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16 in 16: Efficient 16-bit Synthesis Project

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby chris_c » April 18th, 2017, 4:10 pm

16.349 in 15G:

x = 162, y = 134, rule = B3/S23
47bo$48bo$46b3o9$71bo85b2o$69b2o86bo2b2o$70b2o86b2obo$159bo$159bo$157b
2o$157bo$47b2o110bo$48b2o108b2o$47bo$139b2o$42b3o94b2o16b2ob2o$44bo
112b2ob2o$43bo3$30bo$30b2o26b2o$29bobo19b3o4bobo$51bo6bo$23b2o27bo$24b
2o$23bo5$64b3o$64bo$65bo2$37b3o$39bo30b3o$38bo31bo$65b3o3bo$65bo$66bo
30$2o$b2o$o32$57b2o98b2o$57bo2b2o95bo2b2o$58b2obo96b2obo$59bo99bo$59bo
99bo$57b2o98b2o$57bo99bo$59bo99bo$58b2o98b2o2$39b2o$39b2o16b2ob2o$57b
2ob2o5$33b2o$32bobo$34bo$64b2o$64bobo$64bo!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby Extrementhusiast » April 18th, 2017, 5:06 pm

chris_c wrote:16.349 in 15G:

RLE


I used the other soup for ten gliders:
x = 28, y = 32, rule = B3/S23
19bobo$14bo5b2o$7bo7b2o3bo$8bo5b2o10bo$6b3o16bo$25b3o3$21bo$20b2o$7b2o
11bobo$6bobo$8bo4b2o$14b2o$13bo2$17b2o$16b2o$b2o15bo$obo$2bo9$26b2o$
25b2o$27bo!
I Like My Heisenburps! (and others)
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Re: 16 in 16: Efficient 16-bit Synthesis Project (all < 28G)

Postby Goldtiger997 » April 19th, 2017, 2:18 am

Extrementhusiast wrote:I used the other soup for ten gliders:...


Nicely done. I had tried that soup, but the only syntheses for the pattern in the top-right that I found interfered with the formation of the pi.

16.731 in 12 gliders (perhaps improvable through constellations, although I could not find any):

x = 119, y = 53, rule = B3/S23
48bo$46bobo$47b2o12$117bo$116bo$116b3o11$11bo3bo$9bobo2bo$2bo7b2o2b3o
22b3o37b3o$obo$b2o$4bo111b2o$4bobo26b2o38b2o41bo$4b2o26bo2bo36bo2bo37b
2obo$33b2o38b2o37bo2bo$112b2o$114b4o$45b3o37b3o26bo2bo$17bo$16bo26bo5b
o33bo5bo$16b3o24bo5bo13b2o18bo5bo$43bo5bo12bobo18bo5bo$20bo43bo$19b2o
24b3o37b3o$19bobo54b2o$76bobo$71b2o3bo$70bobo$72bo$74b2o$74bobo$74bo!


16.786 in 9 gliders:

x = 50, y = 42, rule = B3/S23
49bo$47b2o$48b2o10$bo$2b2o17bo$b2o16b2o$20b2o$16bo$14b2o$15b2o3$27bo$
26bo$26b3o$20bo$19bo$19b3o3$19b3o$19bo$20bo5$3b3o$3bo$4bo$3o$2bo$bo!


Now all 16-bit still-lifes can be synthesised in under 28 gliders.
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Re: 16 in 16: Efficient 16-bit Synthesis Project (all < 30G)

Postby BobShemyakin » April 19th, 2017, 1:32 pm

Goldtiger997 wrote:...

16.778 in 10 gliders:

x = 44, y = 58, rule = B3/S23
15bo$16b2o$15b2o22$35bobo$36b2o$36bo2$42b2o$32bo8b2o$22b2o7b2o10bo$23b
2o6bobo$22bo4$37bobo$37b2o$38bo$31b2o$30bobo6b2o$32bo5bobo$40bo2$3o$2b
o$bo9$6b2o$7b2o$6bo!

...

This is a mistake. 2 glider (marked on the diagram you will see) interact before:
x = 44, y = 58, rule = LifeHistory
15.A$16.2A$15.2A22$35.A.A$36.2A$36.A2$42.2E$32.A8.2E$22.2A7.2A10.E$
23.2A6.A.A$22.A4$37.E.E$37.2E$38.E$31.2A$30.A.A6.2A$32.A5.A.A$40.A2$
3A$2.A$.A9$6.2A$7.2A$6.A!

To fix it replace the right glider for two (16.778 in 11G):
x = 62, y = 62, rule = B3/S23
15bo$16b2o$15b2o22$35bobo$36b2o$36bo$42bo$43b2o$42b2o2$45bo$44bo$36bo
7b3o$22b2o11b2o$23b2o10bobo$22bo18bobo$41b2o$42bo5$31b2o$30bobo6b2o$
32bo5bobo$40bo$57b2o$3o55bo$2bo55bobo$bo54b2obobo$55bo2bo2bo$55b2o2b2o
7$6b2o$7b2o$6bo!

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Re: 16 in 16: Efficient 16-bit Synthesis Project (all < 28G)

Postby AbhpzTa » April 19th, 2017, 2:09 pm

Goldtiger997 wrote:16.731 in 12 gliders (perhaps improvable through constellations, although I could not find any):

x = 119, y = 53, rule = B3/S23
48bo$46bobo$47b2o12$117bo$116bo$116b3o11$11bo3bo$9bobo2bo$2bo7b2o2b3o
22b3o37b3o$obo$b2o$4bo111b2o$4bobo26b2o38b2o41bo$4b2o26bo2bo36bo2bo37b
2obo$33b2o38b2o37bo2bo$112b2o$114b4o$45b3o37b3o26bo2bo$17bo$16bo26bo5b
o33bo5bo$16b3o24bo5bo13b2o18bo5bo$43bo5bo12bobo18bo5bo$20bo43bo$19b2o
24b3o37b3o$19bobo54b2o$76bobo$71b2o3bo$70bobo$72bo$74b2o$74bobo$74bo!

