16 in 16: Efficient 16-bit Synthesis Project

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

dvgrn wrote: I'm a little worried about 16.3032 / xs16_1784ozx342sg, the last still life on the list, since it only shows up in symmetrical soups, and the only likely-looking soup out of the whole bunch seems as if it's going to end up taking eight pairs of gliders to reproduce the recipe... and I bet that's exactly where the current cost comes from!
The current recipe comes from 14.463 and four extra gliders. There are 27 soups for that still life.

Code: Select all

``````x = 19, y = 17, rule = B3/S23
2o\$bo\$bobo\$2bobo\$4bo\$3bo\$3bobo\$4bobo\$5bo2\$13b2o\$12b2o\$14bo\$17b2o\$2o6b
2o6b2o\$b2o4bobo8bo\$o8bo!
``````
Trickier still could be 16.2323. The best way could be to reduce 15.660 to 11G but there are only 15 soups.

Code: Select all

``````x = 21, y = 27, rule = B3/S23
16bo\$15bo\$15b3o8\$o\$3o14bo\$3bobo10bo\$2o2b2o10b3o\$o\$bo17bo\$2bo15b2o\$b2o
15bobo7\$17bo\$16b2o\$16bobo!
``````

Extrementhusiast
Posts: 1817
Joined: June 16th, 2009, 11:24 pm
Location: USA

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

chris_c wrote:Trickier still could be 16.2323. The best way could be to reduce 15.660 to 11G but there are only 15 soups.

Code: Select all

``RLE``
Whole thing in thirteen gliders via more traditional method (and using the other lengthening):

Code: Select all

``````x = 72, y = 29, rule = B3/S23
3bo\$4bo12bo\$2b3o11bo\$16b3o\$7bo\$5bobo\$6b2o\$41bo23bo\$obo38b3o21b3o\$b2o
41bo23bo\$bo39b2o2bobo17b2o2bobo\$41bo4b2o17bo4b2o\$2b3o37bo23bo\$4bo36b2o
24bo\$3bo11b3o48b2o\$15bo\$11bo4bo\$10b2o\$10bobo\$bo\$b2o\$obo\$10bo\$9b2o19b2o
\$9bobo17bobo9b2o11b2o\$31bo8bobo10b2o\$42bo2b2o8bo\$44b2o\$46bo!
``````
Along the way, I had also found a sixteen-glider method (but obviously, that wasn't enough):

Code: Select all

``````x = 110, y = 25, rule = B3/S23
90bobo\$24bo53bo11b2o\$24bobo52b2o10bo\$24b2o46bo5b2o\$70bobo\$23bo47b2o4bo
\$21bobo53b2o\$22b2o25b2o25bobo6b2o\$48bo2bo32bo2bo21bo\$47bob3o31bob3o19b
3o\$46bobo33bobo21bo\$18b2o5b2o19b2o2b2o30b2o2b2o15bobo2b2o\$19b2o5bo24bo
35bo15b2o4bo\$2o16bo7bobo22bobo32bo21bo\$b2o24b2o23b2o31bo21bo\$o3b2o74b
2o3b2o20b2o\$4bobo73bobo\$4bo69b2o4bo\$41b3o6b2o21bobo\$43bo6bobo22bo\$42bo
7bo\$55b3o23b3o\$48b2o5bo25bo\$47bobo6bo25bo\$49bo!
``````
I Like My Heisenburps! (and others)

Goldtiger997
Posts: 570
Joined: June 21st, 2016, 8:00 am

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

chris_c wrote:
dvgrn wrote: I'm a little worried about 16.3032 / xs16_1784ozx342sg, the last still life on the list, since it only shows up in symmetrical soups, and the only likely-looking soup out of the whole bunch seems as if it's going to end up taking eight pairs of gliders to reproduce the recipe... and I bet that's exactly where the current cost comes from!
The current recipe comes from 14.463 and four extra gliders. There are 27 soups for that still life.
16.3032 in 13 gliders:

Code: Select all

``````x = 116, y = 21, rule = B3/S23
12bobo\$obo10b2o\$b2o10bo56bobo\$bo21bobo45b2o\$16bo6b2o46bo\$9bo5bo8bo\$7bo
bo5b3o55bobo\$8b2o64b2o\$74bo\$19bo\$15bob2o5bo\$13bobo2b2o4bobo42b3o\$14b2o
8b2o45bo\$70bo35bo\$48bo29bo27b3o\$47bobo27bobo29bo\$48bo2b2o25bo2b2o25bo
2b2o\$26b2o21b2o2bo25b2o2bo25b2o2bo\$25b2o25bo17bo11bo29bo\$27bo25b3o14b
2o11b3o27b3o\$55bo13bobo13bo29bo!
``````

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

Nice to see a couple of tricky ones go down. I also had a go at some of the rare ones:

16.380:

