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

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
BobShemyakin
Posts: 214
Joined: June 15th, 2014, 6:24 am

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

16.1696 in 15G:

Code: Select all

``````x = 100, y = 49, rule = B3/S23
32bobo\$32b2o\$33bo11\$69bo\$14bo55b2o\$12b2o55b2o\$13b2o\$73bobo4bo\$14bo54b
2o2b2o4bo\$13b2o54bobo2bo4b3o\$13bobo2bo50bo\$18bobo\$18b2o2\$45bo19bo29bo\$
44bobo2bo14bobo2bo24bobo\$43bo2b4o13bo2b4o23bo2b3o\$44b2o18b2o28b2o3bo\$
46b2o18b2o6bobo19b2obo\$46bobo17bobo5b2o20bobo\$47bo19bo7bo21bo6\$75b2o\$
75bobo\$4b3o68bo\$6bo\$5bo\$b2o\$obo60b3o\$2bo62bo\$64bo\$30b2o\$2b2o25b2o\$bobo
27bo\$3bo!
``````
Bob Shemyakin

chris_c
Posts: 910
Joined: June 28th, 2014, 7:15 am

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

Pushed another update. Here are a couple of improvements I made: 16.823 in 12G and 16.915 in 14G:

Code: Select all

``````x = 365, y = 236, rule = Life
18bo11bo\$19bo10bobo\$17b3o10b2o2\$251bo\$252b2o\$126b3o122b2o102b2o\$355bob
o\$356bo\$129b3o126b3o\$258bo\$259bo2\$26b2o10b3o\$25bobo10bo\$27bo11bo77\$51b
o191bo\$50bo190bobo\$50b3o189b2o2\$270bo\$270bobo\$270b2o2\$9bo\$10bo265bo\$8b
3o264bo\$275b3o\$138b2o222b2o\$138b2o221bo2bo\$26b3o97b3o126b2o104bobo\$
255bobo102b2ob2o\$256bo102bo2bo\$29b3o97b3o228bobo\$118b2o241bo\$118b2o\$
267b2o4bo\$47b3o217bobo2b2o\$47bo219bo4bobo\$48bo\$277b3o\$277bo\$278bo3\$5b
3o\$7bo\$6bo51\$284bo\$233bo50bobo\$234bo49b2o\$232b3o3\$42bobo\$42b2o256bobo\$
43bo256b2o\$301bo\$obo290bo\$b2o290bobo\$bo254bo36b2o\$254bobo\$255b2o15\$
363bo\$38b2o222b2o98bobo\$27bo10b2o88b2o131bo2bo96bo2bo\$27bo98b3obo130bo
bo97bobo\$27bo97bo5bo128b2ob2o95b2ob2o\$30bo95bo5bo126bo2bo96bo2bo\$30bo
96bob3o128bobo97bobo\$18b2o10bo97b2o131bo99bo\$18b2o18\$56bo\$55b2o248b3o\$
55bobo247bo\$306bo\$14bo\$14b2o\$13bobo!
``````
Here are all the improvements since last time:

Code: Select all

``````+16.915     xs16_0gs2pmz1243         14
+16.106     xs16_31246116853         13
+16.557     xs16_1784cggc48c         13
+16.823     xs16_4ai3hik8zx11        12
+16.76      xs16_03lozgjkcz1         11
+16.105     xs16_0mp3zj4cz11         11
+16.114     xs16_c9jz6ahzw23         11
+16.442     xs16_0cai3z4aip          11
+16.1566    xs16_g8e123zpi6          11
+16.1654    xs16_0gs252zj4cz11       11
+16.1696    xs16_4a9mk4ozx121        10
+16.588     xs16_312461164ko         9
+15.396     xs15_8k4ra96zw1          8
+16.142     xs16_5b8raic             8
+16.1716    xs16_4a9mk46zx121        8
+16.626     xs16_69n8jdzx1           7
+16.663     xs16_69r4koz023          7
+16.1500    xs16_0g8e13zo9a6         7
+16.1701    xs16_4a9jc4ozx121        7
+16.641     xs16_c9baiczw32          6
``````
Here is the new list of SLs sorted by frequency:

Code: Select all

``````16.202     xs16_354cgn96                            27  4612
16.657     xs16_695q4ozw321                         16  4403
16.131     xs16_660uhar                             19  3702
16.1856    xs16_39u06a4z32                          16  2408
16.1739    xs16_g88r2qkz121                         20  2219
16.1880    xs16_259q453z032                         25  1975
16.665     xs16_699mkiczx1                          18  1857
16.829     xs16_0md1e8z1226                         23  1475
16.748     xs16_39ege2z321                          17  1372
16.799     xs16_c8al56z311                          17  1176
16.642     xs16_6s1raa4zw1                          53  1101
16.228     xs16_178bp2sg                            20  1047
16.159     xs16_2egmd1e8                            21  960
16.765     xs16_4ap78cz321                          999 926
16.686     xs16_mkkb2acz1                           39  903
16.152     xs16_5b8r9ic                             999 897
16.2309    xs16_8kk31e8z641                         21  779
16.846     xs16_caab8oz0252                         999 684
16.19      xs16_caarz39c                            18  505
16.810     xs16_ca9la4z311                          16  471
16.1992    xs16_25is0cczw65                         16  470
16.1881    xs16_259q453zw32                         19  433
16.813     xs16_c4lb8oz321                          999 425
16.834     xs16_8u15a4z1226                         25  422
16.691     xs16_co2ticz23                           999 419
16.774     xs16_69raa4z32                           21  419
16.360     xs16_2egu16413                           16  360
16.848     xs16_ca9b8oz0252                         18  359
16.2014    xs16_25a8kk8z0253                        17  340
16.827     xs16_ciaj2ak8zw1                         999 329
16.1717    xs16_4aajk46zx121                        999 328
16.995     xs16_0raik8z643                          16  320
16.1722    xs16_4aq32acz032                         17  307
16.1940    xs16_c48q552z321                         999 281
16.716     xs16_3pmk46zx23                          32  272
16.265     xs16_259m861ac                           17  270
16.1757    xs16_g8idik8z123                         18  267
16.2060    xs16_69akg4czx56                         16  260
16.1773    xs16_ciarzx3213                          999 259
16.1703    xs16_4a9la8ozx121                        999 250
16.647     xs16_8k4r2pmzw1                          999 241
16.153     xs16_4a9r8jd                             999 227
16.18      xs16_caarzbd                             19  208
16.1684    xs16_4aab9k8zx32                         19  163
16.2174    xs16_08u164koz32                         27  160
16.353     xs16_321fgc453                           23  155
16.1740    xs16_69acga6zx32                         23  155
16.668     xs16_gbq1daz121                          17  152
16.1990    xs16_8e1tazx1252                         18  143
16.144     xs16_4aar2pm                             999 141
16.1857    xs16_39u0652z32                          16  141
16.243     xs16_2egu16426                           16  138
16.2018    xs16_25a8c826zw33                        18  125
16.819     xs16_ra178cz23                           999 120
16.619     xs16_j9ajkcz11                           999 120
16.126     xs16_69ir9ic                             999 117
16.822     xs16_8ehikozw56                          16  112
16.2445    xs16_ciligzx254c                         16  105
16.1787    xs16_069m4koz311                         16  104
16.953     xs16_0cil56z6221                         16  98
16.1991    xs16_8e1qbzx1252                         17  97
16.1929    xs16_0g5r8b5z121                         16  94
16.213     xs16_35861tic                            23  89
16.15      xs16_178c1f84c                           17  83
16.2295    xs16_0g8go8brz23                         24  74
16.155     xs16_3pabp46                             18  72
16.634     xs16_ca9diczw32                          999 71
16.1694    xs16_4a5p6o8zx121                        19  65
16.2347    xs16_g8861acz0db                         28  64
16.628     xs16_kc32qkz0113                         28  62
16.1847    xs16_39c8a52z033                         17  62
16.1954    xs16_8kk31e8z065                         21  61
16.731     xs16_3iajkcz23                           28  57
16.836     xs16_4aajkczx56                          16  57
16.833     xs16_0mp2sgz1243                         20  56
16.616     xs16_i5pajoz11                           17  53
16.640     xs16_c9bkkozw32                          999 49
16.801     xs16_08eharz321                          19  43
16.1904    xs16_8u164koz32                          32  41
16.795     xs16_c87p46z311                          53  39
16.230     xs16_178jd2ko                            19  39
16.927     xs16_4akgf9zw65                          18  38
16.2132    xs16_0g8it2sgz23                         17  38
16.804     xs16_c871arzx32                          999 36
16.313     xs16_3pm44og4c                           35  36
16.1754    xs16_695m88czx23                         999 35
16.1691    xs16_4a9l6o8zx121                        999 35
16.1106    xs16_0iu0dbz641                          25  35
16.2201    xs16_0ggml96z641                         18  32
16.1304    xs16_0okih3zc8421                        16  32
16.312     xs16_62s53zbd                            29  31
16.1391    xs16_ca168ozc8421                        16  31
16.929     xs16_3iaj2ak8zw1                         999 28
16.2541    xs16_g8861aczc93                         28  28
16.1994    xs16_0g9fgka4z121                        16  28
16.1846    xs16_25a8c93zw33                         23  27
16.623     xs16_o5r8jdz01                           27  23
16.227     xs16_5b8r5426                            17  23
16.856     xs16_kc32acz1252                         16  23
16.914     xs16_8kkja952zx1                         18  22
16.1791    xs16_03lkaa4z3201                        20  19
16.1702    xs16_4a5p68ozx121                        23  18
16.1464    xs16_08o696z6ip                          16  18
16.706     xs16_39s0qmz023                          24  17
16.1766    xs16_kc321e8z123                         16  17
16.621     xs16_g5r8jdz11                           25  14
16.723     xs16_i5p64koz11                          20  14
16.350     xs16_312461tic                           16  14
16.2219    xs16_0oe12koz643                         16  14
16.1962    xs16_4a9eg8ozw65                         999 13
16.1723    xs16_4ap64koz032                         999 13
16.1034    xs16_3lkaa4z065                          24  13
16.1790    xs16_178cia4z0321                        18  12
16.803     xs16_c9bk46z311                          17  12
16.278     xs16_32qj43146                           29  11
16.1323    xs16_031e8gzc9311                        29  11
16.786     xs16_3pa3ia4zw11                         28  11
16.724     xs16_j5o64koz11                          16  11
16.1758    xs16_4a4o796zw121                        17  10
16.996     xs16_2lm853z056                          16  9
16.2546    xs16_j9cz122c84c                         16  9
16.2542    xs16_g88c871zc93                         16  9
16.682     xs16_69j0j9czx11                         999 8
16.3163    xs16_wo443123zbd                         17  8
16.838     xs16_ci9b8ozw56                          16  8
16.2302    xs16_4ap6413z65                          16  8
16.695     xs16_5b8bl8zx32                          25  7
16.872     xs16_2lla8oz065                          20  7
16.1995    xs16_cik8a52z065                         18  7
16.1127    xs16_giligoz104a4                        32  6
16.1680    xs16_8e123ckzx311                        17  6
16.2630    xs16_31e8gzxo9a6                         16  6
16.2322    xs16_raak8zx1252                         16  6
16.147     xs16_32qjap3                             32  5
16.3227    xs16_31e8gzy012ego                       27  5
16.1753    xs16_695q4gozw23                         21  5
16.772     xs16_3h4e1daz011                         16  5
16.2547    xs16_j9cz122c826                         16  5
16.151     xs16_64kr2pm                             999 4
16.778     xs16_69la8oz321                          36  4
16.713     xs16_o8bap3z23                           24  4
16.3066    xs16_4a9jzx12ego                         23  4
16.926     xs16_3iajc4gozw1                         21  4
16.2058    xs16_69akg4czx146                        20  4
16.2805    xs16_0gs2c871z641                        16  4
16.2029    xs16_25ao4a4z2521                        16  4
16.890     xs16_696ki6zw641                         999 3
16.889     xs16_696ki6zx65                          999 3
16.1861    xs16_4ap64koz32                          999 3
16.1685    xs16_c48n98czx23                         999 3
16.842     xs16_cila8oz065                          34  3
16.354     xs16_35s26zbd                            29  3
16.828     xs16_4alhe8z0641                         28  3
16.358     xs16_321fgc2ko                           19  3
16.1911    xs16_69q3213z32                          18  3
16.1107    xs16_02egdbz2521                         18  3
16.1105    xs16_gie0dbz146                          18  3
16.1882    xs16_259m453zx23                         17  3
16.1867    xs16_069q453z311                         17  3
16.762     xs16_jhke1e8z1                           16  3
16.2305    xs16_6413ia4z6421                        16  3
16.2030    xs16_0i5q8a52z121                        16  3
16.1710    xs16_4a9bk46zx32                         16  3
16.1080    xs16_3lo0kcz3421                         16  3
16.2096    xs16_wck5b8oz311                         999 2
16.1094    xs16_cila8oz641                          40  2
16.349     xs16_35s26z39c                           35  2
16.220     xs16_3123qajo                            29  2
16.1901    xs16_08obap3z32                          25  2
16.300     xs16_9fg4czbd                            23  2
16.875     xs16_4a5pa4z2521                         17  2
16.380     xs16_4a40vh248c                          17  2
16.840     xs16_c8idiczw56                          16  2
16.771     xs16_69qb8oz32                           16  2
16.2862    xs16_08u16413z65                         16  2
16.2204    xs16_0gilla4z641                         16  2
16.1720    xs16_4a4o79ozx121                        16  2
16.1675    xs16_xj96z0mdz32                         16  2
16.2784    xs16_woe12koz6221                        999 1
16.1979    xs16_4ap30ga6zw121                       999 1
16.1970    xs16_ckw3lozw1243                        999 1
16.1682    xs16_8k9bkk8zw23                         999 1
16.712     xs16_3pc0qmzw23                          48  1
16.1721    xs16_64kb2acz032                         35  1
16.218     xs16_3pajc48c                            33  1
16.185     xs16_32qk5b8o                            30  1
16.930     xs16_3iaj21e8zw1                         25  1
16.825     xs16_4alhe8zw65                          25  1
16.1064    xs16_39m88cz6221                         24  1
16.2313    xs16_08u16853z32                         23  1
16.1073    xs16_3lkaa4z641                          20  1
16.745     xs16_39qb8oz32                           19  1
16.2162    xs16_0at16426z32                         19  1
16.2050    xs16_6ik8a52z065                         19  1
16.1912    xs16_at16426z32                          19  1
16.2480    xs16_3iaczw1139c                         18  1
16.2447    xs16_0g8it248cz23                        18  1
16.2025    xs16_069q48cz2521                        18  1
16.1711    xs16_c8idik8z023                         18  1
16.843     xs16_4a9liczx56                          17  1
16.3164    xs16_wo443146zbd                         17  1
16.3134    xs16_c9jzw122c826                        17  1
16.2861    xs16_ol3zw343146                         17  1
16.2694    xs16_4ai3gzx11mq                         17  1
16.1715    xs16_64p784czw23                         17  1
16.593     xs16_3123c48gka4                         16  1
16.2699    xs16_08o6413zrm                          16  1
16.2460    xs16_0o861aczc452                        16  1
16.2317    xs16_cik8a52z641                         16  1
16.1864    xs16_31ke1e8z032                         16  1
16.1085    xs16_3h4e12koz011                        16  1
16.104     xs16_0j5ozj4pz11                         16  1
``````

BlinkerSpawn
Posts: 1908
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

16.202 in 10:

Code: Select all

``````x = 162, y = 44, rule = B3/S23
obo\$b2o\$bo5\$40bo\$38bobo\$39b2o3\$95bo\$95bobo\$95b2o\$78bobo\$78b2o\$79bo\$
140b2o\$139bo2bo\$139b3obo\$143bo\$141b2o13b2o\$141bo13bo2bo\$139bobo14b2o\$
139b2o4bo13b3o\$144bobo12bo\$144bo2bo12bo\$145b2o\$148b3o\$148bo\$140b2o7bo\$
54bo85b2o\$53bo\$53b3o82b2o\$57b3o77bobo\$57bo81bo\$58bo4\$76b2o\$76bobo\$76bo
!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Bullet51
Posts: 537
Joined: July 21st, 2014, 4:35 am

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

16.846 in 14G:

Code: Select all

