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

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
chris_c
Posts: 911
Joined: June 28th, 2014, 7:15 am

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

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

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``````x = 28, y = 18, rule = B3/S23
bo\$2bo\$3o3\$13bo\$14b2o5bo\$13b2o4b2o\$20b2o4\$12bo8bob2o\$13bo2bo4b2obo\$11b
3o2b2o7b2o\$15bobo9bo\$24bobo\$24b2o!
``````
Thanks. I added that version of the converter to my collection. Although the clearance is much better than the version I was using before it doesn't actually improve any of the syntheses up to 16-bit in terms of glider count. Maybe it will help if I ever get around to the 17-bitters. For fun I found a 7G synthesis of the 13-bitter involved:

Code: Select all

``````x = 138, y = 147, rule = B3/S23
bo\$2bo\$3o5\$5bo\$6b2o\$5b2o17\$23bobo\$24b2o110b2o\$24bo111b2o3\$135b2o\$135b
2o3\$121bo\$120bobo\$21b3o96bo2bo\$23bo94b2o2b2o\$22bo95bo\$119bo\$118b2o11\$
28b2o\$28bobo\$28bo7\$bo\$b2o\$obo64\$36b2o\$36b2o3\$35b2o\$35b2o3\$21bo99bo\$20b
obo97bobo\$20bo2bo96bo2bo\$18b2o2b2o94b2o2b2o\$18bo99bo\$19bo99bo\$18b2o98b
2o3\$52b3o\$52bo\$53bo!
``````
Goldtiger997 wrote: 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.
Yay! Now 230 after the improvement to the above 13-bitter.
Goldtiger997 wrote: The list that chris_c posted above does not include the still-lifes with no appearances on catalogue.
That's correct. I tweaked the code so that all SLs now appear in the list: 47 have no appearance on Catagolue, 131 have less than 10 appearances. Here is the list of expensive SLs sorted by Catagolue frequency and cost. The permanent homes for these lists are here and here

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``````16.657     xs16_695q4ozw321                         16  4488
16.131     xs16_660uhar                             19  3759
16.1856    xs16_39u06a4z32                          16  2455
16.1739    xs16_g88r2qkz121                         20  2256
16.1880    xs16_259q453z032                         25  2017
16.665     xs16_699mkiczx1                          18  1896
16.829     xs16_0md1e8z1226                         23  1496
16.748     xs16_39ege2z321                          17  1390
16.799     xs16_c8al56z311                          17  1200
16.642     xs16_6s1raa4zw1                          51  1118
16.228     xs16_178bp2sg                            20  1064
16.159     xs16_2egmd1e8                            21  974
16.686     xs16_mkkb2acz1                           38  918
16.2309    xs16_8kk31e8z641                         21  794
16.19      xs16_caarz39c                            18  512
16.1992    xs16_25is0cczw65                         16  477
16.810     xs16_ca9la4z311                          16  476
16.1881    xs16_259q453zw32                         19  441
16.834     xs16_8u15a4z1226                         25  432
16.774     xs16_69raa4z32                           21  432
16.360     xs16_2egu16413                           16  366
16.848     xs16_ca9b8oz0252                         18  363
16.2014    xs16_25a8kk8z0253                        17  348
16.1717    xs16_4aajk46zx121                        16  336
16.827     xs16_ciaj2ak8zw1                         23  335
16.995     xs16_0raik8z643                          16  325
16.1722    xs16_4aq32acz032                         17  319
16.265     xs16_259m861ac                           17  277
16.716     xs16_3pmk46zx23                          17  275
16.1757    xs16_g8idik8z123                         18  271
16.2060    xs16_69akg4czx56                         16  268
16.1703    xs16_4a9la8ozx121                        26  250
16.18      xs16_caarzbd                             19  213
16.1684    xs16_4aab9k8zx32                         19  170
16.2174    xs16_08u164koz32                         27  163
16.353     xs16_321fgc453                           23  157
16.668     xs16_gbq1daz121                          17  156
16.1740    xs16_69acga6zx32                         23  155
16.1990    xs16_8e1tazx1252                         18  146
16.1857    xs16_39u0652z32                          16  141
16.243     xs16_2egu16426                           16  138
16.2018    xs16_25a8c826zw33                        18  127
16.822     xs16_8ehikozw56                          16  114
16.2445    xs16_ciligzx254c                         16  106
16.1787    xs16_069m4koz311                         16  105
16.1991    xs16_8e1qbzx1252                         17  99
16.953     xs16_0cil56z6221                         16  99
16.1929    xs16_0g5r8b5z121                         16  99
16.15      xs16_178c1f84c                           17  85
16.2295    xs16_0g8go8brz23                         24  77
16.155     xs16_3pabp46                             18  73
16.2347    xs16_g8861acz0db                         28  66
16.1694    xs16_4a5p6o8zx121                        19  66
16.1847    xs16_39c8a52z033                         17  64
16.628     xs16_kc32qkz0113                         28  63
16.1954    xs16_8kk31e8z065                         21  62
16.731     xs16_3iajkcz23                           28  58
16.836     xs16_4aajkczx56                          16  58
16.833     xs16_0mp2sgz1243                         20  57
16.616     xs16_i5pajoz11                           17  54
16.640     xs16_c9bkkozw32                          17  50
16.801     xs16_08eharz321                          19  43
16.1904    xs16_8u164koz32                          32  42
16.795     xs16_c87p46z311                          53  39
16.230     xs16_178jd2ko                            19  39
16.2132    xs16_0g8it2sgz23                         17  39
16.1106    xs16_0iu0dbz641                          25  37
16.313     xs16_3pm44og4c                           35  36
16.1691    xs16_4a9l6o8zx121                        26  35
16.2201    xs16_0ggml96z641                         18  35
16.1304    xs16_0okih3zc8421                        16  32
16.1391    xs16_ca168ozc8421                        16  32
16.312     xs16_62s53zbd                            29  31
16.929     xs16_3iaj2ak8zw1                         31  30
16.2541    xs16_g8861aczc93                         28  28
16.1994    xs16_0g9fgka4z121                        16  28
16.1846    xs16_25a8c93zw33                         23  27
16.856     xs16_kc32acz1252                         16  24
16.623     xs16_o5r8jdz01                           25  23
16.914     xs16_8kkja952zx1                         18  23
16.227     xs16_5b8r5426                            17  23
16.1702    xs16_4a5p68ozx121                        23  19
16.1791    xs16_03lkaa4z3201                        20  19
16.1464    xs16_08o696z6ip                          16  18
16.706     xs16_39s0qmz023                          24  17
16.1766    xs16_kc321e8z123                         16  17
16.350     xs16_312461tic                           16  15
16.621     xs16_g5r8jdz11                           23  14
16.723     xs16_i5p64koz11                          20  14
16.1962    xs16_4a9eg8ozw65                         20  14
16.2219    xs16_0oe12koz643                         16  14
16.786     xs16_3pa3ia4zw11                         28  13
16.1034    xs16_3lkaa4z065                          24  13
16.278     xs16_32qj43146                           29  12
16.1323    xs16_031e8gzc9311                        29  12
16.1790    xs16_178cia4z0321                        18  12
16.803     xs16_c9bk46z311                          17  12
16.724     xs16_j5o64koz11                          16  11
16.1758    xs16_4a4o796zw121                        17  10
16.682     xs16_69j0j9czx11                         33  9
16.996     xs16_2lm853z056                          16  9
16.2542    xs16_g88c871zc93                         16  9
16.2546    xs16_j9cz122c84c                         16  9
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
16.2322    xs16_raak8zx1252                         16  6
16.2630    xs16_31e8gzxo9a6                         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
16.762     xs16_jhke1e8z1                           16  4
16.1080    xs16_3lo0kcz3421                         16  4
16.2029    xs16_25ao4a4z2521                        16  4
16.2805    xs16_0gs2c871z641                        16  4
16.890     xs16_696ki6zw641                         35  3
16.842     xs16_cila8oz065                          34  3
16.354     xs16_35s26zbd                            29  3
16.889     xs16_696ki6zx65                          29  3
16.828     xs16_4alhe8z0641                         25  3
16.358     xs16_321fgc2ko                           19  3
16.1105    xs16_gie0dbz146                          18  3
16.1107    xs16_02egdbz2521                         18  3
16.1911    xs16_69q3213z32                          18  3
16.1685    xs16_c48n98czx23                         17  3
16.1867    xs16_069q453z311                         17  3
16.1882    xs16_259m453zx23                         17  3
16.1710    xs16_4a9bk46zx32                         16  3
16.2030    xs16_0i5q8a52z121                        16  3
16.2305    xs16_6413ia4z6421                        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
16.745     xs16_39qb8oz32                           19  2
16.380     xs16_4a40vh248c                          17  2
16.875     xs16_4a5pa4z2521                         17  2
16.771     xs16_69qb8oz32                           16  2
16.840     xs16_c8idiczw56                          16  2
16.1675    xs16_xj96z0mdz32                         16  2
16.1720    xs16_4a4o79ozx121                        16  2
16.2204    xs16_0gilla4z641                         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
16.1073    xs16_3lkaa4z641                          20  1
16.1912    xs16_at16426z32                          19  1
16.2050    xs16_6ik8a52z065                         19  1
16.2162    xs16_0at16426z32                         19  1
16.1711    xs16_c8idik8z023                         18  1
16.2025    xs16_069q48cz2521                        18  1
16.2447    xs16_0g8it248cz23                        18  1
16.2480    xs16_3iaczw1139c                         18  1
16.843     xs16_4a9liczx56                          17  1
16.1715    xs16_64p784czw23                         17  1
16.2694    xs16_4ai3gzx11mq                         17  1
16.2861    xs16_ol3zw343146                         17  1
16.3164    xs16_wo443146zbd                         17  1
16.104     xs16_0j5ozj4pz11                         16  1
16.593     xs16_3123c48gka4                         16  1
16.1085    xs16_3h4e12koz011                        16  1
16.1864    xs16_31ke1e8z032                         16  1
16.2317    xs16_cik8a52z641                         16  1
16.217     xs16_3146pajo                            39  0
16.3154    xs16_32qkzy0321e8                        27  0
16.1077    xs16_69m88cz6221                         26  0
16.2928    xs16_wggkq23zc452                        26  0
16.1139    xs16_kq23z124871                         25  0
16.1398    xs16_g88c93zc952                         25  0
16.1084    xs16_31ke12kozw11                        21  0
16.1693    xs16_8k8aliczw23                         21  0
16.2555    xs16_4a9jzxpia4                          20  0
16.3167    xs16_xok21e8zc93                         20  0
16.2200    xs16_06agc93z2521                        19  0
16.2307    xs16_6ik8a52z641                         19  0
16.2316    xs16_0at16413z32                         19  0
16.3014    xs16_wok21e8zdb                          19  0
16.600     xs16_6421344og84c                        18  0
16.697     xs16_db079ozx32                          18  0
16.1130    xs16_oe12koz01ac                         18  0
16.1558    xs16_3loz1226io                          18  0
16.558     xs16_1784c842ak8                         17  0
16.1097    xs16_ck0ol3z643                          17  0
16.1276    xs16_3iakgozw1ac                         17  0
16.1373    xs16_32q4goz4a43                         17  0
16.1871    xs16_5bo8ge2z32                          17  0
16.1905    xs16_8u16853z32                          17  0
16.2045    xs16_25ao8ge2z032                        17  0
16.2356    xs16_25icggozx1ac                        17  0
16.2467    xs16_0kc3213z34a4                        17  0
16.2763    xs16_ol3zw343123                         17  0
16.115     xs16_0ol3z0mdz32                         16  0
16.302     xs16_5b8o642ac                           16  0
16.1068    xs16_3lo0kcz6421                         16  0
16.1581    xs16_8o6413zrm                           16  0
16.1583    xs16_4a9jzxha6zx11                       16  0
16.1796    xs16_0bt06ioz32                          16  0
16.1959    xs16_4ai31e8zx56                         16  0
16.2028    xs16_25ao48cz2521                        16  0
16.2124    xs16_0g8jd2koz23                         16  0
16.2129    xs16_0g8jt246z23                         16  0
16.2190    xs16_032q4goz6413                        16  0
16.2214    xs16_0mq0c93z641                         16  0
16.2323    xs16_ra248goz056                         16  0
16.2549    xs16_g4c3213zdb                          16  0
16.2710    xs16_xkq23zck3z11                        16  0
16.2711    xs16_xkq23zc4jz011                       16  0
16.2781    xs16_wj9c826z6221                        16  0
16.3032    xs16_1784ozx342sg                        16  0
16.3069    xs16_39cggzx1o9a4                        16  0
``````

