo$33b3o9b3o$35bo9bo2$32b2o13b2o$33b2obo7bob2o$36bo7bo$34bo3b
o3bo3bo$39bobo$39bobo$37bobobobo$36b2obobob2o$39bobo$35bo3bobo3bo$39bo
bo$36bobo3bobo$36b2o5b2o$34b3o7b3o$32b2o2b2o5b2o2b2o2$33bo13bo$33bo13b
o$33bo13bo!


Sokwe,

You asked if I could provide more precision on when the variety of small c/4 ships were found. My records and memory are scattered and sometime between last December and March is a realistic approximation.

The snail was found by a standard search from the front. I have tried some searches from the back and they just don't work well.

Have a happy day,

-Tim Coe
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Re: Spaceship Discussion Thread

Postby Sokwe » June 30th, 2016, 5:03 pm

moebius wrote:I looked through the output file and saw a matching several rows with Sokwe's continuation of Kazyan's asymmetric front end.

That's amazingly convenient. This is now the thinnest known c/6 orthogonal spaceship, although a width 11 or 12 ship probably exists.

muzik wrote:Are there any good c/9 partials?

I ran the c/9 width-15 gutter search with zfind, since I couldn't find any indication that it had been done before. Here are the longest partial results:
x = 135, y = 41, rule = B3/S23
3bo7bo21bo7bo22bo5bo23bo5bo24bo3bo$2bobo5bobo19bobo5bobo20bobo3bobo20b
3o5b3o20b2obobob2o$2bobo5bobo19bobo5bobo19bo2bo3bo2bo19b2obo3bob2o19b
3obobob3o$3bo7bo21bo7bo21b2obobob2o49bo2bobobobo2bo$65b2ob2o24b2o3b2o
19bo5bobo5bo$3bo7bo21bo7bo24bobo23b4o3b4o18b2o9b2o$2bobo5bobo19bobo5bo
bo23bobo22bobobo3bobobo18bob2o3b2obo$bo2bo5bo2bo17bo2bo5bo2bo19bo2bobo
2bo19bo2bo5bo2bo19b3o3b3o$2bobo5bobo19bobo5bobo18bo2bobobobo2bo17bobo
7bobo19bobo3bobo$3b2o5b2o21b2o5b2o18b2o2bobobobo2b2o49b3ob3o$3b3o3b3o
21b3o3b3o23b2ob2o55b2ob2o$2b5ob5o19b5ob5o51bo5bo21b2obo3bob2o$3b2obobo
b2o21b2obobob2o21b3o3b3o21b3o3b3o19bo11bo$4b2o3b2o23b2o3b2o20b2o9b2o
20bobobobo19b2obo7bob2o$3b2o5b2o21b2o5b2o19b3ob2ob2ob3o19bobo3bobo18b
2ob2o5b2ob2o$2bo9bo19bo9bo19b2o2bobo2b2o19b4o3b4o18bo11bo$2bo9bo19bo9b
o19b2ob2ob2ob2o18bo2b2o3b2o2bo18bobo5bobo$b2o9b2o17b2o9b2o18b3o5b3o18b
2obo5bob2o21bo3bo$64bo5bo20bobo7bobo18b5ob5o$obo2bo3bo2bobo15bobo2bo3b
o2bobo17bo9bo19bobo5bobo23bobo$bo11bo17bo11bo17bo3bo3bo3bo16b2o2b2o3b
2o2b2o20bo3bo$b2o9b2o17b2o9b2o19bob2ob2obo18b2o11b2o15bo4bo3bo4bo$60bo
4bo3bo4bo16b3obo3bob3o16bo2bo7bo2bo$4b2o3b2o23bo5bo20b2ob2o3b2ob2o18b
4o3b4o18b3obo3bob3o$4bobobobo22bobo3bobo18b3ob2o3b2ob3o18bo7bo22b3ob3o
$4bobobobo21bo3bobo3bo18bo3bo3bo3bo21b2ob2o21b2o9b2o$o4bo3bo4bo16bo4bo
bo4bo16b2o2b2o3b2o2b2o45bo4b2ob2o4bo$ob3o5b3obo15bo5bobo5bo15b5o5b5o
17b2obo3bob2o18b2o2b2ob2o2b2o$5bo3bo20bo5bobo5bo20bo3bo20b2obob2ob2obo
b2o$b3obo3bob3o17bo4bobo4bo17bobo7bobo17bo11bo$b4o5b4o46bo2b3o3b3o2bo$
4bo5bo20b2ob3ob3ob2o$bobo7bobo22bobo$o5bobo5bo$3b4ob4o19bo3bo3bo3bo$
32b3obobob3o$2bo3bobo3bo$2bo3bobo3bo18b2o9b2o$3bo2bobo2bo20b4o3b4o$2b
2obo3bob2o20bo7bo$2b3o5b3o18b2ob3ob3ob2o!

