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

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

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

Extrementhusiast wrote:I don't see why you can't just do something like this for 16.2460:
`x = 28, y = 18, rule = B3/S23bo\$2bo\$3o3\$13bo\$14b2o5bo\$13b2o4b2o\$20b2o4\$12bo8bob2o\$13bo2bo4b2obo\$11b3o2b2o7b2o\$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:

`x = 138, y = 147, rule = B3/S23bo\$2bo\$3o5\$5bo\$6b2o\$5b2o17\$23bobo\$24b2o110b2o\$24bo111b2o3\$135b2o\$135b2o3\$121bo\$120bobo\$21b3o96bo2bo\$23bo94b2o2b2o\$22bo95bo\$119bo\$118b2o11\$28b2o\$28bobo\$28bo7\$bo\$b2o\$obo64\$36b2o\$36b2o3\$35b2o\$35b2o3\$21bo99bo\$20bobo97bobo\$20bo2bo96bo2bo\$18b2o2b2o94b2o2b2o\$18bo99bo\$19bo99bo\$18b2o98b2o3\$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

`16.657     xs16_695q4ozw321                         16  448816.131     xs16_660uhar                             19  375916.1856    xs16_39u06a4z32                          16  245516.1739    xs16_g88r2qkz121                         20  225616.1880    xs16_259q453z032                         25  201716.665     xs16_699mkiczx1                          18  189616.829     xs16_0md1e8z1226                         23  149616.748     xs16_39ege2z321                          17  139016.799     xs16_c8al56z311                          17  120016.642     xs16_6s1raa4zw1                          51  111816.228     xs16_178bp2sg                            20  106416.159     xs16_2egmd1e8                            21  97416.686     xs16_mkkb2acz1                           38  91816.2309    xs16_8kk31e8z641                         21  79416.19      xs16_caarz39c                            18  51216.1992    xs16_25is0cczw65                         16  47716.810     xs16_ca9la4z311                          16  47616.1881    xs16_259q453zw32                         19  44116.834     xs16_8u15a4z1226                         25  43216.774     xs16_69raa4z32                           21  43216.360     xs16_2egu16413                           16  36616.848     xs16_ca9b8oz0252                         18  36316.2014    xs16_25a8kk8z0253                        17  34816.1717    xs16_4aajk46zx121                        16  33616.827     xs16_ciaj2ak8zw1                         23  33516.995     xs16_0raik8z643                          16  32516.1722    xs16_4aq32acz032                         17  31916.265     xs16_259m861ac                           17  27716.716     xs16_3pmk46zx23                          17  27516.1757    xs16_g8idik8z123                         18  27116.2060    xs16_69akg4czx56                         16  26816.1703    xs16_4a9la8ozx121                        26  25016.18      xs16_caarzbd                             19  21316.1684    xs16_4aab9k8zx32                         19  17016.2174    xs16_08u164koz32                         27  16316.353     xs16_321fgc453                           23  15716.668     xs16_gbq1daz121                          17  15616.1740    xs16_69acga6zx32                         23  15516.1990    xs16_8e1tazx1252                         18  14616.1857    xs16_39u0652z32                          16  14116.243     xs16_2egu16426                           16  13816.2018    xs16_25a8c826zw33                        18  12716.822     xs16_8ehikozw56                          16  11416.2445    xs16_ciligzx254c                         16  10616.1787    xs16_069m4koz311                         16  10516.1991    xs16_8e1qbzx1252                         17  9916.953     xs16_0cil56z6221                         16  9916.1929    xs16_0g5r8b5z121                         16  9916.15      xs16_178c1f84c                           17  8516.2295    xs16_0g8go8brz23                         24  7716.155     xs16_3pabp46                             18  7316.2347    xs16_g8861acz0db                         28  6616.1694    xs16_4a5p6o8zx121                        19  6616.1847    xs16_39c8a52z033                         17  6416.628     xs16_kc32qkz0113                         28  6316.1954    xs16_8kk31e8z065                         21  6216.731     xs16_3iajkcz23                           28  5816.836     xs16_4aajkczx56                          16  5816.833     xs16_0mp2sgz1243                         20  5716.616     xs16_i5pajoz11                           17  5416.640     xs16_c9bkkozw32                          17  5016.801     xs16_08eharz321                          19  4316.1904    xs16_8u164koz32                          32  4216.795     xs16_c87p46z311                          53  3916.230     xs16_178jd2ko                            19  3916.2132    xs16_0g8it2sgz23                         17  3916.1106    xs16_0iu0dbz641                          25  3716.313     xs16_3pm44og4c                           35  3616.1691    xs16_4a9l6o8zx121                        26  3516.2201    xs16_0ggml96z641                         18  3516.1304    xs16_0okih3zc8421                        16  3216.1391    xs16_ca168ozc8421                        16  3216.312     xs16_62s53zbd                            29  3116.929     xs16_3iaj2ak8zw1                         31  3016.2541    xs16_g8861aczc93                         28  2816.1994    xs16_0g9fgka4z121                        16  2816.1846    xs16_25a8c93zw33                         23  2716.856     xs16_kc32acz1252                         16  2416.623     xs16_o5r8jdz01                           25  2316.914     xs16_8kkja952zx1                         18  2316.227     xs16_5b8r5426                            17  2316.1702    xs16_4a5p68ozx121                        23  1916.1791    xs16_03lkaa4z3201                        20  1916.1464    xs16_08o696z6ip                          16  1816.706     xs16_39s0qmz023                          24  1716.1766    xs16_kc321e8z123                         16  1716.350     xs16_312461tic                           16  1516.621     xs16_g5r8jdz11                           23  1416.723     xs16_i5p64koz11                          20  1416.1962    xs16_4a9eg8ozw65                         20  1416.2219    xs16_0oe12koz643                         16  1416.786     xs16_3pa3ia4zw11                         28  1316.1034    xs16_3lkaa4z065                          24  1316.278     xs16_32qj43146                           29  1216.1323    xs16_031e8gzc9311                        29  1216.1790    xs16_178cia4z0321                        18  1216.803     xs16_c9bk46z311                          17  1216.724     xs16_j5o64koz11                          16  1116.1758    xs16_4a4o796zw121                        17  1016.682     xs16_69j0j9czx11                         33  916.996     xs16_2lm853z056                          16  916.2542    xs16_g88c871zc93                         16  916.2546    xs16_j9cz122c84c                         16  916.3163    xs16_wo443123zbd                         17  816.838     xs16_ci9b8ozw56                          16  816.2302    xs16_4ap6413z65                          16  816.872     