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``````16.795     xs16_c87p46z311          53
16.642     xs16_6s1raa4zw1          51
16.712     xs16_3pc0qmzw23          48
16.1094    xs16_cila8oz641          40
16.217     xs16_3146pajo            39
16.686     xs16_mkkb2acz1           38
16.778     xs16_69la8oz321          36
16.313     xs16_3pm44og4c           35
16.349     xs16_35s26z39c           35
16.890     xs16_696ki6zw641         35
16.842     xs16_cila8oz065          34
16.1721    xs16_64kb2acz032         34
16.218     xs16_3pajc48c            33
16.682     xs16_69j0j9czx11         33
16.147     xs16_32qjap3             32
16.1904    xs16_8u164koz32          32
16.929     xs16_3iaj2ak8zw1         31
16.185     xs16_32qk5b8o            30
16.220     xs16_3123qajo            29
16.278     xs16_32qj43146           29
16.312     xs16_62s53zbd            29
16.354     xs16_35s26zbd            29
16.889     xs16_696ki6zx65          29
16.1323    xs16_031e8gzc9311        29
16.151     xs16_64kr2pm             28
16.628     xs16_kc32qkz0113         28
16.731     xs16_3iajkcz23           28
16.786     xs16_3pa3ia4zw11         28
16.2347    xs16_g8861acz0db         28
16.2541    xs16_g8861aczc93         28
16.1979    xs16_4ap30ga6zw121       27
16.2174    xs16_08u164koz32         27
16.3154    xs16_32qkzy0321e8        27
16.3227    xs16_31e8gzy012ego       27
16.1077    xs16_69m88cz6221         26
16.1691    xs16_4a9l6o8zx121        26
16.1703    xs16_4a9la8ozx121        26
16.2928    xs16_wggkq23zc452        26
16.623     xs16_o5r8jdz01           25
16.828     xs16_4alhe8z0641         25
16.834     xs16_8u15a4z1226         25
16.930     xs16_3iaj21e8zw1         25
16.1106    xs16_0iu0dbz641          25
16.1139    xs16_kq23z124871         25
16.1398    xs16_g88c93zc952         25
16.1880    xs16_259q453z032         25
16.1901    xs16_08obap3z32          25
16.706     xs16_39s0qmz023          24
16.713     xs16_o8bap3z23           24
16.1034    xs16_3lkaa4z065          24
16.1064    xs16_39m88cz6221         24
16.2295    xs16_0g8go8brz23         24
16.300     xs16_9fg4czbd            23
16.353     xs16_321fgc453           23
16.621     xs16_g5r8jdz11           23
16.827     xs16_ciaj2ak8zw1         23
16.829     xs16_0md1e8z1226         23
16.1702    xs16_4a5p68ozx121        23
16.1740    xs16_69acga6zx32         23
16.1846    xs16_25a8c93zw33         23
16.2313    xs16_08u16853z32         23
16.3066    xs16_4a9jzx12ego         23
16.825     xs16_4alhe8zw65          22
16.159     xs16_2egmd1e8            21
16.774     xs16_69raa4z32           21
16.1084    xs16_31ke12kozw11        21
16.1682    xs16_8k9bkk8zw23         21
16.1693    xs16_8k8aliczw23         21
16.1753    xs16_695q4gozw23         21
16.1954    xs16_8kk31e8z065         21
16.2096    xs16_wck5b8oz311         21
16.2309    xs16_8kk31e8z641         21
16.228     xs16_178bp2sg            20
16.723     xs16_i5p64koz11          20
16.833     xs16_0mp2sgz1243         20
16.872     xs16_2lla8oz065          20
16.1073    xs16_3lkaa4z641          20
16.1127    xs16_giligoz104a4        20
16.1739    xs16_g88r2qkz121         20
16.1791    xs16_03lkaa4z3201        20
16.1962    xs16_4a9eg8ozw65         20
16.2058    xs16_69akg4czx146        20
16.2555    xs16_4a9jzxpia4          20
16.3167    xs16_xok21e8zc93         20
16.18      xs16_caarzbd             19
16.131     xs16_660uhar             19
16.230     xs16_178jd2ko            19
16.358     xs16_321fgc2ko           19
16.745     xs16_39qb8oz32           19
16.801     xs16_08eharz321          19
16.1684    xs16_4aab9k8zx32         19
16.1694    xs16_4a5p6o8zx121        19
16.1881    xs16_259q453zw32         19
16.1912    xs16_at16426z32          19
16.2050    xs16_6ik8a52z065         19
16.2162    xs16_0at16426z32         19
16.2200    xs16_06agc93z2521        19
16.2307    xs16_6ik8a52z641         19
16.2316    xs16_0at16413z32         19
16.3014    xs16_wok21e8zdb          19
16.19      xs16_caarz39c            18
16.155     xs16_3pabp46             18
16.600     xs16_6421344og84c        18
16.665     xs16_699mkiczx1          18
16.697     xs16_db079ozx32          18
16.848     xs16_ca9b8oz0252         18
16.914     xs16_8kkja952zx1         18
16.926     xs16_3iajc4gozw1         18
16.1105    xs16_gie0dbz146          18
16.1107    xs16_02egdbz2521         18
16.1130    xs16_oe12koz01ac         18
16.1558    xs16_3loz1226io          18
16.1711    xs16_c8idik8z023         18
16.1757    xs16_g8idik8z123         18
16.1790    xs16_178cia4z0321        18
16.1911    xs16_69q3213z32          18
16.1990    xs16_8e1tazx1252         18
16.1995    xs16_cik8a52z065         18
16.2018    xs16_25a8c826zw33        18
16.2025    xs16_069q48cz2521        18
16.2201    xs16_0ggml96z641         18
16.2447    xs16_0g8it248cz23        18
16.2480    xs16_3iaczw1139c         18
16.15      xs16_178c1f84c           17
16.227     xs16_5b8r5426            17
16.265     xs16_259m861ac           17
16.380     xs16_4a40vh248c          17
16.558     xs16_1784c842ak8         17
16.616     xs16_i5pajoz11           17
16.640     xs16_c9bkkozw32          17
16.668     xs16_gbq1daz121          17
16.716     xs16_3pmk46zx23          17
16.748     xs16_39ege2z321          17
16.799     xs16_c8al56z311          17
16.803     xs16_c9bk46z311          17
16.843     xs16_4a9liczx56          17
16.875     xs16_4a5pa4z2521         17
16.1097    xs16_ck0ol3z643          17
16.1276    xs16_3iakgozw1ac         17
16.1373    xs16_32q4goz4a43         17
16.1685    xs16_c48n98czx23         17
16.1715    xs16_64p784czw23         17
16.1722    xs16_4aq32acz032         17
16.1758    xs16_4a4o796zw121        17
16.1847    xs16_39c8a52z033         17
16.1867    xs16_069q453z311         17
16.1871    xs16_5bo8ge2z32          17
16.1882    xs16_259m453zx23         17
16.1905    xs16_8u16853z32          17
16.1991    xs16_8e1qbzx1252         17
16.2014    xs16_25a8kk8z0253        17
16.2045    xs16_25ao8ge2z032        17
16.2132    xs16_0g8it2sgz23         17
16.2356    xs16_25icggozx1ac        17
16.2467    xs16_0kc3213z34a4        17
16.2694    xs16_4ai3gzx11mq         17
16.2763    xs16_ol3zw343123         17
16.2861    xs16_ol3zw343146         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
16.302     xs16_5b8o642ac           16
16.350     xs16_312461tic           16
16.360     xs16_2egu16413           16
16.593     xs16_3123c48gka4         16
16.657     xs16_695q4ozw321         16
16.724     xs16_j5o64koz11          16
16.762     xs16_jhke1e8z1           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
16.840     xs16_c8idiczw56          16
16.856     xs16_kc32acz1252         16
16.953     xs16_0cil56z6221         16
16.995     xs16_0raik8z643          16
16.996     xs16_2lm853z056          16
16.1068    xs16_3lo0kcz6421         16
16.1080    xs16_3lo0kcz3421         16
16.1085    xs16_3h4e12koz011        16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1464    xs16_08o696z6ip          16
16.1581    xs16_8o6413zrm           16
16.1583    xs16_4a9jzxha6zx11       16
16.1675    xs16_xj96z0mdz32         16
16.1710    xs16_4a9bk46zx32         16
16.1717    xs16_4aajk46zx121        16
16.1720    xs16_4a4o79ozx121        16
16.1766    xs16_kc321e8z123         16
16.1787    xs16_069m4koz311         16
16.1796    xs16_0bt06ioz32          16
16.1856    xs16_39u06a4z32          16
16.1857    xs16_39u0652z32          16
16.1864    xs16_31ke1e8z032         16
16.1929    xs16_0g5r8b5z121         16
16.1959    xs16_4ai31e8zx56         16
16.1992    xs16_25is0cczw65         16
16.1994    xs16_0g9fgka4z121        16
16.2028    xs16_25ao48cz2521        16
16.2029    xs16_25ao4a4z2521        16
16.2030    xs16_0i5q8a52z121        16
16.2060    xs16_69akg4czx56         16
16.2124    xs16_0g8jd2koz23         16
16.2129    xs16_0g8jt246z23         16
16.2190    xs16_032q4goz6413        16
16.2204    xs16_0gilla4z641         16
16.2214    xs16_0mq0c93z641         16
16.2219    xs16_0oe12koz643         16
16.2302    xs16_4ap6413z65          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
16.2542    xs16_g88c871zc93         16
16.2546    xs16_j9cz122c84c         16
16.2547    xs16_j9cz122c826         16
16.2549    xs16_g4c3213zdb          16
16.2630    xs16_31e8gzxo9a6         16
16.2710    xs16_xkq23zck3z11        16
16.2711    xs16_xkq23zc4jz011       16
16.2781    xs16_wj9c826z6221        16
16.2805    xs16_0gs2c871z641        16
16.3032    xs16_1784ozx342sg        16
16.3069    xs16_39cggzx1o9a4        16
``````

Goldtiger997
Posts: 549
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

16.795 in 10 gliders:

Code: Select all