``````x = 142, y = 63, rule = B3/S23
110bo\$110bobo\$110b2o5\$59bo\$57bobo\$58b2o2\$52bo\$50bobo\$51b2o10\$77bo\$76bo
\$76b3o\$138bo\$74bo63b3o\$5bo69bo65bo\$3bobo67b3o60b6o\$4b2o130bo\$b2o136bo\$
obo12bo122bobo\$2bo11bo123b2o\$14b3o\$138bo\$8b2o2b2o123b2o\$9b2obobo122bob
o\$8bo3bo121b2o\$133bobo\$68b3o64bo\$70bo\$69bo10b2o\$80b2o4\$85bo\$84bobo\$85b
o11\$47b2o\$46bobo\$48bo!
``````
I wonder if there is a simpler cleanup.
Still drifting.

dvgrn
Moderator
Posts: 5899
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI
Contact:

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

Bullet51 wrote:16.846 in 14G... I wonder if there is a simpler cleanup.
A few minutes with Seeds of Destruction cuts it down to 13G, anyway:

Code: Select all

``````x = 142, y = 51, rule = B3/S23
43bo68bo\$44bo65b2o\$42b3o66b2o6\$59bo\$57bobo\$58b2o14\$77bo\$76bo\$76b3o\$
138bo\$74bo63b3o\$5bo69bo65bo\$3bobo67b3o60b6o\$4b2o130bo\$b2o136bo\$obo12bo
122bobo\$2bo11bo123b2o\$14b3o\$138bo\$8b2o2b2o123b2o\$9b2obobo122bobo\$8bo3b
o121b2o\$133bobo\$68b3o64bo\$70bo\$69bo10b2o\$80b2o4\$85bo\$84bobo\$85bo!``````
A lucky one-glider cleanup doesn't seem terribly likely, but also doesn't seem impossible. I didn't run an exhaustive search, just tried the most likely places I saw.

chris_c
Posts: 910
Joined: June 28th, 2014, 7:15 am

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

BlinkerSpawn wrote:16.202 in 10
I improved the cleanup by 1G which means that the derived synthesis of 16.213 comes in at 15G:

Code: Select all

``````x = 133, y = 276, rule = B3/S23
55bo\$54bo\$54b3o15\$53bo\$51b2o\$24bo27b2o\$25bo\$23b3o15\$127bo\$126bobo\$31bo
94bobo\$29bobo95bo\$30b2o2\$34bo\$34bobo\$34b2o3\$123bo\$122bobo\$122bo2bo\$
123b2o\$129b2o\$128bo2bo\$118b2o6b3obobo\$118b2o5bo4bobo\$125b2o3b2o4\$59b3o
\$59bo\$60bo36\$67b2o\$66b2o\$68bo25\$4bo\$5bo\$3b3o5\$bo\$2bo\$3o3\$27bo\$26bobo\$
26bobo\$27bo8\$23bo\$22bobo\$22bo2bo\$23b2o\$29b2o98b2o\$28bo2bo96bo2bo\$18b2o
6b3obobo93b3obobo\$18b2o5bo4bobo92bo4bobo\$25b2o3b2o93b2o3b2o80\$9bo\$10bo
\$8b3o24bo\$35bobo\$35b2o12\$29b2o94b2o2b2o\$28bo2bo93bo2bo2bo\$26b3obobo93b
obobobo\$25bo4bobo94bo2bobo\$25b2o3b2o98b2o13\$9b3o5b2o\$11bo4bobo18b2o\$
10bo7bo17b2o\$38bo2\$14b2o\$13bobo\$15bo!
``````
Bullet51 wrote:16.846 in 14G
dvgrn wrote: A few minutes with Seeds of Destruction cuts it down to 13G, anyway
And I saved another glider in the construction of the block and tub:

Code: Select all

``````x = 49, y = 29, rule = B3/S23
29bo\$30b2o\$29b2o8\$5b2o\$5bobo\$b2o2bo\$obo30b3o\$2bo35b2o\$37bo2bo\$38bobo\$
39bo3\$37b2o\$37b2o8bo\$46bobo\$47bo3\$19b3o\$21bo\$20bo!
``````

Bullet51
Posts: 537
Joined: July 21st, 2014, 4:35 am

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

Is it doable in 16?

Code: Select all

``````x = 56, y = 38, rule = B3/S23
5b2o\$5b2o2\$47b2o3b2o\$47bo2bo2bo\$bo46b4o\$obo18b2o\$b2o18bobo24b2o\$21bo
26b2o\$55bo\$53b2o\$obo42b2o3b2o2b2o\$obo43b2o2bobo\$3o42bo4bo13\$47b2o3b2o\$
47bo2bo2bo\$48b4o2\$48b2o\$48b2o\$42bo\$43b2o\$42b2o2b2o3b2o\$10b3o32bobo2b2o
\$10bo36bo4bo\$11bo!
``````
EDIT: Is this even possible?

Code: Select all

``````x = 14, y = 18, rule = LifeHistory
12.2A\$12.2A3\$8.A\$8.A.2A\$10.2A\$11.A\$5.2E.2C\$3.E2.EC.C\$3.2E\$.2E6.A\$2.E
5.2A\$E7.4A\$2E7.3A\$.E\$E\$2E!``````
Some recipes for the 20-cell SL:

Code: Select all

``````x = 95, y = 22, rule = B3/S23
43b2o41b2o\$43b2o40bobo\$85bo\$85b2o4bo\$90b2o\$5b2o33b3o47b2o\$7bo31b4o51bo
\$2b2o3bo26b2o2b2o3bo49b2o\$bo5bo26b2obo3b2o51bo\$o5bo30b2ob3o49b2o\$6o32b
o\$10b3o41b2o\$9bo3bo34bo5b2o18b3o\$8bo4bo32b2ob2o22bo2bo\$2b3o3bo37b2ob2o
22b2o\$2bobo3bo2bo34bo2b2o\$3b2o3bo2bo36b2o\$8bobo34b2obo28b2o\$8b2o36b2o
28b3o\$82bo\$47b2o31bobo\$47b2o30b3o!
``````
Still drifting.

Goldtiger997
Posts: 548
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

16.765 in 8 gliders:

Code: Select all

``````x = 36, y = 24, rule = B3/S23
16bo\$17b2o\$16b2o\$obo\$b2o\$bo2\$6bo\$5bo\$2bo2b3o\$3bo\$b3o2\$14b3o\$16bo\$15bo
7b2o\$23bobo\$23bo3\$12b2o\$11bobo19b3o\$13bo19bo\$34bo!
``````
While looking for 1-glider versions of the outer two gliders in the previous step, I found this 8 glider synthesis for a related 19-bit still-life:

Code: Select all

``````x = 40, y = 34, rule = B3/S23
6bo\$7b2o\$6b2o6\$39bo\$37b2o\$38b2o4\$obo\$b2o\$bo2\$6bo\$5bo\$2bo2b3o\$3bo\$b3o2\$
14b3o\$16bo\$15bo7b2o\$23bobo\$23bo3\$12b2o\$11bobo\$13bo!
``````
Bullet51 wrote:EDIT: Is this even possible?

Code: Select all

``````x = 14, y = 18, rule = LifeHistory
12.2A\$12.2A3\$8.A\$8.A.2A\$10.2A\$11.A\$5.2E.2C\$3.E2.EC.C\$3.2E\$.2E6.A\$2.E
5.2A\$E7.4A\$2E7.3A\$.E\$E\$2E!``````
Do you mean is it possible to make a converter out of it? I think it is definitely possible. I do not know if there already exists a converter that does that.