xs16_2lla8oz065                          20  716.1995    xs16_cik8a52z065                         18  716.1127    xs16_giligoz104a4                        20  616.2322    xs16_raak8zx1252                         16  616.2630    xs16_31e8gzxo9a6                         16  616.147     xs16_32qjap3                             32  516.3227    xs16_31e8gzy012ego                       27  516.1753    xs16_695q4gozw23                         21  516.772     xs16_3h4e1daz011                         16  516.2547    xs16_j9cz122c826                         16  516.778     xs16_69la8oz321                          36  416.151     xs16_64kr2pm                             28  416.713     xs16_o8bap3z23                           24  416.3066    xs16_4a9jzx12ego                         23  416.2058    xs16_69akg4czx146                        20  416.926     xs16_3iajc4gozw1                         18  416.762     xs16_jhke1e8z1                           16  416.1080    xs16_3lo0kcz3421                         16  416.2029    xs16_25ao4a4z2521                        16  416.2805    xs16_0gs2c871z641                        16  416.890     xs16_696ki6zw641                         35  316.842     xs16_cila8oz065                          34  316.354     xs16_35s26zbd                            29  316.889     xs16_696ki6zx65                          29  316.828     xs16_4alhe8z0641                         25  316.358     xs16_321fgc2ko                           19  316.1105    xs16_gie0dbz146                          18  316.1107    xs16_02egdbz2521                         18  316.1911    xs16_69q3213z32                          18  316.1685    xs16_c48n98czx23                         17  316.1867    xs16_069q453z311                         17  316.1882    xs16_259m453zx23                         17  316.1710    xs16_4a9bk46zx32                         16  316.2030    xs16_0i5q8a52z121                        16  316.2305    xs16_6413ia4z6421                        16  316.1094    xs16_cila8oz641                          40  216.349     xs16_35s26z39c                           35  216.220     xs16_3123qajo                            29  216.1901    xs16_08obap3z32                          25  216.300     xs16_9fg4czbd                            23  216.2096    xs16_wck5b8oz311                         21  216.745     xs16_39qb8oz32                           19  216.380     xs16_4a40vh248c                          17  216.875     xs16_4a5pa4z2521                         17  216.771     xs16_69qb8oz32                           16  216.840     xs16_c8idiczw56                          16  216.1675    xs16_xj96z0mdz32                         16  216.1720    xs16_4a4o79ozx121                        16  216.2204    xs16_0gilla4z641                         16  216.712     xs16_3pc0qmzw23                          48  116.1721    xs16_64kb2acz032                         34  116.218     xs16_3pajc48c                            33  116.185     xs16_32qk5b8o                            30  116.1979    xs16_4ap30ga6zw121                       27  116.930     xs16_3iaj21e8zw1                         25  116.1064    xs16_39m88cz6221                         24  116.2313    xs16_08u16853z32                         23  116.825     xs16_4alhe8zw65                          22  116.1682    xs16_8k9bkk8zw23                         21  116.1073    xs16_3lkaa4z641                          20  116.1912    xs16_at16426z32                          19  116.2050    xs16_6ik8a52z065                         19  116.2162    xs16_0at16426z32                         19  116.1711    xs16_c8idik8z023                         18  116.2025    xs16_069q48cz2521                        18  116.2447    xs16_0g8it248cz23                        18  116.2480    xs16_3iaczw1139c                         18  116.843     xs16_4a9liczx56                          17  116.1715    xs16_64p784czw23                         17  116.2694    xs16_4ai3gzx11mq                         17  116.2861    xs16_ol3zw343146                         17  116.3164    xs16_wo443146zbd                         17  116.104     xs16_0j5ozj4pz11                         16  116.593     xs16_3123c48gka4                         16  116.1085    xs16_3h4e12koz011                        16  116.1864    xs16_31ke1e8z032                         16  116.2317    xs16_cik8a52z641                         16  116.217     xs16_3146pajo                            39  016.3154    xs16_32qkzy0321e8                        27  016.1077    xs16_69m88cz6221                         26  016.2928    xs16_wggkq23zc452                        26  016.1139    xs16_kq23z124871                         25  016.1398    xs16_g88c93zc952                         25  016.1084    xs16_31ke12kozw11                        21  016.1693    xs16_8k8aliczw23                         21  016.2555    xs16_4a9jzxpia4                          20  016.3167    xs16_xok21e8zc93                         20  016.2200    xs16_06agc93z2521                        19  016.2307    xs16_6ik8a52z641                         19  016.2316    xs16_0at16413z32                         19  016.3014    xs16_wok21e8zdb                          19  016.600     xs16_6421344og84c                        18  016.697     xs16_db079ozx32                          18  016.1130    xs16_oe12koz01ac                         18  016.1558    xs16_3loz1226io                          18  016.558     xs16_1784c842ak8                         17  016.1097    xs16_ck0ol3z643                          17  016.1276    xs16_3iakgozw1ac                         17  016.1373    xs16_32q4goz4a43                         17  016.1871    xs16_5bo8ge2z32                          17  016.1905    xs16_8u16853z32                          17  016.2045    xs16_25ao8ge2z032                        17  016.2356    xs16_25icggozx1ac                        17  016.2467    xs16_0kc3213z34a4                        17  016.2763    xs16_ol3zw343123                         17  016.115     xs16_0ol3z0mdz32                         16  016.302     xs16_5b8o642ac                           16  016.1068    xs16_3lo0kcz6421                         16  016.1581    xs16_8o6413zrm                           16  016.1583    xs16_4a9jzxha6zx11                       16  016.1796    xs16_0bt06ioz32                          16  016.1959    xs16_4ai31e8zx56                         16  016.2028    xs16_25ao48cz2521                        16  016.2124    xs16_0g8jd2koz23                         16  016.2129    xs16_0g8jt246z23                         16  016.2190    xs16_032q4goz6413                        16  016.2214    xs16_0mq0c93z641                         16  016.2323    xs16_ra248goz056                         16  016.2549    xs16_g4c3213zdb                          16  016.2710    xs16_xkq23zck3z11                        16  016.2711    xs16_xkq23zc4jz011                       16  016.2781    xs16_wj9c826z6221                        16  016.3032    xs16_1784ozx342sg                        16  016.3069    xs16_39cggzx1o9a4                        16  0`

