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

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
AbhpzTa
Posts: 504
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

16.801 in 8 gliders:

Code: Select all

``````x = 98, y = 38, rule = B3/S23
45bobo\$45b2o\$46bo8\$41bobo\$41b2o4b2o\$42bo4bobo\$47bo\$40b2o\$40bobo\$bo38bo
24bobo27bobo\$o29bo33bob2o26bob2o\$3o26bobo32bo29bo\$29bobo31b2ob2o25b2ob
2o\$3b3o24bo34bobo27bobo\$3bo54b2o2bobo27bobo\$4bo53b2o2b2o28b2o2\$55b3o\$
57bo\$56bo9\$9b2o\$8bobo\$10bo!``````
Goldtiger997 wrote:16.228 in 9 gliders:

Code: Select all

``````x = 41, y = 24, rule = B3/S23
6\$13bo\$7bobob2o16bo\$8b2o2b2o4bo9bo\$8bo9bobo7b3o\$18b2o2\$17bo3b2o\$17b2o
2bobo\$12bo3bobo2bo\$13bo11b3o\$11b3o11bo\$15b2o9bo\$14bobo\$16bo!
``````
The NE-most glider is unnecessary:

Code: Select all

``````x = 21, y = 14, rule = B3/S23
6bo\$obob2o\$b2o2b2o4bo\$bo9bobo\$11b2o2\$10bo3b2o\$10b2o2bobo\$5bo3bobo2bo\$
6bo11b3o\$4b3o11bo\$8b2o9bo\$7bobo\$9bo!``````
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: 966
Joined: June 28th, 2014, 7:15 am

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

Goldtiger997 wrote: Yes, I would be very grateful if you could post the code. It would help with many syntheses like the one you reduced to 8G in your last post.
OK, let's start off with the attached program. On Linux it compiles with g++ -O3 popseq.c -o popseq. Then run with ./popseq and paste in some RLE. The program searches through certain 4G collisions and outputs them if they contain a population subsequence that is identical to the population sequence of the pasted RLE in the first 16 generations.

The code is supplied with a very old version of LifeAPI.h. I guess it should work with newer versions although I have not tested. Are you able to compile for your platform? (Note that compilation on Windows is not something that I have attempted in quite some time.)

Back to glider syntheses... Here are 16.2200 and 16.2307 in 15G via 16.1899 in 10G and a 5G ship-to-ac converter:

Code: Select all

``````x = 72, y = 122, rule = Life
7bo\$5bobo\$6b2o5\$28bo\$28bobo\$28b2o6\$16bo48b2o2b2o\$15bobo47bo2bobo\$16b2o
48bob2o\$67bo\$65bobo\$30b3o31bobo\$30bo34bo\$2b2o27bo\$3b2o\$2bo6\$26b2o\$6b3o
16b2o\$8bo18bo\$bo5bo\$b2o\$obo\$27b3o\$27bo\$28bo15\$14bo\$15b2o\$14b2o11bo\$25b
2o\$20bo5b2o\$21bo\$19b3o\$32b3o\$32bo\$33bo2\$69b2o\$15b2o2b2o44b2o3bo\$15bo2b
obo44bo2bo\$16bob2o46bob2o\$17bo49bo\$15bobo47bobo\$14bobo47bobo\$15bo12b3o
34bo\$28bo\$29bo28\$25bo\$23bobo\$24b2o2\$14bo\$12bobo\$13b2o\$28bobo\$28b2o\$29b
o4\$26b2o\$15b2o2b2o5bobo36b2o3b2o\$15bo2bobo5bo38bo2bo2bo\$16bob2o46bob2o
\$17bo49bo\$15bobo13bo33bobo\$14bobo13b2o32bobo\$15bo14bobo32bo!
``````
EDIT: I also found a 6G ship-to-snake converter in Extrementhsiast's collection. It was trivial to make one of the sparks with one glider less so 16.2050 is also done in 15G:

Code: Select all

``````x = 15, y = 13, rule = B3/S23
4bo4bo\$3bobob2o\$3bobo2b2o\$4bo3\$8b2o2b2o\$8bobo2bo\$9b2obo\$5b2o4bo\$bo2b2o
5bobo\$2bo3bo5bobo\$3o10bo!
``````
Attachments
popseq.zip

Goldtiger997
Posts: 627
Joined: June 21st, 2016, 8:00 am

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

chris_c wrote:
Goldtiger997 wrote: Yes, I would be very grateful if you could post the code. It would help with many syntheses like the one you reduced to 8G in your last post.
OK, let's start off with the attached program. On Linux it compiles with g++ -O3 popseq.c -o popseq. Then run with ./popseq and paste in some RLE. The program searches through certain 4G collisions and outputs them if they contain a population subsequence that is identical to the population sequence of the pasted RLE in the first 16 generations.

The code is supplied with a very old version of LifeAPI.h. I guess it should work with newer versions although I have not tested. Are you able to compile for your platform? (Note that compilation on Windows is not something that I have attempted in quite some time.)
Thanks, this is great! It compiles fine on Cygwin, with a few warnings.

16.1694 in 12 gliders:

Code: Select all

``````x = 168, y = 19, rule = B3/S23
137bo\$138b2obo\$137b2o2bobo\$141b2o3\$60bo\$59bo\$59b3o76b2o\$104bo32bobo\$4b
o53bo45bobo32bo\$2bobo54bo44b2o2b2o\$3b2o52b3o47b2o56bo\$109bo15bo20bo17b
obo\$25bo19bo9bo9bo13b2o4bo13b2o4bo13b2o3bobo13b2o3bobo17bobo\$b2o17b2o
2bobo13b2o2bobo8b2o3b2o2bobo12bobo2bobo12bobo2bobo12bobobo2bo13bobobo
2bo14b3o2bo\$obo2bo4b2o8bo3b2o14bo3b2o8bobo3bo3b2o14bo3b2o14bo3b2o14bo
3b2o15bo3b2o14bo3b2o\$2bo2bobo2bobo8b3o17b3o17b3o17b3o17b3o17b3o18b3o
17b3o\$5b2o3bo12bo19bo19bo19bo19bo19bo20bo19bo!
``````
The above synthesis features what I think is a new component. It very conveniently appeared in a very easy form in the soup (gen 1937 top left):

Code: Select all

``````x = 16, y = 16, rule = B3/S23
2obob2o2bo2bob2o\$bo5bo2b2o2b2o\$bob5ob2obo2bo\$3b2obobob2o3bo\$3b2o6b2obo
\$4bob2ob4o2bo\$b2o3b3o3bob2o\$3o2b4ob3ob2o\$o4bo3b2o4bo\$3bob6ob2obo\$obobo
bob2o\$3ob2obo3b5o\$o2b2o2bobo\$3b4o2bobob3o\$b2o2bob2ob2ob2o\$b2ob3o2b2o2b
3o!``````
EDIT:

Used the script to make a synthesis of 16.1912 in 14 gliders:

Code: Select all

``````x = 174, y = 29, rule = B3/S23
11bo\$12bo\$bo8b3o\$2bo35bo\$3o34bo\$26bo10b3o\$25bo\$25b3o2\$54bo\$52b2o\$53b2o
2\$105bo62b2o\$68b2o36b2o10b2o48bo\$68bo36b2o11bo50bo\$18bobo48bo49bo48b2o
\$18b2o48b2o41bo6b2o47bo\$19bo92bo54bob3obo\$67bob3obo36b3o4bob3obo44bobo
b2o\$67b2obob2o32bo10b2obob2o\$4bo99bobo\$5bo2bo3bo92b2o2b2o\$3b3o3b2obobo
93bobo\$8b2o2b2o96bo2\$35bo\$34b2o\$34bobo!
``````

chris_c
Posts: 966
Joined: June 28th, 2014, 7:15 am

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

Goldtiger997 wrote:It compiles fine on Cygwin, with a few warnings...

Used the script to make a synthesis of 16.1912 in 14 gliders
Great!

15.516 in 8G gives 16.1130 in 12G:

Code: Select all

