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 * * * * * * *
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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!