Beehive + blinker = 3 gliders : ( 16.731 in 11 )
x = 118, y = 53, rule = B3/S23
47bo$45bobo$46b2o12$116bo$115bo$16bo98b3o$15bo$15b3o10$5bo$5bobo30b3o
37b3o$obo2b2o$b2o$bo113b2o$32b2o38b2o41bo$31bo2bo36bo2bo37b2obo$32b2o
38b2o37bo2bo$111b2o$113b4o$44b3o37b3o26bo2bo$16bo$15bo26bo5bo33bo5bo$
15b3o24bo5bo13b2o18bo5bo$42bo5bo12bobo18bo5bo$19bo43bo$18b2o24b3o37b3o
$18bobo54b2o$75bobo$70b2o3bo$69bobo$71bo$73b2o$73bobo$73bo!


Goldtiger997 wrote:16.786 in 9 gliders:

x = 50, y = 42, rule = B3/S23
49bo$47b2o$48b2o10$bo$2b2o17bo$b2o16b2o$20b2o$16bo$14b2o$15b2o3$27bo$
26bo$26b3o$20bo$19bo$19b3o3$19b3o$19bo$20bo5$3b3o$3bo$4bo$3o$2bo$bo!

Block -> glider : ( 16.786 in 8 )
x = 62, y = 52, rule = B3/S23
61bo$59b2o$60b2o10$13bo$14b2o17bo$13b2o16b2o$32b2o$28bo$26b2o$27b2o3$
39bo$38bo$38b3o$32bo$31bo$31b3o3$31b3o$31bo$32bo18$b2o$obo$2bo!


BobShemyakin wrote:
Goldtiger997 wrote:...

16.778 in 10 gliders:

x = 44, y = 58, rule = B3/S23
15bo$16b2o$15b2o22$35bobo$36b2o$36bo2$42b2o$32bo8b2o$22b2o7b2o10bo$23b
2o6bobo$22bo4$37bobo$37b2o$38bo$31b2o$30bobo6b2o$32bo5bobo$40bo2$3o$2b
o$bo9$6b2o$7b2o$6bo!

...

This is a mistake. 2 glider (marked on the diagram you will see) interact before:
x = 44, y = 58, rule = LifeHistory
15.A$16.2A$15.2A22$35.A.A$36.2A$36.A2$42.2E$32.A8.2E$22.2A7.2A10.E$
23.2A6.A.A$22.A4$37.E.E$37.2E$38.E$31.2A$30.A.A6.2A$32.A5.A.A$40.A2$
3A$2.A$.A9$6.2A$7.2A$6.A!

To fix it replace the right glider for two (16.778 in 11G):
x = 62, y = 62, rule = B3/S23
15bo$16b2o$15b2o22$35bobo$36b2o$36bo$42bo$43b2o$42b2o2$45bo$44bo$36bo
7b3o$22b2o11b2o$23b2o10bobo$22bo18bobo$41b2o$42bo5$31b2o$30bobo6b2o$
32bo5bobo$40bo$57b2o$3o55bo$2bo55bobo$bo54b2obobo$55bo2bo2bo$55b2o2b2o
7$6b2o$7b2o$6bo!

Bob Shemyakin


Only 2G-loaf timing : ( 16.778 in 10 )
x = 45, y = 58, rule = B3/S23
15bo$16b2o$15b2o21$36bo$37bo$35b3o3$42b2o$32bo9bobo$22b2o7b2o9bo$23b2o
6bobo$22bo4$37bobo$37b2o$38bo$31b2o$30bobo6b2o$32bo5bobo$40bo2$3o$2bo$
bo9$6b2o$7b2o$6bo!
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby Goldtiger997 » April 20th, 2017, 3:24 am

16.3227 in 9 gliders:

x = 51, y = 29, rule = B3/S23
19bo$20bo$18b3o7bo$9bobo16bobo$10b2o16b2o$10bo2$15bo$16bo$14b3o$18b2o$
18bobo$18bo$28bo$26b2o$27b2o3$49bo$48b2o$48bobo5$26bo$bo23b2o$b2o22bob
o$obo!


16.1979 looks hard. What hook flipping components are known?

AbhpzTa wrote:
Goldtiger997 wrote:16.731 in 12 gliders (perhaps improvable through constellations, although I could not find any):...

Beehive + blinker = 3 gliders : ( 16.731 in 11 )
x = 118, y = 53, rule = B3/S23
47bo$45bobo$46b2o12$116bo$115bo$16bo98b3o$15bo$15b3o10$5bo$5bobo30b3o
37b3o$obo2b2o$b2o$bo113b2o$32b2o38b2o41bo$31bo2bo36bo2bo37b2obo$32b2o
38b2o37bo2bo$111b2o$113b4o$44b3o37b3o26bo2bo$16bo$15bo26bo5bo33bo5bo$
15b3o24bo5bo13b2o18bo5bo$42bo5bo12bobo18bo5bo$19bo43bo$18b2o24b3o37b3o
$18bobo54b2o$75bobo$70b2o3bo$69bobo$71bo$73b2o$73bobo$73bo!



Nice! I am wondering what method you use to find 3-glider collisions that make constellations? I use a really slow method of running gencols and a script of chris_c's to find most of the 3-glider collisions that have a certain final population, and then run dvgrn's find.py script to find the appropriate constellation.

Also, happy birthday (for yesterday)!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby yootaa » April 20th, 2017, 9:05 am

Good 16.834 components:
x = 56, y = 13, rule = B3/S23
11bobo19b2o$10bo22b2o$10bo3bo$13b2o$10b2o$9bo$9bobo$9b2o24b2o10bo$bo
34bo10bo$b2o31b3o10bo$ob2o50b2o$obo50bobo$2o52bo!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby BlinkerSpawn » April 20th, 2017, 10:41 am

yootaa wrote:Good 16.834 components:
rle

10G:
x = 60, y = 39, rule = B3/S23
o$b2o$2o2$21bo$22bo$20b3o5$22bo$23bo$21b3o10$35bo$26bo7bo$27bo6b3o11bo
8bobo$25b3o19bo9b2o$47b3o8bo$28b3o$30bo$29bo16b2o$45bobo$47bo4$43b2o$
42bobo$44bo!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby Goldtiger997 » April 21st, 2017, 8:06 pm

I wrote:Now all 16-bit still-lifes can be synthesised in under 28 gliders.


