## 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

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.

`x = 19, y = 17, rule = B3/S232o\$bo\$bobo\$2bobo\$4bo\$3bo\$3bobo\$4bobo\$5bo2\$13b2o\$12b2o\$14bo\$17b2o\$2o6b2o6b2o\$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.

`x = 21, y = 27, rule = B3/S2316bo\$15bo\$15b3o8\$o\$3o14bo\$3bobo10bo\$2o2b2o10b3o\$o\$bo17bo\$2bo15b2o\$b2o15bobo7\$17bo\$16b2o\$16bobo!`
chris_c

Posts: 893
Joined: June 28th, 2014, 7:15 am

### 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.

`RLE`

Whole thing in thirteen gliders via more traditional method (and using the other lengthening):
`x = 72, y = 29, rule = B3/S233bo\$4bo12bo\$2b3o11bo\$16b3o\$7bo\$5bobo\$6b2o\$41bo23bo\$obo38b3o21b3o\$b2o41bo23bo\$bo39b2o2bobo17b2o2bobo\$41bo4b2o17bo4b2o\$2b3o37bo23bo\$4bo36b2o24bo\$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):
`x = 110, y = 25, rule = B3/S2390bobo\$24bo53bo11b2o\$24bobo52b2o10bo\$24b2o46bo5b2o\$70bobo\$23bo47b2o4bo\$21bobo53b2o\$22b2o25b2o25bobo6b2o\$48bo2bo32bo2bo21bo\$47bob3o31bob3o19b3o\$46bobo33bobo21bo\$18b2o5b2o19b2o2b2o30b2o2b2o15bobo2b2o\$19b2o5bo24bo35bo15b2o4bo\$2o16bo7bobo22bobo32bo21bo\$b2o24b2o23b2o31bo21bo\$o3b2o74b2o3b2o20b2o\$4bobo73bobo\$4bo69b2o4bo\$41b3o6b2o21bobo\$43bo6bobo22bo\$42bo7bo\$55b3o23b3o\$48b2o5bo25bo\$47bobo6bo25bo\$49bo!`
I Like My Heisenburps! (and others)

Extrementhusiast

Posts: 1768
Joined: June 16th, 2009, 11:24 pm
Location: USA

### 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:

`x = 116, y = 21, rule = B3/S2312bobo\$obo10b2o\$b2o10bo56bobo\$bo21bobo45b2o\$16bo6b2o46bo\$9bo5bo8bo\$7bobo5b3o55bobo\$8b2o64b2o\$74bo\$19bo\$15bob2o5bo\$13bobo2b2o4bobo42b3o\$14b2o8b2o45bo\$70bo35bo\$48bo29bo27b3o\$47bobo27bobo29bo\$48bo2b2o25bo2b2o25bo2b2o\$26b2o21b2o2bo25b2o2bo25b2o2bo\$25b2o25bo17bo11bo29bo\$27bo25b3o14b2o11b3o27b3o\$55bo13bobo13bo29bo!`

Goldtiger997

Posts: 523
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### 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:
`x = 69, y = 62, rule = B3/S2312bo50b2o\$13b2o45bo2bobobo\$12b2o45bobobo2b2o\$bobo56bo2bo\$2b2o59b2o\$2bo8b3o\$13bo\$12bo\$19b2o\$18bobo\$19bo4\$6b2o\$7b2o\$6bo8\$37bo\$b2o33b2o\$obo33bobo\$2bo17\$23bobo\$23b2o\$24bo4\$13b2o48b2o\$10bo2bobobo42bo2bobo\$9bobobo2b2o41bobobo2bobo\$10bo2bo46bo2bo3b2o\$13b2o11bo36b2o\$26bobo\$26b2o2\$19b2o\$18bobo3b2o\$20bo2b2o\$25bo!`