BlinkerSpawn
Posts: 1908
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

Easier:

Code: Select all

``````x = 12, y = 13, rule = B3/S23
9b2o\$10bo2\$5b2ob2o\$3bo2b2obo\$3b2o\$b2o6b2o\$2bo5b2obo\$o\$2o\$bo\$o\$2o!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

BobShemyakin
Posts: 214
Joined: June 15th, 2014, 6:24 am

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

BlinkerSpawn wrote:Easier:

Code: Select all

``````x = 12, y = 13, rule = B3/S23
9b2o\$10bo2\$5b2ob2o\$3bo2b2obo\$3b2o\$b2o6b2o\$2bo5b2obo\$o\$2o\$bo\$o\$2o!
``````
16.2699 in 14G:

Code: Select all

``````x = 118, y = 36, rule = B3/S23
41bo\$40bo\$37bo2b3o\$35bobo\$36b2o23b2o18b2o28b2o\$5bobo15b2o18b2o16bo2bo
16bo2bo26bo2bo\$5b2o16bo19bo19b2o18b2o10bobo15b2o\$2bo3bo19bo19bo18b2o
18b2o8b2o18b2o\$obo22b2o18b2o18bo19bo10bo18bo\$b2o46bo17bo19bo29bo\$49bob
o14b2o18b2o28b2o\$b2o46b2o65bo\$obo114bo\$2bo113b2o\$47b3o\$47bo\$48bo41b2o
2b3o\$91b2obo\$90bo4bo2\$77bo\$77b2o6b2o\$76bobo5b2o\$86bo5\$94b2o\$93b2o\$95bo
3\$106b2o\$105b2o\$107bo!
``````
16.819 in 12G:

Code: Select all

``````x = 79, y = 20, rule = B3/S23
8bo34bobo\$2bo6b2o33b2o\$obo5b2o34bo\$b2o\$11bo10b2ob2obo13b2o8b2ob2obo13b
2ob2obo\$7bo3bobo9bobob2o12bobo9bobob2o14bobob2o\$b3o2b2o3b2o9bo20bo8bo
19bo\$3bo2bobo14b2o28b2o17b3o\$2bo21bo20bo8bo20bo\$23bo21b2o6bo20b2o\$23b
2o19bobo6b2o\$b3o\$3bo\$2bo\$5b3o\$5bo41b3o\$6bo42bo\$2b3o43bo\$4bo\$3bo!
``````
Bob Shemyakin

BlinkerSpawn
Posts: 1908
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

BlinkerSpawn wrote:Easier:

Code: Select all

``````x = 12, y = 13, rule = B3/S23
9b2o\$10bo2\$5b2ob2o\$3bo2b2obo\$3b2o\$b2o6b2o\$2bo5b2obo\$o\$2o\$bo\$o\$2o!
``````
Here we are:

Code: Select all

``````x = 19, y = 15, rule = B3/S23
12bo\$12bobo\$12b2o\$5b2ob2o\$3bo2b2obo\$3b2o11bo\$b2o13bobo\$2bo7bo5b2o\$o8b
2o\$2o7bobo\$bo4bo\$o4b3o\$2o2b2obo\$4b3o\$5b2o!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Extrementhusiast
Posts: 1798
Joined: June 16th, 2009, 11:24 pm
Location: USA

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

BlinkerSpawn wrote:
BlinkerSpawn wrote:Easier:

Code: Select all

``RLE``
Here we are:

Code: Select all

``RLE``
Even better:

Code: Select all

``````x = 13, y = 15, rule = B3/S23
11bo\$10bo\$10b3o3\$5b2ob2o\$3bo2b2obo\$3b2o\$b2o7b3o\$2bo7bo\$o10bo\$2o\$bo\$o\$
2o!
``````
I Like My Heisenburps! (and others)

Goldtiger997
Posts: 548
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

16.152 in 9 gliders:

Code: Select all

``````x = 33, y = 52, rule = B3/S23
o\$b2o\$2o27\$14b2o\$15b2obobo\$14bo3b2o\$19bo3\$14b2o\$13bobo\$15bo\$30bo\$30bob
o\$30b2o4\$7b3o17bo\$9bo16bo\$8bo17b3o\$10b3o\$10bo\$11bo13b2o\$24b2o\$26bo!
``````
EDIT:

Predecessor for 16.813 that I was unable to make into a synthesis, because I could not find a suitable TL inserter:

Code: Select all

``````x = 39, y = 18, rule = B3/S23
35bo\$36bo\$o33b3o\$b2o3b2o\$2o4b2o23b2o\$31b2o3\$4bo29bo\$2b2ob2o25b2ob2o\$4b
o29bo2\$5b3o27b3o\$5bo2bo26bo2bo\$5bo2bo26bo2bo\$8bo29bo\$6b2o28b2o\$5bo29bo
!``````
Here are two 3-glider syntheses for the part at the bottom:

Code: Select all

``````x = 33, y = 15, rule = B3/S23
bobo22bobo\$b2o24b2o\$2bo24bo6\$bo29bo\$o29bo\$3o27b3o2\$bo29bo\$2o28b2o\$obo
27bobo!``````
EDIT 2:

16.691 in 8 gliders:

Code: Select all

``````x = 27, y = 22, rule = B3/S23
14bo\$12bobo\$o12b2o\$b2o21bo\$2o20b2o\$23b2o6\$26bo\$8bo15b2o\$9bo2bo12b2o\$7b
3o2b2o\$11bobo\$16b2o\$16bobo\$16bo\$21b2o\$20b2o\$22bo!``````

chris_c
Posts: 910
Joined: June 28th, 2014, 7:15 am

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

Goldtiger997 wrote: Predecessor for 16.813 that I was unable to make into a synthesis, because I could not find a suitable TL inserter:
Here is 16.813 in 8G:

Code: Select all

``````x = 30, y = 32, rule = B3/S23
3bobo\$4b2o\$4bo\$28bo\$27bo\$o26b3o\$b2o\$2o2\$25bobo\$25b2o\$5bo20bo\$6bo\$4b3o
4\$20bobo\$20b2o\$21bo6\$20bo\$19bo\$19b3o2\$20bo\$19b2o\$19bobo!
``````
I also added your other syntheses along with Bob's and the converters featured in Bob's post.

I added a 6G synthesis of 16.1935:

Code: Select all

``````x = 81, y = 27, rule = B3/S23
15bo\$14bo\$14b3o5\$9bo\$9bobo55bo10bobo\$2bo6b2o55bobo5b2obob2o\$obo63bobo
5bob2o\$b2o64bo11b2o\$80bo\$78bo\$78b2o\$61b3o\$63bo\$62bo5\$6bo\$5b2o\$5bobo2b
2o\$10bobo\$10bo!
``````
I analysed all of Mark Niemiec's syntheses in the zip file on the 16 bit SL page. Now there are just 12 SLs in my lists without synthesis. I don't think any of them have explicit synthesis on Mark's website except for 16.126 which I was too lazy to include because it uses quite a number of *WSS.

Now 249 16-bit SLs have synthesis in greater than 15 gliders in my list. I think about 50 of them have no appearance on Catagolue. Here is the updated list sorted by Catagolue frequency:

Code: Select all