``````x = 34, y = 37, rule = B3/S23
24bo\$23bo\$23b3o\$4bo\$5b2o\$4b2o26bo\$31bo\$31b3o3\$21bo\$20bo\$20b3o\$obo\$b2o\$
bo4\$4bo\$2bobo\$3b2o3\$2b3o\$4bo\$3bo4\$10bo\$8bobo\$9b2o2\$10bo6bo\$10b2o4b2o\$
9bobo4bobo!
``````
16.3154 in 10 gliders:

Code: Select all

``````x = 102, y = 24, rule = B3/S23
69bo\$67b2o\$61bo6b2o\$62bo\$60b3o\$56bo\$57b2o\$56b2o7bo\$65bobo\$65b2o\$93b2o\$
63b3o28bo\$65bo28bob2o\$64bo30bobo\$3bo34b2o28b2o28b2o\$4b2obo31bo29bo29bo
\$3b2o2bobo28bo29bo29bo\$7b2o30b3o9bo17b3o27b3o\$41bo9b2o18bo29bo\$50bobo\$
bo\$b2o12b2o\$obo11b2o\$16bo!
``````
EDIT:

16.2928 in 12 gliders:

Code: Select all

``````x = 29, y = 26, rule = B3/S23
14bo\$14bobo\$8bo5b2o\$9b2o\$8b2o\$5bo\$3bobo20bobo\$4b2o20b2o\$12bo14bo\$12bob
o\$8b3ob2o\$10bo\$9bo\$19bo\$18bo\$15b2ob3o\$14bobo\$bo14bo\$b2o20b2o\$obo20bobo
\$23bo\$19b2o\$18b2o\$13b2o5bo\$12bobo\$14bo!
``````

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

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

16.1992 in 14G:

Code: Select all

``````x = 199, y = 25, rule = B3/S23
108bo\$108bobo\$108b2o\$103bo\$104b2o\$103b2o\$2bo97b2o31bo29bo29bo\$obo20b2o
28b2o23b2o19bobo6b2o22bobo16bo10bobo27bobo\$b2o20bobob2o24bobob2o19bobo
b2o17bo6bobob2o19bobob2o13bo10bobob2o24bobob2o\$25bob2o26bob2o21bob2o
26bob2o21bob2o11b3o12bob2o26bob2o\$25bo29bo24bo29bo24bo29bo28b2o\$bo4b2o
15bobo27bobo22bobo27bobo22bobo27bobo29bo\$2b2o2bobo13bobo27bobo22bobo
27bobo22bobo27bobo29bo\$b2o3bo16bo29bo23b2o28b2o23b2o28b2o30b2o\$173b2o\$
46b2o126b2o\$47b2o2bo121bo3b2o\$46bo3b2o125bobo\$5b3o42bobo124bo\$7bo\$6bo\$
176bo\$153b2o20b2o\$152bobo20bobo\$154bo!
``````
Bob Shemyakin

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

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

BobShemyakin wrote:16.1992 in 14G
Reduced to 12G:

Code: Select all

``````x = 143, y = 25, rule = B3/S23
52bo41bo\$52bobo40bo\$52b2o39b3o\$47bo\$48b2o\$47b2o\$o43b2o31bo29bo29bo\$b2o
19b2o19bobo6b2o22bobo27bobo27bobo\$2o20bobob2o17bo6bobob2o19bobob2o24bo
bob2o24bobob2o\$24bob2o26bob2o21bob2o26bob2o26bob2o\$24bo29bo24bo29bo28b
2o\$bo3b2o15bobo27bobo22bobo27bobo29bo\$2bob2o15bobo27bobo22bobo27bobo
29bo\$3o3bo15bo29bo24bo29bo30b2o\$117b2o\$118b2o\$117bo3b2o\$5bo115bobo\$5b
2o114bo\$4bobo2\$120bo\$93b3o23b2o\$95bo23bobo\$94bo!``````
-Matthias Merzenich

Goldtiger997
Posts: 549
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

16.641 in 11 gliders (actually 16.642 thanks AbhpzTa):

Code: Select all

``````x = 135, y = 84, rule = B3/S23
132bo\$132bobo\$132b2o22\$77bo\$78b2o\$77b2o9bo\$86b2o\$87b2o\$84bo\$82bobo\$83b
2o4\$114b2o\$112b3o\$111bo4bo\$112b2ob2o\$113bobo\$13bo24bo13b2o24bo13b2o19b
obo\$10bo2bobo22bo13b2o24bo13b2o20bo\$8bobo2b2o23bo39bo\$9b2o5\$bo103bo\$b
2o101bo\$obo93bo7b3o\$95bo\$95b3o3\$94b3o\$94bo\$95bo24\$30bo\$30b2o\$29bobo!
``````
Last edited by Goldtiger997 on March 26th, 2017, 6:37 pm, edited 1 time in total.

AbhpzTa
Posts: 476
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

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

Goldtiger997 wrote:16.641 in 11 gliders:

Code: Select all

``````x = 135, y = 84, rule = B3/S23
132bo\$132bobo\$132b2o22\$77bo\$78b2o\$77b2o9bo\$86b2o\$87b2o\$84bo\$82bobo\$83b
2o4\$114b2o\$112b3o\$111bo4bo\$112b2ob2o\$113bobo\$13bo24bo13b2o24bo13b2o19b
obo\$10bo2bobo22bo13b2o24bo13b2o20bo\$8bobo2b2o23bo39bo\$9b2o5\$bo103bo\$b
2o101bo\$obo93bo7b3o\$95bo\$95b3o3\$94b3o\$94bo\$95bo24\$30bo\$30b2o\$29bobo!
``````
That is 16.642 . (typo?)

16.686 in 6 gliders:

Code: Select all

``````x = 17, y = 14, rule = B3/S23
5b2o2bo\$6b2obobo\$5bo3b2o3\$14bo\$14bobo\$7bo6b2o\$6bo\$b2o3b3o\$obo\$2bo8b3o\$
13bo\$12bo!``````
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

Goldtiger997 wrote:16.3154 in 10 gliders
The same hook with tail add gives 16.2710 and 16.2711 in 15G:

Code: Select all

``````x = 192, y = 78, rule = B3/S23
128bo\$129bo\$93bo33b3o\$92bo\$92b3o15bo19bo\$110bo19bo\$110bo19bo\$95bobo\$
50bo44b2o14bo19bo19bo19bo19bo\$8bo39bobo18b2o18b2o5bo12b3o17b3o17b3o17b
3o17b3o\$9bo39b2ob3o13bo2bo16bo2bo16bo19bo19bo13bo5bo19bo\$7b3o42bo16bob
o17bobo5b3o9bo19bo19bo10bobo6bo19bo\$53bo16bo19bo6bo10b2o18b2o18b2o11b
2o5b2o18b2o\$11bo12b2obo16b2obo16b2obo16b2obo10bo5b2obo16b2obo16b2obo
16b2obo19bo\$5b2o2b2o13bob2o16bob2o16bob2o16bob2o16bob2o16bob2o16bob2o
16bob2o19bo\$5bobo2b2o173b2o\$5bo154b2o23bo\$b2o158b2o23bo\$obo157bo24b2o\$
2bo163b3o\$166bo\$167bo\$162b3o\$164bo\$163bo\$165b3o\$165bo\$166bo31\$171bo19b
o\$169b3o17b3o\$162bo5bo19bo\$160bobo6bo19bo\$161b2o5b2o18b2o\$164b2obo19bo
\$164bob2o19bo\$185b2o\$160b2o23bo\$161b2o24bo\$160bo25b2o\$167b3o\$167bo\$
168bo\$163b3o\$165bo\$164bo\$166b3o\$166bo\$167bo!``````
-Matthias Merzenich

chris_c
Posts: 911
Joined: June 28th, 2014, 7:15 am

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

I added recent syntheses and added some converters from v2 of Extrementhusiast's component database. There are 55 improvements since last time; 8 of them take the cost of an SL below 16G:

Code: Select all

``````+16.1094    xs16_cila8oz641          38
+16.778     xs16_69la8oz321          34
+16.842     xs16_cila8oz065          32
+16.3014    xs16_wok21e8zdb          18
+16.2694    xs16_4ai3gzx11mq         16
+16.3167    xs16_xok21e8zc93         16
+16.2710    xs16_xkq23zck3z11        15
+16.2711    xs16_xkq23zc4jz011       15
+16.3069    xs16_39cggzx1o9a4        15
+16.1782    xs16_039u066z311         13
+16.2039    xs16_6413kk8zw643        13
+16.2153    xs16_o86164koz23         13
+16.3007    xs16_xok21e8z653         13
+16.1836    xs16_39u06a4z032         12
+16.1849    xs16_39u0652z032         12
+16.1992    xs16_25is0cczw65         12
+16.2343    xs16_4a9jzxd552          12
+16.2568    xs16_0g8o652z1qm         12
+16.2928    xs16_wggkq23zc452        12
+15.1253    xs15_xok21e8z253         11
+16.390     xs16_03ia4z2ehp          11
+16.642     xs16_6s1raa4zw1          11
+16.1521    xs16_0gs253z1qm          11
+16.1644    xs16_3lozwgjl8zw1        11
+16.1889    xs16_0jhe853z121         11
+16.2377    xs16_ck5jzw116a4         11
+16.2463    xs16_08o6512koz32        11
+14.395     xs14_ggc4871z56          10
+15.901     xs15_04aq453z311         10
+16.1425    xs16_4aarzxol3           10
+16.1466    xs16_0gs256z1qm          10
+16.2071    xs16_69diczx1252         10
+16.2687    xs16_0g8o652zpi6         10
+16.2964    xs16_3pmzx321e8          10
+16.3026    xs16_ci52zw123ck8        10
+16.3050    xs16_32qkzy032qk         10
+16.3154    xs16_32qkzy0321e8        10
+16.3224    xs16_25a8ozy15b8o        10
+15.443     xs15_39u066z032          9
+16.795     xs16_c87p46z311          9
+16.954     xs16_0cila4z6226         9
+16.1040    xs16_0c9jz651252         9
+16.1047    xs16_25akl3zx65          9
+16.1159    xs16_0j9cz1259a4         9
+16.1160    xs16_259ak8zwbd          9
+14.171     xs14_31e8gzwbd           8
+15.983     xs15_wck31e8z311         8
+15.1112    xs15_08o6413z254c        8
+16.196     xs16_4al960ui            8
+16.1145    xs16_4aarzwc453          8
+16.1292    xs16_o8bdzw178c          8
+16.2950    xs16_4aarzy0178c         8
+15.445     xs15_0cid96z321          7
+16.686     xs16_mkkb2acz1           6
``````
I also improved a couple of converters myself. A 6G at-corner boat adder and a one-sided 5G boat to carrier are both illustrated in this 16G synthesis of 16.3167:

Code: Select all

``````x = 137, y = 242, rule = B3/S23
38bobo\$38b2o\$39bo2\$134bo\$133bobo\$25bo106bo2bo\$23bobo105bo3b2o\$24b2o9bo
bo93b2o\$35b2o\$36bo2\$27b2o6b2o\$28b2o5bobo\$27bo7bo76\$12bo\$13b2o\$12b2o12\$
34bo99bo\$33bobo97bobo\$32bo2bo96bo2bo\$31bo3b2o94bo3b2o\$31b2o98b2o\$129b
2o\$128bobo\$12b3o114bo\$14bo\$13bo2\$3o\$2bo6b2o\$bo8b2o\$9bo10\$45b3o\$45bo\$8b
2o36bo\$7bobo\$9bo72\$34bo99bo\$33bobo97bobo\$32bo2bo96bo2bo\$31bo3b2o94bo3b
2o\$31b2o98b2o\$29b2o98b2o\$28bobo99bo\$29bo98bo\$128b2o10\$11b3o\$13bo\$12bo
2\$16b2o\$17b2o5b2o\$16bo6bobo\$25bo18bo\$43b2o\$43bobo8\$45bo\$44b2o\$44bobo!
``````
Now 16.712 is 9G more expensive than anything else and has only one soup on Catagolue... hmmmm...

Code: Select all

``````x = 40, y = 29, rule = B3/S23
17b3o5\$22b2o\$22b2o\$13bo18b3o\$13bo\$13bo16bo5bo\$o29bo5bo\$o29bo5bo\$o\$32b
3o6\$24b2o\$22bo2bo\$22bo2bo2\$23b2o13b2o\$23b2o13b2o\$23bo5b2o\$24bo4b2o\$31b
2o\$31b2o!
``````
Latest list:

Code: Select all

``````16.712     xs16_3pc0qmzw23          48
16.217     xs16_3146pajo            39
16.1094    xs16_cila8oz641          38
16.313     xs16_3pm44og4c           35
16.349     xs16_35s26z39c           35
16.890     xs16_696ki6zw641         35
16.778     xs16_69la8oz321          34
16.1721    xs16_64kb2acz032         34
16.218     xs16_3pajc48c            33
16.682     xs16_69j0j9czx11         33
16.147     xs16_32qjap3             32
16.842     xs16_cila8oz065          32
16.1904    xs16_8u164koz32          32
16.929     xs16_3iaj2ak8zw1         31
16.185     xs16_32qk5b8o            30
16.220     xs16_3123qajo            29
16.278     xs16_32qj43146           29
16.312     xs16_62s53zbd            29
16.354     xs16_35s26zbd            29
16.889     xs16_696ki6zx65          29
16.1323    xs16_031e8gzc9311        29
16.151     xs16_64kr2pm             28
16.628     xs16_kc32qkz0113         28
16.731     xs16_3iajkcz23           28
16.786     xs16_3pa3ia4zw11         28
16.2347    xs16_g8861acz0db         28
16.2541    xs16_g8861aczc93         28
16.1979    xs16_4ap30ga6zw121       27
16.2174    xs16_08u164koz32         27
16.3227    xs16_31e8gzy012ego       27
16.1077    xs16_69m88cz6221         26
16.1691    xs16_4a9l6o8zx121        26
16.1703    xs16_4a9la8ozx121        26
16.623     xs16_o5r8jdz01           25
16.828     xs16_4alhe8z0641         25
16.834     xs16_8u15a4z1226         25
16.930     xs16_3iaj21e8zw1         25
16.1106    xs16_0iu0dbz641          25
16.1139    xs16_kq23z124871         25
16.1398    xs16_g88c93zc952         25
16.1880    xs16_259q453z032         25
16.1901    xs16_08obap3z32          25
16.706     xs16_39s0qmz023          24
16.713     xs16_o8bap3z23           24
16.1034    xs16_3lkaa4z065          24
16.1064    xs16_39m88cz6221         24
16.2295    xs16_0g8go8brz23         24
16.300     xs16_9fg4czbd            23
16.353     xs16_321fgc453           23
16.621     xs16_g5r8jdz11           23
16.827     xs16_ciaj2ak8zw1         23
16.829     xs16_0md1e8z1226         23
16.1702    xs16_4a5p68ozx121        23
16.1740    xs16_69acga6zx32         23
16.1846    xs16_25a8c93zw33         23
16.2313    xs16_08u16853z32         23
16.3066    xs16_4a9jzx12ego         23
16.825     xs16_4alhe8zw65          22
16.159     xs16_2egmd1e8            21
16.774     xs16_69raa4z32           21
16.1084    xs16_31ke12kozw11        21
16.1682    xs16_8k9bkk8zw23         21
16.1693    xs16_8k8aliczw23         21
16.1753    xs16_695q4gozw23         21
16.1954    xs16_8kk31e8z065         21
16.2096    xs16_wck5b8oz311         21
16.2309    xs16_8kk31e8z641         21
16.228     xs16_178bp2sg            20
16.723     xs16_i5p64koz11          20
16.833     xs16_0mp2sgz1243         20
16.872     xs16_2lla8oz065          20
16.1073    xs16_3lkaa4z641          20
16.1127    xs16_giligoz104a4        20
16.1739    xs16_g88r2qkz121         20
16.1791    xs16_03lkaa4z3201        20
16.1962    xs16_4a9eg8ozw65         20
16.2058    xs16_69akg4czx146        20
16.2555    xs16_4a9jzxpia4          20
16.18      xs16_caarzbd             19
16.131     xs16_660uhar             19
16.230     xs16_178jd2ko            19
16.358     xs16_321fgc2ko           19
16.745     xs16_39qb8oz32           19
16.801     xs16_08eharz321          19
16.1684    xs16_4aab9k8zx32         19
16.1694    xs16_4a5p6o8zx121        19
16.1881    xs16_259q453zw32         19
16.1912    xs16_at16426z32          19
16.2050    xs16_6ik8a52z065         19
16.2162    xs16_0at16426z32         19
16.2200    xs16_06agc93z2521        19
16.2307    xs16_6ik8a52z641         19
16.2316    xs16_0at16413z32         19
16.19      xs16_caarz39c            18
16.155     xs16_3pabp46             18
16.600     xs16_6421344og84c        18
16.665     xs16_699mkiczx1          18
16.697     xs16_db079ozx32          18
16.848     xs16_ca9b8oz0252         18
16.914     xs16_8kkja952zx1         18
16.926     xs16_3iajc4gozw1         18
16.1105    xs16_gie0dbz146          18
16.1107    xs16_02egdbz2521         18
16.1130    xs16_oe12koz01ac         18
16.1558    xs16_3loz1226io          18
16.1711    xs16_c8idik8z023         18
16.1757    xs16_g8idik8z123         18
16.1790    xs16_178cia4z0321        18
16.1911    xs16_69q3213z32          18
16.1990    xs16_8e1tazx1252         18
16.1995    xs16_cik8a52z065         18
16.2018    xs16_25a8c826zw33        18
16.2025    xs16_069q48cz2521        18
16.2201    xs16_0ggml96z641         18
16.2447    xs16_0g8it248cz23        18
16.2480    xs16_3iaczw1139c         18
16.3014    xs16_wok21e8zdb          18
16.15      xs16_178c1f84c           17
16.227     xs16_5b8r5426            17
16.265     xs16_259m861ac           17
16.380     xs16_4a40vh248c          17
16.558     xs16_1784c842ak8         17
16.616     xs16_i5pajoz11           17
16.640     xs16_c9bkkozw32          17
16.668     xs16_gbq1daz121          17
16.716     xs16_3pmk46zx23          17
16.748     xs16_39ege2z321          17
16.799     xs16_c8al56z311          17
16.803     xs16_c9bk46z311          17
16.843     xs16_4a9liczx56          17
16.875     xs16_4a5pa4z2521         17
16.1097    xs16_ck0ol3z643          17
16.1276    xs16_3iakgozw1ac         17
16.1373    xs16_32q4goz4a43         17
16.1685    xs16_c48n98czx23         17
16.1715    xs16_64p784czw23         17
16.1722    xs16_4aq32acz032         17
16.1758    xs16_4a4o796zw121        17
16.1847    xs16_39c8a52z033         17
16.1867    xs16_069q453z311         17
16.1871    xs16_5bo8ge2z32          17
16.1882    xs16_259m453zx23         17
16.1905    xs16_8u16853z32          17
16.1991    xs16_8e1qbzx1252         17
16.2014    xs16_25a8kk8z0253        17
16.2045    xs16_25ao8ge2z032        17
16.2132    xs16_0g8it2sgz23         17
16.2356    xs16_25icggozx1ac        17
16.2467    xs16_0kc3213z34a4        17
16.2763    xs16_ol3zw343123         17
16.2861    xs16_ol3zw343146         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
16.302     xs16_5b8o642ac           16
16.350     xs16_312461tic           16
16.360     xs16_2egu16413           16
16.593     xs16_3123c48gka4         16
16.657     xs16_695q4ozw321         16
16.724     xs16_j5o64koz11          16
16.762     xs16_jhke1e8z1           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
16.840     xs16_c8idiczw56          16
16.856     xs16_kc32acz1252         16
16.953     xs16_0cil56z6221         16
16.995     xs16_0raik8z643          16
16.996     xs16_2lm853z056          16
16.1068    xs16_3lo0kcz6421         16
16.1080    xs16_3lo0kcz3421         16
16.1085    xs16_3h4e12koz011        16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1464    xs16_08o696z6ip          16
16.1581    xs16_8o6413zrm           16
16.1583    xs16_4a9jzxha6zx11       16
16.1675    xs16_xj96z0mdz32         16
16.1710    xs16_4a9bk46zx32         16
16.1717    xs16_4aajk46zx121        16
16.1720    xs16_4a4o79ozx121        16
16.1766    xs16_kc321e8z123         16
16.1787    xs16_069m4koz311         16
16.1796    xs16_0bt06ioz32          16
16.1856    xs16_39u06a4z32          16
16.1857    xs16_39u0652z32          16
16.1864    xs16_31ke1e8z032         16
16.1929    xs16_0g5r8b5z121         16
16.1959    xs16_4ai31e8zx56         16
16.1994    xs16_0g9fgka4z121        16
16.2028    xs16_25ao48cz2521        16
16.2029    xs16_25ao4a4z2521        16
16.2030    xs16_0i5q8a52z121        16
16.2060    xs16_69akg4czx56         16
16.2124    xs16_0g8jd2koz23         16
16.2129    xs16_0g8jt246z23         16
16.2190    xs16_032q4goz6413        16
16.2204    xs16_0gilla4z641         16
16.2214    xs16_0mq0c93z641         16
16.2219    xs16_0oe12koz643         16
16.2302    xs16_4ap6413z65          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
16.2542    xs16_g88c871zc93         16
16.2546    xs16_j9cz122c84c         16
16.2547    xs16_j9cz122c826         16
16.2549    xs16_g4c3213zdb          16
16.2630    xs16_31e8gzxo9a6         16
16.2694    xs16_4ai3gzx11mq         16
16.2781    xs16_wj9c826z6221        16
16.2805    xs16_0gs2c871z641        16
16.3032    xs16_1784ozx342sg        16
16.3167    xs16_xok21e8zc93         16``````

Goldtiger997
Posts: 549
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

16.313 in 10 gliders:

Code: Select all