16.300:
`x = 69, y = 139, rule = B3/S2322bobo\$22b2o\$23bo11\$8bo49b2o\$7bobo49bo\$8b2o49bob2o\$58b2o2bo\$60bo\$58b2o6b3o\$58bo\$13b2o5bo39bo\$5b2o5b2o5b2o38b2o\$6b2o6bo4bobo\$5bo\$9b2o\$8bobo\$10bo4\$3o\$2bo\$bo3\$b2o8b3o\$2b2o7bo\$bo10bo26\$8b2o48b2o\$9bo49bo\$9bob2o46bob2o\$8b2o2bo45b2o2bo\$10bo6bo42bo\$8b2o7bo40b2o\$8bo8bo40bo\$10bo49bo\$9b2o48b2o2\$21b3o\$21bo\$22bo38\$8b2o48b2o\$9bo49bo\$9bob2o46bob2o\$8b2o2bo45b2o2bo\$10bo49bo\$8b2o48b2o\$8bo49bo\$10bo48bo\$9b2o47b2o7\$2b2o\$3b2o13b2o\$2bo6b2o6b2o\$9bobo7bo\$9bo4\$11b2o\$10b2o\$12bo!`

16.1675:
`x = 75, y = 49, rule = B3/S233bobo\$4b2o\$4bo14\$72b2o\$16bo55bobo\$16b2o56bo\$15bobo8b3o44bo\$3o17b2o4bo45bo\$2bo17bobo4bo43bo\$bo18bo49bo\$70b2o\$71bo\$7b3o60bo\$9bo59bo\$8bo60b2o2\$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):
`x = 19, y = 19, rule = B3/S2313bo\$6bo6bobo\$7bo5b2o\$5b3o\$bo15bo\$2bo13bo\$3o13b3o2\$5b2o5b2o\$4bo2bo3bo2bo\$4bobo5bobo\$5bo7bo2\$7b2ob2o\$7bo3bo\$8b3o\$6bobo\$5bobo\$6bo!`

16.2317:
`x = 76, y = 118, rule = B3/S2366bo\$65bobo\$65bobo\$8bobo7bo47bo\$obo6b2o5b2o\$b2o6bo7b2o42b2o7b2o\$bo59b2o6bo2bo\$70b2o\$7bobo56b2o\$8b2o56b2o\$8bo\$15bobo45b2o5bo2b2o\$16b2o10bo34b2o4bobo2bo\$16bo11bobo38bo2b2o\$28b2o40b2o\$20b3o48bo\$22bo46bo\$21bo47b2o5\$8b2o\$9b2o\$8bo21\$30bo\$18bo11bobo\$16bobo11b2o\$17b2o2\$16bo\$15bobo\$15bobo\$16bo2\$11b2o7b2o\$11b2o6bo2bo\$20b2o\$16b2o\$16b2o2\$13b2o5bo2b2o45bo2b2o\$13b2o4bobo2bo44bobo2bo\$19bo2b2o45bo2b2o\$20b2o48b2o\$21bo49bo\$19bo49bo\$19b2o48b2o31\$25bo\$15bo10bo\$16b2o6b3o\$15b2o3\$26bo4bo\$24bobo2b2o\$25b2o3b2o4\$74bo\$20bo2b2o45bo2bobo\$19bobo2bo9b2o33bobo2bo\$19bo2b2o10bobo32bo2b2o\$20b2o12bo35b2o\$21bo49bo\$19bo49bo\$19b2o48b2o!`

Latest list contains 35 SLs:

`16.640     xs16_c9bkkozw32          1716.716     xs16_3pmk46zx23          1716.748     xs16_39ege2z321          1716.799     xs16_c8al56z311          1716.875     xs16_4a5pa4z2521         1716.1722    xs16_4aq32acz032         1716.1758    xs16_4a4o796zw121        1716.1847    xs16_39c8a52z033         1716.1882    xs16_259m453zx23         1716.243     xs16_2egu16426           1616.302     xs16_5b8o642ac           1616.360     xs16_2egu16413           1616.593     xs16_3123c48gka4         1616.771     xs16_69qb8oz32           1616.772     xs16_3h4e1daz011         1616.810     xs16_ca9la4z311          1616.822     xs16_8ehikozw56          1616.836     xs16_4aajkczx56          1616.838     xs16_ci9b8ozw56          1616.856     xs16_kc32acz1252         1616.995     xs16_0raik8z643          1616.1304    xs16_0okih3zc8421        1616.1391    xs16_ca168ozc8421        1616.1717    xs16_4aajk46zx121        1616.1739    xs16_g88r2qkz121         1616.1766    xs16_kc321e8z123         1616.1787    xs16_069m4koz311         1616.1929    xs16_0g5r8b5z121         1616.1994    xs16_0g9fgka4z121        1616.2028    xs16_25ao48cz2521        1616.2029    xs16_25ao4a4z2521        1616.2219    xs16_0oe12koz643         1616.2305    xs16_6413ia4z6421        1616.2322    xs16_raak8zx1252         1616.2630    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?
chris_c