``````16.657     xs16_695q4ozw321                         16  4403
16.131     xs16_660uhar                             19  3702
16.1856    xs16_39u06a4z32                          16  2408
16.1739    xs16_g88r2qkz121                         20  2219
16.1880    xs16_259q453z032                         25  1975
16.665     xs16_699mkiczx1                          18  1857
16.829     xs16_0md1e8z1226                         23  1475
16.748     xs16_39ege2z321                          17  1372
16.799     xs16_c8al56z311                          17  1176
16.642     xs16_6s1raa4zw1                          51  1101
16.228     xs16_178bp2sg                            20  1047
16.159     xs16_2egmd1e8                            21  960
16.686     xs16_mkkb2acz1                           38  903
16.2309    xs16_8kk31e8z641                         21  779
16.19      xs16_caarz39c                            18  505
16.810     xs16_ca9la4z311                          16  471
16.1992    xs16_25is0cczw65                         16  470
16.1881    xs16_259q453zw32                         19  433
16.834     xs16_8u15a4z1226                         25  422
16.774     xs16_69raa4z32                           21  419
16.360     xs16_2egu16413                           16  360
16.848     xs16_ca9b8oz0252                         18  359
16.2014    xs16_25a8kk8z0253                        17  340
16.827     xs16_ciaj2ak8zw1                         23  329
16.1717    xs16_4aajk46zx121                        16  328
16.995     xs16_0raik8z643                          16  320
16.1722    xs16_4aq32acz032                         17  307
16.1940    xs16_c48q552z321                         29  281
16.716     xs16_3pmk46zx23                          17  272
16.265     xs16_259m861ac                           17  270
16.1757    xs16_g8idik8z123                         18  267
16.2060    xs16_69akg4czx56                         16  260
16.1773    xs16_ciarzx3213                          999 259
16.1703    xs16_4a9la8ozx121                        26  250
16.647     xs16_8k4r2pmzw1                          999 241
16.153     xs16_4a9r8jd                             999 227
16.18      xs16_caarzbd                             19  208
16.1684    xs16_4aab9k8zx32                         19  163
16.2174    xs16_08u164koz32                         27  160
16.353     xs16_321fgc453                           23  155
16.1740    xs16_69acga6zx32                         23  155
16.668     xs16_gbq1daz121                          17  152
16.1990    xs16_8e1tazx1252                         18  143
16.144     xs16_4aar2pm                             999 141
16.1857    xs16_39u0652z32                          16  141
16.243     xs16_2egu16426                           16  138
16.2018    xs16_25a8c826zw33                        18  125
16.619     xs16_j9ajkcz11                           999 120
16.126     xs16_69ir9ic                             999 117
16.822     xs16_8ehikozw56                          16  112
16.2445    xs16_ciligzx254c                         16  105
16.1787    xs16_069m4koz311                         16  104
16.953     xs16_0cil56z6221                         16  98
16.1991    xs16_8e1qbzx1252                         17  97
16.1929    xs16_0g5r8b5z121                         16  94
16.15      xs16_178c1f84c                           17  83
16.2295    xs16_0g8go8brz23                         24  74
16.155     xs16_3pabp46                             18  72
16.634     xs16_ca9diczw32                          999 71
16.1694    xs16_4a5p6o8zx121                        19  65
16.2347    xs16_g8861acz0db                         28  64
16.628     xs16_kc32qkz0113                         28  62
16.1847    xs16_39c8a52z033                         17  62
16.1954    xs16_8kk31e8z065                         21  61
16.731     xs16_3iajkcz23                           28  57
16.836     xs16_4aajkczx56                          16  57
16.833     xs16_0mp2sgz1243                         20  56
16.616     xs16_i5pajoz11                           17  53
16.640     xs16_c9bkkozw32                          17  49
16.801     xs16_08eharz321                          19  43
16.1904    xs16_8u164koz32                          32  41
16.795     xs16_c87p46z311                          53  39
16.230     xs16_178jd2ko                            19  39
16.2132    xs16_0g8it2sgz23                         17  38
16.313     xs16_3pm44og4c                           35  36
16.1754    xs16_695m88czx23                         999 35
16.1691    xs16_4a9l6o8zx121                        26  35
16.1106    xs16_0iu0dbz641                          25  35
16.2201    xs16_0ggml96z641                         18  32
16.1304    xs16_0okih3zc8421                        16  32
16.312     xs16_62s53zbd                            29  31
16.1391    xs16_ca168ozc8421                        16  31
16.929     xs16_3iaj2ak8zw1                         31  28
16.2541    xs16_g8861aczc93                         28  28
16.1994    xs16_0g9fgka4z121                        16  28
16.1846    xs16_25a8c93zw33                         23  27
16.623     xs16_o5r8jdz01                           25  23
16.227     xs16_5b8r5426                            17  23
16.856     xs16_kc32acz1252                         16  23
16.914     xs16_8kkja952zx1                         18  22
16.1791    xs16_03lkaa4z3201                        20  19
16.1702    xs16_4a5p68ozx121                        23  18
16.1464    xs16_08o696z6ip                          16  18
16.706     xs16_39s0qmz023                          24  17
16.1766    xs16_kc321e8z123                         16  17
16.621     xs16_g5r8jdz11                           23  14
16.723     xs16_i5p64koz11                          20  14
16.350     xs16_312461tic                           16  14
16.2219    xs16_0oe12koz643                         16  14
16.1723    xs16_4ap64koz032                         999 13
16.1034    xs16_3lkaa4z065                          24  13
16.1962    xs16_4a9eg8ozw65                         20  13
16.1790    xs16_178cia4z0321                        18  12
16.803     xs16_c9bk46z311                          17  12
16.278     xs16_32qj43146                           29  11
16.1323    xs16_031e8gzc9311                        29  11
16.786     xs16_3pa3ia4zw11                         28  11
16.724     xs16_j5o64koz11                          16  11
16.1758    xs16_4a4o796zw121                        17  10
16.996     xs16_2lm853z056                          16  9
16.2546    xs16_j9cz122c84c                         16  9
16.2542    xs16_g88c871zc93                         16  9
16.682     xs16_69j0j9czx11                         33  8
16.3163    xs16_wo443123zbd                         17  8
16.838     xs16_ci9b8ozw56                          16  8
16.2302    xs16_4ap6413z65                          16  8
16.872     xs16_2lla8oz065                          20  7
16.1995    xs16_cik8a52z065                         18  7
16.1127    xs16_giligoz104a4                        20  6
16.2630    xs16_31e8gzxo9a6                         16  6
16.2322    xs16_raak8zx1252                         16  6
16.147     xs16_32qjap3                             32  5
16.3227    xs16_31e8gzy012ego                       27  5
16.1753    xs16_695q4gozw23                         21  5
16.772     xs16_3h4e1daz011                         16  5
16.2547    xs16_j9cz122c826                         16  5
16.778     xs16_69la8oz321                          36  4
16.151     xs16_64kr2pm                             28  4
16.713     xs16_o8bap3z23                           24  4
16.3066    xs16_4a9jzx12ego                         23  4
16.2058    xs16_69akg4czx146                        20  4
16.926     xs16_3iajc4gozw1                         18  4
16.2805    xs16_0gs2c871z641                        16  4
16.2029    xs16_25ao4a4z2521                        16  4
16.1861    xs16_4ap64koz32                          999 3
16.890     xs16_696ki6zw641                         35  3
16.842     xs16_cila8oz065                          34  3
16.889     xs16_696ki6zx65                          29  3
16.354     xs16_35s26zbd                            29  3
16.828     xs16_4alhe8z0641                         25  3
16.358     xs16_321fgc2ko                           19  3
16.1911    xs16_69q3213z32                          18  3
16.1107    xs16_02egdbz2521                         18  3
16.1105    xs16_gie0dbz146                          18  3
16.1882    xs16_259m453zx23                         17  3
16.1867    xs16_069q453z311                         17  3
16.1685    xs16_c48n98czx23                         17  3
16.762     xs16_jhke1e8z1                           16  3
16.2305    xs16_6413ia4z6421                        16  3
16.2030    xs16_0i5q8a52z121                        16  3
16.1710    xs16_4a9bk46zx32                         16  3
16.1080    xs16_3lo0kcz3421                         16  3
16.1094    xs16_cila8oz641                          40  2
16.349     xs16_35s26z39c                           35  2
16.220     xs16_3123qajo                            29  2
16.1901    xs16_08obap3z32                          25  2
16.300     xs16_9fg4czbd                            23  2
16.2096    xs16_wck5b8oz311                         21  2
16.875     xs16_4a5pa4z2521                         17  2
16.380     xs16_4a40vh248c                          17  2
16.840     xs16_c8idiczw56                          16  2
16.771     xs16_69qb8oz32                           16  2
16.2862    xs16_08u16413z65                         16  2
16.2204    xs16_0gilla4z641                         16  2
16.1720    xs16_4a4o79ozx121                        16  2
16.1675    xs16_xj96z0mdz32                         16  2
16.2784    xs16_woe12koz6221                        999 1
16.1970    xs16_ckw3lozw1243                        999 1
16.712     xs16_3pc0qmzw23                          48  1
16.1721    xs16_64kb2acz032                         34  1
16.218     xs16_3pajc48c                            33  1
16.185     xs16_32qk5b8o                            30  1
16.1979    xs16_4ap30ga6zw121                       27  1
16.930     xs16_3iaj21e8zw1                         25  1
16.1064    xs16_39m88cz6221                         24  1
16.2313    xs16_08u16853z32                         23  1
16.825     xs16_4alhe8zw65                          22  1
16.1682    xs16_8k9bkk8zw23                         21  1
16.1073    xs16_3lkaa4z641                          20  1
16.745     xs16_39qb8oz32                           19  1
16.2162    xs16_0at16426z32                         19  1
16.2050    xs16_6ik8a52z065                         19  1
16.1912    xs16_at16426z32                          19  1
16.2480    xs16_3iaczw1139c                         18  1
16.2447    xs16_0g8it248cz23                        18  1
16.2025    xs16_069q48cz2521                        18  1
16.1711    xs16_c8idik8z023                         18  1
16.843     xs16_4a9liczx56                          17  1
16.3164    xs16_wo443146zbd                         17  1
16.2861    xs16_ol3zw343146                         17  1
16.2694    xs16_4ai3gzx11mq                         17  1
16.1715    xs16_64p784czw23                         17  1
16.593     xs16_3123c48gka4                         16  1
16.2460    xs16_0o861aczc452                        16  1
16.2317    xs16_cik8a52z641                         16  1
16.1864    xs16_31ke1e8z032                         16  1
16.1085    xs16_3h4e12koz011                        16  1
16.104     xs16_0j5ozj4pz11                         16  1
``````

Sokwe
Moderator
Posts: 1480
Joined: July 9th, 2009, 2:44 pm

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

chris_c wrote:16.823 in 12G
Reduced to 9G:

Code: Select all