`16.795     xs16_c87p46z311          5316.642     xs16_6s1raa4zw1          5116.712     xs16_3pc0qmzw23          4816.1094    xs16_cila8oz641          4016.217     xs16_3146pajo            3916.686     xs16_mkkb2acz1           3816.778     xs16_69la8oz321          3616.313     xs16_3pm44og4c           3516.349     xs16_35s26z39c           3516.890     xs16_696ki6zw641         3516.842     xs16_cila8oz065          3416.1721    xs16_64kb2acz032         3416.218     xs16_3pajc48c            3316.682     xs16_69j0j9czx11         3316.147     xs16_32qjap3             3216.1904    xs16_8u164koz32          3216.929     xs16_3iaj2ak8zw1         3116.185     xs16_32qk5b8o            3016.220     xs16_3123qajo            2916.278     xs16_32qj43146           2916.312     xs16_62s53zbd            2916.354     xs16_35s26zbd            2916.889     xs16_696ki6zx65          2916.1323    xs16_031e8gzc9311        2916.151     xs16_64kr2pm             2816.628     xs16_kc32qkz0113         2816.731     xs16_3iajkcz23           2816.786     xs16_3pa3ia4zw11         2816.2347    xs16_g8861acz0db         2816.2541    xs16_g8861aczc93         2816.1979    xs16_4ap30ga6zw121       2716.2174    xs16_08u164koz32         2716.3154    xs16_32qkzy0321e8        2716.3227    xs16_31e8gzy012ego       2716.1077    xs16_69m88cz6221         2616.1691    xs16_4a9l6o8zx121        2616.1703    xs16_4a9la8ozx121        2616.2928    xs16_wggkq23zc452        2616.623     xs16_o5r8jdz01           2516.828     xs16_4alhe8z0641         2516.834     xs16_8u15a4z1226         2516.930     xs16_3iaj21e8zw1         2516.1106    xs16_0iu0dbz641          2516.1139    xs16_kq23z124871         2516.1398    xs16_g88c93zc952         2516.1880    xs16_259q453z032         2516.1901    xs16_08obap3z32          2516.706     xs16_39s0qmz023          2416.713     xs16_o8bap3z23           2416.1034    xs16_3lkaa4z065          2416.1064    xs16_39m88cz6221         2416.2295    xs16_0g8go8brz23         2416.300     xs16_9fg4czbd            2316.353     xs16_321fgc453           2316.621     xs16_g5r8jdz11           2316.827     xs16_ciaj2ak8zw1         2316.829     xs16_0md1e8z1226         2316.1702    xs16_4a5p68ozx121        2316.1740    xs16_69acga6zx32         2316.1846    xs16_25a8c93zw33         2316.2313    xs16_08u16853z32         2316.3066    xs16_4a9jzx12ego         2316.825     xs16_4alhe8zw65          2216.159     xs16_2egmd1e8            2116.774     xs16_69raa4z32           2116.1084    xs16_31ke12kozw11        2116.1682    xs16_8k9bkk8zw23         2116.1693    xs16_8k8aliczw23         2116.1753    xs16_695q4gozw23         2116.1954    xs16_8kk31e8z065         2116.2096    xs16_wck5b8oz311         2116.2309    xs16_8kk31e8z641         2116.228     xs16_178bp2sg            2016.723     xs16_i5p64koz11          2016.833     xs16_0mp2sgz1243         2016.872     xs16_2lla8oz065          2016.1073    xs16_3lkaa4z641          2016.1127    xs16_giligoz104a4        2016.1739    xs16_g88r2qkz121         2016.1791    xs16_03lkaa4z3201        2016.1962    xs16_4a9eg8ozw65         2016.2058    xs16_69akg4czx146        2016.2555    xs16_4a9jzxpia4          2016.3167    xs16_xok21e8zc93         2016.18      xs16_caarzbd             1916.131     xs16_660uhar             1916.230     xs16_178jd2ko            1916.358     xs16_321fgc2ko           1916.745     xs16_39qb8oz32           1916.801     xs16_08eharz321          1916.1684    xs16_4aab9k8zx32         1916.1694    xs16_4a5p6o8zx121        1916.1881    xs16_259q453zw32         1916.1912    xs16_at16426z32          1916.2050    xs16_6ik8a52z065         1916.2162    xs16_0at16426z32         1916.2200    xs16_06agc93z2521        1916.2307    xs16_6ik8a52z641         1916.2316    xs16_0at16413z32         1916.3014    xs16_wok21e8zdb          1916.19      xs16_caarz39c            1816.155     xs16_3pabp46             1816.600     xs16_6421344og84c        1816.665     xs16_699mkiczx1          1816.697     xs16_db079ozx32          1816.848     xs16_ca9b8oz0252         1816.914     xs16_8kkja952zx1         1816.926     xs16_3iajc4gozw1         1816.1105    xs16_gie0dbz146          1816.1107    xs16_02egdbz2521         1816.1130    xs16_oe12koz01ac         1816.1558    xs16_3loz1226io          1816.1711    xs16_c8idik8z023         1816.1757    xs16_g8idik8z123         1816.1790    xs16_178cia4z0321        1816.1911    xs16_69q3213z32          1816.1990    xs16_8e1tazx1252         1816.1995    xs16_cik8a52z065         1816.2018    xs16_25a8c826zw33        1816.2025    xs16_069q48cz2521        1816.2201    xs16_0ggml96z641         1816.2447    xs16_0g8it248cz23        1816.2480    xs16_3iaczw1139c         1816.15      xs16_178c1f84c           1716.227     xs16_5b8r5426            1716.265     xs16_259m861ac           1716.380     xs16_4a40vh248c          1716.558     xs16_1784c842ak8         1716.616     xs16_i5pajoz11           1716.640     xs16_c9bkkozw32          1716.668     xs16_gbq1daz121          1716.716     xs16_3pmk46zx23          1716.748     xs16_39ege2z321          1716.799     xs16_c8al56z311          1716.803     xs16_c9bk46z311          1716.843     xs16_4a9liczx56          1716.875     xs16_4a5pa4z2521         1716.1097    xs16_ck0ol3z643          1716.1276    xs16_3iakgozw1ac         1716.1373    xs16_32q4goz4a43         1716.1685    xs16_c48n98czx23         1716.1715    xs16_64p784czw23         1716.1722    xs16_4aq32acz032         1716.1758    xs16_4a4o796zw121        1716.1847    xs16_39c8a52z033         1716.1867    xs16_069q453z311         1716.1871    xs16_5bo8ge2z32          1716.1882    xs16_259m453zx23         1716.1905    xs16_8u16853z32          1716.1991    xs16_8e1qbzx1252         1716.2014    xs16_25a8kk8z0253        1716.2045    xs16_25ao8ge2z032        1716.2132    xs16_0g8it2sgz23         1716.2356    xs16_25icggozx1ac        1716.2467    xs16_0kc3213z34a4        1716.2694    xs16_4ai3gzx11mq         1716.2763    xs16_ol3zw343123         1716.2861    xs16_ol3zw343146         1716.3163    xs16_wo443123zbd         1716.3164    xs16_wo443146zbd         1716.104     xs16_0j5ozj4pz11         1616.115     xs16_0ol3z0mdz32         1616.243     xs16_2egu16426           1616.302     xs16_5b8o642ac           1616.350     xs16_312461tic           1616.360     xs16_2egu16413           1616.593     xs16_3123c48gka4         1616.657     xs16_695q4ozw321         1616.724     xs16_j5o64koz11          1616.762     xs16_jhke1e8z1           1616.771     xs16_69qb8oz32           1616.772     xs16_3h4e1daz011         1616.810     xs16_ca9la4z311          1616.822     xs16_8ehikozw56          1616.836     xs16_4aajkczx56          1616.838     xs16_ci9b8ozw56          1616.840     xs16_c8idiczw56          1616.856     xs16_kc32acz1252         1616.953     xs16_0cil56z6221         1616.995     xs16_0raik8z643          1616.996     xs16_2lm853z056          1616.1068    xs16_3lo0kcz6421         1616.1080    xs16_3lo0kcz3421         1616.1085    xs16_3h4e12koz011        1616.1304    xs16_0okih3zc8421        1616.1391    xs16_ca168ozc8421        1616.1464    xs16_08o696z6ip          1616.1581    xs16_8o6413zrm           1616.1583    xs16_4a9jzxha6zx11       1616.1675    xs16_xj96z0mdz32         1616.1710    xs16_4a9bk46zx32         1616.1717    xs16_4aajk46zx121        1616.1720    xs16_4a4o79ozx121        1616.1766    xs16_kc321e8z123         1616.1787    xs16_069m4koz311         1616.1796    xs16_0bt06ioz32          1616.1856    xs16_39u06a4z32          1616.1857    xs16_39u0652z32          1616.1864    xs16_31ke1e8z032         1616.1929    xs16_0g5r8b5z121         1616.1959    xs16_4ai31e8zx56         1616.1992    xs16_25is0cczw65         1616.1994    xs16_0g9fgka4z121        1616.2028    xs16_25ao48cz2521        1616.2029    xs16_25ao4a4z2521        1616.2030    xs16_0i5q8a52z121        1616.2060    xs16_69akg4czx56         1616.2124    xs16_0g8jd2koz23         1616.2129    xs16_0g8jt246z23         1616.2190    xs16_032q4goz6413        1616.2204    xs16_0gilla4z641         1616.2214    xs16_0mq0c93z641         1616.2219    xs16_0oe12koz643         1616.2302    xs16_4ap6413z65          1616.2305    xs16_6413ia4z6421        1616.2317    xs16_cik8a52z641         1616.2322    xs16_raak8zx1252         1616.2323    xs16_ra248goz056         1616.2445    xs16_ciligzx254c         1616.2542    xs16_g88c871zc93         1616.2546    xs16_j9cz122c84c         1616.2547    xs16_j9cz122c826         1616.2549    xs16_g4c3213zdb          1616.2630    xs16_31e8gzxo9a6         1616.2710    xs16_xkq23zck3z11        1616.2711    xs16_xkq23zc4jz011       1616.2781    xs16_wj9c826z6221        1616.2805    xs16_0gs2c871z641        1616.3032    xs16_1784ozx342sg        1616.3069    xs16_39cggzx1o9a4        16`
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