Posts: 893
Joined: June 28th, 2014, 7:15 am

### 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)

Extrementhusiast

Posts: 1768
Joined: June 16th, 2009, 11:24 pm
Location: USA

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

16.2028 in 14 gliders:

`x = 112, y = 39, rule = B3/S2339bo\$o38bobo\$b2o36b2o\$2o2\$21bo\$22bo\$20b3o\$78bobo\$78b2o\$79bo\$72bo\$73bo\$20bo29bo20b3o6bo29bo\$18bobo28bobo27bobo27bobo\$19b2o8bo16b2o2bo17b3o5b2o2bo24bobo2bo\$28bo17bob2o20bo5bob2o25b2ob2o\$19bo8b3o17bo20bo8bo29bo\$19b2o27bobo27bobo27bobo\$18bobo10b3o15bobo27bobo27bobo\$31bo18bo29bo29bo\$3b2o27bo\$4b2o17bo\$3bo14b2o2b2o\$19b2obobo\$18bo11\$30b2o\$30bobo\$30bo!`

16.302 in 12 gliders:

`x = 30, y = 31, rule = B3/S2328bo\$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.

Goldtiger997

Posts: 523
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

16.640 in 8:
`x = 33, y = 31, rule = B3/S2322bo\$21bo\$21b3o\$13bo\$11bobo\$12b2o2\$32bo\$30b2o\$31b2o10\$16bo13bobo\$16b2o13b2o\$2o13bobo13bo\$b2o24b3o\$o28bo\$28bo4\$25b3o\$27bo\$26bo!`

EDIT: 16.716 in no more than 14:
`x = 122, y = 63, rule = B3/S2330bo\$29bo\$29b3o24\$107b2o\$b2o12b3o8b2o78bo2bo\$b2o14bo8b2o79b2o\$15b3o2\$b2o\$b2o6bo75b2o15bo\$8bobo70bo2bobo14bobo\$8bobo70b4o16bo2bo\$9bo75bo16b2o\$83b3o\$82bo36b2o\$82b2o35bobo\$119bo2\$111b2o\$111bobo\$111bo10\$45bo\$44b2o\$44bobo5\$bo\$b2o\$obo!`

16.748 in 12, maybe 11:
`x = 62, y = 53, rule = B3/S2311bobo45bobo\$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:
`x = 15, y = 13, rule = B3/S233bo\$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]

Posts: 1876
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### 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:

`x = 52, y = 55, rule = B3/S23bo\$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\$5bobo37bobo2bo\$6bo2b2o6b3o26bo2bobo\$7b2obo6bo29b2obo\$8bo9bo29bo\$6bobo37bobo\$5bobo37bobo\$6bo39bo!`

16.875:

`x = 80, y = 122, rule = B3/S232bo35bobo\$obo35b2o\$b2o30bobo3bo\$33b2o\$34bo4\$18bo\$19b2o\$18b2o4\$16bo\$17bo54bo2b2ob2o\$15b3o53bobo2bob2o\$72bob2o\$74bo\$19bo15b2o35bobo\$19b2o13b2o35bobo\$18bobo15bo35bo8\$12b2o\$11bobo\$13bo29\$33bo\$32bo\$32b3o3\$22bo2b2ob2o42bo2b2o\$21bobo2bob2o41bobo2bo\$22bob2o46bob2o\$24bo49bo\$22bobo47bobo\$21bobo47bobo\$22bo49bo34\$23bobo9bo\$23b2o8b2o\$18bo5bo9b2o\$19b2o\$18b2o5\$73b2o\$11b3o8bo2b2o45bo2bo\$13bo7bobo2bo44bobo2bo\$12bo9bob2o46bob2o\$24bo49bo\$22bobo47bobo\$21bobo47bobo\$22bo49bo!`

I made a component for 16.593:

`x = 69, y = 66, rule = B3/S2314bo\$13bo\$13b3o4\$2bo\$3b2o\$2b2o\$58b2obo\$58bob2o\$6bo55b2o\$6b2o54bobo\$5bobo2b2o51b2o\$10bobo\$10bo9\$bo\$b2o\$obo4\$17bo\$18bo\$16b3o4\$22bo\$22bobo\$22b2o\$8b2obo46b2obo\$8bob2o46bob2o5bo\$12b2o5b2o41b2o2bobo\$12bobo4bobo40bobo2bo\$13b2o4bo45b2o10\$33b2o\$33bobo\$33bo2\$8b2o\$9b2o\$8bo21b2o\$29b2o\$31bo3b2o\$34b2o\$8b2o26bo\$9b2o\$8bo!`

It was based on this soup (roughly generation 90):

`x = 16, y = 16, rule = B3/S23bo2bob4ob3o\$bo2bob2o2b4obo\$bob2ob2ob2o3bo\$7o2bo4b2o\$3b2o2bobob3o\$3b2obobo2bob2o\$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):

`16.716     xs16_3pmk46zx23          1716.748     xs16_39ege2z321          1716.799     xs16_c8al56z311          1716.1722    xs16_4aq32acz032         1716.1758    xs16_4a4o796zw121        1716.1847    xs16_39c8a52z033         1716.1882    xs16_259m453zx23         1716.243     xs16_2egu16426           1616.360     xs16_2egu16413           1616.771     xs16_69qb8oz32           1616.772     xs16_3h4e1daz011         1616.810     xs16_ca9la4z311          1616.822     xs16_8ehikozw56          1616.836     xs16_4aajkczx56          1616.838     xs16_ci9b8ozw56          1616.856     xs16_kc32acz1252         1616.995     xs16_0raik8z643          1616.1304    xs16_0okih3zc8421        1616.1391    xs16_ca168ozc8421        1616.1717    xs16_4aajk46zx121        1616.1739    xs16_g88r2qkz121         1616.1766    xs16_kc321e8z123         1616.1787    xs16_069m4koz311         1616.1929    xs16_0g5r8b5z121         1616.1994    xs16_0g9fgka4z121        1616.2219    xs16_0oe12koz643         1616.2305    xs16_6413ia4z6421        1616.2322    xs16_raak8zx1252         1616.2630    xs16_31e8gzxo9a6         16`
chris_c

Posts: 893
Joined: June 28th, 2014, 7:15 am

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

16.716 in 8 gliders:

`x = 72, y = 25, rule = B3/S2316bo\$14b2o\$2bo12b2o\$3b2o\$2b2o5\$11bo\$12bo13bo2b2o15bo2b2o19b2o\$10b3o13b4obo14b4obo14bo2bobo\$6b3o22bo19bo14b4o\$8bo19b3o17b3o19bo\$7bo19bo19bo20b3o\$27b2o18b2o18bo\$2o65b2o\$b2o53b2o2b2o\$o54bobob2o\$57bo3bo3\$45bo\$45b2o\$44bobo!`

I haven't seen that converter before, but it's probably not new.

BlinkerSpawn wrote:16.748 in 12, maybe 11:
`x = 62, y = 53, rule = B3/S2311bobo45bobo\$12b2o45b2o\$12bo47bo14\$34b2o\$33bo2bo\$34bobo\$35bo\$30b3o8\$29b2o\$29bobo\$30bo4\$31bo\$30b3o7\$57bo\$56b2o\$56bobo6\$bo\$b2o\$obo!`

16.748 in 11 gliders:

`x = 64, y = 57, rule = B3/S2311bo51bo\$12b2o47b2o\$11b2o49b2o19\$33bo\$34b2o\$33b2o4\$33b3ob3o\$35bobo\$28bo5bo3bo\$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.

Goldtiger997

Posts: 523
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

16.1847 in 10G.
It must be a better way...
`x = 103, y = 28, rule = B3/S2317bobo\$18b2o\$18bo6\$bo\$2bo77bo3b2o\$3o76bobo3bo\$70bo9bo2bo\$12bo55bobo10b4o\$13bo55b2o\$11b3o12bo56b2o\$7b2o15b2o57b2o\$6bobo16b2o45b2o\$8bo63b2o\$100b2o\$59b2o38bo2bo\$59b2o39b2o2\$5b2o59bo29bo\$4bobo21b3o34bobo27bobo\$6bo21bo36bobo27bobo\$29bo31b2o3bo29bo3b2o\$60bobo37bobo\$62bo37bo!`