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``````x = 69, y = 62, rule = B3/S23
12bo50b2o\$13b2o45bo2bobobo\$12b2o45bobobo2b2o\$bobo56bo2bo\$2b2o59b2o\$2bo
8b3o\$13bo\$12bo\$19b2o\$18bobo\$19bo4\$6b2o\$7b2o\$6bo8\$37bo\$b2o33b2o\$obo33bo
bo\$2bo17\$23bobo\$23b2o\$24bo4\$13b2o48b2o\$10bo2bobobo42bo2bobo\$9bobobo2b
2o41bobobo2bobo\$10bo2bo46bo2bo3b2o\$13b2o11bo36b2o\$26bobo\$26b2o2\$19b2o\$
18bobo3b2o\$20bo2b2o\$25bo!
``````
16.300:

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``````x = 69, y = 139, rule = B3/S23
22bobo\$22b2o\$23bo11\$8bo49b2o\$7bobo49bo\$8b2o49bob2o\$58b2o2bo\$60bo\$58b2o
6b3o\$58bo\$13b2o5bo39bo\$5b2o5b2o5b2o38b2o\$6b2o6bo4bobo\$5bo\$9b2o\$8bobo\$
10bo4\$3o\$2bo\$bo3\$b2o8b3o\$2b2o7bo\$bo10bo26\$8b2o48b2o\$9bo49bo\$9bob2o46bo
b2o\$8b2o2bo45b2o2bo\$10bo6bo42bo\$8b2o7bo40b2o\$8bo8bo40bo\$10bo49bo\$9b2o
48b2o2\$21b3o\$21bo\$22bo38\$8b2o48b2o\$9bo49bo\$9bob2o46bob2o\$8b2o2bo45b2o
2bo\$10bo49bo\$8b2o48b2o\$8bo49bo\$10bo48bo\$9b2o47b2o7\$2b2o\$3b2o13b2o\$2bo
6b2o6b2o\$9bobo7bo\$9bo4\$11b2o\$10b2o\$12bo!
``````
16.1675:

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``````x = 75, y = 49, rule = B3/S23
3bobo\$4b2o\$4bo14\$72b2o\$16bo55bobo\$16b2o56bo\$15bobo8b3o44bo\$3o17b2o4bo
45bo\$2bo17bobo4bo43bo\$bo18bo49bo\$70b2o\$71bo\$7b3o60bo\$9bo59bo\$8bo60b2o
2\$48b3o\$48bo\$49bo3\$30b2o\$30bobo\$30bo\$6b2o\$7b2o\$6bo7\$50bo\$49b2o\$49bobo!
``````
16.2030 (just a two glider cleanup instead of three for an old component):

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``````x = 19, y = 19, rule = B3/S23
13bo\$6bo6bobo\$7bo5b2o\$5b3o\$bo15bo\$2bo13bo\$3o13b3o2\$5b2o5b2o\$4bo2bo3bo
2bo\$4bobo5bobo\$5bo7bo2\$7b2ob2o\$7bo3bo\$8b3o\$6bobo\$5bobo\$6bo!
``````
16.2317:

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``````x = 76, y = 118, rule = B3/S23
66bo\$65bobo\$65bobo\$8bobo7bo47bo\$obo6b2o5b2o\$b2o6bo7b2o42b2o7b2o\$bo59b
2o6bo2bo\$70b2o\$7bobo56b2o\$8b2o56b2o\$8bo\$15bobo45b2o5bo2b2o\$16b2o10bo
34b2o4bobo2bo\$16bo11bobo38bo2b2o\$28b2o40b2o\$20b3o48bo\$22bo46bo\$21bo47b
2o5\$8b2o\$9b2o\$8bo21\$30bo\$18bo11bobo\$16bobo11b2o\$17b2o2\$16bo\$15bobo\$15b
obo\$16bo2\$11b2o7b2o\$11b2o6bo2bo\$20b2o\$16b2o\$16b2o2\$13b2o5bo2b2o45bo2b
2o\$13b2o4bobo2bo44bobo2bo\$19bo2b2o45bo2b2o\$20b2o48b2o\$21bo49bo\$19bo49b
o\$19b2o48b2o31\$25bo\$15bo10bo\$16b2o6b3o\$15b2o3\$26bo4bo\$24bobo2b2o\$25b2o
3b2o4\$74bo\$20bo2b2o45bo2bobo\$19bobo2bo9b2o33bobo2bo\$19bo2b2o10bobo32bo
2b2o\$20b2o12bo35b2o\$21bo49bo\$19bo49bo\$19b2o48b2o!
``````
Latest list contains 35 SLs:

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``````16.640     xs16_c9bkkozw32          17
16.716     xs16_3pmk46zx23          17
16.748     xs16_39ege2z321          17
16.799     xs16_c8al56z311          17
16.875     xs16_4a5pa4z2521         17
16.1722    xs16_4aq32acz032         17
16.1758    xs16_4a4o796zw121        17
16.1847    xs16_39c8a52z033         17
16.1882    xs16_259m453zx23         17
16.243     xs16_2egu16426           16
16.302     xs16_5b8o642ac           16
16.360     xs16_2egu16413           16
16.593     xs16_3123c48gka4         16
16.771     xs16_69qb8oz32           16
16.772     xs16_3h4e1daz011         16
16.810     xs16_ca9la4z311          16
16.822     xs16_8ehikozw56          16
16.836     xs16_4aajkczx56          16
16.838     xs16_ci9b8ozw56          16
16.856     xs16_kc32acz1252         16
16.995     xs16_0raik8z643          16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1717    xs16_4aajk46zx121        16
16.1739    xs16_g88r2qkz121         16
16.1766    xs16_kc321e8z123         16
16.1787    xs16_069m4koz311         16
16.1929    xs16_0g5r8b5z121         16
16.1994    xs16_0g9fgka4z121        16
16.2028    xs16_25ao48cz2521        16
16.2029    xs16_25ao4a4z2521        16
16.2219    xs16_0oe12koz643         16
16.2305    xs16_6413ia4z6421        16
16.2322    xs16_raak8zx1252         16
16.2630    xs16_31e8gzxo9a6         16
``````
EDIT:
Extrementhusiast wrote:Along the way, I had also found a sixteen-glider method (but obviously, that wasn't enough)
The eater-to-python component contained in that sequence reduces 29 still lifes in my list (although nothing above 15G). Is it new or have I just missed it previously?