BlinkerSpawn wrote:16.628:
x = 51, y = 30, rule = B3/S23
21bo28bo$19b2o27b2o$9bo10b2o27b2o$10b2o$9b2o2$39bo$39bobo$18bobo18b2o$
17bo$17bo3bo$5b2o11b4o$6b2o13bo$5bo3$45bo$29bo13b2o$29b4o11b2o$29bo3bo
$33bo$10b2o18bobo$9bobo$11bo2$40b2o$39b2o$2o27b2o10bo$b2o27b2o$o28bo!


Whoops... I had had mistakenly thought that it was a synthesis

16.628 in 8 gliders:

x = 35, y = 23, rule = B3/S23
21bobo$21b2o$22bo2$23bo$24bo$22b3o4$24b3o$24bo$20b2o3bo$21b2o$20bo11bo
$32bobo$32b2o$29b2o$29bobo$29bo$2o18bo$b2o16b2o$o18bobo!


Now all 16-bit still-lifes can be synthesised in under 28 gliders.

Only one 16-bit still-life left taking 27 gliders (16.1979):

x = 8, y = 7, rule = B3/S23
2b2o$bobo2b2o$o6bo$b2o3bo$2bo2bo$2bobo$3bo!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby Sokwe » April 22nd, 2017, 1:23 am

Goldtiger997 wrote:Only one 16-bit still-life left taking 27 gliders (16.1979)

It can be done in 19, but I doubt that this method could give a sub-16 synthesis:
x = 283, y = 32, rule = B3/S23
250bo$251bo$249b3o$9bo$7b2o$8b2o$256bobo$2bo253b2o$obo246bobo5bo$b2o6b
obo238b2o$9b2o239bo$10bo2$37b2o28b2o28b2o28b2o28b2o28b2o6bo21b2o28b2o
28b2o$36bobo27bobo27bobo27bobo5bo21bobo27bobo5bo21bobo27bobo27bobo2b2o
$35bo29bo7bo21bo29bo7bo21bo29bo8b3o18bo6bo22bo6bo22bo6bo$17b3o16b2o28b
2o4bo23b2o28b2o5b3o20b2o3bo24b2o3bo24b2o3bobo22b2o3bobo22b2o3bo$13bo3b
o19bo29bo4b3o22bo2bo26bo2bo26bo2bobo24bo2bobo4b2o18bo2bobo24bo2bobo24b
o2bo$3bo10b2o2bo18bobo27bobo27bobobo25bobobo4b2o19bobobo25bobobo5bobo
17bobobo25bobobo25bobo$3b2o8b2o23bobo27bobo4b2o21bobo27bobo5bobo19bobo
27bobo6bo20bobo27bobo27bo$2bobo3b2o29bo29bo5bobo21bo29bo6bo22bo29bo29b
o29bo6bobo$9b2o64bo180b2o$8bo248bo2$255b2o$254b2o$256bo3$261b2o$260b2o
$262bo!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby chris_c » April 22nd, 2017, 1:47 pm

I added all of those so now we are below 27G for all 16-bit still lifes. Looking ahead at a few of the expensive but rare still life shows that this 16G snake -> hook-with-tail sequence is used in quite a few (16.930, 16.1064, 16.1077, 16.1139 for example):

x = 50, y = 91, rule = Life
19bobo$19b2o$15bo4bo$13b2o$10b2o2b2o3bo$9bobo6b2o26bo$11bo6bobo23b3o$
14b2o27bo$14bo29bo$15bo29bo$14b2o28b2o13$19bo3bo$17b2o3bo$18b2o2b3o2$
2bo$obo$b2o4$30bo$29bo$16bo12b3o13bo2b2o$14b3o27bobo2bo$13bo18b2o10bob
3o$14bo17bobo10bo$15bo16bo13bo$14b2o29b2o3$28b2o$27b2o$29bo7$6bobo$7b
2o$7bo$19bo5bo$18bo6bobo$18b3o4b2o3$6bo$7bo$5b3o40b2o$48b2o$3b2o$2bobo
9bo2b2o$4bo8bobo2bo28bo$13bob3o27b3o$14bo29bo$15bo29bo$14b2o28b2o5$23b
o$23bobo$23b2o5$18b2o$18b2o3$17bo29bo$15b3o27b3o$14bo29bo$15bo29bo$14b
2o28b2o!


I wonder if there is a cheaper way? Anyway, here is the list from 20-26G:

16.1077    xs16_69m88cz6221         26
16.1691    xs16_4a9l6o8zx121        26
16.1703    xs16_4a9la8ozx121        26
16.623     xs16_o5r8jdz01           25
16.828     xs16_4alhe8z0641         25
16.930     xs16_3iaj21e8zw1         25
16.1139    xs16_kq23z124871         25
16.1398    xs16_g88c93zc952         25
16.706     xs16_39s0qmz023          24
16.713     xs16_o8bap3z23           24
16.1034    xs16_3lkaa4z065          24
16.1064    xs16_39m88cz6221         24
16.1323    xs16_031e8gzc9311        24
16.1880    xs16_259q453z032         24
16.2295    xs16_0g8go8brz23         24
16.353     xs16_321fgc453           23
16.621     xs16_g5r8jdz11           23
16.829     xs16_0md1e8z1226         23
16.1702    xs16_4a5p68ozx121        23
16.1740    xs16_69acga6zx32         23
16.825     xs16_4alhe8zw65          22
16.1846    xs16_25a8c93zw33         22
16.2313    xs16_08u16853z32         22
16.159     xs16_2egmd1e8            21
16.218     xs16_3pajc48c            21
16.774     xs16_69raa4z32           21
16.1084    xs16_31ke12kozw11        21
16.1682    xs16_8k9bkk8zw23         21
16.1693    xs16_8k8aliczw23         21
16.1753    xs16_695q4gozw23         21
16.1954    xs16_8kk31e8z065         21
16.2096    xs16_wck5b8oz311         21
16.2309    xs16_8kk31e8z641         21
16.217     xs16_3146pajo            20
16.228     xs16_178bp2sg            20
16.712     xs16_3pc0qmzw23          20
16.723     xs16_i5p64koz11          20
16.833     xs16_0mp2sgz1243         20
16.872     xs16_2lla8oz065          20
16.1073    xs16_3lkaa4z641          20
16.1127    xs16_giligoz104a4        20
16.1739    xs16_g88r2qkz121         20
16.1791    xs16_03lkaa4z3201        20
16.1962    xs16_4a9eg8ozw65         20
16.2058    xs16_69akg4czx146        20