``````x = 102, y = 18, rule = B3/S23
62bo19bo\$2bo58bo20bobo\$obo58b3o18b2o\$b2o\$60bo\$61bo\$59b3o35b2o\$13bo21b
3o27b3o27b3obo\$11b2o81bo5bo\$9bo2b2o81bo5bo\$7bobo28b3o27b3o25bob3o\$8b2o
64b3o20b2o\$74bo\$75bo2\$52b2o18b3o\$51bobo20bo\$53bo19bo!``````
Edit: 16.1940 was one of the last to be solved in the original 16-bit synthesis project. Here's 16.1940 in 10G:

Code: Select all

``````x = 23, y = 31, rule = B3/S23
15bobo\$6b2o7b2o\$5bobo8bo\$7bo\$13b3o\$13bo\$14bo6\$18bobo\$14b2o2b2o\$13bobo
3bo\$15bo3\$21bo\$13b2o5b2o\$6b3o4bobo4bobo\$8bo4bo\$7bo6\$3o\$2bo\$bo!``````
Edit 2: 16.2784 in 10G:

Code: Select all

``````x = 107, y = 18, rule = B3/S23
36bo\$37bo\$35b3o\$40bo\$38b2o\$2bobo34b2o18b2o18b2o18b2o\$3b2o4bo50bo19bo
19bo\$3bo5bobo10bo10b3o6bo17bobo17bobo8bo8bob2o\$9b2o10bobo11bo5bobo17bo
bo17bobo7bobo7bob3o\$bo20b2o10bo7b2o18b2o18b2o7b2o13bo\$o87b2o15bo\$3o17b
4o16b4o16b4o16b4o3b2o13bobo\$20bo2bo16bo2bo16bo2bo16bo2bo5bo12b2o2\$b3o\$
bo80b2o\$2bo78bobo\$83bo!``````
Edit 3: 16.1861 in 12G (very messy):

Code: Select all

``````x = 105, y = 59, rule = B3/S23
31bobo55b2o\$31b2o56bobo\$32bo10bo47bo\$41b2o48b2o\$42b2o45b2o2bo\$87bo2bob
o\$87b2o2bo10\$2o\$2o\$96bo\$28bo67bo\$27b2o67bo\$27bobo\$6bo\$6b2o86b2o\$5bobo
86b2o6bo\$101bobo\$11bobo87bobo\$11b2o5b3o81bo\$12bo5bo\$10bo8bo83b2o\$9b2o
91bobo\$9bobo92bo10\$68b3o\$68bo\$69bo13\$29b3o\$29bo\$30bo!``````
-Matthias Merzenich

Goldtiger997
Posts: 548
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

16.1773 in 9 gliders:

Code: Select all

``````x = 52, y = 30, rule = B3/S23
46bo\$46bobo\$46b2o2\$35bo\$33b2o13bo\$34b2o12bobo\$30b3o11bo3b2o\$32bo9b2o\$
31bo11b2o2\$49b3o\$37b2o3bo6bo\$36bobob2o8bo\$38bo2b2o13\$b2o\$obo\$2bo!
``````

AbhpzTa
Posts: 475
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

16.144 in 7 gliders:

Code: Select all

``````x = 72, y = 82, rule = B3/S23
bo\$2bo\$3o28\$12bobo\$13b2o\$13bo\$56bo\$56bobo\$56b2o10\$56bo\$57bo\$55b3o3\$54b
3o\$56bo\$55bo26\$69b3o\$9b2o58bo\$8bobo59bo\$10bo!``````
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).

Sokwe
Moderator
Posts: 1480
Joined: July 9th, 2009, 2:44 pm

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

I wrote:16.1861 in 12G
I reduced 16.1861 to 11G by playing around with Seeds of Destruction for a while:

Code: Select all

``````x = 97, y = 44, rule = B3/S23
57bobo\$57b2o\$58bo10bo\$67b2o\$68b2o7\$bo\$2bo\$3o3\$26b2o\$26b2o2\$54bo\$53b2o\$
53bobo\$32bo\$32b2o\$31bobo2\$37bobo\$37b2o5b3o\$38bo5bo\$36bo8bo\$35b2o\$35bob
o10\$94b3o\$94bo\$95bo!``````
Edit: 16.1723 in 10G:

Code: Select all

``````x = 161, y = 64, rule = B3/S23
46bo\$46bobo\$46b2o4\$bo40bo\$2bo39bobo\$3o39b2o23\$24bobo\$24b2o52bo39bo39bo
\$25bo51bobo37bobo37bobo\$75b3o2bo34b3o2bo34b3o2bo\$24b3o47bo3b2o34bo3b2o
34bo3b2o\$24bo20b3o25bobo2bo34bobo2bo35b2o2bo\$25bo19bo27bobo3bo33bobo3b
o39bo\$46bo27bo3b2o34bo3b2o38b2o\$111b2o\$110bobo\$112bo16\$55bo\$54b2o\$54bo
bo\$60bo\$18bo40b2o\$18b2o39bobo\$17bobo!``````
-Matthias Merzenich

Goldtiger997
Posts: 548
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

chris_c wrote:...except for 16.126 which I was too lazy to include because it uses quite a number of *WSS.
16.126 in 9 gliders:

Code: Select all

``````x = 47, y = 50, rule = B3/S23
9bo\$10bo\$8b3o16\$24bobo\$25b2o\$25bo2\$38bobo\$11bobo24b2o\$12b2o25bo\$12bo5\$
21bo\$21b2o\$20bobo8bobo\$27b2o2b2o11b2o\$27bobo2bo11bobo\$27bo16bo12\$3o\$2b
o\$bo!``````
My ATFBPEWIAHGOD (Always Try to Find a Better Predecessor Even When I Already Have a Good One Disorder, very rare) made finding this synthesis take much longer than usual.

EDIT:

16.153 in 9 gliders:

Code: Select all

``````x = 66, y = 63, rule = B3/S23
50bo\$50bobo\$50b2o19\$20bo\$20bobo\$20b2o3\$4bo\$4bobo\$4b2o2\$4b2o\$4bobo\$2o2b
o8bo\$b2o10bobo\$o12b2o2\$10b3o\$10bo\$11bo\$23b2o\$23bobo\$23bo19\$64b2o\$63b2o
\$65bo!
``````
EDIT2:

16.619 in 8 gliders, found from a C4_4 soup:

Code: Select all