Extrementhusiast
Posts: 1817
Joined: June 16th, 2009, 11:24 pm
Location: USA

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

chris_c wrote:EDIT:
Extrementhusiast wrote:Along the way, I had also found a sixteen-glider method (but obviously, that wasn't enough)
The eater-to-python component contained in that sequence reduces 29 still lifes in my list (although nothing above 15G). Is it new or have I just missed it previously?
No, it's new.
I Like My Heisenburps! (and others)

Goldtiger997
Posts: 570
Joined: June 21st, 2016, 8:00 am

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

16.2028 in 14 gliders:

Code: Select all

``````x = 112, y = 39, rule = B3/S23
39bo\$o38bobo\$b2o36b2o\$2o2\$21bo\$22bo\$20b3o\$78bobo\$78b2o\$79bo\$72bo\$73bo\$
20bo29bo20b3o6bo29bo\$18bobo28bobo27bobo27bobo\$19b2o8bo16b2o2bo17b3o5b
2o2bo24bobo2bo\$28bo17bob2o20bo5bob2o25b2ob2o\$19bo8b3o17bo20bo8bo29bo\$
19b2o27bobo27bobo27bobo\$18bobo10b3o15bobo27bobo27bobo\$31bo18bo29bo29bo
\$3b2o27bo\$4b2o17bo\$3bo14b2o2b2o\$19b2obobo\$18bo11\$30b2o\$30bobo\$30bo!
``````
16.302 in 12 gliders:

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``````x = 30, y = 31, rule = B3/S23
28bo\$27bo\$27b3o3\$20bo\$19bo\$14bo4b3o\$13bo\$13b3o\$2bo\$obo19b3o\$b2o15bo3bo
\$13b2ob2o5bo\$12bobo2b2o\$14bo3\$20bobo\$21b2o\$21bo\$17b2o\$16bobo\$18bo2\$5bo
\$5b2o\$4bobo\$17bo9bo\$16b2o8b2o\$16bobo7bobo!
``````
Now all remaining still-lifes have appearances on catagolue.

Posts: 1938
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

16.640 in 8:

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``````x = 33, y = 31, rule = B3/S23
22bo\$21bo\$21b3o\$13bo\$11bobo\$12b2o2\$32bo\$30b2o\$31b2o10\$16bo13bobo\$16b2o
13b2o\$2o13bobo13bo\$b2o24b3o\$o28bo\$28bo4\$25b3o\$27bo\$26bo!
``````
EDIT: 16.716 in no more than 14:

Code: Select all

``````x = 122, y = 63, rule = B3/S23
30bo\$29bo\$29b3o24\$107b2o\$b2o12b3o8b2o78bo2bo\$b2o14bo8b2o79b2o\$15b3o2\$b
2o\$b2o6bo75b2o15bo\$8bobo70bo2bobo14bobo\$8bobo70b4o16bo2bo\$9bo75bo16b2o
\$83b3o\$82bo36b2o\$82b2o35bobo\$119bo2\$111b2o\$111bobo\$111bo10\$45bo\$44b2o\$
44bobo5\$bo\$b2o\$obo!
``````
16.748 in 12, maybe 11:

Code: Select all

``````x = 62, y = 53, rule = B3/S23
11bobo45bobo\$12b2o45b2o\$12bo47bo14\$34b2o\$33bo2bo\$34bobo\$35bo\$30b3o8\$
29b2o\$29bobo\$30bo4\$31bo\$30b3o7\$57bo\$56b2o\$56bobo6\$bo\$b2o\$obo!
``````
16.799 in around 10, I hope:

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``````x = 15, y = 13, rule = B3/S23
3bo\$4b2o\$3b2o2\$13bo\$12b2o\$7b2o3bo\$6b2obo2bo\$2o5bob2o2b2o\$8b2o3bo\$2b3o\$
4bo\$2b2o!
``````
Last edited by BlinkerSpawn on May 19th, 2017, 8:23 pm, edited 4 times in total.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

Goldtiger997 wrote:16.2028 in 14 gliders:
The base still life there also would have given 16.2029 in 14G. Anyhow I reduced both to 10G:

Code: Select all

``````x = 52, y = 55, rule = B3/S23
bo\$2b2o\$b2o2\$10bobo\$10b2o\$11bo\$46bo\$45bobo\$12bo33bo2b2o\$11bo35b2obo\$
11b3o34bo\$46bobo\$10bo34bobo\$8bobo35bo\$9b2o3\$b2o\$obo\$2bo\$12b2o\$12bobo\$
12bo\$3b2o\$2bobo\$4bo15\$9bo\$10bo\$8b3o2\$14bobo\$14b2o\$6bo8bo30bo\$5bobo37bo
bo2bo\$6bo2b2o6b3o26bo2bobo\$7b2obo6bo29b2obo\$8bo9bo29bo\$6bobo37bobo\$5bo
bo37bobo\$6bo39bo!
``````
16.875:

Code: Select all

