Small Spaceship Syntheses

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
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dvgrn
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Re: Small Spaceship Syntheses

Post by dvgrn » September 3rd, 2020, 11:18 am

mniemiec wrote:
September 3rd, 2020, 3:24 am
In my attempt, I just built a line of interlocking blinker-like objects (a bit like Dave Buckingham's edge-shooting pentadecathlon inserter). I did have the idea of infrastructure mostly in place on both sides, with a hole in the middle that got patched as soon as the escorts passed through.
What's the cheapest patchable horizontal line of junk that ignites a long horizontal line? A row of beehives separated by two cells seems to work fine, but I don't know offhand how painful it is to patch a three-beehive-wide hole in the middle.

Waveguides can be used to extend the length of time that the line travels at light speed, but given how easily long snakes can be lengthened, the waveguide/superstring method probably ends up a good bit more expensive:

Code: Select all

x = 131, y = 74, rule = B3/S23
9bo119bo$8bobo117bobo$9bo119bo2$9bo119bo$8bobo117bobo$9bo119bo2$9bo
119bo$8bobo117bobo$9bo119bo2$9bo119bo$8bobo117bobo$9bo119bo2$9bo119bo$
8bobo117bobo$9bo119bo2$9bo119bo$8bobo117bobo$9bo119bo2$9bo119bo$8bobo
117bobo$9bo119bo2$9bo119bo$8bobo117bobo$9bo119bo2$9bo119bo$8bobo117bob
o$9bo119bo2$9bo119bo$8bobo117bobo$9bo119bo2$9bo119bo$8bobo117bobo$9bo
119bo2$9bo119bo$8bobo117bobo$9bo119bo2$9bo119bo$8bobo117bobo$9bo119bo
2$9bo119bo$8bobo117bobo$9bo119bo2$9bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo
4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo$8bobo2bobo2bobo2bobo2bobo2bobo
2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo
2bobo2bobo2bobo2bobo2bobo$8bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bob
o2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bobo2bob
o2bobo2bobo$9bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo
4bo4bo4bo4bo4bo4bo12$3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b
3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o2b3o$2bo4bo4bo4bo4bo4bo4bo4b
o4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo$bo4bo4bo4bo4bo4bo4bo
4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo4bo!
Maybe some combination of structures could be found that's cheap to build and burns relatively cleanly, though.
mniemiec wrote:
September 3rd, 2020, 3:24 am
I also don't relish the thought of attempting to turn this into an actual recipe (i.e. cleaning up the leftover debris). For now, I'll have to be content with "It can be done".
Heh, it does look awful, but all that junk would melt away surprisingly quickly with the addition of a few dozen gliders. It would be fine as long as nobody got stuck trying to find the minimum number of cleanup gliders -- please let's not go there!

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Macbi
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Re: Small Spaceship Syntheses

Post by Macbi » September 3rd, 2020, 11:25 am

dvgrn wrote:
September 3rd, 2020, 11:18 am
mniemiec wrote:
September 3rd, 2020, 3:24 am
In my attempt, I just built a line of interlocking blinker-like objects (a bit like Dave Buckingham's edge-shooting pentadecathlon inserter). I did have the idea of infrastructure mostly in place on both sides, with a hole in the middle that got patched as soon as the escorts passed through.
What's the cheapest patchable horizontal line of junk that ignites a long horizontal line? A row of beehives separated by two cells seems to work fine, but I don't know offhand how painful it is to patch a three-beehive-wide hole in the middle.
This reminded me of one of my very first posts on the forum. Would this

Code: Select all

x = 160, y = 11, rule = B3/S23
13b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o
3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o$13bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo
5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo$14bo5bo5bo5bo5bo5bo5bo5bo5bo5b
o5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo4$b3o3b3o3b3o3b3o3b3o3b
3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o3b3o
3b3o3b3o$o2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo$3bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo
5bo5bo5bo5bo5bo5bo5bo5bo$3bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo
5bo5bo5bo5bo5bo5bo5bo5bo5bo5bo$obo3bobo3bobo3bobo3bobo3bobo3bobo3bobo
3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo3bobo
3bobo3bobo3bobo!
have any advantage?

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Re: Small Spaceship Syntheses

Post by mniemiec » September 3rd, 2020, 11:36 am

Macbi wrote:
September 3rd, 2020, 11:25 am
This reminded me of one of my very first posts on the forum. Would this ... have any advantage?
Something like this could work; unfortunately, synthesizing such a unbroken row of spaceships so close together would be difficult. The hardest part would be that the main spaceship would have to pass through the middle of it; there would have to be a gap that would be closed later. Adding spaceships at the end of a row of existing ones is easy, but inserting the last one into the narrow gap in the middle would be much more challenging. (Given the levels of expertise we have in these forums, I have no doubt that someone might find a way to do it.)

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Macbi
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Re: Small Spaceship Syntheses

Post by Macbi » September 3rd, 2020, 11:45 am

mniemiec wrote:
September 3rd, 2020, 11:36 am
Macbi wrote:
September 3rd, 2020, 11:25 am
This reminded me of one of my very first posts on the forum. Would this ... have any advantage?
Something like this could work; unfortunately, synthesizing such a unbroken row of spaceships so close together would be difficult. The hardest part would be that the main spaceship would have to pass through the middle of it; there would have to be a gap that would be closed later. Adding spaceships at the end of a row of existing ones is easy, but inserting the last one into the narrow gap in the middle would be much more challenging. (Given the levels of expertise we have in these forums, I have no doubt that someone might find a way to do it.)
My thought was that since LWSSs are faster than 2c/5, the entire line could be constructed behind the ship and then allowed to catch up.

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wwei23
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Re: Small Spaceship Syntheses

Post by wwei23 » September 3rd, 2020, 1:06 pm

Could some forwards-burning fuse of XWSSes work? I'm not at my computer right now so can't test this out on Golly.
EDIT: Apparently not, but this might work if someone can find the right combination of XWSSes:

Code: Select all

x = 79, y = 55, rule = B3/S23
76b3o$75bo2bo$70b3o5bo$70bo2bo4bo$64b3o3bo7bo$63bo2bo3bo7bo$58b3o5bo3b
o4bobo$58bo2bo4bo3bo$52b3o3bo7bo4bobo$51bo2bo3bo7bo$2b3o4bo36b3o5bo3bo
4bobo$bo2bo3b3o35bo2bo4bo3bo$4bo3bob2o3b3o22b3o3bo7bo4bobo$o3bo4b3o2bo
2bo21bo2bo3bo7bo$4bo4b3o5bo16b3o5bo3bo4bobo$bobo5b3obo3bo16bo2bo4bo3bo
$10b2obo3bo10b3o3bo7bo4bobo$9b2o6bo9bo2bo3bo7bo$14bobo5b3o5bo3bo4bobo$
22bo2bo4bo3bo$10bo11bo7bo4bobo$10bo4b3o4bo7bo$10bo3bo2bo4bo4bobo$17bo
4bo$10bo6bo5bobo$10bo3bobo$10bo2$10bo$10bo$10bo2$10bo$10bo$10bo2$10bo$
10bo$10bo2$10bo$10bo$10bo2$10bo$10bo$10bo2$10bo$10bo$9bobo$9bobo$8b2ob
2o$8bo3bo$8b2ob2o!
EDIT 2: Actually put in the right RLE this time.

MathAndCode
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Re: Small Spaceship Syntheses

Post by MathAndCode » September 3rd, 2020, 7:58 pm

Macbi wrote:
September 3rd, 2020, 11:45 am
mniemiec wrote:
September 3rd, 2020, 11:36 am
Macbi wrote:
September 3rd, 2020, 11:25 am
This reminded me of one of my very first posts on the forum. Would this ... have any advantage?
Something like this could work; unfortunately, synthesizing such a unbroken row of spaceships so close together would be difficult. The hardest part would be that the main spaceship would have to pass through the middle of it; there would have to be a gap that would be closed later. Adding spaceships at the end of a row of existing ones is easy, but inserting the last one into the narrow gap in the middle would be much more challenging. (Given the levels of expertise we have in these forums, I have no doubt that someone might find a way to do it.)
My thought was that since LWSSs are faster than 2c/5, the entire line could be constructed behind the ship and then allowed to catch up.
While LWSSs are faster than 44P5H2V0s, gliders aren't, at least not if one only cares about the orthogonal velocity. This means that the glider stream would fall three cells farther behind the pair of 44P5H2V0s for each five cells that it traveled to the side. Each generation, your lightspeed wave goes forwards three-fifths of a cell relative to the pair of 44P5H2V0s and gets shorter by one cell on each side. This means that for each three cells that the wave gets closer to the 44P5H2V0s, it becomes five cells shorter on each side. Let's suppose that your gliders are coming from below and to the right from a stationary reference frame (from above and to the right from the 44P5H2V0s' reference frame) as in your post. In this case, making sure that the line extends for long enough on the right will not be a problem in terms of clearing the 44P5H2V0s. However, making sure that the line will extend far enough to the left will be. Using the 44P5H2V0s' reference frame, imagine a line with a slope of 0.6 passing just below and to the right of the rightmore 44P5H2V0. One cannot get gliders above that line if they must clear the 44P5H2V0s on the bottom-right side. Because the left edge of the wavefront travels upwards and to the right along a line of slope 0.6 (still from the 44P5H2V0s' reference frame), the lightspeed wave will never get above that same line of slope 0.6 passing just below and to the right of the rightmore 44P5H2V0, so it will not be able to reach a point just below and to the left of the rightmore 44P5H2V0. There is a possible solution, finding a way to create the lightspeed wave using gliders coming from both the bottom-left (top-left from the 44P5H2V0s' reference frame) and the bottom-right (top-right from the 44P5H2V0s' reference frame) so that the middle is patched, but besides that, I don't think that your method will work.

Since at least three or four different users have shared different ideas about how to do this, I may as well contribute mine: I'm wondering whether or not there's some unstable c/2 "spaceship" whose front part decays into the traffic light predecessor in just the right place. This isn't far-fetched—generation 17 of the B-heptomino has the same traffic light predecessor at the front—but unfortunately, it's upside-down relative to how we would want it (and it then reacts with the dodecomino just behind, preventing a traffic light from forming). There doesn't seem to be any viable way to do that using a T-pentomino, but it might be possible using another ancestor of the traffic light predecessor that we want.
Marine has a non-centered Moore neighborhood and at least one elementary gun with a very high period (11,843).
I'm in the process of reducing the glider cost of universal construction.

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Re: Small Spaceship Syntheses

Post by mniemiec » September 4th, 2020, 12:05 am

MathAndCode wrote:
September 3rd, 2020, 7:58 pm
Since at least three or four different users have shared different ideas about how to do this, I may as well contribute mine: I'm wondering whether or not there's some unstable c/2 "spaceship" whose front part decays into the traffic light predecessor in just the right place. This isn't far-fetched—generation 17 of the B-heptomino has the same traffic light predecessor at the front—but unfortunately, it's upside-down relative to how we would want it (and it then reacts with the dodecomino just behind, preventing a traffic light from forming). There doesn't seem to be any viable way to do that using a T-pentomino, but it might be possible using another ancestor of the traffic light predecessor that we want.
That might be possible. However, such a spaceship would have to be "mostly stable" for a very long time to be able to be created a safe distance away, and then slowly creep up to the front ships, and last long enough to spontaneously erupt into a traffic light. It might be possible to do this with a spaceship wick (as has been mentioned earlier) that is ignited like a fuse from the sides sufficiently far away; such a signal could theoretically travel at a speed of c horizontally towards the center. Unfortunately, this method could would be quite painful to implement for an insertion behing the middle ships in a wide flotilla; even more so if multiple similar insertions are desired.

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calcyman
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Re: Small Spaceship Syntheses

Post by calcyman » September 4th, 2020, 7:37 am

We can patch the reaction using NE- and NW-travelling gliders. Here's a simple example that ensures the back part forms correctly; what remains is to construct the two missing ponds:

Code: Select all

x = 337, y = 47, rule = LifeHistory
174.2C$174.C.C$174.C$164.3C$166.C$165.C12$.2C4.2C4.2C4.2C4.2C4.2C4.2C
4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C
4.2C43.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C
4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C4.2C$C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.
C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C
.C3.C.C3.C.C3.C.C3.C.C43.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C
3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.
C3.C.C3.C.C$2.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C
5.C5.C5.C5.C5.C5.C43.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.
C5.C5.C5.C5.C5.C5.C5.C5.C23$31.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C
3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C5.3C3.3C3.3C3.3C
3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C3.3C
3.3C3.3C$30.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.
C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.
C2.C2.C2.C5.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.
C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.C2.
C2.C2.C2.C$33.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C
5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C
5.C5.C5.C5.C$33.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C
5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C5.C
5.C5.C5.C5.C5.C$30.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.
C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C7.C.C
3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.
C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C3.C.C!
...but we can actually use an arbitrary glider synthesis from the front to patch the reaction, because those gliders can be emplaced using kickback reactions.
What do you do with ill crystallographers? Take them to the mono-clinic!