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

16.795 in 10 gliders:

`x = 34, y = 37, rule = B3/S2324bo\$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:

`x = 102, y = 24, rule = B3/S2369bo\$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:

`x = 29, y = 26, rule = B3/S2314bo\$14bobo\$8bo5b2o\$9b2o\$8b2o\$5bo\$3bobo20bobo\$4b2o20b2o\$12bo14bo\$12bobo\$8b3ob2o\$10bo\$9bo\$19bo\$18bo\$15b2ob3o\$14bobo\$bo14bo\$b2o20b2o\$obo20bobo\$23bo\$19b2o\$18b2o\$13b2o5bo\$12bobo\$14bo!`

Goldtiger997

Posts: 515
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

16.1992 in 14G:
`x = 199, y = 25, rule = B3/S23108bo\$108bobo\$108b2o\$103bo\$104b2o\$103b2o\$2bo97b2o31bo29bo29bo\$obo20b2o28b2o23b2o19bobo6b2o22bobo16bo10bobo27bobo\$b2o20bobob2o24bobob2o19bobob2o17bo6bobob2o19bobob2o13bo10bobob2o24bobob2o\$25bob2o26bob2o21bob2o26bob2o21bob2o11b3o12bob2o26bob2o\$25bo29bo24bo29bo24bo29bo28b2o\$bo4b2o15bobo27bobo22bobo27bobo22bobo27bobo29bo\$2b2o2bobo13bobo27bobo22bobo27bobo22bobo27bobo29bo\$b2o3bo16bo29bo23b2o28b2o23b2o28b2o30b2o\$173b2o\$46b2o126b2o\$47b2o2bo121bo3b2o\$46bo3b2o125bobo\$5b3o42bobo124bo\$7bo\$6bo\$176bo\$153b2o20b2o\$152bobo20bobo\$154bo!`