``````x = 80, y = 122, rule = B3/S23
2bo35bobo\$obo35b2o\$b2o30bobo3bo\$33b2o\$34bo4\$18bo\$19b2o\$18b2o4\$16bo\$17b
o54bo2b2ob2o\$15b3o53bobo2bob2o\$72bob2o\$74bo\$19bo15b2o35bobo\$19b2o13b2o
35bobo\$18bobo15bo35bo8\$12b2o\$11bobo\$13bo29\$33bo\$32bo\$32b3o3\$22bo2b2ob
2o42bo2b2o\$21bobo2bob2o41bobo2bo\$22bob2o46bob2o\$24bo49bo\$22bobo47bobo\$
21bobo47bobo\$22bo49bo34\$23bobo9bo\$23b2o8b2o\$18bo5bo9b2o\$19b2o\$18b2o5\$
73b2o\$11b3o8bo2b2o45bo2bo\$13bo7bobo2bo44bobo2bo\$12bo9bob2o46bob2o\$24bo
49bo\$22bobo47bobo\$21bobo47bobo\$22bo49bo!
``````
I made a component for 16.593:

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``````x = 69, y = 66, rule = B3/S23
14bo\$13bo\$13b3o4\$2bo\$3b2o\$2b2o\$58b2obo\$58bob2o\$6bo55b2o\$6b2o54bobo\$5bo
bo2b2o51b2o\$10bobo\$10bo9\$bo\$b2o\$obo4\$17bo\$18bo\$16b3o4\$22bo\$22bobo\$22b
2o\$8b2obo46b2obo\$8bob2o46bob2o5bo\$12b2o5b2o41b2o2bobo\$12bobo4bobo40bob
o2bo\$13b2o4bo45b2o10\$33b2o\$33bobo\$33bo2\$8b2o\$9b2o\$8bo21b2o\$29b2o\$31bo
3b2o\$34b2o\$8b2o26bo\$9b2o\$8bo!
``````
It was based on this soup (roughly generation 90):

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``````x = 16, y = 16, rule = B3/S23
bo2bob4ob3o\$bo2bob2o2b4obo\$bob2ob2ob2o3bo\$7o2bo4b2o\$3b2o2bobob3o\$3b2ob
obo2bob2o\$3obobobob2o2bo\$2bob2obob2o3bo\$obob2ob2obobo2bo\$3ob3o3bob4o\$
3b3o2bobob2obo\$ob2obob3obo2b2o\$2o3b3o2bo2bo\$2obobo3bo2bo\$o2b3ob3o2b4o\$
2bo2b6o3bo!
``````
Now 29 remain (BlinkerSpawn's recent synth is taken out of the list by hand but is not in the repo yet):

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``````16.716     xs16_3pmk46zx23          17
16.748     xs16_39ege2z321          17
16.799     xs16_c8al56z311          17
16.1722    xs16_4aq32acz032         17
16.1758    xs16_4a4o796zw121        17
16.1847    xs16_39c8a52z033         17
16.1882    xs16_259m453zx23         17
16.243     xs16_2egu16426           16
16.360     xs16_2egu16413           16
16.771     xs16_69qb8oz32           16
16.772     xs16_3h4e1daz011         16
16.810     xs16_ca9la4z311          16
16.822     xs16_8ehikozw56          16
16.836     xs16_4aajkczx56          16
16.838     xs16_ci9b8ozw56          16
16.856     xs16_kc32acz1252         16
16.995     xs16_0raik8z643          16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1717    xs16_4aajk46zx121        16
16.1739    xs16_g88r2qkz121         16
16.1766    xs16_kc321e8z123         16
16.1787    xs16_069m4koz311         16
16.1929    xs16_0g5r8b5z121         16
16.1994    xs16_0g9fgka4z121        16
16.2219    xs16_0oe12koz643         16
16.2305    xs16_6413ia4z6421        16
16.2322    xs16_raak8zx1252         16
16.2630    xs16_31e8gzxo9a6         16
``````

Goldtiger997
Posts: 570
Joined: June 21st, 2016, 8:00 am

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

16.716 in 8 gliders:

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``````x = 72, y = 25, rule = B3/S23
16bo\$14b2o\$2bo12b2o\$3b2o\$2b2o5\$11bo\$12bo13bo2b2o15bo2b2o19b2o\$10b3o13b
4obo14b4obo14bo2bobo\$6b3o22bo19bo14b4o\$8bo19b3o17b3o19bo\$7bo19bo19bo
20b3o\$27b2o18b2o18bo\$2o65b2o\$b2o53b2o2b2o\$o54bobob2o\$57bo3bo3\$45bo\$45b
2o\$44bobo!
``````
I haven't seen that converter before, but it's probably not new.
BlinkerSpawn wrote:16.748 in 12, maybe 11:

Code: Select all

``````x = 62, y = 53, rule = B3/S23
11bobo45bobo\$12b2o45b2o\$12bo47bo14\$34b2o\$33bo2bo\$34bobo\$35bo\$30b3o8\$
29b2o\$29bobo\$30bo4\$31bo\$30b3o7\$57bo\$56b2o\$56bobo6\$bo\$b2o\$obo!
``````
16.748 in 11 gliders:

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``````x = 64, y = 57, rule = B3/S23
11bo51bo\$12b2o47b2o\$11b2o49b2o19\$33bo\$34b2o\$33b2o4\$33b3ob3o\$35bobo\$28b
o5bo3bo\$29bo\$27b3o3bo\$32b2o\$32bobo5\$33b2o\$32b2o\$34bo\$27b3o\$29bo\$28bo3\$
59b2o\$58b2o\$60bo6\$2o\$b2o\$o!
``````
Last edited by Goldtiger997 on May 20th, 2017, 6:31 am, edited 2 times in total.

yootaa
Posts: 35
Joined: May 26th, 2016, 1:08 am
Location: Japan

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

16.1847 in 10G.
It must be a better way...