``````x = 137, y = 118, rule = B3/S23
o\$b2o\$2o28\$79bobo\$80b2o\$70bo9bo\$71bo\$69b3o12bobo\$84b2o\$85bo3\$67bobo\$
68b2o\$68bo\$64b3o\$66bo12bo\$65bo11b2o\$78b2o5\$74bo\$75bo\$73b3o2b2o\$77bobo\$
79bo61\$135bo\$134b2o\$134bobo!
``````

Posts: 1909
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

chris_c wrote:Now 16.712 is 9G more expensive than anything else and has only one soup on Catagolue... hmmmm...
Looking at the official 48G synthesis, I see that the only requirement for the complex base is this component here:

Code: Select all

``````x = 11, y = 17, rule = B3/S23
7b2o\$7bo\$8bo\$5b4o\$5bo\$7b2o\$3bo2b2o2bo\$bobo5b2o\$2b2o2b3o\$5bo2bo\$4bobo\$b
2o2bo\$obo\$2bo\$5b2o\$4b2o\$6bo!
``````
Provided another way to create the snake (which may or may not be possible), the rest can be done in as few as 14 gliders:

Code: Select all

``````x = 81, y = 27, rule = B3/S23
60bo\$61bo\$59b3o\$65bo\$65bobo\$54bo10b2o\$b2o10bo41b2o\$obobo7bo41b2o\$2bobo
bo5b3o64bo\$4b2o72bo\$10bo17b2o38b2o8b3o\$8b2o19bo39bo\$9b2o13b2obo36b2obo
\$17bo7bob2o36bob2o\$16b2o7bo2bo36bo2bo\$16bobo7b2o38b2o2\$50b2o\$49bobo\$
51bo\$73b2o\$73bobo\$73bo\$43b2o22b3o\$42bobo13bo10bo\$44bo13b2o8bo\$57bobo!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Extrementhusiast
Posts: 1799
Joined: June 16th, 2009, 11:24 pm
Location: USA

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

Well, this pushes 16.712 down to 30 gliders:

Code: Select all

``````x = 224, y = 40, rule = B3/S23
159bo\$160bo\$158b3o3\$41bo135bo\$39bobo135bobo\$40b2o129bo5b2o\$144bo27bo\$
142b2o26b3o\$137bobo3b2o\$72bobo42bobo18b2o\$23bo48b2o44b2o3bo14bo5bo\$23b
2o4bo43bo44bo2b2o20b2o\$22bobo5bo91b2o19bobo\$28b3o64bo87b2o37b2o\$57b2ob
2o25b2ob2ob2o14b2ob2o2bo16b2ob2o2b2o34b2ob2o3bo33b2o3bo\$39b2o6bo10bobo
13b2o12bobo3b2o14bobo2bobo16bobo2bobo4b2o29bobo2bo35bo2bo\$bo25b3o8bo2b
o4b2o10bo2bo12bobo11bo2bo18bo2bob2o17bo2bob2o4b2o22bo7bo2bob2o12bo22bo
b2o\$2bo26bo9bobo4bobo10bobo12bo14bobo19bobo21bobo9bo22bo7bobo15bobo19b
2o2bo\$3o25bo11bob2o16bob2o26bob2obo16bob2obo18bob2obo26b3o8bob2obo11b
2o22bo\$4b2o35bo2bo16bo2bo7bo18bo2b2o17bo2b2o19bo2b2o38bo2b2o35b2o\$3b2o
5bo31bobo17bobo6b2o19bo21bo23bo42bo12b2o\$5bo2b2o33bo19bo7bobo19b3o19b
3o21b3o40b3o8b2o\$9b2o84bo21bo23bo42bo10bo4\$204b3o\$170b2o32bo\$171b2o32b
o\$66b2o102bo\$62b2o2bobo\$61bobo2bo117b2o\$63bo119b2o\$185bo2\$67b2o\$68b2o\$
67bo!
``````
A nice related component:

Code: Select all

``````x = 18, y = 18, rule = B3/S23
7b2o\$2ob2o3bo\$bobo2bo\$bo2bob2o\$2bobo11bo\$3bob2obo6bo\$4bo2b2o6b3o\$5bo6b
2o\$6b3o2b2o\$8bo4bo6\$14b3o\$14bo\$15bo!
``````
I Like My Heisenburps! (and others)

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

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

Goldtiger997 wrote:16.313 in 10 gliders:

Code: Select all

``````x = 137, y = 118, rule = B3/S23
o\$b2o\$2o28\$79bobo\$80b2o\$70bo9bo\$71bo\$69b3o12bobo\$84b2o\$85bo3\$67bobo\$
68b2o\$68bo\$64b3o\$66bo12bo\$65bo11b2o\$78b2o5\$74bo\$75bo\$73b3o2b2o\$77bobo\$
79bo61\$135bo\$134b2o\$134bobo!
``````
You can continue to 16.312 in 15G:

Code: Select all

``````x = 38, y = 14, rule = B3/S23
9bo\$7bobo\$8b2o\$13bo4bo\$11b2o5bobo\$12b2o4b2o\$2b2o2b2o8bo11b2o2b2obo\$2bo
3bo2bo5b2o11bo3bob2o\$3b3o2b2o5bobo11b3o\$bobo23bobo\$b2o8b3o13b2o\$11bo\$
12bo!
``````
Bob Shemyakin

Goldtiger997
Posts: 549
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

16.657 in 8 gliders:

Code: Select all

``````x = 54, y = 77, rule = B3/S23
52bo\$51bo\$51b3o22\$30bo\$28b2o\$29b2o3\$43bo\$42bo\$42b3o\$38bobo\$39b2o\$39bo
6bo\$24bo20b2o\$24b2o19bobo\$23bobo15bo\$41b2o\$40bobo35\$b2o\$obo\$2bo!
``````
EDIT:

16.3167 in 13 gliders:

Code: Select all

``````x = 135, y = 27, rule = B3/S23
96bobo\$96b2o\$97bo2\$101bo\$100bo\$100b3o3\$8bo43bo39bo40b2o\$6bobo42bobo37b
obo37bo2bo\$7b2o42b2o38b2o38b2o\$10b3o8bo27b2o38b2o12bo25b2o\$12bo8bobo
24bobo37bobo10b2o25bobo\$11bo9b2o24bo39bo14b2o23bo\$46bo39bo39bo\$47b3o
37b3o14b2o21b3o\$bo11b3o33bo39bo14bobo7b2o13bo\$b2o10bo90bo9bobo\$obo6b2o
3bo4b3o92bo\$8b2o9bo\$10bo9bo3\$22b2o\$22bobo\$22bo!
``````
The above improved 8-glider synthesis of the 15-bit still-life also improves these other 16-bit still-lifes:

Code: Select all

``````x = 38, y = 10, rule = B3/S23
6b2o17b2o\$7bo18bo9b2o\$5bo9bob2o6bo9bobo\$5b2o8b2obo6b2o8b2o\$3b2o8b2o8b
2o8b2o\$2bobo7bobo7bobo7bobo\$bo9bo9bo9bo\$o9bo9bo9bo\$b3o7b3o7b3o7b3o\$3bo
9bo9bo9bo!
``````

chris_c
Posts: 911
Joined: June 28th, 2014, 7:15 am

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

I pushed an update yesterday. Unfortunately it looks like I missed out Goldtiger's 16.313. Oh well, that can wait until next time.

A couple of things that I added were a very ugly 20G synthesis of 16.712 and a 5G snake-to-ac converter. I think it took 6G before:

Code: Select all

``````x = 158, y = 405, rule = B3/S23
138bo\$138bo\$46bo91bo\$44b2o\$45b2o2\$41bo100b2o\$40b2o100b2o\$40bobo5\$45b2o
\$45bobo\$45bo73\$17bo\$18b2o\$17b2o\$4bo\$5b2o\$4b2o2\$69bo\$67b2o\$68b2o3\$38bo
99bo\$38bo99bo\$38bo99bo4\$42b2o98b2o\$42b2o98b2o9bo\$153bo\$132b3o18bo2\$
149b3o3b3o\$119b3o\$153bo\$153bo\$153bo7\$17bo\$17b2o\$16bobo\$4bo\$4b2o\$3bobo\$
70b3o\$70bo\$71bo64\$87bo\$86bo\$86b3o49b2o\$138bo3b2o\$140bo2bo\$139b2obo\$
139bo2b2o\$37b3o101bo\$140b2o4\$42b2o98b2o\$42b2o73b2o23b2o\$33bo18b3o62b2o
\$33bo90b2o\$33bo16bo5bo67b2o\$20bo29bo5bo\$20bo29bo5bo\$20bo\$52b3o69b2o\$
124b2o8\$133b2o\$132bo2bo\$132bo2bo\$115b2o16b2o\$115b2o5\$127b2o\$126bo2bo\$
127b2o13\$71b3o\$71bo6b3o\$72bo5bo\$79bo\$15b2o\$14bobo\$16bo2\$90b3o\$82b2o6bo
\$82bobo6bo\$82bo43\$143b2o\$142b2o\$144bo11\$138b2o\$137b2o\$139bo30\$38b2o98b
2o\$38bo3b2o94bo3b2o\$40bo2bo96bo2bo\$39b2obo96b2obo\$39bo2b2o95bo2b2o\$41b
o99bo\$40b2o98b2o4\$42b2o\$17b2o23b2o\$17b2o\$24b2o\$24b2o4\$24b2o\$24b2o8\$33b
2o\$32bo2bo\$32bo2bo\$15b2o16b2o\$15b2o5\$27b2o\$26bo2bo\$27b2o4\$11b2o\$10bobo
\$12bo6\$6b2o\$5bobo\$7bo4\$3o\$2bo\$bo!
``````

Code: Select all

``````x = 13, y = 21, rule = B3/S23
10bo\$bo8bobo\$2bo7b2o\$3o5\$2bo\$3bo5b2obo\$b3o5bob2o4\$obo\$b2o\$bo2\$2b2o\$bob
o\$3bo!
``````
Here is the latest list of 16G and above syntheses:

Code: Select all

``````16.217     xs16_3146pajo            38
16.1094    xs16_cila8oz641          37
16.313     xs16_3pm44og4c           34
16.349     xs16_35s26z39c           34
16.778     xs16_69la8oz321          34
16.890     xs16_696ki6zw641         34
16.1721    xs16_64kb2acz032         34
16.218     xs16_3pajc48c            33
16.682     xs16_69j0j9czx11         33
16.147     xs16_32qjap3             32
16.842     xs16_cila8oz065          32
16.929     xs16_3iaj2ak8zw1         31
16.1904    xs16_8u164koz32          31
16.185     xs16_32qk5b8o            30
16.220     xs16_3123qajo            29
16.312     xs16_62s53zbd            29
16.354     xs16_35s26zbd            29
16.889     xs16_696ki6zx65          29
16.1323    xs16_031e8gzc9311        29
16.151     xs16_64kr2pm             28
16.278     xs16_32qj43146           28
16.628     xs16_kc32qkz0113         28
16.731     xs16_3iajkcz23           28
16.786     xs16_3pa3ia4zw11         28
16.2347    xs16_g8861acz0db         28
16.2541    xs16_g8861aczc93         28
16.1979    xs16_4ap30ga6zw121       27
16.3227    xs16_31e8gzy012ego       27
16.1077    xs16_69m88cz6221         26
16.1691    xs16_4a9l6o8zx121        26
16.1703    xs16_4a9la8ozx121        26
16.2174    xs16_08u164koz32         26
16.623     xs16_o5r8jdz01           25
16.828     xs16_4alhe8z0641         25
16.834     xs16_8u15a4z1226         25
16.930     xs16_3iaj21e8zw1         25
16.1106    xs16_0iu0dbz641          25
16.1139    xs16_kq23z124871         25
16.1398    xs16_g88c93zc952         25
16.1901    xs16_08obap3z32          25
16.706     xs16_39s0qmz023          24
16.713     xs16_o8bap3z23           24
16.1034    xs16_3lkaa4z065          24
16.1064    xs16_39m88cz6221         24
16.1880    xs16_259q453z032         24
16.2295    xs16_0g8go8brz23         24
16.300     xs16_9fg4czbd            23
16.353     xs16_321fgc453           23
16.621     xs16_g5r8jdz11           23
16.827     xs16_ciaj2ak8zw1         23
16.829     xs16_0md1e8z1226         23
16.1702    xs16_4a5p68ozx121        23
16.1740    xs16_69acga6zx32         23
16.3066    xs16_4a9jzx12ego         23
16.825     xs16_4alhe8zw65          22
16.1846    xs16_25a8c93zw33         22
16.2313    xs16_08u16853z32         22
16.159     xs16_2egmd1e8            21
16.774     xs16_69raa4z32           21
16.1084    xs16_31ke12kozw11        21
16.1682    xs16_8k9bkk8zw23         21
16.1693    xs16_8k8aliczw23         21
16.1753    xs16_695q4gozw23         21
16.1954    xs16_8kk31e8z065         21
16.2096    xs16_wck5b8oz311         21
16.2309    xs16_8kk31e8z641         21
16.228     xs16_178bp2sg            20
16.712     xs16_3pc0qmzw23          20
16.723     xs16_i5p64koz11          20
16.833     xs16_0mp2sgz1243         20
16.872     xs16_2lla8oz065          20
16.1073    xs16_3lkaa4z641          20
16.1127    xs16_giligoz104a4        20
16.1739    xs16_g88r2qkz121         20
16.1791    xs16_03lkaa4z3201        20
16.1962    xs16_4a9eg8ozw65         20
16.2058    xs16_69akg4czx146        20
16.2555    xs16_4a9jzxpia4          20
16.18      xs16_caarzbd             19
16.131     xs16_660uhar             19
16.230     xs16_178jd2ko            19
16.358     xs16_321fgc2ko           19
16.745     xs16_39qb8oz32           19
16.801     xs16_08eharz321          19
16.1684    xs16_4aab9k8zx32         19
16.1694    xs16_4a5p6o8zx121        19
16.1881    xs16_259q453zw32         19
16.1912    xs16_at16426z32          19
16.2050    xs16_6ik8a52z065         19
16.2162    xs16_0at16426z32         19
16.2200    xs16_06agc93z2521        19
16.2307    xs16_6ik8a52z641         19
16.2316    xs16_0at16413z32         19
16.19      xs16_caarz39c            18
16.155     xs16_3pabp46             18
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
16.1130    xs16_oe12koz01ac         18
16.1558    xs16_3loz1226io          18
16.1711    xs16_c8idik8z023         18
16.1757    xs16_g8idik8z123         18
16.1790    xs16_178cia4z0321        18
16.1911    xs16_69q3213z32          18
16.1990    xs16_8e1tazx1252         18
16.1995    xs16_cik8a52z065         18
16.2025    xs16_069q48cz2521        18
16.2201    xs16_0ggml96z641         18
16.2447    xs16_0g8it248cz23        18
16.2480    xs16_3iaczw1139c         18
16.15      xs16_178c1f84c           17
16.227     xs16_5b8r5426            17
16.265     xs16_259m861ac           17
16.380     xs16_4a40vh248c          17
16.558     xs16_1784c842ak8         17
16.616     xs16_i5pajoz11           17
16.640     xs16_c9bkkozw32          17
16.668     xs16_gbq1daz121          17
16.697     xs16_db079ozx32          17
16.716     xs16_3pmk46zx23          17
16.748     xs16_39ege2z321          17
16.799     xs16_c8al56z311          17
16.803     xs16_c9bk46z311          17
16.843     xs16_4a9liczx56          17
16.875     xs16_4a5pa4z2521         17
16.1097    xs16_ck0ol3z643          17
16.1105    xs16_gie0dbz146          17
16.1276    xs16_3iakgozw1ac         17
16.1373    xs16_32q4goz4a43         17
16.1685    xs16_c48n98czx23         17
16.1715    xs16_64p784czw23         17
16.1722    xs16_4aq32acz032         17
16.1758    xs16_4a4o796zw121        17
16.1847    xs16_39c8a52z033         17
16.1867    xs16_069q453z311         17
16.1871    xs16_5bo8ge2z32          17
16.1882    xs16_259m453zx23         17
16.1905    xs16_8u16853z32          17
16.1991    xs16_8e1qbzx1252         17
16.2014    xs16_25a8kk8z0253        17
16.2018    xs16_25a8c826zw33        17
16.2045    xs16_25ao8ge2z032        17
16.2132    xs16_0g8it2sgz23         17
16.2356    xs16_25icggozx1ac        17
16.2467    xs16_0kc3213z34a4        17
16.2763    xs16_ol3zw343123         17
16.2861    xs16_ol3zw343146         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
16.302     xs16_5b8o642ac           16
16.350     xs16_312461tic           16
16.360     xs16_2egu16413           16
16.593     xs16_3123c48gka4         16
16.724     xs16_j5o64koz11          16
16.762     xs16_jhke1e8z1           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
16.840     xs16_c8idiczw56          16
16.856     xs16_kc32acz1252         16
16.953     xs16_0cil56z6221         16
16.995     xs16_0raik8z643          16
16.996     xs16_2lm853z056          16
16.1068    xs16_3lo0kcz6421         16
16.1080    xs16_3lo0kcz3421         16
16.1085    xs16_3h4e12koz011        16
16.1304    xs16_0okih3zc8421        16
16.1391    xs16_ca168ozc8421        16
16.1581    xs16_8o6413zrm           16
16.1583    xs16_4a9jzxha6zx11       16
16.1675    xs16_xj96z0mdz32         16
16.1710    xs16_4a9bk46zx32         16
16.1717    xs16_4aajk46zx121        16
16.1720    xs16_4a4o79ozx121        16
16.1766    xs16_kc321e8z123         16
16.1787    xs16_069m4koz311         16
16.1796    xs16_0bt06ioz32          16
16.1856    xs16_39u06a4z32          16
16.1857    xs16_39u0652z32          16
16.1864    xs16_31ke1e8z032         16
16.1929    xs16_0g5r8b5z121         16
16.1959    xs16_4ai31e8zx56         16
16.1994    xs16_0g9fgka4z121        16
16.2028    xs16_25ao48cz2521        16
16.2029    xs16_25ao4a4z2521        16
16.2030    xs16_0i5q8a52z121        16
16.2060    xs16_69akg4czx56         16
16.2124    xs16_0g8jd2koz23         16
16.2129    xs16_0g8jt246z23         16
16.2190    xs16_032q4goz6413        16
16.2204    xs16_0gilla4z641         16
16.2214    xs16_0mq0c93z641         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
16.2549    xs16_g4c3213zdb          16
16.2630    xs16_31e8gzxo9a6         16
16.2781    xs16_wj9c826z6221        16
16.3032    xs16_1784ozx342sg        16``````
EDIT: Fairly nice predecessor for 16.218 from (I think) the only soup on Catagolue. If the lower piece of junk can be made in 5G or less it would give 16.217 in 15G:

Code: Select all

``````x = 14, y = 10, rule = B3/S23
12bo\$10b3o\$11bo\$8b2o\$4bo\$4bo7bo\$4bo\$9bo2b2o\$3o6b2ob2o\$10b4o!
``````
Alternatively there is a related still-life with a handful of appearances on Catagolue. How expensive is it to convert to 16.217 I wonder?

Goldtiger997
Posts: 549
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: EDIT: Fairly nice predecessor for 16.218 from (I think) the only soup on Catagolue. If the lower piece of junk can be made in 5G or less it would give 16.217 in 15G...
...Alternatively there is a related still-life with a handful of appearances on Catagolue. How expensive is it to convert to 16.217 I wonder?
Unfortunately I could not find a way to use either of those. However, I found some different related objects with soups on catalogue. Two have a beehive instead of a hook, and a third has a bun instead of a snake.

Here are the most promising soups for each of the first two related still-lifes:

Code: Select all

``````x = 64, y = 41, rule = B3/S23
17b2o\$17b2o9\$8b2o\$8b2o2\$59b3o2\$16bo40bo5bo\$15b3o39bo5bo\$15bob2o38bo5bo
\$55bo\$8bo45bobo2b3o\$7bobo43b2obo\$7bobo45bo\$8bo\$52b2o3b2o\$51b3o3b2o\$50b
obo5bo\$50b2o5b2obo\$2b2o47b2o4b5o\$2ob2o47bo2b3o3bo\$o4bo49b2o\$o3b3o\$b2o
4bo\$5bobo\$5b2o2\$10b2o\$10b2o3\$11b2o\$11b2o!
``````

Posts: 1909
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

The first reduces to this component reaction:

Code: Select all

``````x = 11, y = 8, rule = B3/S23
2obobo2b2o\$5obo2b2o\$2b2obo2\$2bo4b2o\$2b2o3bo\$b3o5bo\$b2o5b2o!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Goldtiger997
Posts: 549
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

Can anyone convert any of these 17 and 18-bit still-lifes into 16.217?:

Code: Select all

``````x = 38, y = 71, rule = B3/S23
20bobo2\$19bo3bo\$14bo\$4bob2o14bo11bob2o\$4b2obo4bobobo3bo13b2obo\$2b2o28b
2o\$o2bob2o7bo5bo9bo2bob2o\$2o2bo2bo22b2o2bobo\$5b2o\$20bo20\$20bobo2\$19bo
3bo\$5b2o7bo\$4bo2bo14bo11bob2o\$4b3o5bobobo3bo13b2obo\$2b2o28b2o\$o2bob2o
7bo5bo9bo2bob2o\$2o2bobo23b2o2bobo2\$20bo20\$20bobo2\$19bo3bo\$6b2o6bo\$4bo
2bo14bo11bob2o\$4b3o5bobobo3bo13b2obo\$2b2o28b2o\$o2bob2o7bo5bo9bo2bob2o\$
2o2bobo23b2o2bobo2\$20bo!
``````
EDIT:

Possibility for one of those. Turn the red cells on at generation 4:

Code: Select all

``````x = 12, y = 11, rule = LifeHistory
10.A\$9.A\$9.3A2\$6.2A\$4.A2.A\$4.3A\$2.2A4.D\$A2.A.2A.D\$2A2.A.A\$8.D!
``````

chris_c
Posts: 911
Joined: June 28th, 2014, 7:15 am

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

Goldtiger997 wrote:Can anyone convert any of these 17 and 18-bit still-lifes into 16.217?:

Code: Select all

``````x = 38, y = 71, rule = B3/S23
20bobo2\$19bo3bo\$14bo\$4bob2o14bo11bob2o\$4b2obo4bobobo3bo13b2obo\$2b2o28b
2o\$o2bob2o7bo5bo9bo2bob2o\$2o2bo2bo22b2o2bobo\$5b2o\$20bo20\$20bobo2\$19bo
3bo\$5b2o7bo\$4bo2bo14bo11bob2o\$4b3o5bobobo3bo13b2obo\$2b2o28b2o\$o2bob2o
7bo5bo9bo2bob2o\$2o2bobo23b2o2bobo2\$20bo20\$20bobo2\$19bo3bo\$6b2o6bo\$4bo
2bo14bo11bob2o\$4b3o5bobobo3bo13b2obo\$2b2o28b2o\$o2bob2o7bo5bo9bo2bob2o\$
2o2bobo23b2o2bobo2\$20bo!
``````
I looked at the first one with JLS and it seemed fairly hopeless For the second one I made a little extra clearance in the old method at the cost of 3G. That brings the cost of 16.217 down to 26G. Not particularly satisfying but there we go.

Code: Select all

``````x = 136, y = 329, rule = B3/S23
13bo4bo13bobo\$7bo6b2o3b2o11b2o\$8b2o3b2o3b2o13bo\$7b2o3\$124bobo\$120b2obo
b2o\$120bob2o\$124b3o\$31bobo90bo2bo\$31b2o92b2o\$32bo2\$10b2o\$11b2o5b3o\$10b
o9bo\$19bo4\$28b3o\$28bo\$21b2o6bo\$22b2o\$21bo60\$17bo39bo\$15bobo38bo\$16b2o
38b3o18\$133b3o\$24bobo97bobo\$20b2obob2o93b2obob2o\$20bob2o96bob2o\$24b3o
97b3o\$24bo2bo96bo2bo\$25b2o98b2o70\$8bobo\$9b2o\$9bo2\$12bo41bo\$13bo39bo\$
11b3o39b3o7\$2bo\$obo\$b2o56bo\$57b2o\$51bo6b2o\$4bo40bobo2bo\$5bo39b2o3b3o\$
3b3o40bo3\$34bo\$34bo\$24bobo7bo89bobo\$20b2obob2o93b2obob2o\$20bob2o96bob
2o\$24b3o97b2obo\$24bo2bo96bob2o\$25b2o15\$47b2o\$46b2o\$48bo5\$8bo\$8b2o\$7bob
o53\$31bobo\$bo29b2o\$2b2o28bo\$b2o5\$2bo\$3b2o\$2b2o3\$2bo\$3bo\$b3o3\$24bobo93b
2o2bobo\$20b2obob2o93bo2bob2o\$20bob2o98b2o\$24b2obo96b2obo\$24bob2o96bob
2o16\$3bo\$3b2o\$2bobo!
``````
These are the SLs with synthesis above 30G in my list:

Code: Select all

``````16.778     xs16_69la8oz321          34
16.890     xs16_696ki6zw641         34
16.1721    xs16_64kb2acz032         34
16.682     xs16_69j0j9czx11         33
16.147     xs16_32qjap3             32
16.929     xs16_3iaj2ak8zw1         31
16.1904    xs16_8u164koz32          31
``````

Goldtiger997
Posts: 549
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: 16 in 16: Efficient 16-bit Synthesis Project (all < 30G)

chris_c wrote: ...That brings the cost of 16.217 down to 26G. Not particularly satisfying but there we go...
By synthesising a different 17-bit still life (carrier instead of snake), 16.217 can be reduced to 20G:

Code: Select all

``````x = 171, y = 51, rule = B3/S23
obo\$b2o\$bo16\$3bo119bo\$bobo120b2o\$2b2o3bo115b2o\$5b2o\$6b2o9bo\$16bo110bo
17bo\$16b3o106bobo17bobo\$11b3o112b2o17b2o\$11bo7b3o\$o11bo6bo\$b2o17bo\$2o
75bo\$78b2obobo23bo29bo\$77b2o2b2o24bo8bo20bo\$33b2o2bobo23b2o2bobo12bo
10b2o2bobo7bo9bo5b2o2bobo7bo25b2o2bobo\$33bo2bob2o23bo2bob2o23bo2bob2o
15b3o5bo2bob2o33bo2bob2o\$35b2o28b2o28b2o28b2o22bobo13b2o\$37b3o27b3o27b
3o27b3o19b2o16b2obo\$14bo22bo2bo26bo2bo26bo2bo26bo2bo7bo3bo7bo16bob2o\$
13b2o23b2o28b2o28b2o19bo8b2o6b2o4bobo\$13bobo101bobo17b2o3b2o\$118b2o\$
139bo\$138b2o\$138bobo6\$122b2o\$123b2o\$122bo!
``````
16.778 in 10 gliders:

Code: Select all

``````x = 44, y = 58, rule = B3/S23
15bo\$16b2o\$15b2o22\$35bobo\$36b2o\$36bo2\$42b2o\$32bo8b2o\$22b2o7b2o10bo\$23b
2o6bobo\$22bo4\$37bobo\$37b2o\$38bo\$31b2o\$30bobo6b2o\$32bo5bobo\$40bo2\$3o\$2b
o\$bo9\$6b2o\$7b2o\$6bo!
``````
16.890 in 11 gliders:

Code: Select all

``````x = 46, y = 22, rule = B3/S23
43bobo\$43b2o\$o43bo\$b2o\$2o26bo\$25bo2bobo7bobo\$23bobo2b2o8b2o\$24b2o13bo\$
6bo\$4bobo\$5b2o19b3o\$28bo\$7b2o18bo\$8b2o\$7bo4\$28bo\$12b2o13b2o4b2o\$11bobo
13bobo3bobo\$13bo19bo!
``````
EDIT:

16.1721 in 14 gliders:

Code: Select all

``````x = 48, y = 35, rule = B3/S23
45bo\$45bobo\$45b2o\$15bo\$16b2o\$15b2o\$23bo18bobo\$2bo21b2o16b2o\$obo20b2o2b
o15bo\$b2o24bobo\$27b2o3\$23bo\$24b2o\$23b2o3\$5bo\$3bo3bo\$8bo\$3bo4bo\$4b5o4\$
36b3o\$20b2o14bo\$19bobo15bo\$21bo2\$10b2o\$11b2o32b2o\$10bo34bobo\$45bo!
``````
It is annoyingly expensive for such as simple reaction, mostly due to a very bulky synthesis of a 2-block-constellation predecessor. Perhaps someone can reduce it...

EDIT2:

16.682 in 9 gliders:

Code: Select all

``````x = 35, y = 39, rule = B3/S23
19bo\$18bo\$18b3o12\$13bobo\$14b2o8bo\$bo12bo8bo\$2bo20b3o\$3o\$14bo\$12bobo\$4b
2o7b2ob3o\$5b2o9bo\$4bo12bo5\$10b2o\$10bobo\$10bo6\$33b2o\$32b2o\$34bo!
``````
EDIT3:

16.147 in 13 gliders:

Code: Select all

``````x = 41, y = 46, rule = B3/S23
39bo\$38bo\$38b3o10\$10bo\$8bobo\$9b2o\$5b3o12bo\$7bo13b2o\$6bo13b2o8bobo\$30b
2o\$9b2o20bo\$9bobo\$9bo11bo\$5b2o14bobo\$6b2o13b2o\$5bo4\$9b2o\$10b2o\$9bo8b3o
13b2o\$18bo15bobo\$19bo14bo6\$2o\$b2o\$o3\$31b2o\$30b2o\$32bo!
``````
EDIT4:

16.929 in 9 gliders:

Code: Select all

``````x = 29, y = 33, rule = B3/S23
bo\$2bo\$3o\$22bobo\$22b2o\$23bo\$4bobo\$5b2o\$5bo\$20bo\$20bobo\$20b2o7\$2bo\$obo\$
b2o3\$13b2o3bo\$14b2ob2o\$13bo3bobo4\$27b2o\$13b2o11b2o\$13bobo12bo\$13bo!
``````
16.1904 in 13 gliders:

Code: Select all

``````x = 114, y = 38, rule = B3/S23
61bo\$62bo\$60b3o4\$73bobo\$74b2o\$74bo\$81bobo\$81b2o\$8bo73bo\$6bobo100b2o\$7b
2o100bobo\$10bo100bo\$10bobo36b2o15bo13bo8b2o20b2o\$10b2o36bo2bo12b2o13b
2o7bo2bo21bo\$49b2o14b2o12bobo7b2o16bob4o\$107b2obo\$77b2o\$76bobo\$78bo\$
64bo\$64b2o\$bobo59bobo\$b2o38bo39bo\$2bo37bobo37bobo\$40b2o38b2o\$3o\$2bo\$bo
51b2o\$52bobo\$54bo3\$97bo\$96b2o\$96bobo!
``````
Now all 16-bit still-lifes cost less than 30 gliders!