Bob Shemyakin
BobShemyakin

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

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

BobShemyakin wrote:16.1992 in 14G

Reduced to 12G:
`x = 143, y = 25, rule = B3/S2352bo41bo\$52bobo40bo\$52b2o39b3o\$47bo\$48b2o\$47b2o\$o43b2o31bo29bo29bo\$b2o19b2o19bobo6b2o22bobo27bobo27bobo\$2o20bobob2o17bo6bobob2o19bobob2o24bobob2o24bobob2o\$24bob2o26bob2o21bob2o26bob2o26bob2o\$24bo29bo24bo29bo28b2o\$bo3b2o15bobo27bobo22bobo27bobo29bo\$2bob2o15bobo27bobo22bobo27bobo29bo\$3o3bo15bo29bo24bo29bo30b2o\$117b2o\$118b2o\$117bo3b2o\$5bo115bobo\$5b2o114bo\$4bobo2\$120bo\$93b3o23b2o\$95bo23bobo\$94bo!`
-Matthias Merzenich
Sokwe
Moderator

Posts: 1458
Joined: July 9th, 2009, 2:44 pm

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

16.641 in 11 gliders (actually 16.642 thanks AbhpzTa):

`x = 135, y = 84, rule = B3/S23132bo\$132bobo\$132b2o22\$77bo\$78b2o\$77b2o9bo\$86b2o\$87b2o\$84bo\$82bobo\$83b2o4\$114b2o\$112b3o\$111bo4bo\$112b2ob2o\$113bobo\$13bo24bo13b2o24bo13b2o19bobo\$10bo2bobo22bo13b2o24bo13b2o20bo\$8bobo2b2o23bo39bo\$9b2o5\$bo103bo\$b2o101bo\$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.

Goldtiger997

Posts: 515
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

Goldtiger997 wrote:16.641 in 11 gliders:

`x = 135, y = 84, rule = B3/S23132bo\$132bobo\$132b2o22\$77bo\$78b2o\$77b2o9bo\$86b2o\$87b2o\$84bo\$82bobo\$83b2o4\$114b2o\$112b3o\$111bo4bo\$112b2ob2o\$113bobo\$13bo24bo13b2o24bo13b2o19bobo\$10bo2bobo22bo13b2o24bo13b2o20bo\$8bobo2b2o23bo39bo\$9b2o5\$bo103bo\$b2o101bo\$obo93bo7b3o\$95bo\$95b3o3\$94b3o\$94bo\$95bo24\$30bo\$30b2o\$29bobo!`

That is 16.642 . (typo?)

16.686 in 6 gliders:
`x = 17, y = 14, rule = B3/S235b2o2bo\$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).
AbhpzTa

Posts: 467
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### 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:
`x = 192, y = 78, rule = B3/S23128bo\$129bo\$93bo33b3o\$92bo\$92b3o15bo19bo\$110bo19bo\$110bo19bo\$95bobo\$50bo44b2o14bo19bo19bo19bo19bo\$8bo39bobo18b2o18b2o5bo12b3o17b3o17b3o17b3o17b3o\$9bo39b2ob3o13bo2bo16bo2bo16bo19bo19bo13bo5bo19bo\$7b3o42bo16bobo17bobo5b3o9bo19bo19bo10bobo6bo19bo\$53bo16bo19bo6bo10b2o18b2o18b2o11b2o5b2o18b2o\$11bo12b2obo16b2obo16b2obo16b2obo10bo5b2obo16b2obo16b2obo16b2obo19bo\$5b2o2b2o13bob2o16bob2o16bob2o16bob2o16bob2o16bob2o16bob2o16bob2o19bo\$5bobo2b2o173b2o\$5bo154b2o23bo\$b2o158b2o23bo\$obo157bo24b2o\$2bo163b3o\$166bo\$167bo\$162b3o\$164bo\$163bo\$165b3o\$165bo\$166bo31\$171bo19bo\$169b3o17b3o\$162bo5bo19bo\$160bobo6bo19bo\$161b2o5b2o18b2o\$164b2obo19bo\$164bob2o19bo\$185b2o\$160b2o23bo\$161b2o24bo\$160bo25b2o\$167b3o\$167bo\$168bo\$163b3o\$165bo\$164bo\$166b3o\$166bo\$167bo!`
-Matthias Merzenich
Sokwe
Moderator

Posts: 1458
Joined: July 9th, 2009, 2:44 pm

### 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:

`+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:

`x = 137, y = 242, rule = B3/S2338bobo\$38b2o\$39bo2\$134bo\$133bobo\$25bo106bo2bo\$23bobo105bo3b2o\$24b2o9bobo93b2o\$35b2o\$36bo2\$27b2o6b2o\$28b2o5bobo\$27bo7bo76\$12bo\$13b2o\$12b2o12\$34bo99bo\$33bobo97bobo\$32bo2bo96bo2bo\$31bo3b2o94bo3b2o\$31b2o98b2o\$129b2o\$128bobo\$12b3o114bo\$14bo\$13bo2\$3o\$2bo6b2o\$bo8b2o\$9bo10\$45b3o\$45bo\$8b2o36bo\$7bobo\$9bo72\$34bo99bo\$33bobo97bobo\$32bo2bo96bo2bo\$31bo3b2o94bo3b2o\$31b2o98b2o\$29b2o98b2o\$28bobo99bo\$29bo98bo\$128b2o10\$11b3o\$13bo\$12bo2\$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...