Code: Select all

``````x = 103, y = 28, rule = B3/S23
17bobo\$18b2o\$18bo6\$bo\$2bo77bo3b2o\$3o76bobo3bo\$70bo9bo2bo\$12bo55bobo10b
4o\$13bo55b2o\$11b3o12bo56b2o\$7b2o15b2o57b2o\$6bobo16b2o45b2o\$8bo63b2o\$
100b2o\$59b2o38bo2bo\$59b2o39b2o2\$5b2o59bo29bo\$4bobo21b3o34bobo27bobo\$6b
o21bo36bobo27bobo\$29bo31b2o3bo29bo3b2o\$60bobo37bobo\$62bo37bo!``````

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

BlinkerSpawn wrote: 16.748 in 12, maybe 11:
In 10G (improved cleanup compared to Goldtiger's implementation):

Code: Select all

``````x = 89, y = 165, rule = B3/S23
29bo\$27bobo\$28b2o56b2o\$85bo2bo\$28b2o4bo51bobo\$27bobo3b2o52bo\$29bo3bobo
48bo\$84bo\$84bo44\$36b2o48b2o\$35bo2bo46bo2bo\$36bobo47bobo\$23bo13bo49bo\$
21bobo10bo49bo\$22b2o10bo40bo8bo\$29bo4bo39bobo7bo\$28b2o45b2o\$28bobo17\$
46bo\$46bobo\$46b2o23\$36b2o37b2o\$35bo2bo36bobob2o\$36bobo38bobo\$16bobo18b
o38b2obo\$17b2o15bo43bo8bo\$17bo7bo8bo40bobo8bobo\$24bobo7bo40b2o9bobo\$
25b2o60bo\$14b2o\$13bobo\$15bo25\$bo\$b2o\$obo13\$25b2o48b2o\$25bobob2o44bobob
2o\$27bobo47bobo\$26b2obo46b2obo\$28bo8bo40bo\$25bobo8bobo36bobo\$25b2o9bob
o36b2o\$37bo3\$41b2o\$41bobo\$41bo!
``````
BlinkerSpawn wrote: 16.799 in around 10, I hope:
In 8G:

Code: Select all

``````x = 27, y = 27, rule = B3/S23
obo\$b2o\$bo2\$23bo\$22bo\$15bo6b3o\$15bobo\$15b2o\$24bo\$23bo\$23b3o3\$3o3bo\$2bo
2b2o\$bo3bobo4\$18bo\$17b2o\$17bobo2\$25b2o\$24b2o\$26bo!
``````
Goldtiger997 wrote: 16.716 in 8 gliders. I haven't seen that converter before, but it's probably not new.
I don't know if it's new or not but it also reduces 16.717 to 10G.
yootaa wrote:16.1847 in 10G.
It must be a better way...
Reduced the cleanup by 1G:

Code: Select all

``````x = 76, y = 80, rule = B3/S23
60bo\$58bobo\$59b2o7\$41bobo\$42b2o\$42bo2\$52bobo\$53b2o15bo\$53bo15bo\$69b3o
3\$48b2o\$49b2o\$48bo5\$46b2o26bo\$47b2o24b2o\$46bo26bobo49\$3o\$2bo\$bo!
``````
Some others.....16.1882:

Code: Select all

``````x = 139, y = 170, rule = B3/S23
27bo\$27bobo96b2o\$27b2o97b2o2\$27b2o97b2o\$27bobo96b2o\$27bo21\$bo\$2bo63bo\$
3o61b2o\$65b2o9\$41bo\$39b2o\$40b2o94bo\$135bobo\$135bo2bo\$136b2o\$35bo5b2o\$
36bo4bobo\$34b3o4bo\$48bo\$48bobo\$48b2o\$26b2o\$26b2o103b2o2b2o\$130bo2bo2bo
\$26b2o103bob3o\$26b2o104bo\$133bo\$132b2o\$47b3o\$47bo\$48bo26\$41bo\$41bobo\$
41b2o3\$36bo\$35bobo\$35bo2bo\$36b2o7\$79bo\$31b2o2b2o41b2o51b2o2b2o\$30bo2bo
2bo41bobo49bo2bo2bo\$31bob3o95bob3o\$32bo99bo\$33bo99bo\$32b2o98b2o45\$31b
2o2b2o94b2o2b2o\$30bo2bo2bo93bo2bo2bo\$31bob3o95bob3o\$32bo99bo\$33bo99bo\$
32b2o7bo92bo\$40bo92b2o\$40b3o5\$24b2o16bo\$25b2o14b2o\$24bo16bobo\$34b3o\$
36bo\$35bo!
``````
16.771:

Code: Select all

``````x = 72, y = 70, rule = B3/S23
5bo22bo\$3bobo21bo\$4b2o21b3o\$12bo\$10bobo\$11b2o2\$21bobo\$21b2o\$22bo4\$69bo
\$67b3o\$66bo\$67b5o\$68bo2bo\$26bo39bo\$17b2o6b2o39b2o\$16bobo6bobo\$18bo5\$
31bo\$30b2o\$30bobo2\$8b2o\$7bobo\$9bo16\$24bo5bo\$24bobob2o\$24b2o3b2o2\$obo\$b
2o\$bo9\$19bo47bobo\$17b3o46bob2o\$16bo49bo\$17b5o45b5o\$18bo2bo46bo2bo\$16bo
49bo\$16b2o48b2o!
``````
16.2305 using a standard converter but where the pre-block construction has a thinner envelope:

Code: Select all