``````x = 128, y = 138, rule = B3/S23
31bo\$29b2o\$30b2o\$22bo\$22bobo\$7bo14b2o\$8bo115bo\$6b3o114bobo\$123bo2bo\$ob
o119b2o3bo\$b2o119bo3b2o\$bo121bo\$124bo\$22b2o99b2o\$21b2o\$23bo4\$13b3o\$15b
o\$14bo\$25b3o\$25bo\$26bo2\$41b2o\$40b2o\$42bo73\$44bo\$43bo\$43b3o3\$24bo99bo\$
23bobo97bobo\$23bo2bo96bo2bo\$22b2o3bo94b2o3bo\$22bo3b2o94bo3b2o\$23bo99bo
\$24bo99bo\$23b2o100bo\$124b2o18\$3b2o40bo\$4b2o38b2o\$3bo40bobo\$13b3o\$15bo\$
14bo!
``````
Recent contributions mean that 16.712 is looking slightly alone at the top of the leaderboard. Now 85 SLs remain:

Code: Select all

``````16.712     xs16_3pc0qmzw23          20
16.600     xs16_6421344og84c        18
16.665     xs16_699mkiczx1          18
16.848     xs16_ca9b8oz0252         18
16.914     xs16_8kkja952zx1         18
16.926     xs16_3iajc4gozw1         18
16.1107    xs16_02egdbz2521         18
16.1558    xs16_3loz1226io          18
16.1757    xs16_g8idik8z123         18
16.1790    xs16_178cia4z0321        18
16.1911    xs16_69q3213z32          18
16.1990    xs16_8e1tazx1252         18
16.2201    xs16_0ggml96z641         18
16.2447    xs16_0g8it248cz23        18
16.2480    xs16_3iaczw1139c         18
16.227     xs16_5b8r5426            17
16.265     xs16_259m861ac           17
16.380     xs16_4a40vh248c          17
16.616     xs16_i5pajoz11           17
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
16.1064    xs16_39m88cz6221         17
16.1097    xs16_ck0ol3z643          17
16.1276    xs16_3iakgozw1ac         17
16.1398    xs16_g88c93zc952         17
16.1722    xs16_4aq32acz032         17
16.1758    xs16_4a4o796zw121        17
16.1847    xs16_39c8a52z033         17
16.1871    xs16_5bo8ge2z32          17
16.1882    xs16_259m453zx23         17
16.1905    xs16_8u16853z32          17
16.2045    xs16_25ao8ge2z032        17
16.2132    xs16_0g8it2sgz23         17
16.2162    xs16_0at16426z32         17
16.2316    xs16_0at16413z32         17
16.2356    xs16_25icggozx1ac        17
16.2467    xs16_0kc3213z34a4        17
16.2555    xs16_4a9jzxpia4          17
16.3163    xs16_wo443123zbd         17
16.3164    xs16_wo443146zbd         17
16.104     xs16_0j5ozj4pz11         16
16.115     xs16_0ol3z0mdz32         16
16.243     xs16_2egu16426           16
16.300     xs16_9fg4czbd            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
16.1068    xs16_3lo0kcz6421         16
16.1080    xs16_3lo0kcz3421         16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1583    xs16_4a9jzxha6zx11       16
16.1675    xs16_xj96z0mdz32         16
16.1693    xs16_8k8aliczw23         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
16.2025    xs16_069q48cz2521        16
16.2028    xs16_25ao48cz2521        16
16.2029    xs16_25ao4a4z2521        16
16.2030    xs16_0i5q8a52z121        16
16.2190    xs16_032q4goz6413        16
16.2204    xs16_0gilla4z641         16
16.2219    xs16_0oe12koz643         16
16.2305    xs16_6413ia4z6421        16
16.2317    xs16_cik8a52z641         16
16.2322    xs16_raak8zx1252         16
16.2323    xs16_ra248goz056         16
16.2445    xs16_ciligzx254c         16
16.2630    xs16_31e8gzxo9a6         16
16.3032    xs16_1784ozx342sg        16
``````

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

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

16.2447 in 11G:

Code: Select all

``````x = 95, y = 35, rule = B3/S23
51bo\$50bo\$50b3o\$87bo\$46bo38bobo\$47bo38b2o\$22bo22b3o\$21bo\$21b3o60b2o3b
2o\$83bo2bobo2bo\$16bo37bo28bobo3bobo\$16bobo34bo30bo5bo\$16b2o35b3o3\$86b
2o\$4bo49b2o30b2o\$5bo42b3o3b2o34bo\$3b3o83bobo\$46bo39bobobo\$46bo39b2o2bo
bo\$46bo43b2obo\$55bo37bo\$48b3o4bo37b2o\$bo53bo\$b2o\$obo\$24b3o\$24bo\$19b2o
4bo\$19bobo\$19bo\$9b3o\$11bo\$10bo!
``````
EDIT: 16.2201 in 11G:

Code: Select all

``````x = 96, y = 63, rule = B3/S23
2bo\$obo\$b2o22\$19bo\$20b2o\$19b2o3\$38bo\$37bo4bobo\$37b3o2b2o47bobo\$43bo47b
2o\$31bobo58bo\$32b2o\$32bo3\$86b3o\$94b2o\$26bo65bo2bo\$27bo64b2o\$25b3o61b2o
bo\$78bo9bobobo\$77bobo8bo2bo\$77b2o10b2o2\$22b3o\$24bo\$23bo59b2o\$83bobo\$
83bo6\$59b2o\$59bobo\$59bo\$21b2o\$22b2o\$21bo!``````

chris_c
Posts: 966
Joined: June 28th, 2014, 7:15 am

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

yootaa wrote:16.2447 in 11G, 16.2201 in 11G
I reduced both of these to 10G. The first via constellations, the second via improved cleanup:

Code: Select all

``````x = 87, y = 85, rule = Life
64bo\$62b2o\$63b2o\$54bo\$55bo\$53b3o\$39bobo\$39b2o\$40bo23bo10bo\$17bo45bo12b
o\$16bo15bo30b3o8b3o\$16b3o11bobo\$31b2o\$78b2o\$64b2o12b2o\$28b3o27b3o3b2o
16bo\$8bo72bobo\$6bobo17bo29bo21bobobo\$7b2o17bo29bo21b2o2bobo\$26bo29bo
25b2obo\$65bo19bo\$4b2o22b3o27b3o4bo19b2o\$5b2o58bo\$4bo4\$30b3o\$32bo\$31bo
17\$o\$b2o\$2o3\$19bo\$18bo4bobo32b3o\$18b3o2b2o\$24bo31bo5bo\$12bobo41bo5bo\$
13b2o41bo5bo\$13bo53bobo\$58b3o6b2o\$68bo4bo\$73bo\$73bo6b2o\$7bo70bo2bo\$8bo
69b2o\$6b3o66b2obo\$64bo9bobobo\$63bobo8bo2bo\$63b2o10b2o2\$3b3o\$5bo\$4bo\$
62b2o\$61bobo\$63bo5\$40b2o\$40bobo\$40bo\$2b2o\$3b2o\$2bo!
``````
Note that these syntheses also reduce 16.2132 and 16.2480 to below 16G.