yootaa

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

### 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):

`x = 89, y = 165, rule = B3/S2329bo\$27bobo\$28b2o56b2o\$85bo2bo\$28b2o4bo51bobo\$27bobo3b2o52bo\$29bo3bobo48bo\$84bo\$84bo44\$36b2o48b2o\$35bo2bo46bo2bo\$36bobo47bobo\$23bo13bo49bo\$21bobo10bo49bo\$22b2o10bo40bo8bo\$29bo4bo39bobo7bo\$28b2o45b2o\$28bobo17\$46bo\$46bobo\$46b2o23\$36b2o37b2o\$35bo2bo36bobob2o\$36bobo38bobo\$16bobo18bo38b2obo\$17b2o15bo43bo8bo\$17bo7bo8bo40bobo8bobo\$24bobo7bo40b2o9bobo\$25b2o60bo\$14b2o\$13bobo\$15bo25\$bo\$b2o\$obo13\$25b2o48b2o\$25bobob2o44bobob2o\$27bobo47bobo\$26b2obo46b2obo\$28bo8bo40bo\$25bobo8bobo36bobo\$25b2o9bobo36b2o\$37bo3\$41b2o\$41bobo\$41bo!`

BlinkerSpawn wrote:16.799 in around 10, I hope:

In 8G:

`x = 27, y = 27, rule = B3/S23obo\$b2o\$bo2\$23bo\$22bo\$15bo6b3o\$15bobo\$15b2o\$24bo\$23bo\$23b3o3\$3o3bo\$2bo2b2o\$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:

`x = 76, y = 80, rule = B3/S2360bo\$58bobo\$59b2o7\$41bobo\$42b2o\$42bo2\$52bobo\$53b2o15bo\$53bo15bo\$69b3o3\$48b2o\$49b2o\$48bo5\$46b2o26bo\$47b2o24b2o\$46bo26bobo49\$3o\$2bo\$bo!`

Some others.....16.1882:

`x = 139, y = 170, rule = B3/S2327bo\$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\$30bo2bo2bo41bobo49bo2bo2bo\$31bob3o95bob3o\$32bo99bo\$33bo99bo\$32b2o98b2o45\$31b2o2b2o94b2o2b2o\$30bo2bo2bo93bo2bo2bo\$31bob3o95bob3o\$32bo99bo\$33bo99bo\$32b2o7bo92bo\$40bo92b2o\$40b3o5\$24b2o16bo\$25b2o14b2o\$24bo16bobo\$34b3o\$36bo\$35bo!`

16.771:

`x = 72, y = 70, rule = B3/S235bo22bo\$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\$b2o\$bo9\$19bo47bobo\$17b3o46bob2o\$16bo49bo\$17b5o45b5o\$18bo2bo46bo2bo\$16bo49bo\$16b2o48b2o!`

16.2305 using a standard converter but where the pre-block construction has a thinner envelope:

`x = 27, y = 21, rule = B3/S23o\$b2o\$2o19bo\$20bo\$20b3o3\$9bo\$10b2o\$9b2o3\$17b2o\$10bobo5b2o3bo\$11b2o4bo5b3o\$11bo14bo\$25bo\$7b3o5b2o7bo\$9bo6b2o5bo\$8bo6bo4bobo\$20b2o!`

Latest list contains 22 SLs:

`16.1722    xs16_4aq32acz032         1716.1758    xs16_4a4o796zw121        1716.243     xs16_2egu16426           1616.360     xs16_2egu16413           1616.772     xs16_3h4e1daz011         1616.810     xs16_ca9la4z311          1616.822     xs16_8ehikozw56          1616.836     xs16_4aajkczx56          1616.838     xs16_ci9b8ozw56          1616.856     xs16_kc32acz1252         1616.995     xs16_0raik8z643          1616.1304    xs16_0okih3zc8421        1616.1391    xs16_ca168ozc8421        1616.1717    xs16_4aajk46zx121        1616.1739    xs16_g88r2qkz121         1616.1766    xs16_kc321e8z123         1616.1787    xs16_069m4koz311         1616.1929    xs16_0g5r8b5z121         1616.1994    xs16_0g9fgka4z121        1616.2219    xs16_0oe12koz643         1616.2322    xs16_raak8zx1252         1616.2630    xs16_31e8gzxo9a6         16`
chris_c