``````x = 27, y = 21, rule = B3/S23
o\$b2o\$2o19bo\$20bo\$20b3o3\$9bo\$10b2o\$9b2o3\$17b2o\$10bobo5b2o3bo\$11b2o4bo
5b3o\$11bo14bo\$25bo\$7b3o5b2o7bo\$9bo6b2o5bo\$8bo6bo4bobo\$20b2o!
``````
Latest list contains 22 SLs:

Code: Select all

``````16.1722    xs16_4aq32acz032         17
16.1758    xs16_4a4o796zw121        17
16.243     xs16_2egu16426           16
16.360     xs16_2egu16413           16
16.772     xs16_3h4e1daz011         16
16.810     xs16_ca9la4z311          16
16.822     xs16_8ehikozw56          16
16.836     xs16_4aajkczx56          16
16.838     xs16_ci9b8ozw56          16
16.856     xs16_kc32acz1252         16
16.995     xs16_0raik8z643          16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1717    xs16_4aajk46zx121        16
16.1739    xs16_g88r2qkz121         16
16.1766    xs16_kc321e8z123         16
16.1787    xs16_069m4koz311         16
16.1929    xs16_0g5r8b5z121         16
16.1994    xs16_0g9fgka4z121        16
16.2219    xs16_0oe12koz643         16
16.2322    xs16_raak8zx1252         16
16.2630    xs16_31e8gzxo9a6         16
``````

Goldtiger997
Posts: 570
Joined: June 21st, 2016, 8:00 am

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

16.1722 in 6 gliders:

Code: Select all

``````x = 22, y = 11, rule = B3/S23
o9bo10bo\$b2o5bobo8b2o\$2o7b2o9b2o3\$16b2o\$16bobo\$12b2o2bo\$4b2o7b2o\$3bobo
6bo\$5bo!``````

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

Goldtiger997 wrote:16.1722 in 6 gliders
And here is 161758 in 8G:

Code: Select all

``````x = 30, y = 25, rule = B3/S23
7bo\$5bobo\$6b2o3\$14bo13bo\$12bobo12bo\$13b2o12b3o6\$2bo\$obo10b2o\$b2o9bo2bo
\$13b2o5b2o\$20bobo\$20bo4\$12b2o\$13b2o\$12bo!
``````
Now everything is at most 16G and there are just 20 left:

Code: Select all

``````16.243     xs16_2egu16426           16
16.360     xs16_2egu16413           16
16.772     xs16_3h4e1daz011         16
16.810     xs16_ca9la4z311          16
16.822     xs16_8ehikozw56          16
16.836     xs16_4aajkczx56          16
16.838     xs16_ci9b8ozw56          16
16.856     xs16_kc32acz1252         16
16.995     xs16_0raik8z643          16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1717    xs16_4aajk46zx121        16
16.1739    xs16_g88r2qkz121         16
16.1766    xs16_kc321e8z123         16
16.1787    xs16_069m4koz311         16
16.1929    xs16_0g5r8b5z121         16
16.1994    xs16_0g9fgka4z121        16
16.2219    xs16_0oe12koz643         16
16.2322    xs16_raak8zx1252         16
16.2630    xs16_31e8gzxo9a6         16
``````

dvgrn
Moderator
Posts: 6271
Joined: May 17th, 2009, 11:00 pm
Contact:

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

chris_c wrote:Now everything is at most 16G and there are just 20 left...
The rate of progress has been impressive lately -- and @chris_c, I'd say it really wouldn't have been possible without your organization of the effort. Thanks!

I've been thinking a little bit about what to do next with all these syntheses, along the lines of making online access a little easier. Apple Bottom has added a link to the up-to-12-bit synthesis builder in the LifeWiki infobox -- see for example beehive at beehive.

The link shows up for some still lifes but not others, and I haven't looked into why that is exactly -- work in progress. How hard will it be to get that page working for everything up to 16 bits -- and might it make sense to host it somewhere else, like maybe on conwaylife.com?

-- Just by the way: if the title of this thread were to be taken literally, y'all would suddenly be done already...!

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

dvgrn wrote:@chris_c, I'd say it really wouldn't have been possible without your organization of the effort. Thanks!
No problem. Just please nobody mention 17-bit still lifes for at least a little while!
dvgrn wrote: I've been thinking a little bit about what to do next with all these syntheses, along the lines of making online access a little easier. Apple Bottom has added a link to the up-to-12-bit synthesis builder in the LifeWiki infobox -- see for example beehive at beehive.

The link shows up for some still lifes but not others, and I haven't looked into why that is exactly -- work in progress. How hard will it be to get that page working for everything up to 16 bits -- and might it make sense to host it somewhere else, like maybe on conwaylife.com?
Not hard at all. The website just consists of these two files and a copy of lv-plugin.js. The glider synthesis data is taken from here and dumped line by line within quotes toward the end of display_synth.js. To go up to 16-bit still lifes would make the size of display_synth.js roughly 500K.

The system is capable of holding syntheses of oscillators as well as still lifes. If someone can supply a list of apgcodes that the wiki should provide syntheses for then I can provide a corresponding version of display_synth.js.