Similarly by making 14.344 in 7G, 15.439 in 8G and 15.475 in 12G I knocked 16.1871, 16.2045, 16.1990, 16.2162 and 16.2316 off the list:

Code: Select all

``````x = 122, y = 47, rule = Life
40bo13bo\$41bo12bobo\$39b3o12b2o2\$o\$b2o52bo\$2o51b2o\$13bo40b2o\$13bobo\$13b
2o\$19bo\$18bo85bo\$18b3o35bobo46bo\$56b2o45b3o\$5bobo49bo51bo\$6b2o100bobo\$
6bo37b2o51bo10bobo\$43bobo50bobo10bo\$10bo34bo50b2o\$10bobo\$10b2o87b2o\$
60b2o36bo2bo\$14b2o44bobo36b2o\$3bo10bobo43bo59b2o\$3b2o9bo104b2o\$2bobo
116bo\$115bo\$91bo22b2o\$92bo21bobo\$90b3o5b2o\$98bobo\$98bo13\$31bo\$31b2o\$
30bobo!
``````
Now 75 SLs remain:

Code: Select all

``````16.712     xs16_3pc0qmzw23          20
16.600     xs16_6421344og84c        18
16.665     xs16_699mkiczx1          18
16.848     xs16_ca9b8oz0252         18
16.914     xs16_8kkja952zx1         18
16.926     xs16_3iajc4gozw1         18
16.1107    xs16_02egdbz2521         18
16.1757    xs16_g8idik8z123         18
16.1790    xs16_178cia4z0321        18
16.1911    xs16_69q3213z32          18
16.227     xs16_5b8r5426            17
16.265     xs16_259m861ac           17
16.380     xs16_4a40vh248c          17
16.616     xs16_i5pajoz11           17
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
16.1064    xs16_39m88cz6221         17
16.1097    xs16_ck0ol3z643          17
16.1276    xs16_3iakgozw1ac         17
16.1398    xs16_g88c93zc952         17
16.1722    xs16_4aq32acz032         17
16.1758    xs16_4a4o796zw121        17
16.1847    xs16_39c8a52z033         17
16.1882    xs16_259m453zx23         17
16.1905    xs16_8u16853z32          17
16.2356    xs16_25icggozx1ac        17
16.2467    xs16_0kc3213z34a4        17
16.2555    xs16_4a9jzxpia4          17
16.3163    xs16_wo443123zbd         17
16.3164    xs16_wo443146zbd         17
16.104     xs16_0j5ozj4pz11         16
16.115     xs16_0ol3z0mdz32         16
16.243     xs16_2egu16426           16
16.300     xs16_9fg4czbd            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
16.1068    xs16_3lo0kcz6421         16
16.1080    xs16_3lo0kcz3421         16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1583    xs16_4a9jzxha6zx11       16
16.1675    xs16_xj96z0mdz32         16
16.1693    xs16_8k8aliczw23         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
16.2025    xs16_069q48cz2521        16
16.2028    xs16_25ao48cz2521        16
16.2029    xs16_25ao4a4z2521        16
16.2030    xs16_0i5q8a52z121        16
16.2190    xs16_032q4goz6413        16
16.2204    xs16_0gilla4z641         16
16.2219    xs16_0oe12koz643         16
16.2305    xs16_6413ia4z6421        16
16.2317    xs16_cik8a52z641         16
16.2322    xs16_raak8zx1252         16
16.2323    xs16_ra248goz056         16
16.2445    xs16_ciligzx254c         16
16.2630    xs16_31e8gzxo9a6         16
16.3032    xs16_1784ozx342sg        16
``````
EDIT: 16.1558 via a 5G block to python converter:

Code: Select all

``````x = 125, y = 421, rule = B3/S23
21bobo\$21b2o\$22bo\$117b3o2\$11bo\$12bo\$10b3o\$116b2o\$115bo2bo\$21b2o93b2o\$
20b2o\$22bo61\$51bo\$50bo\$50b3o11\$9bo\$10b2o\$9b2o14\$18bo\$18bo101b2o\$18bo
101b2o2\$120b4o\$119bo2bo\$16b2o101b2o3bo\$15bo2bo96b2o6b2o\$16b2o97bobo\$
116bo3\$43b2o\$43bobo\$43bo4\$11bo\$11b2o\$10bobo81\$20b2o98b2o\$20b2o98b2o2\$
20b4o96b4o\$19bo2bo96bo2bo\$19b2o3bo94b2o3bo\$15b2o6b2o98b2o\$15bobo\$16bo
9\$27b2o\$27bobo\$27bo59\$9bo28bo\$10b2o24b2o\$9b2o26b2o2\$6bo\$4bobo24bo\$5b2o
24bobo\$31b2o12\$119b2o\$119bo\$120bo\$20b2o99bo\$20b2o98b2o2\$20b4o96b4o\$19b
o2bo96bo2bo\$19b2o3bo94b2o3bo\$23b2o98b2o3\$3o\$2bo\$bo81\$6bo\$7bo\$5b3o3\$19b
2o98b2o\$19bo99bo\$20bo99bo\$21bo99bo\$20b2o98b2o\$119bo\$20b4o96b4o\$19bo2bo
99bo\$19b2o3bo99bo\$23b2o98b2o9\$3bo\$3b2o\$2bobo!
``````

Goldtiger997
Posts: 627
Joined: June 21st, 2016, 8:00 am

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

16.665 in 8 gliders:

Code: Select all

``````x = 33, y = 28, rule = B3/S23
16bo\$14bobo\$15b2o5\$10b2o8b3o\$9bobo8bo\$11bo9bo\$13b2o\$13bobo\$13bo\$b2o\$ob
o2b2o\$2bo2bobo\$5bo6\$4b2o\$3b2o\$5bo\$31bo\$30b2o\$30bobo!
``````
I wasn't able to find a synthesis for 16.600. The best predecessor I found is below. I was able to find syntheses for the junk on the outside, but not the reacting beehives (i.e. No good 1-sided 4G synths).

Code: Select all

``````x = 57, y = 29, rule = B3/S23
41b3o\$5bob2o34bo\$4b2ob3o32bo\$5bo2b3o37b3o\$5b2o3b2o36bo4b3o\$5b3o29bo11b
o3bo\$6b2o29b2o15bo\$6b2o28bobo\$8bob2o\$10bo\$10b2o\$12bo\$4b2o6bo\$3bo2bo\$4b
2o\$7b2o27b2o\$6bo2bo25bobo2b2o\$o6b2o28bob2o\$o40bo\$b2o\$2bo\$b2obo\$5b2o\$5b
2o\$5b3o\$b2o3b2o47bo\$2b3o2bo46b2o\$3b3ob2o45bobo\$4b2obo!
``````
chris_c wrote:...a 5G block to python converter:...
Nice! I think this means all pseudo still-lifes up to 15-bits cost < 1G/bit.

chris_c
Posts: 966
Joined: June 28th, 2014, 7:15 am

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

Goldtiger997 wrote: I wasn't able to find a synthesis for 16.600. The best predecessor I found is below.
Aha! I completely forgot about the possibility of using C2 soups.
Goldtiger997 wrote:I was able to find syntheses for the junk on the outside, but not the reacting beehives (i.e. No good 1-sided 4G synths).
I already had some code for searching 180 degree symmetric glider syntheses from when I was trying to synthesise a clock in the "Splitters from common SL" thread. A bit of hacking yielded a 14G solution:

Code: Select all

``````x = 41, y = 34, rule = B3/S23
33bobo\$15bo17b2o\$16bo17bo\$14b3o\$32bo\$30b2o\$31b2o3\$15bo\$13bobo\$14b2o\$o\$
b2o\$2o3bo7bo\$6b2o6bo\$5b2o5b3o\$26b3o5b2o\$26bo6b2o\$27bo7bo3b2o\$38b2o\$40b
o\$25b2o\$25bobo\$25bo3\$8b2o\$9b2o\$8bo\$24b3o\$6bo17bo\$6b2o17bo\$5bobo!
``````

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

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

16.914 in 11G:

Code: Select all

``````x = 56, y = 33, rule = B3/S23
37bo\$35bobo\$36b2o6bobo\$44b2o\$38bo6bo\$38bobo\$bo36b2o\$o\$3o22b2o\$24bo2bo\$
24bo2bo\$25b2o15bobo\$42b2o\$43bo2\$2bo\$b2o30bo\$bobo28b2o13bo\$28bo3bobo11b
2o\$27b2o17bobo\$20b2o5bobo\$21b2o\$20bo8\$53b2o\$53bobo\$53bo!``````

Goldtiger997
Posts: 627
Joined: June 21st, 2016, 8:00 am

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

yootaa wrote:16.914 in 11G:

Code: Select all

``````x = 56, y = 33, rule = B3/S23
37bo\$35bobo\$36b2o6bobo\$44b2o\$38bo6bo\$38bobo\$bo36b2o\$o\$3o22b2o\$24bo2bo\$
24bo2bo\$25b2o15bobo\$42b2o\$43bo2\$2bo\$b2o30bo\$bobo28b2o13bo\$28bo3bobo11b
2o\$27b2o17bobo\$20b2o5bobo\$21b2o\$20bo8\$53b2o\$53bobo\$53bo!``````
Wow, I had created a synthesis of 16.914 earlier today, and was yet to post it. yootaa's synthesis is almost identical to the one I created!:

Code: Select all

``````x = 41, y = 28, rule = B3/S23
40bo\$38b2o\$39b2o3\$17bo\$15bobo7bo\$16b2o5b2o\$24b2o\$5bo12bo\$3bobo12bobo\$
4b2o12b2o2\$5bo\$5b2o\$4bobo\$24bo\$22b2o\$23b2o3\$13bo\$12b2o\$8bo3bobo\$7b2o\$
2o5bobo15b3o\$b2o22bo\$o25bo!
``````
16.848 in 8 gliders:

Code: Select all

``````x = 30, y = 44, rule = B3/S23
2bo2bobo\$obo3b2o\$b2o3bo2\$6b3o\$8bo\$7bo3\$2b2o\$bobo\$3bo5\$14bo\$7bo6bobo\$7b
2o5b2o\$6bobo2b2o\$10b2o\$12bo20\$27b2o\$27bobo\$27bo!
``````
EDIT:

16.926 in 15 gliders:

Code: Select all

``````x = 72, y = 22, rule = B3/S23
19bo24bo\$17b2o26b2o4bo\$18b2o24b2o6bo\$7bobo40b3o\$8b2o34bo\$8bo4bo30b2o\$
12bo30bobo6bobo\$12b3o37b2o\$3bo49bo\$3bobo20b2o18b2o18b2o\$3b2o2b3o17bo
13b2o4bo19bo2bo\$7bo19bob2o11b2o3bob2o4b2o10bobobo\$b2o5bo17b2o2bo10bo4b
2o2bo4bobo8b2o2bo\$obo25b2o18b2o5bo12b2o\$2bo12bo12bo19bo19bo\$14bo15bo
19bo19bo\$14b3o12b2o18b2o18b2o2\$12bo\$5bo5b2o\$5b2o4bobo\$4bobo!
``````
EDIT2:

16.1107 in 13 gliders:

Code: Select all

``````x = 71, y = 72, rule = B3/S23
68bo\$68bobo\$68b2o8\$2bo\$obo\$b2o11\$9bobo\$10b2o\$10bo31bo\$40b2o\$41b2o3\$12b
o\$13b2o\$12b2o4\$45bo\$43b2o\$44b2o\$17bo\$15bobo\$16b2o7\$25bo\$25bobo\$18b2o5b
2o\$17b2o\$14b2o3bo\$15b2o\$14bo11\$22b2o\$15b2o4b2o\$14b2o7bo\$16bo\$12b2o\$11b
obo\$13bo!
``````

chris_c
Posts: 966
Joined: June 28th, 2014, 7:15 am

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

I think I've added everything except 16.1107 in Goldtiger's second edit above. I made some new synths of my own as well. The new list contains 62 SLs:

Code: Select all

``````16.712     xs16_3pc0qmzw23          20
16.1757    xs16_g8idik8z123         18
16.1790    xs16_178cia4z0321        18
16.227     xs16_5b8r5426            17
16.265     xs16_259m861ac           17
16.380     xs16_4a40vh248c          17
16.616     xs16_i5pajoz11           17
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
16.1064    xs16_39m88cz6221         17
16.1097    xs16_ck0ol3z643          17
16.1398    xs16_g88c93zc952         17
16.1722    xs16_4aq32acz032         17
16.1758    xs16_4a4o796zw121        17
16.1847    xs16_39c8a52z033         17
16.1882    xs16_259m453zx23         17
16.2467    xs16_0kc3213z34a4        17
16.3163    xs16_wo443123zbd         17
16.3164    xs16_wo443146zbd         17
16.104     xs16_0j5ozj4pz11         16
16.243     xs16_2egu16426           16
16.300     xs16_9fg4czbd            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
16.1068    xs16_3lo0kcz6421         16
16.1080    xs16_3lo0kcz3421         16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1583    xs16_4a9jzxha6zx11       16
16.1675    xs16_xj96z0mdz32         16
16.1693    xs16_8k8aliczw23         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
16.2025    xs16_069q48cz2521        16
16.2028    xs16_25ao48cz2521        16
16.2029    xs16_25ao4a4z2521        16
16.2030    xs16_0i5q8a52z121        16
16.2204    xs16_0gilla4z641         16
16.2219    xs16_0oe12koz643         16
16.2305    xs16_6413ia4z6421        16
16.2317    xs16_cik8a52z641         16
16.2322    xs16_raak8zx1252         16
16.2323    xs16_ra248goz056         16
16.2445    xs16_ciligzx254c         16
16.2630    xs16_31e8gzxo9a6         16
16.3032    xs16_1784ozx342sg        16
``````
These are the SLs with new costs since last time:

Code: Select all

``````+16.926     xs16_3iajc4gozw1         15
+16.600     xs16_6421344og84c        14
+16.1107    xs16_02egdbz2521         14
+16.1276    xs16_3iakgozw1ac         14
+16.2190    xs16_032q4goz6413        14
+16.2356    xs16_25icggozx1ac        14
+16.1273    xs16_32q4goz0db          13
+16.1381    xs16_32q4gozc93          13
+16.1785    xs16_2eg88bdzx23         13
+16.1905    xs16_8u16853z32          13
+16.2555    xs16_4a9jzxpia4          13
+15.1205    xs15_0g8gka23z343        12
+16.115     xs16_0ol3z0mdz32         12
+16.948     xs16_04s0fpz6221         12
+16.2215    xs16_04s0cp3z6221        12
+16.2216    xs16_0g8ie0dbz23         12
+15.552     xs15_69m88czx56          11
+16.1911    xs16_69q3213z32          11
+15.598     xs15_3iakgozw56          10
+16.914     xs16_8kkja952zx1         10
+15.97      xs15_354qajo             9
+15.179     xs15_3146pb8o            9
+15.620     xs15_39m88czx56          9
+16.3066    xs16_4a9jzx12ego         9
+15.6       xs15_ol3zmdz11           8
+16.665     xs16_699mkiczx1          8
+16.848     xs16_ca9b8oz0252         8
+16.1904    xs16_8u164koz32          8
+16.3227    xs16_31e8gzy012ego       8
``````