Posts: 893
Joined: June 28th, 2014, 7:15 am

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

16.1722 in 6 gliders:

`x = 22, y = 11, rule = B3/S23o9bo10bo\$b2o5bobo8b2o\$2o7b2o9b2o3\$16b2o\$16bobo\$12b2o2bo\$4b2o7b2o\$3bobo6bo\$5bo!`

Goldtiger997

Posts: 523
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

Goldtiger997 wrote:16.1722 in 6 gliders

And here is 161758 in 8G:

`x = 30, y = 25, rule = B3/S237bo\$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:

`16.243     xs16_2egu16426           1616.360     xs16_2egu16413           1616.772     xs16_3h4e1daz011         1616.810     xs16_ca9la4z311          1616.822     xs16_8ehikozw56          1616.836     xs16_4aajkczx56          1616.838     xs16_ci9b8ozw56          1616.856     xs16_kc32acz1252         1616.995     xs16_0raik8z643          1616.1304    xs16_0okih3zc8421        1616.1391    xs16_ca168ozc8421        1616.1717    xs16_4aajk46zx121        1616.1739    xs16_g88r2qkz121         1616.1766    xs16_kc321e8z123         1616.1787    xs16_069m4koz311         1616.1929    xs16_0g5r8b5z121         1616.1994    xs16_0g9fgka4z121        1616.2219    xs16_0oe12koz643         1616.2322    xs16_raak8zx1252         1616.2630    xs16_31e8gzxo9a6         16`
chris_c

Posts: 893
Joined: June 28th, 2014, 7:15 am

### 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...!

dvgrn
Moderator

Posts: 5709
Joined: May 17th, 2009, 11:00 pm

### 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.
chris_c

Posts: 893
Joined: June 28th, 2014, 7:15 am

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

16.822 in 10G:
`x = 49, y = 19, rule = B3/S2346bo\$8bo37bobo\$2o4b2o7bo30b2o\$2o5b2o6bobo17b2o\$15b2o19bo6bo\$35bo6bobo\$12bo22b4o2bo2bo\$12bo20b2o3bo3b2o\$3bo8bo21bo2bo\$3b2o29bobo\$2bobo30bo3\$9b2o\$9bobo\$9bo\$b2o\$obo\$2bo!`

EDIT: Components:
`x = 89, y = 42, rule = B3/S2331bo\$30bobo51bo\$29bo2bo51bo\$30b2o52bo2\$80b3o3b3o\$30bo\$30b2o4b3o45bo\$29b2o53bo\$84bo3\$78bo\$77bobo5b3o\$77bobo5bo2bo\$27b2o49bo6bo2bo\$28bo6b3o48b2o\$25bo2bo\$26b2o46b2o\$74b2o2\$79bo\$78bobo\$77bo2bo\$55b2o21b2o\$56b2o\$55bo13\$b2o\$obo\$2bo!`

yootaa

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

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

got 16.1739 (aka xs16_g88r2qkz121) in 8 gliders!
`x = 60, y = 74, rule = B3/S2357bobo\$57b2o\$58bo16\$50bo\$50bobo\$50b2o14\$31bobo\$20bo11b2o\$18bobo11bo\$19b2o\$30b2o\$29b2o\$21b3o7bo\$23bo\$22bo12\$54b3o\$54bo\$55bo15\$2o\$b2o\$o!`

Enjoy!
Jormungant

Posts: 97
Joined: May 27th, 2016, 1:01 am

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

Jormungant wrote:got 16.1739 (aka xs16_g88r2qkz121) in 8 gliders!
`x = 60, y = 74, rule = B3/S2357bobo\$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:
`x = 60, y = 74, rule = B3/S2357bobo\$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).
AbhpzTa

Posts: 468
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

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

`16.243     xs16_2egu16426           1616.360     xs16_2egu16413           1616.810     xs16_ca9la4z311          1616.836     xs16_4aajkczx56          1616.995     xs16_0raik8z643          1616.1304    xs16_0okih3zc8421        1616.1391    xs16_ca168ozc8421        1616.1717    xs16_4aajk46zx121        1616.1766    xs16_kc321e8z123         1616.1787    xs16_069m4koz311         1616.1929    xs16_0g5r8b5z121         1616.2219    xs16_0oe12koz643         16`
chris_c