MathAndCode
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Re: Small Spaceship Syntheses

Post by MathAndCode » September 4th, 2020, 9:42 am

mniemiec wrote:
September 4th, 2020, 12:05 am
MathAndCode wrote:
September 3rd, 2020, 7:58 pm
Since at least three or four different users have shared different ideas about how to do this, I may as well contribute mine: I'm wondering whether or not there's some unstable c/2 "spaceship" whose front part decays into the traffic light predecessor in just the right place. This isn't far-fetched—generation 17 of the B-heptomino has the same traffic light predecessor at the front—but unfortunately, it's upside-down relative to how we would want it (and it then reacts with the dodecomino just behind, preventing a traffic light from forming). There doesn't seem to be any viable way to do that using a T-pentomino, but it might be possible using another ancestor of the traffic light predecessor that we want.
That might be possible. However, such a spaceship would have to be "mostly stable" for a very long time to be able to be created a safe distance away, and then slowly creep up to the front ships, and last long enough to spontaneously erupt into a traffic light. It might be possible to do this with a spaceship wick (as has been mentioned earlier) that is ignited like a fuse from the sides sufficiently far away; such a signal could theoretically travel at a speed of c horizontally towards the center. Unfortunately, this method could would be quite painful to implement for an insertion behing the middle ships in a wide flotilla; even more so if multiple similar insertions are desired.
Yes; unless there's a still-life or small constellation that a 44P5H2V0 can preturb to create a mutated B-heptomino (which, depending on what is meant by mutated, would either be illegal or probably still would not work because of the butterfly effect), my method probably won't work. (My first idea was actually crashing XWSSes into the backsparks, but I had already eliminated that by the time that I made my post.) I guess that my Life sense will get better as I participate on the forums and in Conway's Game of Life more. Also, it seems that my my suggestion of having gliders come from two directions could be made to work, although it still looks like the long lines of gliders and LWSSes would be very expensive, and I don't think that the lines of LWSSes could be made with a rake.
Last edited by MathAndCode on September 7th, 2020, 3:42 pm, edited 1 time in total.
Marine has a non-centered Moore neighborhood and at least one elementary gun with a very high period (11,843).
I'm in the process of reducing the glider cost of universal construction.

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wwei23
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Re: Small Spaceship Syntheses

Post by wwei23 » September 7th, 2020, 3:18 pm

When I try the still life core thing with JLS, it basically can't get anywhere?

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Goldtiger997
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Re: Small Spaceship Syntheses

Post by Goldtiger997 » September 19th, 2020, 4:03 am

55P9H3V0 in 271 gliders, which is the first p9 spaceship to be synthesized. I've been working on this one for quite a while:

Code: Select all

x = 4380, y = 341, rule = B3/S23
4065bo$4065bobo$4065b2o23$4036bo$4037b2o6bo6bo$4036b2o5b2o7bobo$4044b
2o6b2o4$3724bo153bobo$2435bo1286b2o154b2o$2421bo13bobo1268bo16b2o154bo
319bo$2422bo12b2o1269bobo489bo$2414bo5b3o1129bo153b2o4b2o160bo323b3o$
43bobo2369b2o1136b2o157bobo153bo5bobo317bo$43b2o2369b2o15bo154bo965b2o
151bo6bo153bobo5b2o319bo$44bo2385bo154bo1120b2o159b2o324b3o$2103bo159b
o166b3o152b3o970bo146b2o164bobo326bo$2101b2o161b2o151bo165bo815bo156b
2o314b2o325bo$2102b2o159b2o153b2o161bobo815bobo151bo3b2o313bo156b2o
168b3o$10bo2406b2o163b2o815b2o153b2o474bo$8bobo19bo1409bobo651bo177bo
1280b2o314b2o158bo159b2o2b2o$9b2o13b3o2b2o1410b2o6bo645bo175bo1137bo
459b2o158b2o158b2o2b2o$26bo2bobo1409bo5bobo643b3o175b3o321b3o146b2o
150bo7b2o4bo153b2o12bo129bo15b2o158b2o21b2o135b2o158b2o158b2o158b2o
158b2o$2bo22bo1422b2o1145bo147bo2bo147bobo6bo2bo3bobo150bo2bo2b2o8b2o
125b2o8b2o5bo2bo2b2o145b2o5bo2bo2b2o17b2o126b2o5bo2bo2b2o145b2o5bo2bo
2b2o2b2o141b2o5bo2bo2b2o2b2o141b2o5bo2bo2b2o2b2o141b2o5bo2bo2b2o2b2o$o
bo2580b2o11bo130bo15bobo13bo135b2o6bobo4b2o151bobo3b2o7b2o2bobo117bobo
2b2o7b2o5bobo3bo2bo141bo2bo5bobo3bo2bo141bo2bo5bobo3bo2bo2bob2o135bo2b
o5bobo3bo2bo2bob2o135bo2bo5bobo3bo2bo2bob2o135bo2bo5bobo3bo2bo2bob2o
135bo2bo5bobo3bo2bo2bob2o$b2o2581bo143bo15bo13bo133b2o10bo8b2o149bo17b
2o119b2o19bo6b2o141b2o8bo6b2o141b2o8bo6b2o2b2obo135b2o8bo6b2o2b2obo
135b2o8bo6b2o2b2obo135b2o8bo6b2o2b2obo135b2o8bo6b2o2b2obo5bo$196bo
1891bo4b2o177b2o4bo302b3o142b3o12b3o14b3o130bobo7b3o9bobo145b3o19bo
119bo17b3o157b3o15b3o139b3o157b3o157b3o157b3o157b3o18b2o$194b2o1892b2o
4b2o164bo10b2o4b2o141bo5bo153bo5bo153bo5bo146bo6bo5bo6bo146bo5bo153bo
5bo153bo5bo12bo140bo5bo153bo5bo153bo5bo153bo5bo153bo5bo16b2o$181bo3bo
9b2o144bo3b2o153b2o3b2o153b2o3b2o153b2o3b2o153b2o3b2o153b2o3b2o153b2o
3b2o153b2o3b2o153b2o3b2o153b2o3b2o153b2o3b2o140bobo3bo6b2o3b2o152bobo
3b2o6bo3bobo139bobo3bobo151bobo3bobo151bobo3bobo148bo2bobo3bobo2bo145b
o2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo9bo135bo2bobo3bobo2b
o145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo
2bo8b2o$180bobobobo146bo6bobobobo153bobobobo153bobobobo153bobobobo153b
obobobo153bobobobo153bobobobo141bo11bobobobo153bobobobo153bobobobo153b
obobobo153bobobobo153bobobobo153bobobobo153bobobobo153bobobobo148bobo
2bobobobo2bobo143bobo2bobobobo2bobo143bobo2bobobobo2bobo143bobo2bobobo
bo2bobo143bobo2bobobobo2bobo143bobo2bobobobo2bobo143bobo2bobobobo2bobo
143bobo2bobobobo2bobo143bobo2bobobobo2bobo8b2o$180bobobobo5bo140bobo4b
obobo157bobo157bobo157bobo157bobo157bobo157bobo144b2o11bobo157bobo157b
obo157bobo157bobo157bobo157bobo157bobo157bobo151bo5bobo5bo145bo5bobo5b
o145bo5bobo5bo145bo5bobo5bo11b2o132bo5bobo5bo145bo5bobo5bo145bo5bobo5b
o145bo5bobo5bo145bo5bobo5bo8bo$181b2ob2o4b2o141b2o6b2ob2o155b2ob2o155b
2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o142b2o11b2ob2o155b2ob2o155b2o
b2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o155b
2ob2o155b2ob2o155b2ob2o16bobo136b2ob2o155b2ob2o155b2ob2o155b2ob2o155b
2ob2o$183bo7b2o150bo159bo159bo145bobo11bo159bo159bo159bo139bo19bo159bo
159bo159bo159bo159bo159bo159bo159bo159bo159bo13bo131bo13bo159bo18bo
140bo159bo159bo159bo159bo20b3o$183bo159bo159bo159bo146b2o11bo159bo159b
o149bo9bo140b2o17bo148bo10bo144bobo12bo159bo12bobo144bo159bo159bo159bo
142bo16bo16bo142bo159bo13b2o129b2o13bo159bo159bo159bo159bo159bo159bo
20bo$184b2o158b2o158b2o158b2o144bo13b2o158b2o158b2o145bobo10b2o137b2o
4b2o13b2o144bobo8b2ob2o143b2o10b2ob2o155b2ob2o10b2o143b2ob2o155b2ob2o
155b2ob2o155b2ob2o140b2o13b2ob2o13b2o140b2ob2o155b2ob2o10bobo129bobo
10b2ob2o155b2ob2o14b2o139b2ob2o155b2ob2o155b2ob2o155b2ob2o37b2o116b2ob
2o19bo$185bo7b2o138b2o10bo159bo159bo147bobo10bo154b3o2bo154b3o2bo145b
2o7b3o2bo143b2o9b3o2bo144b2o7bo2bo2bo142bo10bo2bo2bo153bo2bo2bo10bo
142bo2bo2bo153bo2bo2bo153bo2bo2bo153bo2bo2bo138bobo12bo2bo2bo12bobo
138bo2bo2bo153bo2bo2bo153bo2bo2bo153bo2bo2bo12bobo138bo2bo2bo153bo2bo
2bo153bo2bo2bo153bo2bo2bo35b2o116bo2bo2bo$183bo8b2o138bobo8bo159bo160b
o149b2o7bobo155bo3b2o154bo3b2o153bo4b2o142bo10bo4b2o153bobo2b2o153b2o
3b2o152bobo3b2o141b3o8bobo3bobo151bobo3bobo8b3o140bobo3bobo151bobo3bob
o151bobo3bobo151bobo3bobo151bobo3bobo151bobo3bobo151bobo3bobo13bo137bo
bo3bobo151bobo3bobo151bobo3bobo151bobo3bobo36bo114bobo3bobo$183b2o9bo
139bo8b2o158b2o159b2o148bo8b2o301bo12bobo154bo3b2o159bo159bo318bo149bo
9bo5bo153bo5bo9bo143bo5bo153bo5bo153bo5bo153bo5bo153bo5bo23bo105bo23bo
5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo$668bobo304b2o147bo
bo12b2o153bobo163b2o151b2o474bo187bo446b2o35b2o140bo159bo25b2o105b2o
25bo159bo159bo159bo159bo159bo159bo$336b3o329b2o144b3o159b2o147b2o168b
2o140b3o172bobo1108bobo35bobo138bobo157bobo24bobo103bobo24bobo157bobo
157bobo157bobo157bobo157bobo157bobo$336bo332bo146bo158bo3b3o457bo174bo
1110bo35bo141bo159bo159bo159bo159bo159bo159bo159bo159bo$18bo318bo328bo
148bo11b3o2b3o144bo318b2o138bo334b2o4bo167bo4b2o$19b2o645b2o161bo2bo
147bo317bobo306bo164bobo3b2o167b2o3bobo$18b2o489b2o154bobo4b2o154bo4bo
294b2o168bo308b2o165bo3bobo165bobo3bo$44bo450b2o11b2o162bobo454b2o318b
2o155bobo$36bobo4b2o5b3o443b2o6b2o4bo161bo455bo321b2o161bo15bo$36b2o5b
obo4bo444bo7bobo616b3o324bo22bo140b2o13b2o158b2o147b2o$37bo13bo453bo
314b3o301bo329bo16b2o139bobo13bobo148b2o7bobo145bobo7b2o798b2o$822bo
300bo330b2o15bobo304b2o8bo149bo8b2o788b2o7bobo$821bo623bo7bobo324bo
165bo791b2o6bo$1445b2o159bo1125b3o2bo$502b2o940bobo159b2o1126bo$3bo
499b2o1100bobo1125bo$3b2o497bo611b2o$2bobo1110b2o$1114bo2$18b3o1139b2o
$20bo1138b2o$19bo1089bo51bo$1109b2o$1108bobo6$44b3o$44bo$45bo157$941bo
$939bobo$940b2o14$4379bo$4363bobo11b2o$4363b2o7bo5b2o$4353bo10bo5b2o$
4353bobo15b2o$4353b2o2$4335bo$4336b2o$970bo3364b2o$954bo6bo6b2o3337bo$
952bobo7b2o5b2o3337b2o12bobo$953b2o6b2o3344b2o14b2o$3859bo167bo295bo5b
obo23bobo$3859bobo163bobo302b2o18bo4b2o9bo$3855bo3b2o165b2o3bo285bo12b
o19bobo3bo9bobo$642bo163bobo3047b2o171b2o287bo31b2o14b2o$643b2o162b2o
3046b2o173b2o284b3o26bo$642b2o16bo146bo319bo2724bo181bo309bo$37bo620bo
bo467bo160bo2560bobo181bobo307b3o$37bobo454bo158b2o4b2o151bo313b3o158b
obo2561b2o161bo19b2o138bo17bo141bo5bobo9bo$37b2o453b2o158bobo155bobo5b
o313bo155b2o2723bobo157bobo15bobo139bobo5b2o8bobo$205bo287b2o159bo6bo
149b2o5bobo310bo309bo2571b2o158b2o17b2o124bo14b2o6bo10b2o14bo$36bo166b
obo453b2o157b2o311b3o156bo150bobo2875bo47bo$37b2obobo161b2o282bo171b2o
151bobo310bo157bobob2o151b2o2874b3o47b3o$36b2o2b2o285bo161b2o322b2o
312bo157b2o2b2o$41bo160b2o121bobo160b2o3bo320bo161b2o147b3o157bo157b2o
$198bo3bobo121b2o163b2o483bo465bobo3bo$29b2o2b2o2b2o150b2o2b2o2bobo2bo
146b2o2b2o2bo2bo131b2o15b2o2b2o2bo2bo148b2o2b2o2bo2bo135b2o11b2o2b2o2b
o2bo136bo11b2o2b2o2bo2bo131b2o2b2o11b2o2b2o2bo2bo127b2o2b2o2b2o11b2o2b
2o2bo2bo123bo2bobo2b2o2b2o11b2o2b2o2bo2bo125bo2bo2b2o2b2o11b2o2b2o2bo
2bo125bo2bo2b2o2b2o11b2o2b2o2bo2bo125bo2bo2b2o2b2o11b2o2b2o2bo2bo125bo
2bo2b2o2b2o11b2o2b2o2bo2bo125bo2bo2b2o2b2o11b2o2b2o2bo2bo125bo2bo2b2o
2b2o11b2o2b2o2bo2bo125bo2bo2b2o2b2o11b2o2b2o2bo2bo125bo2bo2b2o2b2o11b
2o2b2o2bo2bo125bo2bo2b2o2b2o11b2o2b2o2bo2bo125bo2bo2b2o2b2o11b2o2b2o2b
o2bo125bo2bo2b2o2b2o11b2o2b2o2bo2bo125bo2bo2b2o2b2o11b2o2b2o2bo2bo125b
o2bo2b2o2b2o11b2o2b2o2bo2bo125bo2bo2b2o2b2o11b2o2b2o2bo2bo125bo2bo2b2o
2b2o11b2o2b2o2bo2bo125bo2bo2b2o2b2o11b2o2b2o2bo2bo125bo2bo2b2o2b2o11b
2o2b2o2bo2bo112bo12bo2bo2b2o2b2o11b2o2b2o2bo2bo12bo$29b2o2b2o2b2o150b
2o2b2o2b2o118bo31b2o2b2o2b4o148b2o2b2o2b4o148b2o2b2o2b4o135b2o11b2o2b
2o2b4o135b2o11b2o2b2o2b4o131b2o2b2o11b2o2b2o2b4o127b2o2b2o2b2o11b2o2b
2o2b4o127b2o2b2o2b2o11b2o2b2o2b4o125b4o2b2o2b2o11b2o2b2o2b4o125b4o2b2o
2b2o11b2o2b2o2b4o125b4o2b2o2b2o11b2o2b2o2b4o125b4o2b2o2b2o11b2o2b2o2b
4o125b4o2b2o2b2o11b2o2b2o2b4o125b4o2b2o2b2o11b2o2b2o2b4o125b4o2b2o2b2o
11b2o2b2o2b4o125b4o2b2o2b2o11b2o2b2o2b4o125b4o2b2o2b2o11b2o2b2o2b4o
125b4o2b2o2b2o11b2o2b2o2b4o125b4o2b2o2b2o11b2o2b2o2b4o125b4o2b2o2b2o
11b2o2b2o2b4o125b4o2b2o2b2o11b2o2b2o2b4o125b4o2b2o2b2o11b2o2b2o2b4o
125b4o2b2o2b2o11b2o2b2o2b4o125b4o2b2o2b2o11b2o2b2o2b4o125b4o2b2o2b2o
11b2o2b2o2b4o110bobo12b4o2b2o2b2o11b2o2b2o2b4o12bobo$24b2o158b2o132b2o
24b2o158b2o158b2o158b2o158b2o158b2o158b2o158b2o158b2o158b2o158b2o158b
2o158b2o158b2o158b2o158b2o158b2o158b2o158b2o158b2o158b2o158b2o158b2o
158b2o158b2o126b2o30b2o27b2o$16b2o5bo2bo2b2o2b2o2b2o137b2o5bo2bo2b2o2b
2o2b2o118b2o17b2o5bo2bo2b2o2b2o2b2o137b2o5bo2bo2b2o2b2o2b2o133b2o2b2o
5bo2bo2b2o2b2o2b2o133b2o2b2o5bo2bo2b2o2b2o2b2o133b2o2b2o5bo2bo2b2o2b2o
2b2o133b2o2b2o5bo2bo2b2o2b2o2b2o129b2o2b2o2b2o5bo2bo2b2o2b2o2b2o129b2o
2b2o2b2o5bo2bo2b2o2b2o2b2o129b2o2b2o2b2o5bo2bo2b2o2b2o2b2o129b2o2b2o2b
2o5bo2bo2b2o2b2o2b2o129b2o2b2o2b2o5bo2bo2b2o2b2o2b2o129b2o2b2o2b2o5bo
2bo2b2o2b2o2b2o129b2o2b2o2b2o5bo2bo2b2o2b2o2b2o129b2o2b2o2b2o5bo2bo2b
2o2b2o2b2o129b2o2b2o2b2o5bo2bo2b2o2b2o2b2o129b2o2b2o2b2o5bo2bo2b2o2b2o
2b2o129b2o2b2o2b2o5bo2bo2b2o2b2o2b2o129b2o2b2o2b2o5bo2bo2b2o2b2o2b2o
129b2o2b2o2b2o5bo2bo2b2o2b2o2b2o129b2o2b2o2b2o5bo2bo2b2o2b2o2b2o129b2o
2b2o2b2o5bo2bo2b2o2b2o2b2o129b2o2b2o2b2o5bo2bo2b2o2b2o2b2o129b2o2b2o2b
2o5bo2bo2b2o2b2o2b2o129b2o2b2o2b2o5bo2bo2b2o2b2o2b2o129b2o2b2o2b2o5bo
2bo2b2o2b2o2b2o129b2o2b2o2b2o5bo2bo2b2o2b2o2b2o$14bo2bo5bobo3bo2bo2bo
2bo135bo2bo5bobo3bo2bo2bo2bo135bo2bo5bobo3bo2bo2bo2bo129b2obo2bo2bo5bo
bo3bo2bo2bo2bo129b2obo2bo2bo5bobo3bo2bo2bo2bo129b2obo2bo2bo5bobo3bo2bo