Sokwe
Moderator
Posts: 1674
Joined: July 9th, 2009, 2:44 pm

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

chris_c wrote:
Sokwe wrote:I tried to reduce 16.1693 via the honeycomb, but I was only able to get it down to 18
By keeping your glider in the lower right and finding a 3G collision that worked for the rest, I reduced this by two. Sadly that still means 16G if the honeycomb costs 7G:

Code: Select all

``````x = 24, y = 26, rule = B3/S23
10bo12bo\$9bo11b2o\$9b3o3bo6b2o\$15bobo\$15b2o3\$15b2o\$15bobo\$9b2o4bo\$b3o4b
o2bo\$3bo3bob2obo\$2bo5bo2bo\$9b2o4\$18b2o\$18bobo\$9b2o7bo\$9bobo\$b2o6bo\$obo
\$2bo10b2o\$13bobo\$13bo!
``````
I've spent some time looking for a 6G honeycomb synthesis, but I haven't been unsuccessful so far. Maybe someone else can get it from one of these "good looking" predecessors:

Code: Select all

``````x = 206, y = 28, rule = B3/S23
142bo\$140bobo\$141b2o5\$117b2o\$28bo57bo29bo2bo\$2bo3bobo18bobo30bo26b2o
28bobo43b2o\$3bo3bo20b2o31bo27bo30bo42b2o37b2o\$2obob3o52bobo23b3obo28b
2o77bo2b2o\$o2bo2bo55bobo24b3o107bo2bo\$3bo28b2obo22bo4b3o16bo7bobo106b
3o\$4bobo24bo4bo20bobo4bo18bo8b2o67bo\$5bo22b2o27bobo21b3o7b3o65bobo43bo
\$27bo30bo23bo8b2o67b2o31b2o10bo\$27b2o2bo3bo19bo27b2o33b2o73b2o10bo\$27b
2ob2o3bo19b2o25bobo34b2o\$10bo19b3obo19bobo27bo32b2o2bo41b3o\$8b2o18bo4b
2o81bob4o41bo\$9b2o18b3obo81bo3bo44bo\$30b3o79bo2bo2bo\$31bo80bo4bo\$113b
3o45bobo\$162b2o2b2o\$162bo2b2o\$167bo!``````
-Matthias Merzenich

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

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

16.3163 in 7G. It can be continued to 16.3164 synthesis (12G).

Code: Select all

``````x = 69, y = 32, rule = B3/S23
obo\$b2o\$bo2\$65bobo\$65b2o\$66bo3\$2bo\$3b2o\$2b2o62b3o\$29bo36bo\$29bobo35bo\$
29b2o\$55b2obo\$55bob2o7b2o\$53b2o10b2o\$52bo14bo\$2b3o19bo27bo\$4bo19bobo
23b2o\$3bo20b2o24bo\$51bo\$50b2o15b2o\$25b2o28bo10b2o\$25bobo27b2o11bo\$25bo
28bobo3\$28b2o\$28bobo\$28bo!
``````
EDIT: 16.1757 in 8G:

Code: Select all

``````x = 40, y = 42, rule = B3/S23
9bobo\$9b2o\$o9bo\$b2o\$2o\$21bo\$20bo\$20b3o13\$24b3o\$24bo\$5bobo17bo\$b2o3b2o\$
2b2o2bo\$bo3\$5b3o\$7bo\$6bo9\$37b2o\$37bobo\$37bo!
``````

Goldtiger997
Posts: 627
Joined: June 21st, 2016, 8:00 am

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

16.1790 in 9 gliders:

Code: Select all

``````x = 24, y = 29, rule = B3/S23
5bo\$3b2o16bo\$4b2o15bobo\$21b2o\$o\$b2o\$2o2\$11bo\$9b2o\$10b2o2\$bo3b2o\$b2ob2o
\$obo3bo6\$11b2o\$10b2o\$12bo\$6b2o\$5bobo\$7bo\$13b2o\$13bobo\$13bo!
``````
Now all but one 16-bit still-lifes cost less than 18 gliders.
Sokwe wrote:I've spent some time looking for a 6G honeycomb synthesis, but I haven't been unsuccessful so far. Maybe someone else can get it from one of these "good looking" predecessors:

Code: Select all

``````x = 206, y = 28, rule = B3/S23
142bo\$140bobo\$141b2o5\$117b2o\$28bo57bo29bo2bo\$2bo3bobo18bobo30bo26b2o
28bobo43b2o\$3bo3bo20b2o31bo27bo30bo42b2o37b2o\$2obob3o52bobo23b3obo28b
2o77bo2b2o\$o2bo2bo55bobo24b3o107bo2bo\$3bo28b2obo22bo4b3o16bo7bobo106b
3o\$4bobo24bo4bo20bobo4bo18bo8b2o67bo\$5bo22b2o27bobo21b3o7b3o65bobo43bo
\$27bo30bo23bo8b2o67b2o31b2o10bo\$27b2o2bo3bo19bo27b2o33b2o73b2o10bo\$27b
2ob2o3bo19b2o25bobo34b2o\$10bo19b3obo19bobo27bo32b2o2bo41b3o\$8b2o18bo4b
2o81bob4o41bo\$9b2o18b3obo81bo3bo44bo\$30b3o79bo2bo2bo\$31bo80bo4bo\$113b
3o45bobo\$162b2o2b2o\$162bo2b2o\$167bo!``````
Hmm...The first one looks particularly promising. I've had a quick go at a few, with no success so far.

AbhpzTa
Posts: 504
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

yootaa wrote:16.3163 in 7G. It can be continued to 16.3164 synthesis (12G).

Code: Select all

``````x = 69, y = 32, rule = B3/S23
obo\$b2o\$bo2\$65bobo\$65b2o\$66bo3\$2bo\$3b2o\$2b2o62b3o\$29bo36bo\$29bobo35bo\$
29b2o\$55b2obo\$55bob2o7b2o\$53b2o10b2o\$52bo14bo\$2b3o19bo27bo\$4bo19bobo
23b2o\$3bo20b2o24bo\$51bo\$50b2o15b2o\$25b2o28bo10b2o\$25bobo27b2o11bo\$25bo
28bobo3\$28b2o\$28bobo\$28bo!
``````
Reduced by 1:

Code: Select all

``````x = 43, y = 35, rule = B3/S23
bo\$2bo\$3o8\$3bo\$bobo\$2b2o6\$41bo\$40bo\$40b3o8\$2b2o\$3b2o22b2o\$2bo23b2o\$28b
o\$24b2o\$23bobo\$25bo!``````
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: 966
Joined: June 28th, 2014, 7:15 am

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

Sokwe wrote: I've spent some time looking for a 6G honeycomb synthesis, but I haven't been unsuccessful so far. Maybe someone else can get it from one of these "good looking" predecessors:
Eventually I did find a 6G honeycomb synthesis:

Code: Select all