``````x = 71, y = 61, rule = B3/S23
2bo\$obo\$b2o4\$55bo\$54bo\$54b3o23\$17bo\$18bo\$16b3o\$20b3o\$13b3o6bo\$15bo5bo\$
14bo\$37bo\$28b3o5b2o\$30bo5bobo\$29bo17\$68b2o\$68bobo\$68bo!
``````

chris_c
Posts: 910
Joined: June 28th, 2014, 7:15 am

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

I pushed an update with the recent syntheses. Also I added Bob's 3G tail adder as a component and worked out how to make 16.1970 from a 15-bit still life. The 3G carrier to long long snake was worked out by me, mimicking a 2G version that does not work in this scenario. I guess that something equivalent or possibly identical was already known. (EDIT: prepended a 8G synthesis of the 15-bitter)

Code: Select all

``````x = 166, y = 41, rule = B3/S23
16bo\$14b2o13bobo\$15b2o12b2o34bo\$30bo33bo44bo\$64b3o40b2o\$108b2o\$10bobo
131bo\$10b2o27b2o18b2o84bo\$5bobo3bo27b2o18b2o37bo6bo37b3o\$6b2o91bo4bo
34bo\$6bo90b3o4b3o30bobo6bobo\$138b2o6b2o\$147bo2\$122b2o18b2o\$122bo19bo
20b2o\$43b2o18b2o18b2o18b2o18bo19bo19bo\$39b2o2bo15b2o2bo15b2o2bo15b2o2b
o15b2o3bo14b2o3bo14b2o3bo\$39bo5bo13bo5bo13bo5bo13bo5bo13bo5bo13bo5bo
13bo5bo\$40bo3b2o14bo3b2o14bo3b2o14bo3b2o14bo3b2o14bo3b2o14bo3b2o\$41bo
2bo16bo2bo16bo2bo16bo2bo16bo2bo16bo2bo16bo2bo\$42bobo17bobo17bobo17bobo
17bobo17bobo17bobo\$43bo19bo19bo19bo19bo19bo19bo5\$27bo\$26b2o\$26bobo5\$2o
\$b2o\$o2\$26b2o\$25b2o\$27bo!
``````
Now there are just 4 still lifes that remain unsynthesised on my list and all of them have at least 35 soups on Catagolue (EDIT: Now just 3 since I missed Goldtiger's 16.619 in the second edit above)

Code: Select all

``````x = 7, y = 47, rule = Life
b2o\$o2bo\$ob2o2bo\$bo2b3o\$3bo\$4bo\$3b2o14\$3bobo\$3b2obo\$b2o3bo\$o2bobo\$bobo
b2o\$2bo15\$2b2o\$bo2bo\$o2bobo\$4obo\$4bo\$2bo\$2b2o!
``````

Code: Select all

``````16.657     xs16_695q4ozw321                         16  4403
16.131     xs16_660uhar                             19  3702
16.1856    xs16_39u06a4z32                          16  2408
16.1739    xs16_g88r2qkz121                         20  2219
16.1880    xs16_259q453z032                         25  1975
16.665     xs16_699mkiczx1                          18  1857
16.829     xs16_0md1e8z1226                         23  1475
16.748     xs16_39ege2z321                          17  1372
16.799     xs16_c8al56z311                          17  1176
16.642     xs16_6s1raa4zw1                          51  1101
16.228     xs16_178bp2sg                            20  1047
16.159     xs16_2egmd1e8                            21  960
16.686     xs16_mkkb2acz1                           38  903
16.2309    xs16_8kk31e8z641                         21  779
16.19      xs16_caarz39c                            18  505
16.810     xs16_ca9la4z311                          16  471
16.1992    xs16_25is0cczw65                         16  470
16.1881    xs16_259q453zw32                         19  433
16.834     xs16_8u15a4z1226                         25  422
16.774     xs16_69raa4z32                           21  419
16.360     xs16_2egu16413                           16  360
16.848     xs16_ca9b8oz0252                         18  359
16.2014    xs16_25a8kk8z0253                        17  340
16.827     xs16_ciaj2ak8zw1                         23  329
16.1717    xs16_4aajk46zx121                        16  328
16.995     xs16_0raik8z643                          16  320
16.1722    xs16_4aq32acz032                         17  307
16.716     xs16_3pmk46zx23                          17  272
16.265     xs16_259m861ac                           17  270
16.1757    xs16_g8idik8z123                         18  267
16.2060    xs16_69akg4czx56                         16  260
16.1703    xs16_4a9la8ozx121                        26  250
16.647     xs16_8k4r2pmzw1                          999 241
16.18      xs16_caarzbd                             19  208
16.1684    xs16_4aab9k8zx32                         19  163
16.2174    xs16_08u164koz32                         27  160
16.353     xs16_321fgc453                           23  155
16.1740    xs16_69acga6zx32                         23  155
16.668     xs16_gbq1daz121                          17  152
16.1990    xs16_8e1tazx1252                         18  143
16.1857    xs16_39u0652z32                          16  141
16.243     xs16_2egu16426                           16  138
16.2018    xs16_25a8c826zw33                        18  125
16.822     xs16_8ehikozw56                          16  112
16.2445    xs16_ciligzx254c                         16  105
16.1787    xs16_069m4koz311                         16  104
16.953     xs16_0cil56z6221                         16  98
16.1991    xs16_8e1qbzx1252                         17  97
16.1929    xs16_0g5r8b5z121                         16  94
16.15      xs16_178c1f84c                           17  83
16.2295    xs16_0g8go8brz23                         24  74
16.155     xs16_3pabp46                             18  72
16.634     xs16_ca9diczw32                          999 71
16.1694    xs16_4a5p6o8zx121                        19  65
16.2347    xs16_g8861acz0db                         28  64
16.628     xs16_kc32qkz0113                         28  62
16.1847    xs16_39c8a52z033                         17  62
16.1954    xs16_8kk31e8z065                         21  61
16.731     xs16_3iajkcz23                           28  57
16.836     xs16_4aajkczx56                          16  57
16.833     xs16_0mp2sgz1243                         20  56
16.616     xs16_i5pajoz11                           17  53
16.640     xs16_c9bkkozw32                          17  49
16.801     xs16_08eharz321                          19  43
16.1904    xs16_8u164koz32                          32  41
16.795     xs16_c87p46z311                          53  39
16.230     xs16_178jd2ko                            19  39
16.2132    xs16_0g8it2sgz23                         17  38
16.313     xs16_3pm44og4c                           35  36
16.1754    xs16_695m88czx23                         999 35
16.1691    xs16_4a9l6o8zx121                        26  35
16.1106    xs16_0iu0dbz641                          25  35
16.2201    xs16_0ggml96z641                         18  32
16.1304    xs16_0okih3zc8421                        16  32
16.312     xs16_62s53zbd                            29  31
16.1391    xs16_ca168ozc8421                        16  31
16.929     xs16_3iaj2ak8zw1                         31  28
16.2541    xs16_g8861aczc93                         28  28
16.1994    xs16_0g9fgka4z121                        16  28
16.1846    xs16_25a8c93zw33                         23  27
16.623     xs16_o5r8jdz01                           25  23
16.227     xs16_5b8r5426                            17  23
16.856     xs16_kc32acz1252                         16  23
16.914     xs16_8kkja952zx1                         18  22
16.1791    xs16_03lkaa4z3201                        20  19
16.1702    xs16_4a5p68ozx121                        23  18
16.1464    xs16_08o696z6ip                          16  18
16.706     xs16_39s0qmz023                          24  17
16.1766    xs16_kc321e8z123                         16  17
16.621     xs16_g5r8jdz11                           23  14
16.723     xs16_i5p64koz11                          20  14
16.350     xs16_312461tic                           16  14
16.2219    xs16_0oe12koz643                         16  14
16.1034    xs16_3lkaa4z065                          24  13
16.1962    xs16_4a9eg8ozw65                         20  13
16.1790    xs16_178cia4z0321                        18  12
16.803     xs16_c9bk46z311                          17  12
16.278     xs16_32qj43146                           29  11
16.1323    xs16_031e8gzc9311                        29  11
16.786     xs16_3pa3ia4zw11                         28  11
16.724     xs16_j5o64koz11                          16  11
16.1758    xs16_4a4o796zw121                        17  10
16.996     xs16_2lm853z056                          16  9
16.2546    xs16_j9cz122c84c                         16  9
16.2542    xs16_g88c871zc93                         16  9
16.682     xs16_69j0j9czx11                         33  8
16.3163    xs16_wo443123zbd                         17  8
16.838     xs16_ci9b8ozw56                          16  8
16.2302    xs16_4ap6413z65                          16  8
16.872     xs16_2lla8oz065                          20  7
16.1995    xs16_cik8a52z065                         18  7
16.1127    xs16_giligoz104a4                        20  6
16.2630    xs16_31e8gzxo9a6                         16  6
16.2322    xs16_raak8zx1252                         16  6
16.147     xs16_32qjap3                             32  5
16.3227    xs16_31e8gzy012ego                       27  5
16.1753    xs16_695q4gozw23                         21  5
16.772     xs16_3h4e1daz011                         16  5
16.2547    xs16_j9cz122c826                         16  5
16.778     xs16_69la8oz321                          36  4
16.151     xs16_64kr2pm                             28  4
16.713     xs16_o8bap3z23                           24  4
16.3066    xs16_4a9jzx12ego                         23  4
16.2058    xs16_69akg4czx146                        20  4
16.926     xs16_3iajc4gozw1                         18  4
16.2805    xs16_0gs2c871z641                        16  4
16.2029    xs16_25ao4a4z2521                        16  4
16.890     xs16_696ki6zw641                         35  3
16.842     xs16_cila8oz065                          34  3
16.889     xs16_696ki6zx65                          29  3
16.354     xs16_35s26zbd                            29  3
16.828     xs16_4alhe8z0641                         25  3
16.358     xs16_321fgc2ko                           19  3
16.1911    xs16_69q3213z32                          18  3
16.1107    xs16_02egdbz2521                         18  3
16.1105    xs16_gie0dbz146                          18  3
16.1882    xs16_259m453zx23                         17  3
16.1867    xs16_069q453z311                         17  3
16.1685    xs16_c48n98czx23                         17  3
16.762     xs16_jhke1e8z1                           16  3
16.2305    xs16_6413ia4z6421                        16  3
16.2030    xs16_0i5q8a52z121                        16  3
16.1710    xs16_4a9bk46zx32                         16  3
16.1080    xs16_3lo0kcz3421                         16  3
16.1094    xs16_cila8oz641                          40  2
16.349     xs16_35s26z39c                           35  2
16.220     xs16_3123qajo                            29  2
16.1901    xs16_08obap3z32                          25  2
16.300     xs16_9fg4czbd                            23  2
16.2096    xs16_wck5b8oz311                         21  2
16.875     xs16_4a5pa4z2521                         17  2
16.380     xs16_4a40vh248c                          17  2
16.840     xs16_c8idiczw56                          16  2
16.771     xs16_69qb8oz32                           16  2
16.2204    xs16_0gilla4z641                         16  2
16.1720    xs16_4a4o79ozx121                        16  2
16.1675    xs16_xj96z0mdz32                         16  2
16.712     xs16_3pc0qmzw23                          48  1
16.1721    xs16_64kb2acz032                         34  1
16.218     xs16_3pajc48c                            33  1
16.185     xs16_32qk5b8o                            30  1
16.1979    xs16_4ap30ga6zw121                       27  1
16.930     xs16_3iaj21e8zw1                         25  1
16.1064    xs16_39m88cz6221                         24  1
16.2313    xs16_08u16853z32                         23  1
16.825     xs16_4alhe8zw65                          22  1
16.1682    xs16_8k9bkk8zw23                         21  1
16.1970    xs16_ckw3lozw1243                        20  1
16.1073    xs16_3lkaa4z641                          20  1
16.745     xs16_39qb8oz32                           19  1
16.2162    xs16_0at16426z32                         19  1
16.2050    xs16_6ik8a52z065                         19  1
16.1912    xs16_at16426z32                          19  1
16.2480    xs16_3iaczw1139c                         18  1
16.2447    xs16_0g8it248cz23                        18  1
16.2025    xs16_069q48cz2521                        18  1
16.1711    xs16_c8idik8z023                         18  1
16.843     xs16_4a9liczx56                          17  1
16.3164    xs16_wo443146zbd                         17  1
16.2861    xs16_ol3zw343146                         17  1
16.2694    xs16_4ai3gzx11mq                         17  1
16.1715    xs16_64p784czw23                         17  1
16.593     xs16_3123c48gka4                         16  1
16.2460    xs16_0o861aczc452                        16  1
16.2317    xs16_cik8a52z641                         16  1
16.1864    xs16_31ke1e8z032                         16  1
16.1085    xs16_3h4e12koz011                        16  1
16.104     xs16_0j5ozj4pz11                         16  1
``````

AbhpzTa
Posts: 475
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

16.1754 in 7 gliders:

Code: Select all