2bo2bo129b2obo2bo2bo5bobo3bo2bo2bo2bo129b2obo2bo2bo5bobo3bo2bo2bo2bo
129bo2bo2bo2bo5bobo3bo2bo2bo2bo129bo2bo2bo2bo5bobo3bo2bo2bo2bo129bo2bo
2bo2bo5bobo3bo2bo2bo2bo129bo2bo2bo2bo5bobo3bo2bo2bo2bo129bo2bo2bo2bo5b
obo3bo2bo2bo2bo129bo2bo2bo2bo5bobo3bo2bo2bo2bo129bo2bo2bo2bo5bobo3bo2b
o2bo2bo129bo2bo2bo2bo5bobo3bo2bo2bo2bo129bo2bo2bo2bo5bobo3bo2bo2bo2bo
129bo2bo2bo2bo5bobo3bo2bo2bo2bo129bo2bo2bo2bo5bobo3bo2bo2bo2bo129bo2bo
2bo2bo5bobo3bo2bo2bo2bo129bo2bo2bo2bo5bobo3bo2bo2bo2bo129bo2bo2bo2bo5b
obo3bo2bo2bo2bo129bo2bo2bo2bo5bobo3bo2bo2bo2bo129bo2bo2bo2bo5bobo3bo2b
o2bo2bo129bo2bo2bo2bo5bobo3bo2bo2bo2bo129bo2bo2bo2bo5bobo3bo2bo2bo2bo
129bo2bo2bo2bo5bobo3bo2bo2bo2bo129bo2bo2bo2bo5bobo3bo2bo2bo2bo$14b2o8b
o6b2o2bobo136b2o8bo6b2o2bobo136b2o8bo6b2o2bobo130bob2o2b2o8bo6b2o2bobo
130bob2o2b2o8bo6b2o2bobo130bob2o2b2o8bo6b2o2bobo130bob2o2b2o8bo6b2o2bo
bo124bo5bob2o2b2o8bo6b2o2bobo131bobo2b2o8bo6b2o2bobo131bobo2b2o8bo6b2o
2bobo131bobo2b2o8bo6b2o2bobo131bobo2b2o8bo6b2o2bobo131bobo2b2o8bo6b2o
2bobo131bobo2b2o8bo6b2o2bobo131bobo2b2o8bo6b2o2bobo131bobo2b2o8bo6b2o
2bobo131bobo2b2o8bo6b2o2bobo131bobo2b2o8bo6b2o2bobo131bobo2b2o8bo6b2o
2bobo131bobo2b2o8bo6b2o2bobo131bobo2b2o8bo6b2o2bobo131bobo2b2o8bo6b2o
2bobo131bobo2b2o8bo6b2o2bobo131bobo2b2o8bo6b2o2bobo131bobo2b2o8bo6b2o
2bobo131bobo2b2o8bo6b2o2bobo131bobo2b2o8bo6b2o2bobo118b2o11bobo2b2o8bo
6b2o2bobo11b2o$21b3o12bo144b3o12bo128b3o13b3o12bo144b3o12bo144b3o12bo
144b3o12bo144b3o12bo126b2o16b3o12bo133bo10b3o12bo133bo10b3o12bo133bo
10b3o12bo133bo10b3o12bo133bo10b3o12bo133bo10b3o12bo133bo10b3o12bo133bo
10b3o12bo133bo10b3o12bo133bo10b3o12bo133bo10b3o12bo133bo10b3o12bo133bo
10b3o12bo133bo10b3o12bo133bo10b3o12bo133bo10b3o12bo133bo10b3o12bo133bo
10b3o12bo133bo10b3o12bo118bobo12bo10b3o12bo12bobo$20bo5bo153bo5bo140bo
12bo5bo153bo5bo153bo5bo153bo5bo153bo5bo135b2o16bo5bo153bo5bo153bo5bo
153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo
5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo
130bo22bo5bo22bo$16bo2bobo3bobo2bo145bo2bobo3bobo2bo135bo9bo2bobo3bobo
2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bo
bo2bo135b2o8bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2b
obo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo
2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo
145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo
2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bo
bo2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo$15bobo2bobobobo2bobo143bobo
2bobobobo2bobo143bobo2bobobobo2bobo143bobo2bobobobo2bobo143bobo2bobobo
bo2bobo143bobo2bobobobo2bobo143bobo2bobobobo2bobo133b2o8bobo2bobobobo
2bobo143bobo2bobobobo2bobo143bobo2bobobobo2bobo143bobo2bobobobo2bobo
143bobo2bobobobo2bobo143bobo2bobobobo2bobo143bobo2bobobobo2bobo143bobo
2bobobobo2bobo143bobo2bobobobo2bobo143bobo2bobobobo2bobo143bobo2bobobo
bo2bobo143bobo2bobobobo2bobo143bobo2bobobobo2bobo143bobo2bobobobo2bobo
143bobo2bobobobo2bobo143bobo2bobobobo2bobo143bobo2bobobobo2bobo143bobo
2bobobobo2bobo143bobo2bobobobo2bobo143bobo2bobobobo2bobo143bobo2bobobo
bo2bobo$16bo5bobo5bo145bo5bobo5bo132b2o11bo5bobo5bo145bo5bobo5bo145bo
5bobo5bo145bo5bobo5bo145bo5bobo5bo136bo8bo5bobo5bo145bo5bobo5bo145bo5b
obo5bo145bo5bobo5bo145bo5bobo5bo145bo5bobo5bo145bo5bobo5bo145bo5bobo5b
o145bo5bobo5bo122bo22bo5bobo5bo22bo117b2o3bo5bobo5bo3b2o135b2o3bo5bobo
5bo3b2o135b2o3bo5bobo5bo3b2o135b2o3bo5bobo5bo3b2o135b2o3bo5bobo5bo3b2o
135b2o3bo5bobo5bo3b2o135b2o3bo5bobo5bo3b2o135b2o3bo5bobo5bo3b2o135b2o
3bo5bobo5bo3b2o135b2o3bo5bobo5bo3b2o135b2o3bo5bobo5bo3b2o$21b2ob2o155b
2ob2o136bobo16b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o155b
2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o
128bo26b2ob2o26bo117bo2bo7b2ob2o7bo2bo133bo2bo7b2ob2o7bo2bo133bo2bo7b
2ob2o7bo2bo133bo2bo7b2ob2o7bo2bo133bo2bo7b2ob2o7bo2bo133bo2bo7b2ob2o7b
o2bo133bo2bo7b2ob2o7bo2bo133bo2bo7b2ob2o7bo2bo133bo2bo7b2ob2o7bo2bo
133bo2bo7b2ob2o7bo2bo133bo2bo7b2ob2o7bo2bo$23bo159bo140bo18bo159bo159b
o159bo159bo136b3o20bo159bo159bo159bo159bo159bo159bo159bo159bo128b3o28b
o28b3o116b2o10bo10b2o135b2o10bo10b2o135b2o10bo10b2o135b2o10bo10b2o135b
2o10bo10b2o135b2o10bo10b2o135b2o10bo10b2o135b2o10bo10b2o135b2o10bo10b
2o135b2o10bo10b2o135b2o10bo10b2o$23bo159bo159bo159bo159bo159bo159bo
138bo20bo159bo159bo159bo159bo159bo159bo21bo115bo21bo143bo15bo15bo116bo
26bo26bo111bo20bo20bo138bo159bo159bo159bo159bo159bo159bo159bo159bo159b
o$21b2ob2o155b2ob2o139b2o14b2ob2o155b2ob2o155b2ob2o155b2ob2o116b2o37b
2ob2o135bo19b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob
2o18bo117bo18b2ob2o139bobo13b2ob2o13bobo114b2o23b2ob2o23b2o112b2o16b2o
b2o16b2o137b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob2o155b2ob
2o155b2ob2o155b2ob2o155b2ob2o$20bo2bo2bo153bo2bo2bo138bobo12bo2bo2bo
153bo2bo2bo153bo2bo2bo153bo2bo2bo116b2o35bo2bo2bo153bo2bo2bo153bo2bo2b
o153bo2bo2bo153bo2bo2bo153bo2bo2bo153bo2bo2bo153bo2bo2bo17b3o113b3o17b
o2bo2bo139b2o12bo2bo2bo12b2o114bobo22bo2bo2bo22bobo110b2o16bo2bo2bo16b
2o135bo2bo2bo153bo2bo2bo153bo2bo2bo153bo2bo2bo153bo2bo2bo153bo2bo2bo
153bo2bo2bo153bo2bo2bo153bo2bo2bo153bo2bo2bo$19bobo3bobo151bobo3bobo
137bo13bobo3bobo151bobo3bobo151bobo3bobo151bobo3bobo114bo36bobo3bobo
151bobo3bobo151bobo3bobo151bobo3bobo151bobo3bobo151bobo3bobo151bobo3bo
bo151bobo3bobo151bobo3bobo151bobo3bobo151bobo3bobo151bobo3bobo148bo2bo
bo3bobo2bo12bo119bo12bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo
2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bobo2bo145bo2bobo3bo
bo2bo145bo2bobo3bobo2bo128b2o11bo6bobo3bobo6bo11b2o$20bo5bo153bo5bo
153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo
5bo153bo5bo153bo5bo153bo5bo153bo5bo153bo5bo148b3o2bo5bo2b3o143b3o2bo5b
o2b3o139b3o2bo3bo5bo3bo2b3o6bo121bo6b3o2bo3bo5bo3bo2b3o135b3o2bo3bo5bo
3bo2b3o135b3o2bo3bo5bo3bo2b3o135b3o2bo3bo5bo3bo2b3o135b3o2bo3bo5bo3bo
2b3o135b3o2bo3bo5bo3bo2b3o135b3o2bo3bo5bo3bo2b3o135b3o2bo3bo5bo3bo2b3o
124b2o10bo2b3o2bo5bo2b3o2bo10b2o$23bo159bo159bo159bo159bo159bo159bo
159bo159bo159bo149bobo7bo7bobo149bo159bo159bo159bo159bo159bo159bo152bo
6bo6bo11b3o117b3o11bo6bo6bo7b2ob2o121b2ob2o7bo6bo6bo7b2ob2o121b2ob2o7b
o6bo6bo7b2ob2o121b2ob2o7bo6bo6bo7b2ob2o121b2ob2o7bo6bo6bo7b2ob2o121b2o
b2o7bo6bo6bo7b2ob2o121b2ob2o7bo6bo6bo7b2ob2o121b2ob2o7bo6bo6bo7b2ob2o
116bo4b2ob2o3bo10bo10bo3b2ob2o4bo$22bobo157bobo157bobo157bobo157bobo
157bobo157bobo157bobo157bobo157bobo149b2o6bobo6b2o149bobo157bobo157bob
o157bobo157bobo157bobo157bobo157bobo157bobo13b2ob2o121b2ob2o13bobo13b
2ob2o121b2ob2o13bobo13b2ob2o121b2ob2o13bobo13b2ob2o121b2ob2o13bobo13b
2ob2o121b2ob2o13bobo13b2ob2o121b2ob2o13bobo13b2ob2o121b2ob2o13bobo13b
2ob2o121b2ob2o13bobo13b2ob2o$23bo159bo159bo159bo159bo159bo159bo159bo
159bo159bo150bo8bo8bo146bo3bo3bo151bo3bo3bo151bo3bo3bo151bo3bo3bo151bo
3bo3bo151bo3bo3bo151bo3bo3bo151bo3bo3bo18bo113bo18bo3bo3bo151bo3bo3bo
151bo3bo3bo151bo3bo3bo151bo3bo3bo151bo3bo3bo151bo3bo3bo151bo3bo3bo151b
o3bo3bo$1777b3o7b3o147b3o7b3o147b3o7b3o147b3o7b3o147b3o7b3o147b3o7b3o
147b3o7b3o147b3o7b3o15bo115bo15b3o7b3o147b3o7b3o147b3o7b3o147b3o7b3o
147b3o7b3o147b3o7b3o147b3o7b3o147b3o7b3o147b3o7b3o$1776bo13bo145bo13bo
145bo13bo145bo13bo145bo13bo145bo13bo134bo10bo13bo10bo134bo13bo14b3o
111b3o14bo13bo145bo13bo145bo13bo145bo13bo145bo13bo145bo13bo145bo13bo
145bo13bo129bo15bo13bo15bo$1776b2o11b2o145b2o11bo147bo11bo14bo117bo14b
o11bo138b3o6bo11bo6b3o138bo11bo135b2o10bo11bo10b2o135bo11bo147bo11bo
147bo11bo147bo11bo4b2o135b2o4bo11bo4b2o10bo113bo10b2o4bo11bo4b2o135b2o
4bo11bo4b2o135b2o4bo11bo4b2o135b2o4bo11bo4b2o124b2o9b2o4bo11bo4b2o9b2o
$1948bo149bo9bo13b2o119b2o13bo9bo141bo7bo9bo7bo141bo9bo135bobo11bo9bo
11bobo135bo9bo12b3o119b3o12bo9bo149bo9bo149bo9bo4bo2bob2o127b2obo2bo4b
o9bo4bo2bob2o6bobo109bobo6b2obo2bo4bo9bo4bo2bob2o127b2obo2bo4bo9bo4bo
2bob2o127b2obo2bo4bo9bo4bo2bob2o127b2obo2bo4bo9bo4bo2bob2o119bobo5b2ob
o2bo4bo9bo4bo2bob2o5bobo$1792bobo137bobo13b2o147b2o9b2o13b2o117b2o13b
2o8bo141bo9bo7bo9bo141bo7bo151bo7bo151bo7bo15bo119bo15bo7bo151bo7bo
151bo7bo5bo2bob2o127b2obo2bo5bo7bo5bo2bob2o6b2o111b2o6b2obo2bo5bo7bo5b
o2bob2o127b2obo2bo5bo7bo5bo2bob2o127b2obo2bo5bo7bo5bo2bob2o127b2obo2bo
5bo7bo5bo2bob2o127b2obo2bo5bo7bo5bo2bob2o$1611b3o19b3o156b2o139b2o332b
2o149b2o7b2o112bo36b2o7b2o36bo112b2o7b2o149b2o7b2o13bo121bo13b2o7b2o
149b2o7b2o149b2o7b2o5b2o135b2o5b2o7b2o5b2o135b2o5b2o7b2o5b2o6bo121bo6b
2o5b2o7b2o5b2o6bo121bo6b2o5b2o7b2o5b2o6bo121bo6b2o5b2o7b2o5b2o6bo121bo
6b2o5b2o2b3o2b2o5b2o6bo$1613bo19bo148b2o9bo139bo9b2o596b2o81b2o1095bob
o119bobo35bobo119bobo35bobo119bobo35bobo119bobo35bobo$1612bo21bo148b2o
2bo151bo2b2o183b2o109b2o300bobo81bobo609b3o3bo121bo3b3o349bo2bo119bo2b
o33bo2bo119bo2bo33bo2bo119bo2bo33bo2bo119bo2bo33bo2bo$1782bo3b2o6b3o
133b3o6b2o3bo181b2o111b2o997bo2b2o121b2o2bo352b2o121b2o35b2o121b2o35b
2o121b2o35b2o121b2o35b2o$1786bobo5bo137bo5bobo187bo109bo998bo3bobo119b
obo3bo$1795bo135bo$2118b3o125b3o$2118bo129bo2069b2o10bo25bo10b2o$2119b
o127bo983b2o141b2o181b3o127b3o487b2o140b2o9b2o23b2o9b2o$2094b3o171b2o
960bobo141bobo182bo127bo490b2o6b2o126bo3bo10bobo5b3o15bobo10bo3bo$
2096bo15b2o154bobo961bo141bo183bo129bo488bo8bobo125b2o23bo31b2o$2095bo
16bobo153bo1917bo126bobo22bo32bobo$2112bo2237b2o$4349b2o$2268b2o2081bo
$2267b2o976b3o111b3o824b2o$2269bo975bo115bo823b2o126bo59bo$3246bo113bo
826bo125b2o57b2o$2258b2o2052bobo57bobo$2257bobo$2259bo!
Continuous synthesis:

Code: Select all

x = 1173, y = 1173, rule = B3/S23
1171bo$1156bo13bo$1156bobo5bo5b3o$1147bo8b2o5bo$1145b2o16b3o$1146b2o2$
29bo$30bo$28b3o$bo$2bo14bo$3o12bobo$16b2o6bo1123bo$22bobo1119bo3bobo9b
o$23b2o1117b2o4b2o8b2o$9bobo1131b2o14b2o$10b2o$10bo1126bobo$1137b2o$
35bo1102bo$33bobo$34b2o$10bobo1147bobo$11b2o1147b2o$11bo1149bo3$5bo
1161bo$6b2o1157b2o$5b2o1159b2o27$17bobo$18b2o$18bo3$1149bo$1147b2o$
1148b2o8$98bo$99b2o$44bobo51b2o984bo$45b2o1036bo$45bo1037b3o$1069bo19b
o$41bobo1023b2o18b2o$42b2o49bo974b2o18b2o31bobo$42bo51bo1026b2o$92b3o
1027bo$88bo$89b2o1033bobo$59bo28b2o1023bo10b2o$60bo1051bo12bo$58b3o
1051b3o14$77bobo1013bobo$78b2o1013b2o$78bo1015bo$69bobo1029bobo$70b2o
1029b2o$70bo1031bo14$92bo$90bobo$91b2o4$1011bobo$1011b2o$1012bo59bo$
1071bo$92bobo37bo938b3o$93b2o38bo$93bo37b3o3$128bo882bobo$129b2o880b2o
$128b2o8bo873bo$136bobo932bo$137b2o930b2o$112bo894bo62b2o$113b2o892bob
o$112b2o893b2o$137bo$135bobo$136b2o3$128bo915bo6bo$129b2o27bo883b2o6bo
$128b2o26bobo884b2o5b3o$157b2o$132bobo$133b2o$133bo20$959bo$171bo6bo
778b2o$169bobo7b2o777b2o$170b2o6b2o2$183bo$181bobo$182b2o2$186bo$187b
2o781bo$186b2o780b2o$969b2o$964bo$964bobo$964b2o9$197bo$195bobo$196b2o
14bobo$213b2o$213bo2$952bo$952bobo$952b2o6$935bo$935bobo$935b2o2$213bo
$211bobo$212b2o720bo$934bobo$934b2o3$256bobo$257b2o$257bo2$943bo$942bo
$942b3o3$256bobo688bo$257b2o686b2o$257bo679bo8b2o$937bobo$937b2o$262bo
$260bobo$261b2o$938bo$938bobo$938b2o4$917bo$917bobo$917b2o$941bobo$
941b2o$942bo20$310bo$311b2o584bo6bo$310b2o583b2o7bobo$896b2o6b2o2$892b
o$892bobo$892b2o2$889bo$299bo587b2o$300b2o586b2o$299b2o$305bo$303bobo$
280bo23b2o$281bo$279b3o3$270bobo$271b2o$271bo2$878bo$878bobo$861bobo
14b2o$861b2o$862bo2$317bo$315bobo$316b2o11$339bo$337bobo$338b2o2$857bo
$857bobo$340bo516b2o$338bobo$339b2o$856bo$854b2o$855b2o2$864bo$863bo$
863b3o11$811bo$325bo485bobo$326bo484b2o$324b3o2$364bobo$365b2o476bo$
365bo475b2o$842b2o6$351bo469bo$352b2o465b2o$351b2o467b2o10$796bo$795bo
$795b3o$379bo$377bobo$378b2o$794bo$388bo405bobo$389bo404b2o$360bobo18b
o5b3o420bobo$361b2o19b2o426b2o$361bo19b2o407bo20bo$789bo$789b3o$384bo$
385b2o$384b2o2$776bo$775bo$775b3o3$385bobo$386b2o$386bo8$411bo$409bobo
379bo$410b2o379bobo$791b2o$772bo$770b2o$771b2o5$390bo$391b2o$390b2o10$
404bo$405b2o$404b2o3bo$410b2o5bo$409b2o7bo$416b3o7$416bobo$417b2o$417b
o$411bobo$412b2o$412bo3$425bo$426b2o$425b2o2$428bo$429b2o$428b2o40$
460bo$461b2o$460b2o2$474bo$475b2o$474b2o$478bo$479b2o$478b2o6$685bo$
684bo$684b3o$658bo$657bo$657b3o5$670bobo$670b2o$671bo2$666bobo$666b2o$
667bo3$656bobo$656b2o$657bo4$523bo$521bobo$522b2o2$515bo$513bobo$514b
2o16$531bo$532b2o$531b2o2$649bobo$649b2o$650bo73$643bo$537b3o102b2o$
539bo102bobo$538bo21$657bo$656b2o5b3o$656bobo4bo$664bo5$516bo$516b2o$
515bobo3$531b3o135bo$533bo134b2o$532bo135bobo8$494b3o160b3o$496bo160bo
$495bo162bo$661b2o$661bobo$661bo2$673b2o$497b2o174bobo$496bobo7bo166bo
$498bo7b2o$505bobo4$504b2o$503bobo$505bo$495b3o$497bo191bo$479b2o15bo
191b2o$478bobo207bobo$480bo11b2o200b2o$491bobo200bobo$493bo200bo4$485b
2o$484bobo$486bo$468b2o$467bobo$469bo223b2o$463b3o226b2o$465bo228bo$
458bo5bo$458b2o$457bobo6$449b3o$451bo$450bo2$710b3o$710bo$444b2o265bo$
443bobo$445bo19$418bo$418b2o$417bobo$731b2o$730b2o$406b2o324bo$405bobo
$407bo3$418bo$418b2o$417bobo$749b2o$422b2o324b2o21b2o$423b2o325bo20bob
o2b3o$413b2o7bo348bo4bo$414b2o361bo$413bo2$406b2o$407b2o$406bo2$400b2o
374b2o$399bobo373b2o$401bo375bo$406b2o353b2o$405bobo353bobo$380b2o3b3o
19bo353bo$379bobo5bo$381bo4bo$399b2o$398bobo$400bo$394b3o366b2o$396bo
365b2o$395bo368bo$381bo$381b2o$380bobo381bo7b3o$763b2o7bo32b3o$763bobo
7bo31bo$806bo2$398b2o387b2o$397bobo386b2o$399bo388bo3$388b2o$389b2o6b
3o$388bo10bo$398bo$360b2o449b2o$359bobo449bobo$361bo449bo3$358b2o453b
2o$359b2o451b2o$358bo455bo3$348b2o473b2o$349b2o471b2o$348bo475bo2$798b
2o$371b3o423b2o$367bo5bo425bo$367b2o3bo$366bobo9$363b2o$364b2o$363bo3$
812b3o34b2o$812bo35b2o$813bo36bo2$856bo$317b3o535b2o$319bo535bobo$318b
o2$858b2o$857b2o9bo$859bo7b2o$867bobo$350b2o$351b2o$350bo26$279b2o$
278bobo$280bo3$276b3o$278bo$277bo$915b2o$857b3o54b2o$857bo58bo$858bo
37$267bo$267b2o$266bobo2$943b2o$943bobo10bo$943bo11b2o$955bobo11$207bo
$207b2o$206bobo37$159b2o$160b2o$159bo38$1002bo$1001b2o$1001bobo2$131b
2o$119bo10bobo$119b2o11bo$118bobo27$126b2o917b2o$125bobo917bobo$127bo
917bo6$130b2o$129bobo$131bo912b3o6b2o$1044bo7b2o$1045bo8bo4$1050bo$
1049b2o$110b2o6b2o929bobo22b2o$109bobo7b2o952b2o$111bo6bo956bo2$1065b
3o$1065bo$1066bo$73b2o38b3o982b2o$72bobo14bo25bo943b2o37bobo$74bo14b2o
23bo944bobo36bo$88bobo968bo2$97b2o$96bobo$98bo2$1063b3o$1063bo$1064bo
2$58b2o1004bo48b2o$57bobo1003b2o48bobo$59bo20b2o981bobo25b2o20bo$81b2o
1007b2o$80bo1011bo$108b3o$110bo$95bo13bo$95b2o$94bobo977b3o$1074bo$
1075bo3$1075bo$1074b2o$1074bobo$61b2o1047b2o$60bobo1047bobo$62bo1047bo
8$89bo$89b2o$88bobo3$1088bo$1087b2o$1087bobo3$78bo$78b2o1046b2o$77bobo
1046bobo$1126bo3$9b2o1151b2o$10b2o60b2o1087b2o$9bo63b2o1088bo$72bo3$
1105b2o$33b3o1068b2o25bo$35bo1070bo23b2o$34bo1095bobo2$12b3o1143b3o$
14bo1096bo46bo$13bo1096b2o47bo$1110bobo3$13b2o47bo1095b2o$12bobo47b2o
1094bobo$14bo14b2o30bobo1094bo$30b2o$29bo2$1115b2o$1114b2o$1116bo3$11b
3o9b2o1123b2o9b3o$13bo8bobo6bo1116bobo8bo$7b2o3bo11bo6b2o1115bo11bo3b
2o$6bobo21bobo1131bobo$8bo1155bo$1142b3o$1142bo$1143bo2$6b2o1157b2o$5b
obo1157bobo$7bo1157bo!
We now have syntheses of spaceships of all periods from 2 to 10 (which we'll be able to seen on Catagolue once the update process happens)! At the end of last year we only had 6 out of those 9 periods.

User avatar
wwei23
Posts: 1557
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

Re: Small Spaceship Syntheses

Post by wwei23 » September 19th, 2020, 9:07 am

Goldtiger997 wrote:
September 19th, 2020, 4:03 am
55P9H3V0 in 271 gliders, which is the first p9 spaceship to be synthesized. I've been working on this one for quite a while:
AMAZING!!! How, though? I see blinkers in the final seed, which would make the LLS still life method useless.
(I've also tried similar things using JLS instead of LLS. It didn't work for me.)

User avatar
Goldtiger997
Posts: 628
Joined: June 21st, 2016, 8:00 am

Re: Small Spaceship Syntheses

Post by Goldtiger997 » October 1st, 2020, 9:18 am

wwei23 wrote:
September 19th, 2020, 9:07 am
AMAZING!!! How, though? I see blinkers in the final seed, which would make the LLS still life method useless.
(I've also tried similar things using JLS instead of LLS. It didn't work for me.)
Thanks! I'll try to give an explanation for how I found the synthesis. Sorry for not replying earlier.

Actually I did use LLS to assist in finding the synthesis (I did many different LLS searches). With LLS I can still restrict a region to be period 2 for the first few generations, so it's not a problem for LLS to find methods that involve blinkers. However, I don't usually bother to try this and instead just stick to restricting areas to be stable for simplicity and faster searching. In fact, in all of my LLS searches that I did for this synthesis, I restricted regions to being completely stable (not p2). All the blinkers were placed by me.

What follows is a simplified timeline:

I initially tried searches for the entire spaceship at once, but any search with a reasonable population bound was taking too long, so I realised I needed to break up the search and do it in regions. The spaceship is "linked together" by region of stable cells (marked on left in the pattern below), so I decided to try to individually search for the different parts of the spaceship that connect to the stable regions (specifically the p9 part at the bottom and the wings at the top).

Code: Select all

x = 21, y = 13, rule = LifeHistory
6.3A3.3A$2.A.2A3.A.A3.2A.A$.3A3.A.C.C.A3.3A$A3.A4.C.C4.A3.A$.A7.C.C7.
A$8.A.A.A$8.A.A.A2$10.A$9.A.A$7.2A3.2A$7.A.A.A.A$7.2A3.2A!
The Top

After some playing around with the stable area and population restriction, I found the following predecessor for the top:

Code: Select all

x = 35, y = 12, rule = LifeHistory
10.2A11.2A$10.A13.A$9.3A3.C3.C3.3A$9.A5.C3.C5.A$9.A.A2.A5.A2.A.A$2.A
2.2A2.2A2.A.A3.A.A2.2A2.2A2.A$A.A2.A3.2A3.A.A.A.A3.2A3.A2.A.A$.2A7.A
5.A.A5.A7.2A$6.A3.A4.A.A.A4.A3.A$6.A3.A4.A.A.A4.A3.A$6.A2.A6.A.A6.A2.
A$7.A.A7.A7.A.A!
The majority of the good-looking predecessors used those tub-hooks and the duoplets marked above in white, so I continued doing searches, but with the assumption of the existence of the aforementioned tub-hooks and duoplets to speed up the searches. Nothing was looking too promising, but eventually I found the pattern shown on the left in the codebox below. It doesn't look that good at first glance, but advancing it 4 generations looked a lot more promising (shown in the middle, with a simplification shown on the right) as it looked quite simple. Also, I found a method of placing the douplets through manual experimentation (shown at the bottom):

Code: Select all

x = 79, y = 35, rule = B3/S23
2b2o$14b3o14bo12bo$bo8b2o4bo14b2o12b2o$o2bo4bo2b7o12bobo5bo29bo$bobo4b
2o6b2o20b2obo6bo19b2obo$2bo10b3o15b2o2bo4bo6b2o16bo4bo$3b3o10bo18bo5bo
bob2o18bo5bobo$6bo4b3o2b2o18bo3b2o24bo3b2o$5bobo2bo2bo2b2o17bobo2b2o
23bobo2b2o$4bobo2bobo2b2obo16bobo2bobo2b2o2b2o14bobo2bobo2b2o2bo$4bo5b
o4bo2bo15bo5bo2bo2bo17bo5bo2bo2bo$5bo8bo3bo16bo7bo2bo18bo7bo2bo$3bobo
8b2o17bobo8b2o17bobo8b2o$3b2o28b2o28b2o5$37b2o$36b3o$36b2o2$34b2o$33bo
2bo$34bobo$35bo$36b3o$33bo5bo$32bobo3bobo$33bobobobo$35bobo$34bobobo$
34bobobo$35bobo$36bo!
The pond+spark didn't look particularly specific, so I looked for some replacements with spark search, and I found a glider+beehive method that would leave good clearance for the bottom. I then searched for a pattern that could react with a tub (boat didn't work out) from the top as required. Spark_search couldn't find anything, so I did more LLS searches. It was difficult to find things that didn't interfere with the addition of the douplets: I was only able to find one method (on the left in the codebox below). It was looking good after some manual rewinding (next two patterns). Using spark_search I found that the top could be done with a boat+glider, but the left still eluded me. I did find a method (see next pattern), but it interfered with the glider+beehive, so I turned to LLS and spark_search, finding the rightmost pattern in the following codebox which left plenty of clearance for the glider+beehive:

Code: Select all

x = 98, y = 33, rule = B3/S23
84bo$85b2o$84b2o5bo$92b2o$64bo26b2o$62bobo$63b2o2$64bo29bo$63bobo27bob
o$54bo8b2o28b2o$55bo$53b3o24bo$43b2o33bobo$20b5o19bo11b3o20b2o$22b2o$
4bobobo14bo2b2o14b2o2b2o14b2o2b2o18bo2bo2b2o2b2o$2b2o2b2o14b2o2b2o10bo
3b2o2b2o14b2o2b2o6bo11b4o2b2o2b2o$bo19bo14bob2o35bo$2b2o2b2o14b2o2b2o
11bo2b2o2b2o10b2o2b2o2b2o5b3o12b2o2b2o2b2o$4bo2bo16bo2bo13bo2bo2bo10bo
2bo2bo2bo9b3o8bo2bo2bo2bo$2o2b2o14bo3b2o15bo2b2o13bobo2b2o13bo9bobo2b
2o$20b2o18bo19bo17bo11bo$19b3o$6bo12b2o5bo19bo6bo12bo29bo$5bobo17bobo
17bobo5b2o10bobo27bobo$6bo19bo19bo5bobo6b2o3bo24b2o3bo$60bo2bo26bo2bo$
61b2o28b2o2$81bo$81b2o$80bobo!
I could now assemble the top after doing one final spark_search for the activation of the loaf with tail:

Code: Select all

x = 65, y = 44, rule = B3/S23
42bobo$42b2o$43bo2$25bo$23bobo$24b2o$12bo$13bo$11b3o5bo25bo$20bo23bo$
18b3o18bobo2b3o$39b2o$40bo$35bo$33b2o$30bo3b2o$23bo7bo9bo$22bobo4b3o8b
obo$6bo15b2o17b2o15bo$7b2o47b2o$6b2o49b2o4$obo12bo2bo2b2o2b2o11b2o2b2o
2bo2bo12bobo$b2o12b4o2b2o2b2o11b2o2b2o2b4o12b2o$bo31b2o28bo$17b2o2b2o
2b2o5bo2bo2b2o2b2o2b2o$17bo2bo2bo2bo5bobo3bo2bo2bo2bo$5bo12bobo2b2o8bo
6b2o2bobo12bo$5b2o12bo10b3o12bo12b2o$4bobo22bo5bo22bobo$25bo2bobo3bobo
2bo$24bobo2bobobobo2bobo$20b2o3bo5bobo5bo3b2o$19bo2bo7bobobo7bo2bo$20b
2o8bobobo8b2o$31bobo$32bo2$8b2o45b2o$7bobo45bobo$9bo45bo!
The Bottom

The hardest part was now done, so I needed to work on the bottom part. Using LLS, the least-population method I found was the first pattern in the codebox below. It looked good, but the bits on the sides looked hard to make. A very simple modification would turn those bits into pre-TLs, so I searched for predecessors that used pre-TL's instead. Meanwhile, I tried to find a method of inserting the pre-TLs that fit with the synthesis for the top part. I found a nice result inspired by spark_search (the next pattern in the code box below). This is where the blinkers came from. Anyway, after a bunch of fiddling around with stable area and population restrictions, I found a method that looked viable (see next pattern). I found out that the eater-plus-loaf structures could be built from a still-life + a douplet spark and a glider, and the TL could be inserted by sparking a blinker (see below):

Code: Select all

x = 105, y = 22, rule = B3/S23
64bo5bo$5b2o3b2o51bobo3bobo$5bobobobo52bobobobo24bo6bo$7bobo56bobo24b
3o6bo$6b2ob2o54b2ob2o17b2o3bo9bo$8bo58bo19b4o2bo$8bo58bo20b2o4bo6bobo$
6b2ob2o54b2ob2o25bo5bo2bo$5bo2bo2bo52bo2bo2bo23b2o4bo2bo$b2obobo3bobob
2o29bo10bo2bo3bobo3bobo3bo2bo22bo2bo$3o2bo5bo2b3o23b3o2bo11bo2b2o2bo5b
o2b2o2bo13b3o7bo2bo$2bo11bo18b2ob2o7bo13bo7bo7bo17bo8bobo$33b2ob2o28bo
bo23bo$4bo7bo50bo3bo3bo$4b3o3b3o48b3o7b3o$2bo2bob3obo2bo45bo13bo$6b2ob
2o17b3o29b2o11b2o$30bo31bo9bo$29bo32b2o7b2o$62b3ob3ob3o$67bo$67bo!
After I found a method of inserting the douplet spark that fit with everything else and did some assembly, I had a complete method for the bottom:

Code: Select all

x = 51, y = 39, rule = B3/S23
26b2o$25bo2bo$25bobo$26bo$23b3o$22bo5bo$21bobo3bobo$22bobobobo$24bobo$
23b2ob2o$25bo$25bo$23b2ob2o$22bo2bo2bo$14bo6bobo3bobo6bo$14bo2b3o2bo5b
o2b3o2bo$6b2ob2o3bo10bo10bo3b2ob2o$6b2ob2o13bobo13b2ob2o$21bo3bo3bo$
19b3o7b3o$2bo15bo13bo15bo$2b2o9b2o4bo11bo4b2o9b2o$bobo5b2obo2bo4bo9bo
4bo2bob2o5bobo$9b2obo2bo5bo7bo5bo2bob2o$6bo6b2o5b2o2b3o2b2o5b2o6bo$5bo
bo35bobo$5bo2bo33bo2bo$6b2o35b2o4$2o10bo25bo10b2o$b2o9b2o23b2o9b2o$o
10bobo5b3o15bobo10bo$21bo$20bo$32b2o$31b2o$33bo!
Assembling the Synthesis

Combing this with what I already had for the top and adding some cleanup gliders resulted in a working final step (!):

Code: Select all

x = 73, y = 73, rule = B3/S23
72bo$56bobo11b2o$56b2o7bo5b2o$46bo10bo5b2o$46bobo15b2o$46b2o2$28bo$29b
2o$28b2o$o$b2o12bobo$2o14b2o$16bo5bobo23bobo$23b2o18bo4b2o9bo$10bo12bo
19bobo3bo9bobo$11bo31b2o14b2o$9b3o26bo$37bo$37b3o$27bo5bobo9bo$26bobo
5b2o8bobo$11bo14b2o6bo10b2o14bo$12bo47bo$10b3o47b3o4$6bo12bo2bo2b2o2b
2o11b2o2b2o2bo2bo12bo$4bobo12b4o2b2o2b2o11b2o2b2o2b4o12bobo$5b2o30b2o
27b2o$21b2o2b2o2b2o5bo2bo2b2o2b2o2b2o$21bo2bo2bo2bo5bobo3bo2bo2bo2bo$
9b2o11bobo2b2o8bo6b2o2bobo11b2o$8bobo12bo10b3o12bo12bobo$10bo22bo5bo
22bo$29bo2bobo3bobo2bo$28bobo2bobobobo2bobo$24b2o3bo5bobo5bo3b2o$23bo
2bo7b2ob2o7bo2bo$24b2o10bo10b2o$36bo$34b2ob2o$33bo2bo2bo$12b2o11bo6bob
o3bobo6bo11b2o$13b2o10bo2b3o2bo5bo2b3o2bo10b2o$12bo4b2ob2o3bo10bo10bo
3b2ob2o4bo$17b2ob2o13bobo13b2ob2o$32bo3bo3bo$30b3o7b3o$13bo15bo13bo15b
o$13b2o9b2o4bo11bo4b2o9b2o$12bobo5b2obo2bo4bo9bo4bo2bob2o5bobo$20b2obo
2bo5bo7bo5bo2bob2o$17bo6b2o5b2o2b3o2b2o5b2o6bo$16bobo35bobo$16bo2bo33b
o2bo$17b2o35b2o4$11b2o10bo25bo10b2o$12b2o9b2o23b2o9b2o$7bo3bo10bobo5b
3o15bobo10bo3bo$7b2o23bo31b2o$6bobo22bo32bobo$43b2o$42b2o$44bo2$6bo59b
o$6b2o57b2o$5bobo57bobo!
The only thing left was to construct the base constellation which had it's own problems, but that was comparatively easy and less interesting so I won't go into that.

LLS Sample

I don't have access to the specific LLS searches that I did for this synthesis (I didn't record the parameters), but here's one of the input files I ended up using (see this post for an input file for a different spaceship for which I did remember the parameters):

Code: Select all

0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 
0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 c d e * * * * * * * *
0 0 0 f4 f g h i j * * * * * * * * 
g1 g2 g3 g4 k l m n o * * * * * * * * 
h1 h2 h3 h4 p q r s t * * * * * * * * 
i1 i2 i3 i4 u v w x y * * * * * * * * 
* * * * a1 a2 a3 a4 a5 * * * * * * * * 
* * * * b1 b2 b3 b4 b5 * * * * * * * * 
* * * * c1 c2 c3 c4 c5 * * * * * * * *
* * * * d1 d2 d3 d4 d5 * * * * * * * * 
* * * * e1 e2 e3 e4 e5 * * * * * * * * 
* * * * * * * * * * * * * * * * * 
* * * * * * * * * * * * * * * * * 
* * * * * * * * * * * * * * * * *

0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 
0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 0 c d e * * * * * * * *
0 0 0 f4 f g h i j * * * * * * * * 
g1 g2 g3 g4 k l m n o * * * * * * * * 
h1 h2 h3 h4 p q r s t * * * * * * * * 
i1 i2 i3 i4 u v w x y * * * * * * * * 
* * * * a1 a2 a3 a4 a5 * * * * * * * * 
* * * * b1 b2 b3 b4 b5 * * * * * * * * 
* * * * c1 c2 c3 c4 c5 * * * * * * * *
* * * * d1 d2 d3 d4 d5 * * * * * * * * 
* * * * e1 e2 e3 e4 e5 * * * * * * * * 
* * * * * * * * * * * * * * * * * 
* * * * * * * * * * * * * * * * * 
* * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * *
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* * * 0 0 1 1 0 0 0 1 1 0 0 * * * 
* * * 0 0 1 0 1 0 1 0 1 0 0 * * * 
* * * 0 0 0 0 1 0 1 0 0 0 0 * * * 
* * * * 0 0 1 0 1 0 1 0 0 * * * * 
* * * * 0 0 1 0 1 0 1 0 0 * * * * 
* * * * 0 0 0 0 0 0 0 0 0 * * * * 
* * * * * 0 0 0 1 0 0 0 * * * * * 
* * * 0 0 0 0 1 0 1 0 0 0 * * * * 
* * * 0 0 1 1 0 0 0 1 1 0 * * * * 
* * * 0 0 1 0 1 0 1 * * * * * * *
* * * 0 0 1 1 0 0 * * * * * * * *
* * * 0 0 0 0 0 * * * * * * * * *
* * * 0 0 0 0 0 * * * * * * * * *
* * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * *
What Next?

Anyway, after this success, I think a good (albeit ambitious) next target would be 77P6H1V1. Although it has a minimum population of 77 cells, it is long and skinny and it can be divided into multiple regions which could be individually searched for. I recently started some investigation myself, and found something that looked very nice for the sections marked in white (see below), but sadly it turns out that it won't fit with the middlemost section:

Code: Select all

x = 91, y = 35, rule = LifeHistory
32.3A$32.3A$31.A$28.C.2A$27.C$26.C4.A$26.C41.A$24.2C.2C38.A$23.C3.2C
40.2A$26.2C41.3A$26.2C41.3A$20.6C45.2A$73.A$17.A56.A$16.3A56.A$18.A4.
A46.A5.A$14.A.2A3.2A48.A5.A$13.2A.A2.2A48.3A6.A$14.2A50.A6.A5.A$17.A
46.A.A6.A6.A$11.C5.A47.2A6.A2.2A3.A$11.C4.A60.A4.A$11.C4.A51.2A6.A6.A
$8.C2.C3.A52.A.A5.2A3.A.A$7.C3.C59.A6.A.A.A3.A$7.C3.C60.A.5A.A4.A.A$
5.2C2.2C62.2A5.A3.A.A$4.C2.4C66.2A.2A3.A3.2A$3.C3.2C68.2A.A7.2A$81.A
8.A$3.A78.A$2.2A.A75.2A2.2A$2A83.A.A$2A83.A$2A!

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dvgrn
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Re: Small Spaceship Syntheses

Post by dvgrn » October 10th, 2020, 1:38 pm

Just finally took a good look at current pufferfish spaceship syntheses, and they seem to be suboptimal in a couple of ways.

First, the 1G cleanup after the pufferfish construction takes longer than it needs to. Seeds of Destruction suggested a couple of better 1G options; the best one I saw was

Code: Select all

x = 88, y = 97, rule = B3/S23
2bo83bo$obo82bo$b2o82b3o2$8bo$6bobo$7b2o12$12bo$13bo$11b3o$29bo$30b2o
33bo$29b2o33bo$64b3o4$53bobo$53b2o$54bo3$37bo$38b2o$37b2o4$21bo$19bobo
33bobo$20b2o33b2o$56bo10$26b3o$28bo$27bo$46b2o$47b2o$46bo20b2o$67bobo$
67bo11$24b3o$26bo2b2o$18b3o4bo4b2o$20bo8bo33bo$19bo42b2o$62bobo2$28b2o
$29b2o$28bo11$7b3o$9bo$8bo$85b2o$b3o81bobo$3bo81bo$2bo!
but there could be something a little faster, especially if one more glider is used. This should allow for the construction of somewhat shorter pufferfish block puffers.

Second, the octohash database knows 65 ways to make the trailing c/2 fuse, from a glider hitting a two-still-life constellation. Current recipes use one of these, a block+boat combination, but another boat is needed to turn an input glider so that it comes in from the right direction.