``````x = 42, y = 43, rule = B3/S23
4bobo\$5b2o\$5bo4\$9bo\$7bobo\$8b2o3\$11bo\$9bobo\$10b2o5\$o13bo\$b2o11bobo\$2o
12b2o20\$39b3o\$39bo\$40bo!
``````
It is much like the first of your predecessors in that the main piece of the junk would evolve into this without any further interaction:

Code: Select all

``````x = 5, y = 5, rule = LifeHistory
2.D\$.D.D\$D.D.D\$D.D.D\$4D!
``````
Here is 16.1097 in 11G by improving 15.477:

Code: Select all

``````x = 45, y = 56, rule = B3/S23
21bobo2bobo\$21b2o3b2o\$22bo4bo5\$15bobo\$15b2o\$16bo\$38b2o3b2o\$38bo2bo2bo\$
39bob2o\$40bo\$4b3o31bobo\$4bo33b2o\$2o3bo\$b2o\$o20b2o5bo\$21bobo3b2o\$21bo5b
obo5\$13bo\$12b2o\$12bobo15\$10bo\$11bo\$9b3o4bobo\$16b2o\$17bo2\$42b2o\$43bo\$8b
2o3b2o23b2o2bo\$8bo2bo2bo5b2o16bo2bo\$9bob2o7bobo16bob2o\$10bo9bo19bo\$8bo
bo27bobo\$8b2o28b2o!
``````
The latest list contains 56 SLs:

Code: Select all

``````16.712     xs16_3pc0qmzw23          20
16.227     xs16_5b8r5426            17
16.265     xs16_259m861ac           17
16.380     xs16_4a40vh248c          17
16.616     xs16_i5pajoz11           17
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
16.1064    xs16_39m88cz6221         17
16.1398    xs16_g88c93zc952         17
16.1722    xs16_4aq32acz032         17
16.1758    xs16_4a4o796zw121        17
16.1847    xs16_39c8a52z033         17
16.1882    xs16_259m453zx23         17
16.2467    xs16_0kc3213z34a4        17
16.104     xs16_0j5ozj4pz11         16
16.243     xs16_2egu16426           16
16.300     xs16_9fg4czbd            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
16.1068    xs16_3lo0kcz6421         16
16.1080    xs16_3lo0kcz3421         16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1583    xs16_4a9jzxha6zx11       16
16.1675    xs16_xj96z0mdz32         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
16.2025    xs16_069q48cz2521        16
16.2028    xs16_25ao48cz2521        16
16.2029    xs16_25ao4a4z2521        16
16.2030    xs16_0i5q8a52z121        16
16.2204    xs16_0gilla4z641         16
16.2219    xs16_0oe12koz643         16
16.2305    xs16_6413ia4z6421        16
16.2317    xs16_cik8a52z641         16
16.2322    xs16_raak8zx1252         16
16.2323    xs16_ra248goz056         16
16.2445    xs16_ciligzx254c         16
16.2630    xs16_31e8gzxo9a6         16
16.3032    xs16_1784ozx342sg        16
``````

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

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

16.265 in 10G:

Code: Select all

``````x = 65, y = 45, rule = B3/S23
2bo\$obo\$b2o5\$9bo\$9bobo\$9b2o2\$10bo\$9b2o\$9bobo4\$49bo\$47bobo\$48b2o2b2o\$
52b2o3\$52b2o\$52b2o\$9bo4b2o43bo\$9b2o2b2o43bobo2b2o\$8bobo4bo41bobobo2bo\$
56bo2bobobo\$57b2o3bo5\$10b3o\$12bo7b2o\$11bo8bobo\$20bo3\$6b2o\$5bobo\$7bo11b
o\$18b2o\$18bobo!
``````

Goldtiger997
Posts: 627
Joined: June 21st, 2016, 8:00 am

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

On the reducing 16.712 front, here is a synthesis for a related 19-bit still-life in 10 gliders:

Code: Select all

``````x = 39, y = 38, rule = B3/S23
5bo\$6bo\$4b3o2\$15bo\$16bo\$14b3o2\$29bobo\$15b3o11b2o\$17bo12bo\$16bo19bo\$36b
obo\$36b2o7\$2b2o\$bobo\$3bo3\$31b2o\$30b2o\$32bo\$b3o\$3bo\$2bo2\$23b2o\$22b2o\$
24bo\$3o\$2bo\$bo!
``````
It can probably be reduced to 9 gliders. How expensive is it to convert into 16.712?

chris_c
Posts: 966
Joined: June 28th, 2014, 7:15 am

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

Goldtiger997 wrote:On the reducing 16.712 front, here is a synthesis for a related 19-bit still-life in 10 gliders:

Code: Select all

``````x = 39, y = 38, rule = B3/S23
5bo\$6bo\$4b3o2\$15bo\$16bo\$14b3o2\$29bobo\$15b3o11b2o\$17bo12bo\$16bo19bo\$36b
obo\$36b2o7\$2b2o\$bobo\$3bo3\$31b2o\$30b2o\$32bo\$b3o\$3bo\$2bo2\$23b2o\$22b2o\$
24bo\$3o\$2bo\$bo!
``````
It can probably be reduced to 9 gliders. How expensive is it to convert into 16.712?
I had a play around in JLS and modifying the top spark seems a lot more promising than modifying the still life after it has settled. Any luck in making something like this?

Code: Select all

``````x = 11, y = 12, rule = B3/S23
3bo\$2bo\$bo2bo\$3obo\$o2bob2o\$3b2o\$8b2o\$bo5bo\$b2o4bo\$obo4bo2bo\$9b2o\$2bo!
``````
EDIT: And the 19-bitter can be done in 9G:

Code: Select all

``````x = 32, y = 36, rule = B3/S23
4bo\$5bo\$3b3o2\$14bo\$15bo\$13b3o3\$14b3o\$16bo\$15bo9\$b2o\$obo\$2bo6\$3o3b3o\$2b
o5bo21b2o\$bo5bo21b2o\$31bo\$3b2o\$4b2o20bo\$3bo21b2o\$25bobo!
``````

AbhpzTa
Posts: 504
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

chris_c wrote:I had a play around in JLS and modifying the top spark seems a lot more promising than modifying the still life after it has settled. Any luck in making something like this?

Code: Select all

``````x = 11, y = 12, rule = B3/S23
3bo\$2bo\$bo2bo\$3obo\$o2bob2o\$3b2o\$8b2o\$bo5bo\$b2o4bo\$obo4bo2bo\$9b2o\$2bo!
``````
16.712 in 14 gliders:

Code: Select all

``````x = 58, y = 112, rule = B3/S23
6bo\$7b2o\$6b2o9\$12bo39bo\$6bo3b2o38bo2bo\$4bobo4b2o37bo2bo\$5b2o44bo37\$12b
o39bo\$10bo2bo10bo25bo2bo\$10bo2bo8b2o26bo2bo2bo\$11bo11b2o26bo4bo\$56bo2\$
21bo\$20b2o\$20bobo23\$bo\$2bo11bo\$3o9bobo12bo\$13b2o11bo\$26b3o5\$12bo\$10bo
2bo38b2o\$10bo2bo2bo35bo3b2o\$11bo4bo37bo2bo\$16bo36b2obo\$53bo2b2o\$55bo\$
54b2o3\$3o\$2bo\$bo4b2o4b2o\$7b2o4b2o13b2o\$6bo5bo15bobo\$28bo\$9b2o\$8bobo\$
10bo12b3o\$23bo\$24bo!``````
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: 966
Joined: June 28th, 2014, 7:15 am