``````x = 67, y = 20, rule = B3/S23
49bobo\$44bo4b2o\$42bobo5bo\$39bo3b2o\$37bobo\$38b2o\$61b2o\$60bo2bo\$2bobo21b
o19bo13bob2o2bo\$3b2o19b3o17b3o14bo2b3o\$3bo19bo19bo19bo\$23b2o18b2o19bo\$
3o60b2o\$2bo\$bo38b2o\$39bobo\$41bo\$43b2o\$43bobo\$43bo!``````
16.647 in 8 gliders:

Code: Select all

``````x = 93, y = 62, rule = B3/S23
21bo\$22b2o\$21b2o11\$56bo\$57bo\$55b3o3\$56b3o\$58bo\$57bo5\$64bo\$63b2o\$63bobo
17\$91bo\$90b2o\$90bobo2\$76bo\$75b2o\$75bobo4\$bo\$b2o\$obo3\$13b3o\$15bo\$14bo!``````
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).

Extrementhusiast
Posts: 1798
Joined: June 16th, 2009, 11:24 pm
Location: USA

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

I don't see why you can't just do something like this for 16.2460:

Code: Select all

``````x = 28, y = 18, rule = B3/S23
bo\$2bo\$3o3\$13bo\$14b2o5bo\$13b2o4b2o\$20b2o4\$12bo8bob2o\$13bo2bo4b2obo\$11b
3o2b2o7b2o\$15bobo9bo\$24bobo\$24b2o!
``````
Very nice predecessor to 16.185:

Code: Select all

``````x = 15, y = 12, rule = B3/S23
7b2o\$6bo2bo\$6bobo\$7bo2b3o\$bo8bo\$ob2o6bo\$4bo6b2obo\$4bo8bo\$2b3o2bo\$6bobo
\$5bo2bo\$6b2o!
``````
I Like My Heisenburps! (and others)

Goldtiger997
Posts: 548
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

16.634 in 9 gliders:

Code: Select all

``````x = 40, y = 45, rule = B3/S23
24bo\$23bo\$23b3o18\$2bo\$3b2o\$2b2o23bo\$26bo\$26b3o2\$bo27b2o\$b2o26bobo\$obo
26bo4\$13bo10b2o\$13b2o9bobo\$12bobo9bo6\$38b2o\$37b2o\$30bo8bo\$29b2o\$29bobo
!``````
Now all still-lifes up to 16-bits have syntheses on chris_c's lists!

I think there are now 232 16-bitters with syntheses in 16 gliders or more.
Last edited by Goldtiger997 on March 23rd, 2017, 4:53 am, edited 1 time in total.

dvgrn
Moderator
Posts: 5899
Joined: May 17th, 2009, 11:00 pm
Location: Madison, WI
Contact:

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

Goldtiger997 wrote:I think there are now 233 16-bitters with syntheses in 16 gliders or more.
Why so many? There only seem to be 185 rows in chris_c's latest list of still lifes, not counting the three 999's. Are you including oscillators or pseudo-still-lifes as well, or something like that?

Goldtiger997
Posts: 548
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

dvgrn wrote:
Goldtiger997 wrote:I think there are now 232 16-bitters with syntheses in 16 gliders or more.
Why so many? There only seem to be 185 rows in chris_c's latest list of still lifes, not counting the three 999's. Are you including oscillators or pseudo-still-lifes as well, or something like that?
The list that chris_c posted above does not include the still-lifes with no appearances on catalogue.