`x = 40, y = 29, rule = B3/S2317b3o5\$22b2o\$22b2o\$13bo18b3o\$13bo\$13bo16bo5bo\$o29bo5bo\$o29bo5bo\$o\$32b3o6\$24b2o\$22bo2bo\$22bo2bo2\$23b2o13b2o\$23b2o13b2o\$23bo5b2o\$24bo4b2o\$31b2o\$31b2o!`

Latest list:

`16.712     xs16_3pc0qmzw23          4816.217     xs16_3146pajo            3916.1094    xs16_cila8oz641          3816.313     xs16_3pm44og4c           3516.349     xs16_35s26z39c           3516.890     xs16_696ki6zw641         3516.778     xs16_69la8oz321          3416.1721    xs16_64kb2acz032         3416.218     xs16_3pajc48c            3316.682     xs16_69j0j9czx11         3316.147     xs16_32qjap3             3216.842     xs16_cila8oz065          3216.1904    xs16_8u164koz32          3216.929     xs16_3iaj2ak8zw1         3116.185     xs16_32qk5b8o            3016.220     xs16_3123qajo            2916.278     xs16_32qj43146           2916.312     xs16_62s53zbd            2916.354     xs16_35s26zbd            2916.889     xs16_696ki6zx65          2916.1323    xs16_031e8gzc9311        2916.151     xs16_64kr2pm             2816.628     xs16_kc32qkz0113         2816.731     xs16_3iajkcz23           2816.786     xs16_3pa3ia4zw11         2816.2347    xs16_g8861acz0db         2816.2541    xs16_g8861aczc93         2816.1979    xs16_4ap30ga6zw121       2716.2174    xs16_08u164koz32         2716.3227    xs16_31e8gzy012ego       2716.1077    xs16_69m88cz6221         2616.1691    xs16_4a9l6o8zx121        2616.1703    xs16_4a9la8ozx121        2616.623     xs16_o5r8jdz01           2516.828     xs16_4alhe8z0641         2516.834     xs16_8u15a4z1226         2516.930     xs16_3iaj21e8zw1         2516.1106    xs16_0iu0dbz641          2516.1139    xs16_kq23z124871         2516.1398    xs16_g88c93zc952         2516.1880    xs16_259q453z032         2516.1901    xs16_08obap3z32          2516.706     xs16_39s0qmz023          2416.713     xs16_o8bap3z23           2416.1034    xs16_3lkaa4z065          2416.1064    xs16_39m88cz6221         2416.2295    xs16_0g8go8brz23         2416.300     xs16_9fg4czbd            2316.353     xs16_321fgc453           2316.621     xs16_g5r8jdz11           2316.827     xs16_ciaj2ak8zw1         2316.829     xs16_0md1e8z1226         2316.1702    xs16_4a5p68ozx121        2316.1740    xs16_69acga6zx32         2316.1846    xs16_25a8c93zw33         2316.2313    xs16_08u16853z32         2316.3066    xs16_4a9jzx12ego         2316.825     xs16_4alhe8zw65          2216.159     xs16_2egmd1e8            2116.774     xs16_69raa4z32           2116.1084    xs16_31ke12kozw11        2116.1682    xs16_8k9bkk8zw23         2116.1693    xs16_8k8aliczw23         2116.1753    xs16_695q4gozw23         2116.1954    xs16_8kk31e8z065         2116.2096    xs16_wck5b8oz311         2116.2309    xs16_8kk31e8z641         2116.228     xs16_178bp2sg            2016.723     xs16_i5p64koz11          2016.833     xs16_0mp2sgz1243         2016.872     xs16_2lla8oz065          2016.1073    xs16_3lkaa4z641          2016.1127    xs16_giligoz104a4        2016.1739    xs16_g88r2qkz121         2016.1791    xs16_03lkaa4z3201        2016.1962    xs16_4a9eg8ozw65         2016.2058    xs16_69akg4czx146        2016.2555    xs16_4a9jzxpia4          2016.18      xs16_caarzbd             1916.131     xs16_660uhar             1916.230     xs16_178jd2ko            1916.358     xs16_321fgc2ko           1916.745     xs16_39qb8oz32           1916.801     xs16_08eharz321          1916.1684    xs16_4aab9k8zx32         1916.1694    xs16_4a5p6o8zx121        1916.1881    xs16_259q453zw32         1916.1912    xs16_at16426z32          1916.2050    xs16_6ik8a52z065         1916.2162    xs16_0at16426z32         1916.2200    xs16_06agc93z2521        1916.2307    xs16_6ik8a52z641         1916.2316    xs16_0at16413z32         1916.19      xs16_caarz39c            1816.155     xs16_3pabp46             1816.600     xs16_6421344og84c        1816.665     xs16_699mkiczx1          1816.697     xs16_db079ozx32          1816.848     xs16_ca9b8oz0252         1816.914     xs16_8kkja952zx1         1816.926     xs16_3iajc4gozw1         1816.1105    xs16_gie0dbz146          1816.1107    xs16_02egdbz2521         1816.1130    xs16_oe12koz01ac         1816.1558    xs16_3loz1226io          1816.1711    xs16_c8idik8z023         1816.1757    xs16_g8idik8z123         1816.1790    xs16_178cia4z0321        1816.1911    xs16_69q3213z32          1816.1990    xs16_8e1tazx1252         1816.1995    xs16_cik8a52z065         1816.2018    xs16_25a8c826zw33        1816.2025    xs16_069q48cz2521        1816.2201    xs16_0ggml96z641         1816.2447    xs16_0g8it248cz23        1816.2480    xs16_3iaczw1139c         1816.3014    xs16_wok21e8zdb          1816.15      xs16_178c1f84c           1716.227     xs16_5b8r5426            1716.265     xs16_259m861ac           1716.380     xs16_4a40vh248c          1716.558     xs16_1784c842ak8         1716.616     xs16_i5pajoz11           1716.640     xs16_c9bkkozw32          1716.668     xs16_gbq1daz121          1716.716     xs16_3pmk46zx23          1716.748     xs16_39ege2z321          1716.799     xs16_c8al56z311          1716.803     xs16_c9bk46z311          1716.843     xs16_4a9liczx56          1716.875     xs16_4a5pa4z2521         1716.1097    xs16_ck0ol3z643          1716.1276    xs16_3iakgozw1ac         1716.1373    xs16_32q4goz4a43         1716.1685    xs16_c48n98czx23         1716.1715    xs16_64p784czw23         1716.1722    xs16_4aq32acz032         1716.1758    xs16_4a4o796zw121        1716.1847    xs16_39c8a52z033         1716.1867    xs16_069q453z311         1716.1871    xs16_5bo8ge2z32          1716.1882    xs16_259m453zx23         1716.1905    xs16_8u16853z32          1716.1991    xs16_8e1qbzx1252         1716.2014    xs16_25a8kk8z0253        1716.2045    xs16_25ao8ge2z032        1716.2132    xs16_0g8it2sgz23         1716.2356    xs16_25icggozx1ac        1716.2467    xs16_0kc3213z34a4        1716.2763    xs16_ol3zw343123         1716.2861    xs16_ol3zw343146         1716.3163    xs16_wo443123zbd         1716.3164    xs16_wo443146zbd         1716.104     xs16_0j5ozj4pz11         1616.115     xs16_0ol3z0mdz32         1616.243     xs16_2egu16426           1616.302     xs16_5b8o642ac           1616.350     xs16_312461tic           1616.360     xs16_2egu16413           1616.593     xs16_3123c48gka4         1616.657     xs16_695q4ozw321         1616.724     xs16_j5o64koz11          1616.762     xs16_jhke1e8z1           1616.771     xs16_69qb8oz32           1616.772     xs16_3h4e1daz011         1616.810     xs16_ca9la4z311          1616.822     xs16_8ehikozw56          1616.836     xs16_4aajkczx56          1616.838     xs16_ci9b8ozw56          1616.840     xs16_c8idiczw56          1616.856     xs16_kc32acz1252         1616.953     xs16_0cil56z6221         1616.995     xs16_0raik8z643          1616.996     xs16_2lm853z056          1616.1068    xs16_3lo0kcz6421         1616.1080    xs16_3lo0kcz3421         1616.1085    xs16_3h4e12koz011        1616.1304    xs16_0okih3zc8421        1616.1391    xs16_ca168ozc8421        1616.1464    xs16_08o696z6ip          1616.1581    xs16_8o6413zrm           1616.1583    xs16_4a9jzxha6zx11       1616.1675    xs16_xj96z0mdz32         1616.1710    xs16_4a9bk46zx32         1616.1717    xs16_4aajk46zx121        1616.1720    xs16_4a4o79ozx121        1616.1766    xs16_kc321e8z123         1616.1787    xs16_069m4koz311         1616.1796    xs16_0bt06ioz32          1616.1856    xs16_39u06a4z32          1616.1857    xs16_39u0652z32          1616.1864    xs16_31ke1e8z032         1616.1929    xs16_0g5r8b5z121         1616.1959    xs16_4ai31e8zx56         1616.1994    xs16_0g9fgka4z121        1616.2028    xs16_25ao48cz2521        1616.2029    xs16_25ao4a4z2521        1616.2030    xs16_0i5q8a52z121        1616.2060    xs16_69akg4czx56         1616.2124    xs16_0g8jd2koz23         1616.2129    xs16_0g8jt246z23         1616.2190    xs16_032q4goz6413        1616.2204    xs16_0gilla4z641         1616.2214    xs16_0mq0c93z641         1616.2219    xs16_0oe12koz643         1616.2302    xs16_4ap6413z65          1616.2305    xs16_6413ia4z6421        1616.2317    xs16_cik8a52z641         1616.2322    xs16_raak8zx1252         1616.2323    xs16_ra248goz056         1616.2445    xs16_ciligzx254c         1616.2542    xs16_g88c871zc93         1616.2546    xs16_j9cz122c84c         1616.2547    xs16_j9cz122c826         1616.2549    xs16_g4c3213zdb          1616.2630    xs16_31e8gzxo9a6         1616.2694    xs16_4ai3gzx11mq         1616.2781    xs16_wj9c826z6221        1616.2805    xs16_0gs2c871z641        1616.3032    xs16_1784ozx342sg        1616.3167    xs16_xok21e8zc93         16`
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