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

AbhpzTa wrote: 16.712 in 14 gliders:

Code: Select all

``````x = 58, y = 112, rule = B3/S23
6bo\$7b2o\$6b2o9\$12bo39bo\$6bo3b2o38bo2bo\$4bobo4b2o37bo2bo\$5b2o44bo37\$12b
o39bo\$10bo2bo10bo25bo2bo\$10bo2bo8b2o26bo2bo2bo\$11bo11b2o26bo4bo\$56bo2\$
21bo\$20b2o\$20bobo23\$bo\$2bo11bo\$3o9bobo12bo\$13b2o11bo\$26b3o5\$12bo\$10bo
2bo38b2o\$10bo2bo2bo35bo3b2o\$11bo4bo37bo2bo\$16bo36b2obo\$53bo2b2o\$55bo\$
54b2o3\$3o\$2bo\$bo4b2o4b2o\$7b2o4b2o13b2o\$6bo5bo15bobo\$28bo\$9b2o\$8bobo\$
10bo12b3o\$23bo\$24bo!``````
Nice!!

With some contributions of my own we are down to 50 SLs. Still quite a way to go but hopefully the worst is behind us:

Code: Select all

``````16.227     xs16_5b8r5426            17
16.380     xs16_4a40vh248c          17
16.616     xs16_i5pajoz11           17
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
16.1398    xs16_g88c93zc952         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
16.300     xs16_9fg4czbd            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
16.1068    xs16_3lo0kcz6421         16
16.1080    xs16_3lo0kcz3421         16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1583    xs16_4a9jzxha6zx11       16
16.1675    xs16_xj96z0mdz32         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
16.2030    xs16_0i5q8a52z121        16
16.2204    xs16_0gilla4z641         16
16.2219    xs16_0oe12koz643         16
16.2305    xs16_6413ia4z6421        16
16.2317    xs16_cik8a52z641         16
16.2322    xs16_raak8zx1252         16
16.2323    xs16_ra248goz056         16
16.2445    xs16_ciligzx254c         16
16.2630    xs16_31e8gzxo9a6         16
16.3032    xs16_1784ozx342sg        16
``````
16.1064:

Code: Select all

``````x = 62, y = 116, rule = B3/S23
24bo\$22b2o\$23b2o\$obo\$b2o\$bo12\$59b3o\$54b2o\$54bobo\$56bo\$55bob2obo\$56bo2b
2o\$bo18b3o34bo\$b2o17bo8b2o23b3o\$obo18bo6b2o24bo\$6b2o5b2o15bo\$7b2o3bobo
\$6bo6bo9\$6bo\$6b2o\$5bobo12\$28bo\$26b2o\$27b2o3\$20bo\$20bo\$14b2o4bo33b2o\$
14bobo37bobo\$16bo39bo\$15bob2obo34bob2obo\$16bo2b2o35bo2b2o\$17bo39bo\$14b
3o37b3o\$14bo39bo23\$31bobo\$31b2o\$32bo8\$14b2o38b2o\$14bobo37bobo\$16bo39bo
2bo\$15bob2obo34bob3o\$16bo2b2o35bo\$17bo39bo\$14b3o37b3o\$14bo39bo3\$34b3o\$
34bo\$35bo3\$32b2o\$32bobo\$32bo!
``````
16.2467:

Code: Select all

``````x = 68, y = 106, rule = B3/S23
20bo5bo\$18bobo5bobo\$19b2o5b2o\$61b2o\$60bo2bo\$61b2o\$65b3o\$22bo\$22b2o\$21b
obo18\$9bo\$7bobo\$8b2o8\$25bo\$26bo\$24b3o3bo\$30bobo\$30b2o32bob2o\$64b2obo\$
21b2o39b2o\$20bo2bo39bo\$21b2o39bo\$25b3o33bo\$61b2o4\$3b3o\$5bo\$4bo5\$22b2o\$
23b2o\$2o20bo\$b2o\$o16\$7bo34bo\$5bobo33bo\$6b2o33b3o\$24bob2o36bob2o\$24b2ob
o6bobo27b2obo\$22b2o10b2o26b2o\$23bo11bo27bo\$22bo39bo\$21bo39bo\$21b2o38bo
bo\$62bobo\$63bo5\$26bo\$26bobo\$26b2o3\$28b2o\$28bobo\$28bo2\$7b3o\$9bo\$8bo!
``````
16.104:

Code: Select all

``````x = 76, y = 122, rule = B3/S23
26bobo\$26b2o\$27bo2\$19b2o2b3o42b3o\$18bobo2bo49b3o\$20bo3bo16\$43bo\$41b2o\$
42b2o14\$20bobo\$20b2o\$21bo4\$25b2o\$24b2o\$26bo4\$71b2o\$29b3o39bo\$29bo42bo\$
30bo42bo\$18b3o50bobo\$23b3o44bobo\$13bo56bo\$14bo56bo\$12b3o57bo\$71b2o4\$
17bo\$18b2o\$17b2o4\$22bo\$22b2o\$21bobo14\$2o\$b2o\$o13\$21b2o48b2o\$21bo49bo\$
22bo49bo\$23bo49bo\$21bobo47bobo\$20bobo47bobo\$14bo5bo9bo39bo\$15bo5bo7bo
41bo\$13b3o6bo6b3o40bo\$21b2o47bobo\$70b2o8\$28b2o\$21bo6bobo\$20b2o6bo\$20bo
bo!
``````
16.2025:

Code: Select all

``````x = 65, y = 100, rule = B3/S23
31bobo\$26bo4b2o\$26bobo3bo\$26b2o3\$27b3o29b2o\$17b3o7bo31bobo\$28bo33bobo\$
60b2ob2o\$59bobo\$58bo2bo\$59b2o\$29b3o\$15b2o12bo\$14bobo13bo\$16bo\$24b2o\$
24bobo\$24bo27\$12bo6b2o38b2o\$13bo5bobo37bobo\$11b3o8bobo37bobo\$20b2ob2o
35b2ob2o\$19bobo39bo\$18bo2bo37bobo\$19b2o37bobo\$59bo4\$27b2o\$19bo6b2o\$19b
2o7bo\$18bobo15\$5bo\$6bo\$4b3o9\$19b2o39bo\$19bobo37bobo\$22bobo34bo2bobo\$
20b2ob2o35b2ob2o\$21bo39bo\$3o16bobo37bobo\$2bo15bobo37bobo\$bo4b2o11bo39b
o\$5bobo\$7bo2\$bo\$b2o\$obo!
``````

Goldtiger997
Posts: 627
Joined: June 21st, 2016, 8:00 am

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

AbhpzTa wrote:16.712 in 14 gliders:..
Great work!

The current hardest still life left might be 16.1398.

16.227 in 9 gliders:

Code: Select all

``````x = 45, y = 29, rule = B3/S23
31bo\$31bobo\$31b2o3\$30bo\$28b2o\$11b3o15b2o\$13bo\$12bo2\$13b3o\$7b3o3bo\$9bo
4bo\$8bo8\$3o32b2o\$2bo26b3o3bobo\$bo27bo5bo\$30bo\$42b2o\$42bobo\$42bo!
``````

chris_c
Posts: 966
Joined: June 28th, 2014, 7:15 am

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

Goldtiger997 wrote: The current hardest still life left might be 16.1398.
It was hard but I managed to reduce 16.1323 by 2G to get 16.1398 in 15G:

Code: Select all