EDIT: 16.1323 has soups and has a reasonable conversion to 16.1398. I might look through them later:

x = 25, y = 18, rule = B3/S23
22bo$7bo14bobo$5bobo14b2o$6b2o2$bo$2bo$3o$6bo$7bo4b2o$5b3o4bobo$14bo5b
3o$5bo8b2o4bo$5b2o9bo4bo$4bobo5b4o$13bo$11bo$11b2o!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby yootaa » April 22nd, 2017, 9:00 pm

16.1703 in 10 gliders:
x = 65, y = 80, rule = B3/S23
62bo$62bobo$2bo59b2o$obo$b2o16$30bo$28bobo$29b2o2$51bo$50bo$50b3o10$
36bo$34bobo$35b2o7bo$42b2o$29b2o12b2o$30b2o$29bo3$53b3o$53bo$54bo5$51b
o$50b2o$50bobo23$16b2o$15bobo$17bo!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby Extrementhusiast » April 22nd, 2017, 9:43 pm

chris_c wrote:EDIT: 16.1323 has soups and has a reasonable conversion to 16.1398. I might look through them later:

RLE

Reduced that converter by one:
x = 16, y = 15, rule = B3/S23
15bo$4bo8b2o$5bo8b2o$3b3o$13bo$12b2o$4b2ob2o3bobo$3bobobobo$4bo4bo$9b
2o$3o8bo$2bo4b4o$bo6bo$6bo$6b2o!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby BlinkerSpawn » April 22nd, 2017, 9:46 pm

chris_c wrote:Looking ahead at a few of the expensive but rare still life shows that this 16G snake -> hook-with-tail sequence is used in quite a few (16.930, 16.1064, 16.1077, 16.1139 for example):

How, exactly, are these components used in relation to the still lifes?
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby Extrementhusiast » April 22nd, 2017, 10:27 pm

16.1077 in fourteen gliders:
x = 80, y = 20, rule = B3/S23
49bo$47b2o$44bo3b2o$45b2o$44b2o2$18bo6b2o26b2o17b2o3b2o$18bobo3bo2bo
18bo5bo2bo17bo2bo2bo$18b2o3bob2o18bobo3bob2o18bobob2o$22bobo21b2o2bobo
21bobo$obobo10b3o4bobo25bobo23bo$23bo22b2o3bo3bo20b2o$18b2o19b2o4bobo
7bobo$18bobo19b2o4bo8b2o$18bo20bo$44b2o$43bobo$45bo9b2o$56b2o$55bo!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby Goldtiger997 » April 23rd, 2017, 1:10 am

Despite its large number of soups, 16.1691 does not have many good predecessors. Here are some:

x = 45, y = 31, rule = B3/S23
2o$2o7$2b3o$b2ob2o$b2ob2o31bobo$3bo33bobo$38bob2o$3o37b2o$3o$obo$2bo$
2bo$37b3o$39bo$13b2o21b3o4b2o$13b2o16b2o3bo6b2o$31b2o5$2bo3b2o24bo3b2o
$bobobo2bo22bobobo2bo$2b2obobo24b2obobo$6bo29bo!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby yootaa » April 23rd, 2017, 2:45 am

16.2295 in 13 griders:
x = 86, y = 27, rule = B3/S23
44bo8bo$45b2o7bo$44b2o6b3o3$9bo$8bo$8b3o2$34b2o15bobo14b2o14b2o$11bo
22b2o16b2o2bobo9b2o14b2o$11bobo38bo3b2o$11b2o19b4o21bo5b2ob4o10bob4o$
28b2o2bo2bo27b2obo2bo9bob2o2bo$bo25bobo49bo$b2o26bo48b2o$obo$30b2o$6bo
23bobo$5b2o23bo$5bobo50b3o$60bo$59bo3b2o$63bobo$63bo9b2o$72b2o$74bo!


EDIT: 16.1880 in 8 griders:
x = 33, y = 24, rule = B3/S23
22bo$23bo$21b3o$25bo$25bobo$8bo9bo6b2o$6bobo10b2o$7b2o9b2o3$31bo$30bo$
30b3o$18b2o$17bobo$19bo$26b3o$26bo$27bo3$b2o$obo$2bo!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby chris_c » April 23rd, 2017, 8:00 am

Extrementhusiast wrote:
chris_c wrote:EDIT: 16.1323 has soups and has a reasonable conversion to 16.1398. I might look through them later:

Reduced that converter by one:


Thanks. Immediately that improves 16.213 from 15G to 14G and gives one more glider of leeway for 16.1398 if anyone can make 16.1323 well enough (I couldn't).

Goldtiger997 wrote:Despite its large number of soups, 16.1691 does not have many good predecessors. Here are some.


16.1691 in 15G:

x = 37, y = 41, rule = Life
6bo$7b2o$6b2o3$12bo$bo11bo$2bo8b3o$3o18bo$20bo$20b3o$6bo$7bo$5b3o2bo$
11b2o3bo$10b2o5b2o10bo$16b2o10bo$28b3o3$26b2o$26bobo$14bo11bo$3b2o9b2o
$2bobo8bobo$4bo4$12b3o$14bo$13bo$2bo18b3o$2b2o17bo$bobo18bo4$35bo$34b
2o$34bobo!