Goldtiger997
Posts: 549
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: 16 in 16: Efficient 16-bit Synthesis Project (all < 30G)

16.220 in 13 gliders:

Code: Select all

``````x = 108, y = 45, rule = B3/S23
8bo\$6bobo\$7b2o14\$9bo5bo\$10bo4bobo\$8b3o4b2o2\$9bo60bo\$9b2o59bobo\$2bo5bob
o14bo44b2o\$obo20b2o19bob2o13bo4bo7bob2o26bob2o\$b2o21b2o18b2obo11bobo5b
2o5b2obo26b2obo\$60b2o4b2o\$42b5o16bo8b5o23bob5o\$40bo2bo2bo16b2o5bo2bo2b
o23b2obo2bo\$40b2o20bobo5b2o2\$66b3o\$68bo\$9bo57bo\$9b2o\$8bobo8\$b3o\$3bo\$2b
o!``````

chris_c
Posts: 911
Joined: June 28th, 2014, 7:15 am

### Re: 16 in 16: Efficient 16-bit Synthesis Project (all < 30G)

Goldtiger997 wrote: Now all 16-bit still-lifes cost less than 30 gliders!
Excellent work! Altogether your syntheses get us down to 28G at most.
Goldtiger997 wrote:16.1721 in 14 gliders:
...
It is annoyingly expensive for such as simple reaction, mostly due to a very bulky synthesis of a 2-block-constellation predecessor. Perhaps someone can reduce it...
I got surprisingly lucky and found a 3G collision that produces an edgy loaf and some junk behind that serves to clean up the later beacon. Now the fact that the pond is one glider more expensive than "ideal" seems perfectly tolerable.

Code: Select all

``````x = 129, y = 226, rule = B3/S23
10bo\$8bobo\$9b2o\$18bo\$16bobo\$17b2o8bobo\$27b2o\$28bo3\$18bo\$16bobo\$17b2o2\$
121bo\$118bo2b3o\$118b3o3bo\$obo118bobobo\$b2o7bo109bo3bo\$bo6bobo108bo7bo\$
9b2o108b2o5bobo\$126bobo\$6bo120bo\$6b2o\$5bobo5\$37b2o\$14bo21b2o\$14b2o22bo
\$13bobo82\$21bo99bo\$18bo2b3o94bo2b3o\$18b3o3bo93b3o3bo\$21bobobo95bobobo\$
20bo3bo95bo3bo\$19bo7bo91bo\$19b2o5bobo90b2o\$26bobo\$27bo3\$31b2o\$31bobo\$
31bo82\$33bo\$32bo\$32b3o3\$21bo99bo\$18bo2b3o94bo2b3o\$18b3o3bo93b3o3bo\$21b
obobo95bob2o\$20bo3bo95bo\$19bo99bo\$19b2o98b2o3\$32b3o\$32bo\$33bo!
``````
Goldtiger997 wrote:16.929 in 9 gliders:
I got this one down to 8G by elegantly noticing (*) that 2-glider mess does a reasonably good impression of a phi-spark at some point. The 1G reduction is useful because my system now tells us we have 16.827 in 15G as a bonus:

Code: Select all

``````x = 126, y = 138, rule = B3/S23
32bo\$30b2o\$31b2o2\$43bo\$43bobo\$43b2o6\$22bo\$23bo94bo2bo\$21b3o94b6o\$124bo
\$120bo2bobo\$14b2o103bobo2bo\$15b2o103bo\$14bo2\$21b2o\$20bobo\$22bo\$40b2o\$
39b2o\$41bo5\$15b3o27bo\$17bo26b2o\$16bo27bobo57\$29bo\$29bobo\$29b2o2\$3bo\$bo
bo\$2b2o24bo\$28bobo\$28b2o2\$obo\$b2o\$bo4\$5bobo\$6b2o\$6bo5\$18bo2bo99bo\$18b
6o95b5o\$24bo93bo5bo\$20bo2bobo92bobo2bobo\$19bobo2bo94bobo2bo\$20bo99bo7\$
6b3o\$8bo\$7bo8\$29bo\$28b2o\$28bobo!
``````
Goldtiger997 wrote:16.220 in 13 gliders:
Actually in 12G. There is a 4G ac-to-snake that has been on my machine since Dec 8th. Here are all of the ac-to-snake converters I have:

Code: Select all

``````x = 89, y = 24, rule = LifeHistory
43.A\$43.A.A\$43.2A\$70.A.A\$4.A60.A4.2A\$5.A57.A.A5.A\$3.3A35.A.A20.2A\$14.
A26.2A7.A30.A\$12.2A19.A8.A7.A.A14.A11.2A\$13.2A16.A.A16.2A13.2A13.2A\$
32.2A32.2A\$3.A.A10.A\$4.2A10.A.A\$4.A11.2A\$86.2A\$86.A.A\$86.A2\$10.2E28.
2E28.2E\$11.E29.E29.E\$9.E29.E29.E\$3A6.2E28.2E28.2E\$2.A\$.A!
``````
The first one is old. The second is the cheapest. The third has better clearance in the south-west. I think the 2nd are 3rd were made by me but I could be wrong.

Now there are 192 still life which cost at least 16G. Here are those with cost at least 20:

Code: Select all

``````16.151     xs16_64kr2pm             28
16.278     xs16_32qj43146           28
16.349     xs16_35s26z39c           28
16.628     xs16_kc32qkz0113         28
16.731     xs16_3iajkcz23           28
16.786     xs16_3pa3ia4zw11         28
16.1979    xs16_4ap30ga6zw121       27
16.3227    xs16_31e8gzy012ego       27
16.1077    xs16_69m88cz6221         26
16.1691    xs16_4a9l6o8zx121        26
16.1703    xs16_4a9la8ozx121        26
16.623     xs16_o5r8jdz01           25
16.828     xs16_4alhe8z0641         25
16.834     xs16_8u15a4z1226         25
16.930     xs16_3iaj21e8zw1         25
16.1139    xs16_kq23z124871         25
16.1398    xs16_g88c93zc952         25
16.706     xs16_39s0qmz023          24
16.713     xs16_o8bap3z23           24
16.1034    xs16_3lkaa4z065          24
16.1064    xs16_39m88cz6221         24
16.1323    xs16_031e8gzc9311        24
16.1880    xs16_259q453z032         24
16.2295    xs16_0g8go8brz23         24
16.300     xs16_9fg4czbd            23
16.353     xs16_321fgc453           23
16.354     xs16_35s26zbd            23
16.621     xs16_g5r8jdz11           23
16.829     xs16_0md1e8z1226         23
16.1702    xs16_4a5p68ozx121        23
16.1740    xs16_69acga6zx32         23
16.3066    xs16_4a9jzx12ego         23
16.825     xs16_4alhe8zw65          22
16.1846    xs16_25a8c93zw33         22
16.2313    xs16_08u16853z32         22
16.159     xs16_2egmd1e8            21
16.218     xs16_3pajc48c            21
16.774     xs16_69raa4z32           21
16.1084    xs16_31ke12kozw11        21
16.1682    xs16_8k9bkk8zw23         21
16.1693    xs16_8k8aliczw23         21
16.1753    xs16_695q4gozw23         21
16.1954    xs16_8kk31e8z065         21
16.2096    xs16_wck5b8oz311         21
16.2309    xs16_8kk31e8z641         21
16.217     xs16_3146pajo            20
16.228     xs16_178bp2sg            20
16.712     xs16_3pc0qmzw23          20
16.723     xs16_i5p64koz11          20
16.833     xs16_0mp2sgz1243         20
16.872     xs16_2lla8oz065          20
16.1073    xs16_3lkaa4z641          20
16.1127    xs16_giligoz104a4        20
16.1739    xs16_g88r2qkz121         20
16.1791    xs16_03lkaa4z3201        20
16.1962    xs16_4a9eg8ozw65         20
16.2058    xs16_69akg4czx146        20
16.2555    xs16_4a9jzxpia4          20
``````
(*) in reality it was brute force...

Posts: 1909
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

This should drop 16.151 to about 18G:

Code: Select all

``````x = 95, y = 72, rule = B3/S23
93bo\$92bo\$92b3o18\$36bo\$34bobo\$35b2o\$54bo\$54bobo\$54b2o3\$26bo\$25bobo\$25b
obo\$26bo2\$30b2o\$29bo2bo\$30b2o2\$26bo8b3o\$25bobo9bo25b3o\$25bobo8bo\$26bo\$
48bo\$46b3o\$46bobo9bo\$46bo10b2o\$57bobo2\$54bo\$54b2o\$53bobo20\$2o\$b2o\$o!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Goldtiger997
Posts: 549
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: 16 in 16: Efficient 16-bit Synthesis Project (all < 29G)

Code: Select all

``````x = 95, y = 72, rule = B3/S23
93bo\$92bo\$92b3o18\$36bo\$34bobo\$35b2o\$54bo\$54bobo\$54b2o3\$26bo\$25bobo\$25b
obo\$26bo2\$30b2o\$29bo2bo\$30b2o2\$26bo8b3o\$25bobo9bo25b3o\$25bobo8bo\$26bo\$
48bo\$46b3o\$46bobo9bo\$46bo10b2o\$57bobo2\$54bo\$54b2o\$53bobo20\$2o\$b2o\$o!
``````
16.151 in 15 gliders:

Code: Select all

``````x = 112, y = 97, rule = B3/S23
110bo\$109bo\$109b3o18\$37bo\$35bobo\$36b2o\$71bo\$71bobo\$71b2o8\$21bo\$22b2o\$
21b2o3\$34bo\$35b2o\$34b2o2\$33bo\$33b2o\$32bobo15bo16bo\$48bobo16bobo\$49b2o
16b2o2\$66bo\$48bo18bo\$49b2o14b3o\$48b2o2\$36b3o\$38bo\$37bo2\$73bo\$72b2o\$72b
obo3\$49bo\$49b2o\$48bobo21\$b2o\$2b2o\$bo7\$2o\$b2o\$o!
``````
EDIT:

16.278 in 12 gliders:

Code: Select all

``````x = 79, y = 99, rule = B3/S23
77bo\$76bo\$76b3o5\$55bo\$54bo\$54b3o20\$27bo\$25b2o\$26b2o2\$36bobo\$16b2o7b2o
9b2o\$17b2o5b2o11bo\$16bo9bo3\$22bo\$23b2o\$22b2o2\$21bo\$20b2o\$20bobo5\$34bo\$
33bo\$33b3o2\$34bo\$33b2o\$33bobo3b3o\$39bo\$40bo38\$2o\$b2o\$o!
``````
Got stuck on 16.349...

chris_c
Posts: 911
Joined: June 28th, 2014, 7:15 am

### Re: 16 in 16: Efficient 16-bit Synthesis Project (all < 29G)

Goldtiger997 wrote: Got stuck on 16.349...
I spent quite a while on it too.... Can this be completed cheaply enough? I'm out of time for now.

Code: Select all

``````x = 23, y = 27, rule = B3/S23
4bo\$2bobo5bobo\$3b2o5b2o\$11bo2\$2bo14bo\$obo6bo6b3o\$b2o4bobo6bo\$8b2o\$4b2o
\$3bobo12bo\$5bo12bobo\$18b2o7\$21b2o\$15b2o3b2o\$14b2o6bo\$16bo2\$9b2o\$10b2o\$
9bo!
``````

Posts: 1909
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

16.628:

Code: Select all

``````x = 51, y = 30, rule = B3/S23
21bo28bo\$19b2o27b2o\$9bo10b2o27b2o\$10b2o\$9b2o2\$39bo\$39bobo\$18bobo18b2o\$
17bo\$17bo3bo\$5b2o11b4o\$6b2o13bo\$5bo3\$45bo\$29bo13b2o\$29b4o11b2o\$29bo3bo
\$33bo\$10b2o18bobo\$9bobo\$11bo2\$40b2o\$39b2o\$2o27b2o10bo\$b2o27b2o\$o28bo!
``````
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]