There are other two-object constellations where the glider doesn't need to be turned, like the one outlined in blue here:

Code: Select all

x = 439, y = 226, rule = LifeHistory
22.417F$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.F
31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.F31.F31.F31.F
31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.F31.F31.F31.F31.F31.F31.F
31.F31.F31.F31.F31.F31.F31.F$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F
31.F31.F31.F31.F$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F
31.F$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.F31.
F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.F31.F31.F31.F31.
F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.F31.F31.F31.F31.F31.F31.F31.
F31.F31.F31.F31.F31.F31.F$2.A19.F18.2A11.F11.2A6.2A10.F11.2A6.2A10.F
11.2A6.2A10.F11.2A6.A11.F12.A4.2A12.F12.A6.2A10.F13.A17.F13.2A16.F19.
2A.3A6.F17.2A12.F14.A16.F17.2A12.F$.4A17.F18.A.A10.F11.A.A4.A.A10.F
11.A.A4.A.A10.F11.A.A4.A.A10.F11.A6.A.A10.F11.A.A3.A.A11.F11.A.A6.A
10.F12.A.A16.F14.A2.2A12.F11.A7.A2.A8.F18.A12.F12.3A16.F17.A.A11.F$A.
4A16.F19.2A10.F12.A6.A11.F12.A6.A11.F12.A5.2A11.F12.3A4.A11.F11.2A6.A
11.F12.A4.3A11.F12.A.A16.F11.3A3.A.A11.F11.3A3.A.A3.A7.F14.A3.A.A10.F
11.A19.F19.A2.3A6.F$2A3.2A15.F31.F31.F31.F31.F14.A16.F19.2A10.F17.A
13.F13.A6.2A9.F11.A7.A2.3A6.F14.A2.2A12.F12.3A4.2A10.F11.2A18.F19.2A.
A8.F$.3A.A16.F31.F11.2A18.F19.2A10.F20.2A9.F31.F31.F31.F20.2A9.F19.2A
.A8.F13.2A16.F11.A19.F19.2A.3A6.F11.2A10.A7.F$2.3A17.F31.F11.A.A17.F
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$22.417F$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.
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$22.F.D27.D.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.F.D
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12.A2.A15.F$22.F15.3A2.2A9.F31.F16.2A13.F15.3A2.2A9.F16.A14.F14.A.A
14.F17.2A12.F31.F13.A17.F16.3A2.2A8.F31.F12.A.A3.A12.F13.2A16.F$22.F
17.A.2A10.F31.F31.F17.A.2A10.F31.F15.A15.F31.F31.F31.F18.A.2A9.F31.F
13.2A16.F31.F$22.F13.A7.A9.F13.A17.F13.A17.F13.A7.A9.F31.F31.F13.2A
16.F17.2A12.F17.A13.F14.A7.A8.F12.2A17.F31.F31.F$22.F12.A.A16.F12.A.A
2.2A12.F12.A.A.3A12.F12.A.A16.F16.2A13.F12.2A17.F12.A2.A.3A11.F18.A
12.F16.A.A12.F13.A.A15.F12.A18.F31.F20.3A8.F$22.F13.A17.F13.2A.2A13.F
13.A2.A14.F12.A.A16.F12.2A.2A14.F12.A18.F13.2A2.A13.F15.3A13.F16.A.A
12.F12.A2.A15.F13.3A15.F31.F16.2A2.A10.F$22.F31.F18.A12.F17.A13.F13.A
17.F12.2A3.A13.F13.3A15.F18.A12.F15.A15.F17.A13.F13.2A16.F15.A15.F16.
2A13.F15.A2.A2.A9.F$22.F31.F31.F31.F31.F31.F15.A15.F31.F31.F31.F31.F
31.F16.A.A12.F16.2A13.F$22.F31.F31.F31.F31.F31.F17.3A11.F31.F15.2A14.
F18.3A10.F31.F14.2A15.F17.2A12.F31.F$22.F31.F31.F31.F31.F31.F17.A13.F
31.F15.A.A13.F18.A12.F31.F14.A.A14.F31.F31.F$22.F31.F31.F31.F31.F31.F
18.A12.F31.F15.A15.F19.A11.F31.F14.A16.F31.F31.F$22.F31.F31.F31.F31.F
31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.F31.F31.F31.F31.F31.F31.F31.F
31.F31.F31.F31.F31.F31.F$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F
31.F31.F31.F$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F
$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.F31.F31.
F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.F31.F31.F31.F31.F31.
F31.F31.F31.F31.F31.F31.F31.F31.F$22.F31.F31.F31.F31.F31.F31.F31.F31.
F31.F31.F31.F31.F31.F$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.
F31.F31.F$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$
22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.F31.F31.F
31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.F31.F31.F31.F31.F31.F
31.F31.F31.F31.F31.F31.F31.F31.F$22.F31.F31.F31.F31.F31.F31.F31.F31.F
31.F31.F31.F31.F31.F$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F
31.F31.F$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.
F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.F31.F31.F31.
F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$22.417F$22.F31.F31.F31.F31.
F31.F31.F31.F31.F31.F31.F31.F31.F31BF$22.F31.F31.F31.F31.F31.F31.F31.
F31.F31.F31.F31.F31.F31BF$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.
F31.F31.F31BF$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31B
F$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31BF$22.F31.F
31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31BF$22.F31.F31.F31.F31.F
31.F31.F31.F31.F31.F31.F31.F31.F31BF$22.F31.F31.F31.F31.F31.F31.F31.F
31.F31.F31.F31.F31.F31BF$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F
31.F31.F31BF$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31BF
$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31BF$22.F31.F31.
F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31BF$22.F17.2A12.F12.2A17.F
17.2A12.F12.3A16.F20.2A9.F21.2A8.F14.A16.F14.2A15.F12.A18.F18.A12.F
18.A12.F18.A12.F14BA16BF$22.F16.A.A12.F12.A.A16.F17.A13.F31.F19.A2.A
8.F20.A.A8.F13.A.A15.F14.A16.F12.A18.F18.A12.F18.A12.F18.A12.F13BABA
15BF$22.F16.A14.F13.2A16.F18.3A10.F21.A9.F20.2A2.2A5.F20.2A9.F12.A2.A
2.2A11.F15.3A13.F12.A18.F18.A12.F18.A12.F12.2A4.A12.F12BA2BA15BF$22.F
15.2A2.3A9.F31.F20.A10.F20.A.A8.F24.A.A4.F31.F13.2A2.2A12.F17.A13.F
31.F31.F20.3A8.F12.A.A16.F13B2A3B3A10BF$22.F19.A11.F16.2A4.2A7.F31.F
19.A2.A8.F24.A6.F31.F19.A11.F31.F31.F31.F20.A10.F14.A16.F31BF$22.F20.
A10.F17.A3.2A8.F14.2A15.F20.2A9.F31.F31.F31.F18.3A10.F31.F31.F21.A9.F
14.2A15.F15BA15BF$22.F12.2A17.F17.A.A3.A7.F13.A.A2.2A11.F31.F12.3A16.
F12.3A16.F15.A15.F12.3A3.A12.F31.F31.F31.F17.2A12.F14B2A15BF$22.F12.A
.A16.F18.2A11.F12.A.A2.2A12.F22.A8.F31.F31.F15.A15.F19.A11.F16.A14.F
13.A17.F31.F17.A.A11.F14BABA14BF$22.F13.2A16.F31.F13.A5.A11.F21.2A8.F
31.F15.2A14.F15.A15.F31.F15.A.A13.F12.A.A16.F13.2A16.F17.A13.F31BF$
22.F31.F31.F31.F21.A.A7.F31.F15.A.A13.F31.F31.F14.A2.A2.2A9.F12.A.A
16.F12.A.A16.F31.F31BF$22.F31.F31.F31.F31.F31.F15.A15.F31.F31.F15.2A
2.2A10.F13.A17.F12.2A17.F31.F31BF$22.F31.F31.F31.F31.F31.F31.F31.F31.
F21.A9.F31.F31.F31.F31BF$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F14.
3A14.F31.F31.F31BF$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F14.A16.F
31.F31.F31BF$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F15.A15.F31.F31.F
31BF$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31BF$22.F31.
F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31BF$22.F31.F31.F31.F31.
F31.F31.F31.F31.F31.F31.F31.F31.F31BF$22.F31.F31.F31.F31.F31.F31.F31.
F31.F31.F31.F31.F31.F31BF$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.
F31.F31.F31BF$22.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31B
F$22.417F!
I haven't sorted all of these out yet -- seems like there might be one where the activation glider can come from the SE, passing in front of the preexisting pufferfish block puffer, but I haven't proved that out yet. And/or maybe there's one where the two still lifes can be made simultaneously by three gliders from the NW and NE.

Code: Select all

x = 148, y = 83, rule = LifeSuper
69.U$70.2U73.U.U$61.U7.2U74.2U$62.U83.U$60.3U12.U$76.2U$M17.M17.M38.
2U$.2M16.2M16.2M$2M16.2M16.2M3$67.U$65.U.U$66.2U$130.U$130.U.U$130.2U
$66.W$67.W$65.3W12$92.M$93.2M$92.2M$117.M$115.2M$116.2M$132.2S$132.2S
4.2S$136.2S2.S$136.2S2.2S$117.2S4.2S4.2S.2S.S3.2S$117.2S4.2S4.S4.S.4S
$130.S3.S2.S2$130.S3.S2.S$111.2S4.2S4.2S4.S4.S.4S$111.2S4.2S4.2S4.2S.
2S.S3.2S$136.2S2.2S$136.2S2.S$91.W40.2S4.2S$91.W4.2W34.2S$91.W3.W2.W$
95.W.W$96.W5$27.pA.pA10.pA$28.2pA8.2pA$28.pA10.2pA2$33.pA.pA10.2O3.3O
$34.2pA10.2O2.O.2O.O$34.pA15.O5.O$50.O5.2O$43.2O7.O.3O$43.2O9.2O$49.
2O.2O2$49.2O.2O$43.2O9.2O$43.2O7.O.3O$50.O5.2O$50.O5.O$33.2Q11.2O2.O.
2O.O$34.2Q10.2O3.3O$33.Q$40.Q$27.2Q10.2Q$28.2Q9.Q.Q$27.Q!
Seeds of Destruction also came up with a 1G cleanup to replace the 2G cleanup in (I think) all the current recipes on Catagolue, so new pufferfish spaceships should be a few gliders cheaper as well as smaller.

Another option that might make shorter pufferfish spaceships at slightly greater expense, would be if an octohashWSS database were run on the same set of 12x12 constellations. Odds seem decent that one of those collisions would let the fuse be lit by a *WSS sneaking in from the front between the two pufferfish block puffers.

(Posting this now because I'm out of time for this investigation, at least for this weekend. If anyone wants to pick it up and figure out a good quick synthesis for the loaf + blinker, or one of the other 1G seeds for that c/2 fuse, please be my guest.)

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wwei23
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Re: Small Spaceship Syntheses

Post by wwei23 » October 11th, 2020, 9:56 am

A Sir Robin synthesis is out of the question right now, but what about recipes for adding minstrels given a pre-existing Sir Robin on the board? Would that be feasible to realize today?

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dvgrn
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Re: Small Spaceship Syntheses

Post by dvgrn » October 11th, 2020, 1:36 pm

wwei23 wrote:
October 11th, 2020, 9:56 am
A Sir Robin synthesis is out of the question right now, but what about recipes for adding minstrels given a pre-existing Sir Robin on the board? Would that be feasible to realize today?
Yikes. I guess I wouldn't want to bet against the glider-synth experts being able to pull something like that off, for one of the smaller minstrels -- ragged, or possibly wandering? EDIT in response to question below: Or featherweight.

But since you have to wait for Sir Robin to go by before beginning the construction, it wouldn't look anything at all like the spaceship recipes we've been seeing recently, where you gradually build up a complex stable thing, then pound on it with gliders to turn it into what you want. At least, not unless someone can design a hyperfast edge-shooting minstrel seed that can drop a minstrel in place across a half-Sir-Robin-width of lanes.

Sir Robin always runs away so fast that only *WSSes can really reach the key space behind him quickly enough, possibly with some help from a glider or two coming in from the sides. Someone might have to invent a whole new *WSS-based construction toolkit to make this work -- and even then, there will be painfully little time available to complete the construction before Sir Robin has receded out of reach.

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wwei23
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Re: Small Spaceship Syntheses

Post by wwei23 » October 11th, 2020, 1:48 pm

dvgrn wrote:
October 11th, 2020, 1:36 pm
ragged, or possibly wandering?
What about featherweight?