BlinkerSpawn wrote:
chris_c wrote:Looking ahead at a few of the expensive but rare still life shows that this 16G snake -> hook-with-tail sequence is used in quite a few (16.930, 16.1064, 16.1077, 16.1139 for example):

How, exactly, are these components used in relation to the still lifes?


It would be the following sequences, going downwards through time:

x = 36, y = 68, rule = Life
b2o12b2o14b2o$bo13bo15bo$2bo13bo15bo$b2o2bo9b2o12b3obo$2bobobo8bo3b2o
8bo2bo$2bo2bo10bo2bo12bobo$b2o14bobo13b2o$18bo11$3bo13bo15bo$b3o11b3o
13b3o$o13bo15bo$bo13bo15bo$2bo13bo15bo$b2o2bo9b2o12b3obo$2bobobo8bo3b
2o8bo2bo$2bo2bo10bo2bo12bobo$b2o14bobo13b2o$18bo11$bo2b2o9bo2b2o11bo2b
2o$obo2bo8bobo2bo10bobo2bo$ob3o9bob3o11bob3o$bo13bo15bo$2bo13bo15bo$b
2o2bo9b2o12b3obo$2bobobo8bo3b2o8bo2bo$2bo2bo10bo2bo12bobo$b2o14bobo13b
2o$18bo12$4bo13bo15bo$2b3o11b3o13b3o$bo13bo15bo$2bo13bo15bo$b2o2bo9b2o
12b3obo$2bobobo8bo3b2o8bo2bo$2bo2bo10bo2bo12bobo$b2o14bobo13b2o$18bo!


yootaa wrote:16.2295 in 13 griders:


The converter you use here also improves 4 other still lifes. Most notably it improves 16.558 from 17G to 15G:

x = 148, y = 339, rule = Life
51bobo$41bo9b2o$41bobo8bo$41b2o$55bobo$55b2o87b2o$56bo84bobo2bo$141b2o
2bobo$39b2o105bo$39bobo$39bo2$54b2o$54bobo$46b2o6bo$46bobo$46bo84$34bo
$35bo$33b3o3$44b2o92bo5b2o$41bobo2bo90bobobobo2bo$41b2o2bobo90b2ob2o2b
obo$46bo99bo92$28bo$29bo$27b3o3$38bo5b2o98b2o$37bobobobo2bo91b2obobo2b
o$38b2ob2o2bobo90b2ob2o2bobo$46bo99bo66$67bo$66bo$58bo7b3o$56b2o$57b2o
$14bobo$15b2o$15bo23$137b2o$44b2o92bo5b2o$38b2obobo2bo91bob2obo2bo$38b
2ob2o2bobo91bob2o2bobo$46bo99bo18$50b2o$8b2o40bobo$7bobo40bo$9bo6$9bo$
3o6b2o$2bo5bobo$bo!


Now the maximum cost is 25G:

16.623     xs16_o5r8jdz01           25
16.828     xs16_4alhe8z0641         25
16.930     xs16_3iaj21e8zw1         25
16.1139    xs16_kq23z124871         25
16.1398    xs16_g88c93zc952         25
16.706     xs16_39s0qmz023          24
16.713     xs16_o8bap3z23           24
16.1034    xs16_3lkaa4z065          24
16.1323    xs16_031e8gzc9311        24
16.353     xs16_321fgc453           23
16.621     xs16_g5r8jdz11           23
16.829     xs16_0md1e8z1226         23
16.1702    xs16_4a5p68ozx121        23
16.1740    xs16_69acga6zx32         23
16.825     xs16_4alhe8zw65          22
16.1846    xs16_25a8c93zw33         22
16.2313    xs16_08u16853z32         22
16.159     xs16_2egmd1e8            21
16.218     xs16_3pajc48c            21
16.774     xs16_69raa4z32           21
16.1084    xs16_31ke12kozw11        21
16.1682    xs16_8k9bkk8zw23         21
16.1693    xs16_8k8aliczw23         21
16.1753    xs16_695q4gozw23         21
16.1954    xs16_8kk31e8z065         21
16.2096    xs16_wck5b8oz311         21
16.2309    xs16_8kk31e8z641         21
16.217     xs16_3146pajo            20
16.228     xs16_178bp2sg            20
16.712     xs16_3pc0qmzw23          20
16.723     xs16_i5p64koz11          20
16.833     xs16_0mp2sgz1243         20
16.872     xs16_2lla8oz065          20
16.1073    xs16_3lkaa4z641          20
16.1127    xs16_giligoz104a4        20
16.1739    xs16_g88r2qkz121         20
16.1791    xs16_03lkaa4z3201        20
16.1962    xs16_4a9eg8ozw65         20
16.2058    xs16_69akg4czx146        20


EDIT: We would need a 5G synthesis of 12.103 to solve 16.1064 in 15G using Extrementhusiast's method for 16.1077. I wonder how much brute forcing has been done on 5G syntheses?

x = 16, y = 6, rule = B3/S23
4b2o$2bo2bo$bob2o$obo8bobobo$obo$bo!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby dvgrn » April 23rd, 2017, 9:32 am

chris_c wrote:EDIT: We would need a 5G synthesis of 12.103 to solve 16.1064 in 15G using Extrementhusiast's method for 16.1077. I wonder how much brute forcing has been done on 5G syntheses?

As far as I know, Bob Shemyakin's recent survey has been the most ambitious effort along these lines, and it could only be declared "complete" for 4-glider collisions (and it wasn't really). Running his SpaceBattle search utility with a wide enough variety of targets and angles of attack might turn up something, but that's always going to be just random sampling, luck of the draw.

It's probably about time to attempt a more systematic brute-force approach, exhaustive through 3 gliders, then choosing promising branches to explore from there.
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby chris_c » April 23rd, 2017, 10:23 am

dvgrn wrote:It's probably about time to attempt a more systematic brute-force approach, exhaustive through 3 gliders, then choosing promising branches to explore from there.