Posts: 893
Joined: June 28th, 2014, 7:15 am

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

16.243 in 10 gliders:

`x = 63, y = 47, rule = B3/S2361bo\$60bo\$60b3o2\$2bo\$obo\$b2o19\$17bo\$15bobo8bo\$16b2o6bobo\$20b3o2b2o\$22bo\$21bo2\$15bobo\$16b2o\$16bo3\$33bo\$18b3o10b2o\$20bo11b2o\$19bo3\$31b3o\$12b2o17bo\$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:

`x = 45, y = 41, rule = B3/S2332bo\$31bo\$22bo8b3o\$23bo\$21b3o3\$bo28bo\$2bo27bobo\$3o27b2o\$20bobo\$20b2o\$21bo\$18bo\$18b2o\$17bobo2\$24bo\$23b2o\$23bobo19\$43bo\$42b2o\$42bobo!`

Goldtiger997

Posts: 523
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

16.1304 in 8 gliders:
`x = 69, y = 21, rule = B3/S2346bo\$46bobo\$46b2o9\$47bo19b2o\$47bobo16bobo\$4bo42b2o16bo\$4bobo27b2o6bo7b2o12bo\$3ob2o27bo2bo5bobo5bobo11b4o\$2bo17bo12bobo6b2o6bo16bo\$bo18b2o12bo31bo\$19bobo18b2o21bobo\$39b2o22b2o\$41bo!`

EDIT: 16.1391 in 7 gliders:
`x = 23, y = 23, rule = B3/S239bo\$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).
AbhpzTa

Posts: 468
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### 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.

dvgrn
Moderator

Posts: 5709
Joined: May 17th, 2009, 11:00 pm

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

Two more from me:

16.2219:
`x = 77, y = 121, rule = B3/S2311bo\$11bobo\$11b2o\$67bo\$66bobo\$66bo2bo\$13bo13bo37b2o3bo4b2o\$12bo14bo37bo3b2o4b2o\$12b3o12bo38bo\$65b2o\$13bo\$12b2o\$12bobo2\$19bo\$18b2o\$18bobo10\$bo\$b2o\$obo\$41b2o\$40b2o\$42bo22\$17bo49bo\$16bobo47bobo\$16bo2bo46bo2bo\$15b2o3bo4b2o38b2o3bo\$15bo3b2o4b2o38bo3b2o\$16bo49bo\$15b2o48b2o3\$29b3o\$29bo\$30bo39\$17bo49bo\$16bobo47bobo\$16bo2bo46bo2bo\$15b2o3bo44b2o3bo\$15bo3b2o44bo3b2o\$8bobo5bo49bo\$9b2o4b2o47bobo\$9bo16bo37b2o\$25bo\$19b2o4b3o\$18bobo\$20bo3\$21b2o\$13b2o5b2o\$13bobo6bo\$13bo!`

16.1766 featuring a very nice 4G tail adder (one sided and very unobtrusive):

`x = 72, y = 75, rule = B3/S236bobo\$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:

`16.810     xs16_ca9la4z311          1616.836     xs16_4aajkczx56          1616.995     xs16_0raik8z643          1616.1717    xs16_4aajk46zx121        1616.1787    xs16_069m4koz311         1616.1929    xs16_0g5r8b5z121         16`
chris_c

Posts: 893
Joined: June 28th, 2014, 7:15 am

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

16.810:
`x = 91, y = 58, rule = B3/S2316bo\$17b2o\$16b2o9\$19bo\$18bobo66b2o\$17bo68bo2bo\$18bo2bo63bo2bobo\$19b3o63b3obo\$27b3o14bo43bo\$44bo40b3o\$25bo18bo40bo\$25bo4b2o\$25bo4b2o\$81b2o\$81b2o2\$83b2o\$83bobo\$83bo29\$b2o\$obo\$2bo!`
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Posts: 1876
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### 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).

`x = 21, y = 23, rule = B3/S2313bo\$11b2o\$12b2o\$7bo\$7b2o9b3o\$bo4bobo8bo\$2b2o13bo2bo\$b2o14bo2\$10bo\$9b2o\$9bobo\$5b2o\$4bobo\$6bo4\$b2o\$obo\$2bo11bo\$14b2o\$13bobo!`
Jormungant

Posts: 97
Joined: May 27th, 2016, 1:01 am

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