A preliminary step in this project was creating a translation between Niemiec's still life numbering and apgcodes. The fact that a similar list does not exist for oscillators is the only reason that I didn't reply to Goldtiger's query here.

yootaa
Posts: 35
Joined: May 26th, 2016, 1:08 am
Location: Japan

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

16.822 in 10G:

Code: Select all

``````x = 49, y = 19, rule = B3/S23
46bo\$8bo37bobo\$2o4b2o7bo30b2o\$2o5b2o6bobo17b2o\$15b2o19bo6bo\$35bo6bobo\$
12bo22b4o2bo2bo\$12bo20b2o3bo3b2o\$3bo8bo21bo2bo\$3b2o29bobo\$2bobo30bo3\$
9b2o\$9bobo\$9bo\$b2o\$obo\$2bo!
``````
EDIT: Components:

Code: Select all

``````x = 89, y = 42, rule = B3/S23
31bo\$30bobo51bo\$29bo2bo51bo\$30b2o52bo2\$80b3o3b3o\$30bo\$30b2o4b3o45bo\$
29b2o53bo\$84bo3\$78bo\$77bobo5b3o\$77bobo5bo2bo\$27b2o49bo6bo2bo\$28bo6b3o
48b2o\$25bo2bo\$26b2o46b2o\$74b2o2\$79bo\$78bobo\$77bo2bo\$55b2o21b2o\$56b2o\$
55bo13\$b2o\$obo\$2bo!
``````

Jormungant
Posts: 130
Joined: May 27th, 2016, 1:01 am

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

got 16.1739 (aka xs16_g88r2qkz121) in 8 gliders!

Code: Select all

``````x = 60, y = 74, rule = B3/S23
57bobo\$57b2o\$58bo16\$50bo\$50bobo\$50b2o14\$31bobo\$20bo11b2o\$18bobo11bo\$
19b2o\$30b2o\$29b2o\$21b3o7bo\$23bo\$22bo12\$54b3o\$54bo\$55bo15\$2o\$b2o\$o!
``````
Enjoy!

AbhpzTa
Posts: 485
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

Jormungant wrote:got 16.1739 (aka xs16_g88r2qkz121) in 8 gliders!

Code: Select all

``````x = 60, y = 74, rule = B3/S23
57bobo\$57b2o\$58bo16\$50bo\$50bobo\$50b2o14\$31bobo\$20bo11b2o\$18bobo11bo\$
19b2o\$30b2o\$29b2o\$21b3o7bo\$23bo\$22bo12\$54b3o\$54bo\$55bo15\$2o\$b2o\$o!
``````
Enjoy!
The block can be replaced with a glider:

Code: Select all

``````x = 60, y = 74, rule = B3/S23
57bobo\$57b2o\$58bo16\$50bo\$50bobo\$50b2o14\$31bobo\$32b2o\$32bo2\$30b2o\$29b2o
\$31bo2\$19b2o\$18bobo\$20bo10\$54b3o\$54bo\$55bo15\$2o\$b2o\$o!``````
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).

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

Thanks for the contributions. With a few ones of my own 12 SLs remain:

Code: Select all

``````16.243     xs16_2egu16426           16
16.360     xs16_2egu16413           16
16.810     xs16_ca9la4z311          16
16.836     xs16_4aajkczx56          16
16.995     xs16_0raik8z643          16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1717    xs16_4aajk46zx121        16
16.1766    xs16_kc321e8z123         16
16.1787    xs16_069m4koz311         16
16.1929    xs16_0g5r8b5z121         16
16.2219    xs16_0oe12koz643         16
``````

Goldtiger997
Posts: 570
Joined: June 21st, 2016, 8:00 am

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

16.243 in 10 gliders:

Code: Select all

``````x = 63, y = 47, rule = B3/S23
61bo\$60bo\$60b3o2\$2bo\$obo\$b2o19\$17bo\$15bobo8bo\$16b2o6bobo\$20b3o2b2o\$22b
o\$21bo2\$15bobo\$16b2o\$16bo3\$33bo\$18b3o10b2o\$20bo11b2o\$19bo3\$31b3o\$12b2o
17bo\$11bobo18bo\$13bo!
``````
dvgrn wrote:@chris_c, I'd say it really wouldn't have been possible without your organization of the effort. Thanks!
Agreed!
chris_c wrote: Just please nobody mention 17-bit still lifes for at least a little while!
I sort of feel the same way. When a project like this comes round, I feel obliged to contribute, when sometimes I would rather be doing other things in life (double meaning intended). Considering that this project has taken about 5 months so far, the 17-bit version would take a very long time. If we do eventually attempt the 17-bit still-lifes, perhaps it would be better to start with an easier goal, such as synthesising them all in less than 2 gliders/bit, or just getting explicit syntheses for them all.
chris_c wrote:A preliminary step in this project was creating a translation between Niemiec's still life numbering and apgcodes. The fact that a similar list does not exist for oscillators is the only reason that I didn't reply to Goldtiger's query here.
Ah, thanks, that makes sense.

EDIT:

16.360 in 8 gliders:

Code: Select all

``````x = 45, y = 41, rule = B3/S23
32bo\$31bo\$22bo8b3o\$23bo\$21b3o3\$bo28bo\$2bo27bobo\$3o27b2o\$20bobo\$20b2o\$
21bo\$18bo\$18b2o\$17bobo2\$24bo\$23b2o\$23bobo19\$43bo\$42b2o\$42bobo!
``````

AbhpzTa
Posts: 485
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

16.1304 in 8 gliders:

Code: Select all

``````x = 69, y = 21, rule = B3/S23
46bo\$46bobo\$46b2o9\$47bo19b2o\$47bobo16bobo\$4bo42b2o16bo\$4bobo27b2o6bo7b
2o12bo\$3ob2o27bo2bo5bobo5bobo11b4o\$2bo17bo12bobo6b2o6bo16bo\$bo18b2o12b
o31bo\$19bobo18b2o21bobo\$39b2o22b2o\$41bo!``````
EDIT: 16.1391 in 7 gliders:

Code: Select all

``````x = 23, y = 23, rule = B3/S23
9bo\$9bobo\$9b2o2\$5bobo\$6b2o\$6bo2\$21bo\$20bo\$8bobo9b3o\$9b2o5b3o\$9bo6bo\$
17bo\$9b2o\$8b2o\$10bo4\$bo\$b2o\$obo!``````
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).

dvgrn
Moderator
Posts: 6271
Joined: May 17th, 2009, 11:00 pm
Contact:

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

Goldtiger997 wrote:
chris_c wrote: Just please nobody mention 17-bit still lifes for at least a little while!
I sort of feel the same way. When a project like this comes round, I feel obliged to contribute, when sometimes I would rather be doing other things in life (double meaning intended).
And yet people keep mentioning the darn things.
Goldtiger997 wrote:If we do eventually attempt the 17-bit still-lifes, perhaps it would be better to start with an easier goal, such as synthesising them all in less than 2 gliders/bit, or just getting explicit syntheses for them all.
I still like the idea of an online collection system, preferably connected to Catagolue. It would be nice to be able to gradually accumulate syntheses and converters for a while, and then kick off a new challenge to finish the next group -- sometime in the safely distant future when the number of unknowns has been reduced to something reasonable.

I think that until Catagolue at least reports an up-to-date cost of the current cheapest synthesis for each still life, I'll officially boycott the Interminable Glider Synthesis Project -- not that I'll be much missed, given my current level of contribution...!

But I heartily recommend that everyone else join in the boycott, after the 16-bitters are polished off. If nothing else, collective productivity on other tasks will go way up.

chris_c
Posts: 940
Joined: June 28th, 2014, 7:15 am

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

Two more from me:

16.2219:

Code: Select all

``````x = 77, y = 121, rule = B3/S23
11bo\$11bobo\$11b2o\$67bo\$66bobo\$66bo2bo\$13bo13bo37b2o3bo4b2o\$12bo14bo37b
o3b2o4b2o\$12b3o12bo38bo\$65b2o\$13bo\$12b2o\$12bobo2\$19bo\$18b2o\$18bobo10\$b
o\$b2o\$obo\$41b2o\$40b2o\$42bo22\$17bo49bo\$16bobo47bobo\$16bo2bo46bo2bo\$15b
2o3bo4b2o38b2o3bo\$15bo3b2o4b2o38bo3b2o\$16bo49bo\$15b2o48b2o3\$29b3o\$29bo
\$30bo39\$17bo49bo\$16bobo47bobo\$16bo2bo46bo2bo\$15b2o3bo44b2o3bo\$15bo3b2o
44bo3b2o\$8bobo5bo49bo\$9b2o4b2o47bobo\$9bo16bo37b2o\$25bo\$19b2o4b3o\$18bob
o\$20bo3\$21b2o\$13b2o5b2o\$13bobo6bo\$13bo!
``````
16.1766 featuring a very nice 4G tail adder (one sided and very unobtrusive):

Code: Select all

``````x = 72, y = 75, rule = B3/S23
6bobo\$7b2o\$7bo5\$68bo\$bo65bobo\$b2o3b3o58b2o\$obo5bo56b2o\$7bo58bo\$65bo\$
18b2o45bobo\$11b3o3bobo46b2o\$13bo5bo2b2o\$12bo9bobo\$22bo13\$28bo\$26b2o\$
27b2o5\$18bo49bo\$17bobo5bobo39bobo\$17b2o6b2o40b2obo\$15b2o9bo38b2o3bo\$
16bo49bo3b2o\$15bo11b3o35bo\$15bobo9bo37bobo\$16b2o10bo37b2o7\$28b3o\$28bo\$
29bo9\$16bo3bo\$14bobo3bobo\$15b2o3b2o3\$18bo\$17bobo47bobo\$17b2obo46b2obo\$
15b2o3bo44b2o3bo\$16bo3b2o44bo3b2o\$15bo49bo\$15bobo47bobo\$16b2o48b2o!
``````
With Goldtiger's and Abhpzta's contributions 6 remain and all have at least 50 soups on Catagolue:

Code: Select all

``````16.810     xs16_ca9la4z311          16
16.836     xs16_4aajkczx56          16
16.995     xs16_0raik8z643          16
16.1717    xs16_4aajk46zx121        16
16.1787    xs16_069m4koz311         16
16.1929    xs16_0g5r8b5z121         16
``````

Posts: 1938
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

16.810:

Code: Select all

``````x = 91, y = 58, rule = B3/S23
16bo\$17b2o\$16b2o9\$19bo\$18bobo66b2o\$17bo68bo2bo\$18bo2bo63bo2bobo\$19b3o
63b3obo\$27b3o14bo43bo\$44bo40b3o\$25bo18bo40bo\$25bo4b2o\$25bo4b2o\$81b2o\$
81b2o2\$83b2o\$83bobo\$83bo29\$b2o\$obo\$2bo!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Jormungant
Posts: 130
Joined: May 27th, 2016, 1:01 am

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

I found an approach that may work for 16.1787 (aka xs16_069m4koz311); however, I don't know if there is a 3 or 4 glider construction for a transient group that has 7 cells at some point (found on the upper right).

Code: Select all

``````x = 21, y = 23, rule = B3/S23
13bo\$11b2o\$12b2o\$7bo\$7b2o9b3o\$bo4bobo8bo\$2b2o13bo2bo\$b2o14bo2\$10bo\$9b
2o\$9bobo\$5b2o\$4bobo\$6bo4\$b2o\$obo\$2bo11bo\$14b2o\$13bobo!
``````