Yeah I have thought about that. I would love to see a recursive glider synthesis search program that works as follows:

-Keep track of the active reaction and then copy a new glider into the pattern at the latest moment that is consistent with that glider having come from infinity.

-Prune the search tree if the active reaction gets bigger than a certain bounding box.

-Bonus points if the program is clever enough to realise that the active reaction has settled down to an oscillator or still life so that trying arbitrarily distant gliders is futile.

-Bonus points if the program is clever enough to recognise interesting objects that appear in the soup for a limited number of ticks before being destroyed.

EDIT:Oh there's something I forgot that occurred to me recently. The above method only catches cases where every new glider added interacts with the main part of the pattern. It would not catch reactions like below where both gliders would miss the block on their own:

x = 12, y = 6, rule = B3/S23
5bo4b2o$6bo3b2o$4b3o$3o$2bo$bo!


Since 2-glider interactions are relatively easy to enumerate it should be technically possible to recursively add a 2-glider interaction to an already active pattern. This should do a fairly good job up to 5 gliders in total but would start missing stuff at 6G when 3G-with-3G interactions start to appear. /EDIT


Just so this post is not entirely fantasy here are a few interesting "Top 10" lists:

Top 10 most common SLs with 16 bits or less and having no synthesis in 3 gliders:
12.3       xs12_g8o653z11                           4   312061550510
6.4        xs6_39c                                  4   14920902439
8.3        xs8_35ac                                 4   5896527053
9.4        xs9_31ego                                4   5427491755
8.1        xs8_3pm                                  4   4681094199
10.24      xs10_g8o652z01                           4   4585639472
6.1        xs6_bd                                   4   4100396956
14.36      xs14_g88b96z123                          4   4096975356
9.5        xs9_178ko                                4   1960573686
11.30      xs11_g8o652z11                           4   1621211575


Top 10 most common SLs with 16 bits or less and having no synthesis in 4 gliders:
13.154     xs13_g88m96z121                          5   50821803
10.19      xs10_3542ac                              5   40989491
13.27      xs13_4a960ui                             5   32058011
16.10      xs16_259e0e952                           5   27911390
15.472     xs15_3lk453z121                          5   19308543
13.10      xs13_0g8o653z121                         5   18897513
12.73      xs12_0ggm96z32                           5   15382432
10.1       xs10_g8ka52z01                           5   14915217
15.8       xs15_259e0e96                            5   13454061
11.12      xs11_g0s256z11                           5   12333761


Top 10 most common SLs with 16 bits or less and having no synthesis in 5 gliders:
11.45      xs11_3586246                             6   6932803
10.3       xs10_4al96                               6   6542997
16.617     xs16_j1u0uiz11                           6   3907082
12.8       xs12_0g8o652z23                          6   3577765
16.728     xs16_j1u06acz11                          6   3394633
11.41      xs11_32132ac                             6   3066684
14.9       xs14_g88q552z121                         6   2829709
11.21      xs11_69jzx56                             6   2691884
14.280     xs14_0g8o653z321                         6   2592113
14.12      xs14_g88m552z121                         7   2324684


Top 10 most common SLs with 16 bits or less and having no synthesis in 6 gliders:
14.12      xs14_g88m552z121                         7   2324684
15.969     xs15_0ggca96z3421                        7   1554699
11.20      xs11_3542156                             7   1509087
15.1051    xs15_69ak8zx1256                         8   1381971
15.625     xs15_0ggmp3z346                          7   1160289
15.968     xs15_0g8ka96z3421                        7   1069734
12.55      xs12_3542ako                             7   812154
14.16      xs14_0gbaa4z343                          7   749443
16.736     xs16_2ege96z321                          10  715622
14.587     xs14_08u1acz321                          10  695637


For example the still life 12.103 that I mentioned previously is the 120th most common still life that does not have any known synthesis in 5 gliders.
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby dvgrn » April 23rd, 2017, 10:20 pm

Just started a new thread on enumerating three-glider collisions, as a starting point for a (maybe somewhat) more exhaustive 5G search... or at least a better prebuilt database of small constellations.

I don't think I'll have time to work on any search code for the next few months at least -- too many other things on my To-Do list right now, and I'm trying not to have it be a LIFO stack...! But I do want to pick this topic up again eventually, if no one else gets to it first.

Maybe let's move any future progress on collision enumeration to that thread, to avoid polluting this thread any further...?

chris_c wrote:-Bonus points if the program is clever enough to realise that the active reaction has settled down to an oscillator or still life so that trying arbitrarily distant gliders is futile.

-Bonus points if the program is clever enough to recognise interesting objects that appear in the soup for a limited number of ticks before being destroyed.

The first item I think happens automatically if we keep a list of hashes of each "final initial" state of the 2G collision plus glider #3, at the last generation before they interact. Once we've backed off the T=0 position of glider #3 far enough that the new pre-collision picture is already in the hash table, we can stop investigating that glider lane and move to the next one.

... Unless there's some kind of spark that curls around behind the glider but dies before the glider reaches the stabilized constellation. Bother. To be safe, maybe we have to keep backing the glider off for some number of extra ticks proportional to the size of the 2G collision's total reaction envelope...? Or we could track cells lining the incoming glider's lane and move on to the next lane only if the hash value is in the table AND those lane cells are all undisturbed.

The interesting-objects-for-a-limited-time bonus points are going to be a lot harder to get, I think. For stabilized ash we have code lying around, like recognizer.py and the various apgsearches. It's going to slow things down a lot if we have to hunt through an active reaction every tick, or even every ten ticks or hundred ticks, looking for interesting still-life islands.

We'd also want to look for much more interesting things than still lifes -- things like a temporary loafer, which there really might be one of, out there somewhere unnoticed in an already-censused Catagolue soup. It's so much easier to run through a pattern and recognize-and-remove everything as we get to it, than to have to check every cell against a huge list of interesting stuff, and end up ignoring most cells because they're still active but not recognizable yet.

chris_c wrote:EDIT:Oh there's something I forgot that occurred to me recently. The above method only catches cases where every new glider added interacts with the main part of the pattern. It would not catch reactions like below where both gliders would miss the block on their own...