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

16.313 in 10 gliders:

`x = 137, y = 118, rule = B3/S23o\$b2o\$2o28\$79bobo\$80b2o\$70bo9bo\$71bo\$69b3o12bobo\$84b2o\$85bo3\$67bobo\$68b2o\$68bo\$64b3o\$66bo12bo\$65bo11b2o\$78b2o5\$74bo\$75bo\$73b3o2b2o\$77bobo\$79bo61\$135bo\$134b2o\$134bobo!`

Goldtiger997

Posts: 515
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: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:
`x = 11, y = 17, rule = B3/S237b2o\$7bo\$8bo\$5b4o\$5bo\$7b2o\$3bo2b2o2bo\$bobo5b2o\$2b2o2b3o\$5bo2bo\$4bobo\$b2o2bo\$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:
`x = 81, y = 27, rule = B3/S2360bo\$61bo\$59b3o\$65bo\$65bobo\$54bo10b2o\$b2o10bo41b2o\$obobo7bo41b2o\$2bobobo5b3o64bo\$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]

Posts: 1871
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

Well, this pushes 16.712 down to 30 gliders:
`x = 224, y = 40, rule = B3/S23159bo\$160bo\$158b3o3\$41bo135bo\$39bobo135bobo\$40b2o129bo5b2o\$144bo27bo\$142b2o26b3o\$137bobo3b2o\$72bobo42bobo18b2o\$23bo48b2o44b2o3bo14bo5bo\$23b2o4bo43bo44bo2b2o20b2o\$22bobo5bo91b2o19bobo\$28b3o64bo87b2o37b2o\$57b2ob2o25b2ob2ob2o14b2ob2o2bo16b2ob2o2b2o34b2ob2o3bo33b2o3bo\$39b2o6bo10bobo13b2o12bobo3b2o14bobo2bobo16bobo2bobo4b2o29bobo2bo35bo2bo\$bo25b3o8bo2bo4b2o10bo2bo12bobo11bo2bo18bo2bob2o17bo2bob2o4b2o22bo7bo2bob2o12bo22bob2o\$2bo26bo9bobo4bobo10bobo12bo14bobo19bobo21bobo9bo22bo7bobo15bobo19b2o2bo\$3o25bo11bob2o16bob2o26bob2obo16bob2obo18bob2obo26b3o8bob2obo11b2o22bo\$4b2o35bo2bo16bo2bo7bo18bo2b2o17bo2b2o19bo2b2o38bo2b2o35b2o\$3b2o5bo31bobo17bobo6b2o19bo21bo23bo42bo12b2o\$5bo2b2o33bo19bo7bobo19b3o19b3o21b3o40b3o8b2o\$9b2o84bo21bo23bo42bo10bo4\$204b3o\$170b2o32bo\$171b2o32bo\$66b2o102bo\$62b2o2bobo\$61bobo2bo117b2o\$63bo119b2o\$185bo2\$67b2o\$68b2o\$67bo!`