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dvgrn
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Re: Small Spaceship Syntheses

Post by dvgrn » October 11th, 2020, 3:54 pm

dvgrn wrote:
October 10th, 2020, 1:38 pm
... seems like there might be one where the activation glider can come from the SE, passing in front of the preexisting pufferfish block puffer, but I haven't proved that out yet. And/or maybe there's one where the two still lifes can be made simultaneously by three gliders from the NW and NE.
I had a moment to look at this again, and it seems like the first option might not quite work out -- but it's close enough that maybe if someone else has a fresh look at it, an obvious fix will present itself. Here's an example of it not quite working:

Code: Select all

x = 365, y = 284, rule = LifeHistory
91.A$92.2A261.A.A$91.2A262.2A$356.A$97.A$98.2A$97.2A35$121.C.C$122.2C
$122.C4.C.C$128.2C$128.C8$155.A$153.A.A$154.2A$297.A$296.A$144.A151.
3A$145.2A9.A$144.2A4.A3.A.A$151.2A2.2A$150.2A11$301.A.A$301.2A$173.A
128.A$171.A.A$172.2A$152.A$153.2A$152.2A26$4.A$5.2A80.A$4.2A74.A6.A.A
$80.A.A4.2A$80.2A$95.A$93.2A$10.A83.2A$11.2A70.A$10.2A69.2A$82.2A9$
17.A.A$18.2A$18.A$70.A162.D$68.2A162.3D$9.A59.2A160.2D.2D$7.A.A8.A.A
209.5D$8.2A5.A3.2A$13.A.A3.A$14.2A$233.2D$233.2D4$233.2D$233.2D2$232.
D$74.A156.4D$73.A156.D.4D$73.3A154.2D3.2D$35.A.A193.3D.D$36.2A194.3D$
36.A196.D$17.A$15.A.A$16.2A$51.D$50.3D$49.5D$48.3D.3D$48.6D$49.4D$50.
D2$51.2D$51.2D4$51.2D$51.2D2$50.D$49.4D$48.D.4D$48.2D3.2D$49.3D.D$49.
6D$48.D.4D$49.2D3.D3$48.2D12.2A$9.3A35.D2.D10.2A$11.A35.D2.D12.A$10.A
37.2D3$27.A$27.2A$26.A.A4$60.2A$59.2A$61.A3$71.2A$19.A51.A.A$19.2A50.
A$18.A.A125.A142.3A$.2A143.2A141.A$A.A142.A.A142.A$2.A3$163.2A$162.A.
A$164.A4$82.A204.3A$11.A69.2A204.A$11.2A68.A.A204.A$10.A.A$95.A$94.2A
203.2A$94.A.A58.2A141.2A$79.3A72.A.A143.A$5.A73.A6.3A67.A$5.2A73.A5.A
50.2A$4.A.A80.A50.2A$137.A22$127.2C$126.C.C$128.C3$122.3C$124.C$123.C
30$362.3E$362.E$363.E!
Disregarding the two recipes not actually being rewindable yet, the yellow glider in the southeast is in the correct position to light the interior c/2 fuse on the upper blockpufferfiship, but we'd have to know how to build somewhat shorter blockpufferfiships, to make this work.

The recipe shown on the left here is already quite a bit shorter than previous blockpufferfiships, but it's not quite enough. Lighting the tail end of the previous blockpufferfiship eight ticks sooner -- or rather, lighting the tail end at the same time but building the front end eight ticks later! -- would allow the yellow glider to sneak past.

Alternatively, some other way of triggering the c/2 fuse with a glider from the SE, that's either a couple of cells farther to the right, or takes 8 ticks longer to complete, or some combination of those, would also be enough.

Here's the stamp collection of relevant octohash results that I posted yesterday, with a little more sorting done. Should really buckle down and write the post-processing code that could build a correctly-oriented stamp collection like this, the first time around, without any custom fiddling:

Code: Select all

x = 417, y = 301, rule = LifeHistory
417F$F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$F31.F31.F
31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$F31.F31.F31.F31.F31.F31.
F31.F31.F31.F31.F14.B16.F31.F31.F$F31.F31.F31.F31.F31.F31.F31.F31.F
31.F31.F31.F31.F31.F$F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.
F31.F$F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$F31.F31.F
31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F31.F$F16.2B13.F31.F31.F31.F
31.F31.F31.F31.F31.F31.F31.F31.F31.F$F14.6B11.F31.F31.F31.F31.F31.F
31.F31.F31.F31.F31.F31.F31.F$F13.8B10.F31.F31.F31.F31.F31.F31.F31.F
31.F31.F31.F31.F31.F$F11.4BDBD3B10.F31.F31.F31.F31.F31.F31.F31.F31.F
31.F31.F31.F31.F$F11.4B2D4B10.F31.F31.F31.F31.F31.F31.F31.F31.F31.F
31.F31.F31.F$F11.5BD4B10.F31.F31.F31.F31.F31.F31.F31.F31.F31.F10.B2.
4B14.F31.F31.F$F11.9B11.F31.F31.F31.F31.F31.F31.F31.F31.F31.F8.4B2D4B
13.F31.F31.F$F11.5B2D2B11.F31.F31.F31.F31.F31.F31.F31.F31.F31.F7.6BD
4B13.F31.F31.F$F11.4BDBDB12.F31.F31.F31.F31.F31.F31.F31.F31.F31.F7.2B
D3BDBD2B13.F31.F31.F$F11.4B2DB13.F31.F31.F31.F31.F31.F31.F31.F31.F31.
F7.3D4B2D2B13.F31.F31.F$F11.8B12.F31.F31.F31.F31.F31.F31.F31.F12.B18.
F11.B19.F6.D12B12.F31.F31.F$F12.7B12.F14.B16.F11.B19.F13.B17.F15.BD
14.F16.B14.F13.BD16.F31.F11.3B17.F10.3B18.F6.2D6BD5B11.F8.B22.F6.B24.
F$F12.9B10.F13.3B15.F10.3B18.F12.3B16.F14.D.D2B12.F15.3B13.F11.BD.DB
15.F31.F10.4B17.F9.4B18.F7.6B2D6B10.F7.3B21.F5.3B23.F$F11.10B.3B6.F
13.3B15.F10.3B18.F12.3B16.F15.2D4B10.F15.3B13.F9.4B2D16.F31.F9.6B16.F
8.6B17.F8.5BDBD4B11.F6.5B20.F4.5B22.F$F11.15B5.F12.5B14.F9.5B17.F11.
5B15.F14.8B9.F14.5B12.F8.8B15.F31.F5.D.8B16.F4.B.8B17.F8.13B10.F6.5B
20.F4.5B22.F$F12.11B2D2B4.F12.5B14.F9.5B17.F11.5B15.F14.BD7B8.F14.5B
12.F7.7BDB15.F31.F4.B.DB2D6B15.F3.3DB2D6B16.F8.13B10.F5.5B2D19.F3.5B
2D21.F$F12.3BA6BDBDB5.F12.2BA2B14.F9.2BA2B17.F11.2BA2B15.F10.DB.2BDCD
4B9.F14.2BA2BD11.F8.4BDCD2B.BD11.F12.A.3B14.F4.3D2BD6BAD13.F3.B.D2BD
6BAD14.F9.3BA9B9.F5.D3BDBD2B.A15.F3.4BDBD2B.A17.F$F12.2B4A4B2DB6.F12.
B4AB13.F9.B4AB16.F11.B4AB14.F9.DBD2B4AD2B10.F13.B4AD.B10.F9.2BD4A2BDB
D10.F10.B4A3B13.F5.4BDBD3B3CA12.F4.D3BDBD3B3CA13.F9.2B4A6B10.F4.B.D2B
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dvgrn
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Re: Small Spaceship Syntheses

Post by dvgrn » October 12th, 2020, 8:11 am

dvgrn wrote:
October 11th, 2020, 3:54 pm
Here's the stamp collection of relevant octohash results that I posted yesterday, with a little more sorting done...
Comparatively clever choosing of constellations from that collection can be credited for a 53-glider collision creating a complete pufferfish spaceship:

Code: Select all

x = 663, y = 506, rule = LifeSuper
163.U$164.2U485.U.U$163.2U486.2U$652.U$169.U$170.2U$169.2U21$181.S$
182.S$180.3S$176.S$177.S$175.3S3$209.W$207.W.W$208.2W$611.W$610.W$
198.W411.3W$199.2W9.W$198.2W4.W3.W.W$205.2W2.2W$204.2W11$615.W.W$615.
2W$227.W388.W$225.W.W$226.2W$206.W$207.2W$206.2W53$67.Q$68.2Q286.Q$
67.2Q280.Q6.Q.Q$349.Q.Q4.2Q$349.2Q$364.Q$362.2Q$73.Q289.2Q$74.2Q276.Q
$73.2Q275.2Q$351.2Q9$80.W.W$81.2W$81.W$339.W$337.2W$72.W265.2W$70.W.W
8.W.W$71.2W5.W3.2W$76.W.W3.W$77.2W3$230.pA$3.pA.pA223.pA$4.2pA223.3pA
$4.pA4$343.W$342.W$342.3W$98.W.W$99.2W$99.W$80.W$78.W.W$79.2W209$.pA$
.2pA$pA.pA22$331.2W$72.3W255.2W$74.W257.W$73.W3$90.W$90.2W$89.W.W4$
329.2W$328.2W$330.W3$340.2W$82.W257.W.W$82.2W256.W$81.W.W$64.2W$63.W.
W$65.W9$351.O$74.O275.2O$74.2O274.O.O$73.O.O$364.O$363.2O$363.O.O$
348.3O$68.O279.O6.3O$68.2O279.O5.O$67.O.O286.O5$200.W402.3W$200.2W
401.W$199.W.W402.W4$217.2W$216.W.W$218.W4$601.3W$601.W$602.W3$613.2W$
209.2W401.2W$208.W.W403.W$210.W$191.2W$192.2W$191.W19$183.S$183.2S$
182.S.S5$178.3S$180.S$179.S11$660.2S$660.S.S$660.S!
It would be a little less, but the 21-glider blockpufferfiship --

Code: Select all

x = 95, y = 104, rule = LifeHistory
A$.2A89.A.A$2A90.2A$93.A$6.A$7.2A$6.2A11$28.A$26.A.A$27.2A$70.A$69.A$
17.A51.3A$18.2A9.A$17.2A4.A3.A.A$24.2A2.2A$23.2A11$74.A.A$74.2A$46.A
28.A$44.A.A$45.2A$25.A30.D$26.2A27.3D$25.2A27.2D.2D$53.5D4$56.2D$56.
2D4$56.2D$56.2D2$55.D$54.4D$53.D.4D$53.2D3.2D$54.3D.D$55.3D$19.A36.D
5.3A$19.2A41.A$18.A.A42.A4$36.2A$35.A.A$37.A4$60.3A$60.A$61.A3$72.2A$
28.2A41.2A$27.A.A43.A$29.A$10.2A$11.2A$10.A11$7.A$7.2A$6.A.A2$.A90.2A
$.2A88.2A$A.A90.A!
-- is still slightly too long to work with the eater-and-beehive constellation. So the full recipe uses the 27-glider recipe that allows for a shorter length, instead.

That means there are probably ways to save a few gliders, maybe get below a cost of 50, by using the 21-glider recipe and triggering that internal c/2 fuse with a glider from the NW, like in previous pufferfish spaceship recipes. I hunted around a little but haven't found a really good combination yet.

EDIT: Reduced to 51 gliders. Need a cheaper recipe for the key two-eater constellation, or a workable replacement for it. Currently it's 8 gliders plus the trigger glider, due to the constraint that the pufferfish block trails are already in place nearby. The 53-glider recipe only needed four gliders to build an equivalent constellation triggered from the SE, but then it needed a shorter blockpufferfiship that cost six more gliders.

Code: Select all

x = 385, y = 293, rule = LifeSuper
89.U.U292.U$90.2U290.2U$90.U292.2U2$95.U.U$96.2U$96.U7$91.S$89.S.S$
90.2S8$108.S$109.S$107.3S4$104.S$105.2S$104.2S7.S3.S$114.S3.2S$112.3S
2.2S9$143.W$144.W$142.3W2$334.W$334.W.W$132.W.W9.W189.2W$133.2W10.W$
133.W4.W.W2.3W$139.2W$139.W10$340.W$338.2W$161.W177.2W$162.W$160.3W2$
140.W.W$141.2W$141.W3$3.pA176.pA$4.2pA174.pA.pA$3.2pA175.2pA10$21.Q$
22.2Q171.Q.Q$21.2Q172.2Q$196.Q$27.Q$28.2Q$27.2Q12$30.W.W$31.2W$31.W
17.W$50.W$48.3W124.W.W$175.2W$176.W3$164.W$164.W.W$164.2W3$57.W$58.W$
56.3W4$39.W$40.2W124.W$39.2W125.W.W$166.2W101$46.W$46.2W$45.W.W2$65.
3W$67.W$66.W111.2W$177.2W$179.W2$327.2W$134.2W191.W.W$135.2W190.W$
134.W4$151.3W$44.W108.W$44.2W106.W$38.W4.W.W2.3W$2pA36.2W10.W$.2pA34.
W.W9.W123.2W150.2W$pA172.W.W149.W.W$173.W151.W2$47.3W$49.W287.W$48.W
287.2W$143.3W190.W.W$145.W$126.W17.W$126.2W$125.W.W5$27.Q$27.2Q$26.Q.
Q2$21.Q174.2Q$21.2Q172.2Q$20.Q.Q174.Q10$105.2S$104.S.S$106.S2$99.S$
99.2S$98.S.S2$114.2S$108.S4.S.S$108.2S5.S$107.S.S!

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