Good point. A clearer example for me would be something like this:

x = 11, y = 41, rule = B3/S23
2bo$obo$b2o17$bo6bobo$b2o5b2o$obo6bo17$8b2o$8bobo$8bo!

This constellation can't be found by adding a fourth glider to my proposed three-glider collision database, because none of the subsets of three out of the four gliders are valid three-glider collisions. So if we ever, Heaven forbid, get to the stage of trying to enumerate all four-glider collisions, we can start with the three-glider-database-plus-one-glider approach, but then as you say we'll have to add all two-glider-collision interactions with other-two-glider-collisions.

But for just three gliders I think this isn't a problem yet. There's no way to set up three gliders such that no two of them interact, but the combination of all three does interact. (Right?) So with a decent 3G database we could kinda sorta reach up to 6G before we start missing huge classes of reactions.

-- I'm sure people have thought of all these problems before, and maybe more, and that's why the collision census hasn't been done yet for more than two gliders. It still seems as if an exhaustive 3G search is a lot closer to being possible than 4G and above, though.
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby Goldtiger997 » April 24th, 2017, 1:01 am

16.623 in 9 gliders:

x = 26, y = 24, rule = B3/S23
11bo$10bo$10b3o$bo$2bo$3o7bo$11b2o$10b2o2$20bo$18b2o$19b2o3$23bo$23bob
o$23b2o$10b2o$10bobo7b3o$10bo9bo$15b2o4bo$6b2o7bobo$5bobo7bo$7bo!


dvgrn wrote:... or at least a better prebuilt database of small constellations...


I would find such a thing very useful, as it can take an hour for my computer to find a 3-glider collision to make the constellation I need, with my very slow clumsy method.

EDIT:

16.828 in 12 gliders (ugly):

x = 125, y = 148, rule = B3/S23
obo$b2o$bo65$77bobo$78b2o$78bo2$51bo$52bo$50b3o6bo18b2o$37bo22b2o15b2o
$35bobo21b2o18bo$36b2o15b2o$33b2o19b2o4bo$32bobo18bo6b2o$34bo24bobo2b
2o$63b2o$65bo37$116b2o$116bobo$116bo25$122b2o$122bobo$122bo!


16.930 in 10 gliders:

x = 49, y = 62, rule = B3/S23
22bo$20b2o$21b2o6$48bo$46b2o$47b2o8$3bo$bobo$2b2o$15bo$13b2o$14b2o2$5b
2o9bo$4bobo8b2o$6bo8bobo2$o$b2o$2o3$12b2o$3b2o8b2o$4b2o6bo$3bo22$35bo$
34b2o$34bobo!
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby yootaa » April 24th, 2017, 6:23 am

chris_c wrote:...
Now the maximum cost is 25G:

16.623 xs16_o5r8jdz01 25
16.828 xs16_4alhe8z0641 25
16.930 xs16_3iaj21e8zw1 25
16.1139 xs16_kq23z124871 25
16.1398 xs16_g88c93zc952 25
16.706 xs16_39s0qmz023 24
16.713 xs16_o8bap3z23 24
16.1034 xs16_3lkaa4z065 24
16.1323 xs16_031e8gzc9311 24
16.353 xs16_321fgc453 23
16.621 xs16_g5r8jdz11 23
16.829 xs16_0md1e8z1226 23
16.1702 xs16_4a5p68ozx121 23
16.1740 xs16_69acga6zx32 23
16.825 xs16_4alhe8zw65 22
16.1846 xs16_25a8c93zw33 22
16.2313 xs16_08u16853z32 22
16.159 xs16_2egmd1e8 21
16.218 xs16_3pajc48c 21
16.774 xs16_69raa4z32 21
16.1084 xs16_31ke12kozw11 21
16.1682 xs16_8k9bkk8zw23 21
16.1693 xs16_8k8aliczw23 21
16.1753 xs16_695q4gozw23 21
16.1954 xs16_8kk31e8z065 21
16.2096 xs16_wck5b8oz311 21
16.2309 xs16_8kk31e8z641 21
16.217 xs16_3146pajo 20
16.228 xs16_178bp2sg 20
16.712 xs16_3pc0qmzw23 20
16.723 xs16_i5p64koz11 20
16.833 xs16_0mp2sgz1243 20
16.872 xs16_2lla8oz065 20
16.1073 xs16_3lkaa4z641 20
16.1127 xs16_giligoz104a4 20
16.1739 xs16_g88r2qkz121 20
16.1791 xs16_03lkaa4z3201 20
16.1962 xs16_4a9eg8ozw65 20
16.2058 xs16_69akg4czx146 20

...


Don't miss this 16.1034 synthesis.
x = 62, y = 65, rule = B3/S23
60bo$59bo$59b3o12$33bo$34bo$32b3o$37bo$26b2o7b2o$25bobo8b2o$27bo$29b2o
$29bobo$29bo9$36bobo$36b2o$37bo2$27bo7b2o$28b2o5bobo$27b2o6bo3$24b3o$
26bo$25bo13bo$38bo$38b3o3$38b2o$38bobo$38bo12$bo$b2o$obo!