``````x = 123, y = 158, rule = B3/S23
3bobo\$4b2o\$4bo39bo\$44bobo\$44b2o8\$44bo\$43bo\$43b3o17\$121b2o\$122bo\$120bo\$
30bo87b4o\$29b2o86bo\$29bobo86b2o\$119bo\$119bobo\$25b2o93b2o\$26b2o\$25bo2\$
4bo31b3o\$4b2o30bo\$3bobo9b2o20bo\$14bobo\$16bo34\$75b2o\$75bobo\$75bo18\$72b
2o\$72bobo\$72bo22\$38bo\$3bo32b2o\$4bo32b2o\$2b3o3\$21b2o98b2o\$22bo99bo\$20bo
99bo\$18b4o96b4o\$17bo99bo\$18b2o98b2o\$19bo100bo\$19bobo95bobo\$20b2o95b2o
14\$40b3o\$35b2o3bo\$b2o32bobo3bo\$obo32bo\$2bo!
``````
I saved 2G in making the R + Boat + Blinker but then had to jump through some extra hoops to keep the loaf and the cleanup on that side at only 3G.

Next hardest could be 16.1583. I'm trying to make a relevant 15 bitter in 11G from this soup:

Code: Select all

``````x = 13, y = 27, rule = B3/S23
4bo\$4bo\$4bo2\$3o2\$4bo7bo\$4bo7bo\$4bo7bo11\$3b3o\$3bobo\$3bo4\$2o\$2o!
``````
The plan is 4G + 4G and 3G for cleanup but that's just hope rather than expecation at the moment.

EDIT: Done. The snake can be extend to a python in 4G giving 15G for 16.1583:

Code: Select all

``````x = 99, y = 90, rule = B3/S23
64bo33bo\$62b2o32b2o\$63b2o32b2o\$9b3o37b3o2\$7bo5bo33bo5bo33b2o\$7bo5bo33b
o5bo32bobo\$7bo5bo33bo5bo31bo5b2o\$86b2o3b2o\$9b3o37b3o36bo\$88bo\$59bo29b
2o\$58bo31bo\$58b3o28bo\$89b2o4\$64b2o\$9bo54bobo\$10b2o52bo\$9b2o\$50b2o\$49bo
2bo\$7b3o40b2o\$9bo\$8bo\$46b2o\$46b2o\$9b2o\$9bobo\$9bo37\$80b2o\$80bobo\$80bo
17\$2o\$b2o\$o!
``````
EDIT2: 16.1068 in 11G:

Code: Select all

``````x = 62, y = 55, rule = B3/S23
2bo\$obo21bo\$b2o19b2o\$23b2o\$6bo6bo\$4bobo7b2o\$5b2o6b2o2\$3bo\$4bo50b2o3b2o
\$2b3o50bo2bo2bo\$57b2obo\$59bo\$56bobo\$56b2o\$12bo\$12b2o\$11bobo2\$8b2o\$9b2o
\$8bo\$17b3o\$17bo\$18bo18\$18bo\$12bo5bobo\$13b2o3b2o\$12b2o2\$56b2o\$56bo\$15b
2o3b2o35bo2b2o\$8b3o4bo2bo2bo36bo2bo\$10bo6b2obo36b2obo\$9bo9bo39bo\$16bob
o37bobo\$16b2o38b2o!
``````
Now all 17G SLs have at least two soups on Catagolue and all 16G SLs that have fewer than two soups have a 15-bit predecessor having at least 15 soups and currently costing at least 10G. The latest list contains 45 SLs:

Code: Select all

``````16.380     xs16_4a40vh248c          17
16.616     xs16_i5pajoz11           17
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
16.300     xs16_9fg4czbd            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
16.1675    xs16_xj96z0mdz32         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
16.2030    xs16_0i5q8a52z121        16
16.2204    xs16_0gilla4z641         16
16.2219    xs16_0oe12koz643         16
16.2305    xs16_6413ia4z6421        16
16.2317    xs16_cik8a52z641         16
16.2322    xs16_raak8zx1252         16
16.2323    xs16_ra248goz056         16
16.2445    xs16_ciligzx254c         16
16.2630    xs16_31e8gzxo9a6         16
16.3032    xs16_1784ozx342sg        16
``````

AbhpzTa
Posts: 504
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

16.616 in 10 gliders:

Code: Select all

``````x = 100, y = 49, rule = B3/S23
obo\$b2o\$bo5\$50bo\$50bobo\$50b2o14\$44bo\$43bo\$43b3o2\$35bo44bo\$36b2o9b3o29b
o\$35b2o10bo31b3o\$48bo27b2o\$36bo38bo2bo\$35b2o39b2o\$35bobo\$65b2obo26b2ob
o\$64bo2b2o25bo2b2o\$65bo29bo\$66b2obo26b2obo\$64bobob2o24bobob2o\$64b2o28b
2o3\$3b3o2b2o\$5bob2o23b2o3b2o\$4bo4bo21bo2bo2b2o\$32b2o\$4bo\$4b2o\$3bobo!``````
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: 7173
Joined: May 17th, 2009, 11:00 pm
Contact:

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

Down toward the end of the current list, 16.2445 / xs16_ciligzx254c can be reduced to 14G, based on this soup.

That was the first soup I tried -- it's the black link between the red and purple links. Didn't even look at the dozens of other soups, and didn't try terribly hard to replace blocks with gliders either... so this could almost certainly be improved further, one way or another:

Code: Select all

``````x = 68, y = 72, rule = B3/S23
5bo\$3bobo\$4b2o2\$2bo\$obo\$b2o63bo\$65bo\$65b3o9\$39bobo\$40b2o\$40bo6\$53bo\$
52bo\$52b3o\$8bo2bobo\$6bobo3b2o44b2o\$7b2o3bo44b2o\$59bo22\$56bo\$55b2o\$55bo
bo3\$58b3o\$58bo\$27b2o30bo\$26bobo\$28bo3\$9bo\$9b2o\$8bobo40b3o\$51bo\$18b2o
32bo\$17bobo\$19bo!``````
I also spent some time on the next 16-bitter on the list, 16.2630 / xs16_31e8gzxo9a6, and found what seems like a fairly promising predecessor, from one of the first couple of soups (I looked at all of them for this case):

Code: Select all

``````x = 26, y = 24, rule = B3/S23
6b2o\$6b2o2b2o\$10b2o\$2ob2o\$o3bo\$b3o\$2bo\$7b3o2\$13b2o4bo\$13b2o2bo2bo\$16bo
3bo\$10b2o4bo\$10b2o7bo\$20bo\$15b2o\$14bob3o3bo\$13bo8b2o\$13bo\$13bo7bob2o\$
14bo3b3o2b2o\$15bo6bo2bo\$22bobo\$22bo!``````
But a very speculative 4G search hasn't turned up that modified phi spark yet. Don't think it's likely to, though the script is still running. Seems likely that someone can work out a recipe for it, since there's a fair amount of working room and nine gliders to spare if they're needed.

Another option is

Code: Select all

``````x = 20, y = 24, rule = B3/S23
13bo\$12bobo\$12bo3b3o\$13bo5bo\$17bo2\$15b2o\$2bo14bo\$3o\$3o\$12b3o\$4bo5b2o2b
o\$2b2ob2o3bo2b2o\$4bo5b3o5\$6bo\$6b3o\$6b3o\$5bo3bo\$5b4o\$5bob2o!``````
but that seems a good bit more expensive, though at least the long boat can be removed with a single glider.

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!