The first two look especially interesting, because they have the same loosely-connected front end.
-Matthias Merzenich
Sokwe
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Re: Spaceship Discussion Thread

Postby muzik » June 30th, 2016, 5:06 pm

So how would one actually find the spaceships then? Since they're called "partials" do you simply find a rear end for them all, try to attach some random stuff to the back, or (most likely) run a promising front end through searches?
2c/n spaceships project (new)

Current priorities: see here
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Location: Scotland

Re: Spaceship Discussion Thread

Postby Sokwe » June 30th, 2016, 5:19 pm

muzik wrote:So how would one actually find the spaceships then? Since they're called "partials" do you simply find a rear end for them all, try to attach some random stuff to the back, or (most likely) run a promising front end through searches?

Ususally, it's the last one: use a known partial result as the starting point of a gfind/zfind/knight2/WLS/JLS search.

I described how to extend partial results with zfind here. This is closely related to extending partial results in gfind, which Paul Tooke describes here (row ordering is the same as in zfind). I know that knight2 can also extend partial results, but I don't know how to input the initial rows.
-Matthias Merzenich
Sokwe
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Re: Spaceship Discussion Thread

Postby muzik » June 30th, 2016, 5:23 pm

Whenever I get round to trying to figure out how to work them, what would be a good usable partial to test if it's working?
2c/n spaceships project (new)

Current priorities: see here
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Location: Scotland

Re: Spaceship Discussion Thread

Postby Sokwe » June 30th, 2016, 5:50 pm

muzik wrote:Whenever I get round to trying to figure out how to work them, what would be a good usable partial to test if it's working?

It doesn't matter, as long as you can tell that the output looks right. In my post on extending partials with zfind, I extended the front end of the dragon as an example. I could quickly tell that I had input the rows correctly, because the output partials had the same front end as the dragon. If you mess up, it usually causes the search to terminate almost immediately, with the longest partial being 2 or 3 rows.

Edit:
muzik wrote:Here's a c/8 partial from the other thread

I tried to extend this partial at width 18 using zfind, but it didn't find a ship. Here are the longest partials:
x = 48, y = 53, rule = B3/S23
4bo8bo20bo8bo$3bobo6bobo18bobo6bobo$2bo2bo6bo2bo16bo2bo6bo2bo$3b2o8b2o
18b2o8b2o$8b2o28b2o$6b2o2b2o24b2o2b2o$6bo4bo24bo4bo$6bo4bo24bo4bo$5b8o
22b8o$4b4o2b4o20b4o2b4o$3bo2bo4bo2bo18bo2bo4bo2bo$2bo3bo4bo3bo16bo3bo
4bo3bo$3bo2bo4bo2bo18bo2bo4bo2bo3$3b3o6b3o18b3o6b3o3$4bo8bo$3b3o6b3o
16b3o10b3o$2b2ob3o2b3ob2o15bo2bo8bo2bo$2bobo2bo2bo2bobo16b2o10b2o$3b2o
3b2o3b2o19b3o4b3o$7bo2bo22bo2bo4bo2bo$3bo3b4o3bo18b3o6b3o$32b2obo6bob
2o$3bo2bo4bo2bo17bob3o4b3obo$4b3o4b3o17bo4b2o2b2o4bo$3bo10bo16bo4b2o2b
2o4bo$4bo8bo17bo14bo$4bo8bo18bob4o2b4obo2$4b2o6b2o21bo6bo$2bo4bo2bo4bo
17b2o8b2o$2b3o8b3o14bob2o10b2obo$2bobob2o2b2obobo14bobo2b3o2b3o2bobo$b
2o2bo6bo2b2o16bobo2b2o2bobo$o2bo10bo2bo18b6o$obo12bobo15bo3b4o3bo$34b
2o6b2o$ob2ob2o4b2ob2obo16b2ob4ob2o$bo3b2o4b2o3bo17b2o6b2o$6b2o2b2o26b
2o$5b3o2b3o20bobo6bobo$b3o3bo2bo3b3o15bo5b2o5bo$o3bo3b2o3bo3bo14bobobo
4bobobo$8b2o22bo4b4o4bo$3bo3bo2bo3bo22bo2bo$b2o4bo2bo4b2o15bo3bo4bo3bo
$obo4bo2bo4bobo13b2obo2bo2bo2bob2o$6b2o2b2o18b3obo2bo2bo2bob3o$bo3b8o
3bo$bo2bo8bo2bo!
-Matthias Merzenich
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