This might be useful for 16.1073 and 16.1791 synthesis.
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yootaa
 
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby BlinkerSpawn » April 24th, 2017, 4:01 pm

16.706 in 11:
x = 40, y = 54, rule = B3/S23
5bobo$6b2o$6bo8$23bo$24b2o$23b2o$14bo$12bobo$13b2o2$15b3o$17bo$16bo$
22b2o$21bobo$23bo2$38bo$37b2o$37bobo2$32b3o$32bo$27b2o4bo$26bobo$28bo
3$17b2o$16bobo$18bo2$28b2o$28bobo$28bo10$bo$b2o$obo!
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]
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BlinkerSpawn
 
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Re: 16 in 16: Efficient 16-bit Synthesis Project

Postby chris_c » April 24th, 2017, 7:29 pm

Goldtiger997 wrote:16.828 in 12 gliders (ugly):


Reduced to 11 which gives 16.825 in 15:

x = 156, y = 228, rule = Life
134b2o$33b2o99b2o$34b2o$33bo4bo$37b2o$37bobo23$obo$b2o$bo61$75bo$73bob
o$74b2o3$46bobo$47b2o7bo$47bo9bo94b2o$55b3o17b3o73bo2bo$34b2o39bo74bob
obo$34b2o40bo74bo2b2o$49b3o100b2o$51bo4b2o95bo$50bo4bobo93bo$57bo3b3o
87b2o$61bo$62bo64$120b2o$119b2o$121bo25$52b2o98b2o$51bo2bo96bo2bo$50bo
bobo95bobobo$51bo2b2o95bo2b2o$52b2o98b2o$53bo99bo$51bo100bo$51b2o99b2o
12$63b2o$37b2o23b2o$38b2o6b2o16bo$37bo7bobo$47bo4$44b2o$45b2o$44bo!


Goldtiger997 wrote:16.930 in 10 gliders

Reduced to 9:

x = 123, y = 150, rule = Life
13bo$11bobo$12b2o103bo$116bobo$15b2o99bobo$14bobo100bo$16bo59$56bo$55b
o$55b3o22$10bobo$11b2o$11bo6$4bo35bo$5bo32b2o$3b3o33b2o3$17bo$16bobo$
16bobo$17bo97bo2bobo$115b5obo$121bo$117bo3b2o$116bobo$117bo16$38bo$37b
2o$37bobo2$3o$2bo$bo15$45bo$44b2o$44bobo!


yootaa wrote:Don't miss this 16.1034 synthesis.
x = 62, y = 65, rule = B3/S23
60bo$59bo$59b3o12$33bo$34bo$32b3o$37bo$26b2o7b2o$25bobo8b2o$27bo$29b2o
$29bobo$29bo9$36bobo$36b2o$37bo2$27bo7b2o$28b2o5bobo$27b2o6bo3$24b3o$
26bo$25bo13bo$38bo$38b3o3$38b2o$38bobo$38bo12$bo$b2o$obo!

This might be useful for 16.1073 and 16.1791 synthesis.


Thanks. That synthesis didn't make it into the database because there was a trivial error in the construction of the blinker. It brings 16.1073 down to 17G but doesn't appear to improve 16.1791.

BlinkerSpawn wrote:16.706 in 11:
x = 40, y = 54, rule = B3/S23
5bobo$6b2o$6bo8$23bo$24b2o$23b2o$14bo$12bobo$13b2o2$15b3o$17bo$16bo$
22b2o$21bobo$23bo2$38bo$37b2o$37bobo2$32b3o$32bo$27b2o4bo$26bobo$28bo
3$17b2o$16bobo$18bo2$28b2o$28bobo$28bo10$bo$b2o$obo!


It brings 16.745 down to 16G. Are there any constellations that can reduce this further?

x = 135, y = 432, rule = Life
11bo$9bobo$10b2o3$116b3o2$114bo5bo$114bo5bo$114bo5bo$16bo$14bobo99b3o$
15b2o2$6b2o$5bobo$7bo113b2o$121b2o2$17b3o$19bo$18bo55$55bo$54bo$54b3o$
10bo$8bobo$9b2o23$134bo$16b3o97b3o15bo$134bo$14bo5bo93bo5bo$14bo5bo93b
o5bo$14bo5bo93bo5bo2$16b3o97b3o5$21b2o98b2o$21b2o98b2o56$64bo$64bobo$
64b2o15$8bobo$9b2o$9bo12$17bo96b2o$17bo15b3o78b2o$17bo$118b2obo$13b3o
3b3o96bob2o2$17bo101b5o$17bo99bo2bo2bo$17bo99b2o4$21b2o$21b2o15$54b2o$
54bobo$54bo5$5b2o$4bobo$6bo58$10bo$11bo$9b3o3$14b2o$14b2o2$18b2obo96b
2obo$18bob2o96bob2o2$19b5o95b5o$17bo2bo2bo93bo2bo2bo$17b2o98b2o87$2bo$
obo$b2o6$18b2obo96b2obo$18bob2o96bob2o2$19b5o95b5o$17bo2bo2bo96bo2bo$
17b2o99bo$118b2o13$9bo$2b2o5b2o24bo$bobo4bobo23b2o$3bo9b2o19bobo$12bob
o$14bo!


Still lifes at 20G or above:

16.1139    xs16_kq23z124871         25
16.1398    xs16_g88c93zc952         25
16.713     xs16_o8bap3z23           24
16.1323    xs16_031e8gzc9311        24
16.353     xs16_321fgc453           23
16.621     xs16_g5r8jdz11           23
16.829     xs16_0md1e8z1226         23
16.1702    xs16_4a5p68ozx121        23
16.1740    xs16_69acga6zx32         23
16.1846    xs16_25a8c93zw33         22
16.2313    xs16_08u16853z32         22
16.159     xs16_2egmd1e8            21
16.218     xs16_3pajc48c            21
16.774     xs16_69raa4z32           21
16.1084    xs16_31ke12kozw11        21
16.1682    xs16_8k9bkk8zw23         21
16.1693    xs16_8k8aliczw23         21
16.1753    xs16_695q4gozw23         21
16.1954    xs16_8kk31e8z065         21
16.2096    xs16_wck5b8oz311         21
16.2309    xs16_8kk31e8z641         21
16.217     xs16_3146pajo            20
16.228     xs16_178bp2sg            20
16.712     xs16_3pc0qmzw23          20
16.723     xs16_i5p64koz11          20
16.833     xs16_0mp2sgz1243         20
16.872     xs16_2lla8oz065          20
16.1127    xs16_giligoz104a4        20
16.1739    xs16_g88r2qkz121         20
16.1791    xs16_03lkaa4z3201        20
16.1962    xs16_4a9eg8ozw65         20
16.2058    xs16_69akg4czx146        20
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