A nice related component:
`x = 18, y = 18, rule = B3/S237b2o\$2ob2o3bo\$bobo2bo\$bo2bob2o\$2bobo11bo\$3bob2obo6bo\$4bo2b2o6b3o\$5bo6b2o\$6b3o2b2o\$8bo4bo6\$14b3o\$14bo\$15bo!`
I Like My Heisenburps! (and others)

Extrementhusiast

Posts: 1753
Joined: June 16th, 2009, 11:24 pm
Location: USA

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

Goldtiger997 wrote:16.313 in 10 gliders:

`x = 137, y = 118, rule = B3/S23o\$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:
`x = 38, y = 14, rule = B3/S239bo\$7bobo\$8b2o\$13bo4bo\$11b2o5bobo\$12b2o4b2o\$2b2o2b2o8bo11b2o2b2obo\$2bo3bo2bo5b2o11bo3bob2o\$3b3o2b2o5bobo11b3o\$bobo23bobo\$b2o8b3o13b2o\$11bo\$12bo!`

Bob Shemyakin
BobShemyakin

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

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

16.657 in 8 gliders:

`x = 54, y = 77, rule = B3/S2352bo\$51bo\$51b3o22\$30bo\$28b2o\$29b2o3\$43bo\$42bo\$42b3o\$38bobo\$39b2o\$39bo6bo\$24bo20b2o\$24b2o19bobo\$23bobo15bo\$41b2o\$40bobo35\$b2o\$obo\$2bo!`

EDIT:

16.3167 in 13 gliders:

`x = 135, y = 27, rule = B3/S2396bobo\$96b2o\$97bo2\$101bo\$100bo\$100b3o3\$8bo43bo39bo40b2o\$6bobo42bobo37bobo37bo2bo\$7b2o42b2o38b2o38b2o\$10b3o8bo27b2o38b2o12bo25b2o\$12bo8bobo24bobo37bobo10b2o25bobo\$11bo9b2o24bo39bo14b2o23bo\$46bo39bo39bo\$47b3o37b3o14b2o21b3o\$bo11b3o33bo39bo14bobo7b2o13bo\$b2o10bo90bo9bobo\$obo6b2o3bo4b3o92bo\$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:

`x = 38, y = 10, rule = B3/S236b2o17b2o\$7bo18bo9b2o\$5bo9bob2o6bo9bobo\$5b2o8b2obo6b2o8b2o\$3b2o8b2o8b2o8b2o\$2bobo7bobo7bobo7bobo\$bo9bo9bo9bo\$o9bo9bo9bo\$b3o7b3o7b3o7b3o\$3bo9bo9bo9bo!`

Goldtiger997

Posts: 515
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### 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:

`x = 158, y = 405, rule = B3/S23138bo\$138bo\$46bo91bo\$44b2o\$45b2o2\$41bo100b2o\$40b2o100b2o\$40bobo5\$45b2o\$45bobo\$45bo73\$17bo\$18b2o\$17b2o\$4bo\$5b2o\$4b2o2\$69bo\$67b2o\$68b2o3\$38bo99bo\$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\$38b2o98b2o\$38bo3b2o94bo3b2o\$40bo2bo96bo2bo\$39b2obo96b2obo\$39bo2b2o95bo2b2o\$41bo99bo\$40b2o98b2o4\$42b2o\$17b2o23b2o\$17b2o\$24b2o\$24b2o4\$24b2o\$24b2o8\$33b2o\$32bo2bo\$32bo2bo\$15b2o16b2o\$15b2o5\$27b2o\$26bo2bo\$27b2o4\$11b2o\$10bobo\$12bo6\$6b2o\$5bobo\$7bo4\$3o\$2bo\$bo!`

`x = 13, y = 21, rule = B3/S2310bo\$bo8bobo\$2bo7b2o\$3o5\$2bo\$3bo5b2obo\$b3o5bob2o4\$obo\$b2o\$bo2\$2b2o\$bobo\$3bo!`

Here is the latest list of 16G and above syntheses:

`16.217     xs16_3146pajo            3816.1094    xs16_cila8oz641          3716.313     xs16_3pm44og4c           3416.349     xs16_35s26z39c           3416.778     xs16_69la8oz321          3416.890     xs16_696ki6zw641         3416.1721    xs16_64kb2acz032         3416.218     xs16_3pajc48c            3316.682     xs16_69j0j9czx11         3316.147     xs16_32qjap3             3216.842     xs16_cila8oz065          3216.929     xs16_3iaj2ak8zw1         3116.1904    xs16_8u164koz32          3116.185     xs16_32qk5b8o            3016.220     xs16_3123qajo            2916.312     xs16_62s53zbd            2916.354     xs16_35s26zbd            2916.889     xs16_696ki6zx65          2916.1323    xs16_031e8gzc9311        2916.151     xs16_64kr2pm             2816.278     xs16_32qj43146           2816.628     xs16_kc32qkz0113         2816.731     xs16_3iajkcz23           2816.786     xs16_3pa3ia4zw11         2816.2347    xs16_g8861acz0db         2816.2541    xs16_g8861aczc93         2816.1979    xs16_4ap30ga6zw121       2716.3227    xs16_31e8gzy012ego       2716.1077    xs16_69m88cz6221         2616.1691    xs16_4a9l6o8zx121        2616.1703    xs16_4a9la8ozx121        2616.2174    xs16_08u164koz32         2616.623     xs16_o5r8jdz01           2516.828     xs16_4alhe8z0641         2516.834     xs16_8u15a4z1226         2516.930     xs16_3iaj21e8zw1         2516.1106    xs16_0iu0dbz641          2516.1139    xs16_kq23z124871         2516.1398    xs16_g88c93zc952         2516.1901    xs16_08obap3z32          2516.706     xs16_39s0qmz023          2416.713     xs16_o8bap3z23           2416.1034    xs16_3lkaa4z065          2416.1064    xs16_39m88cz6221         2416.1880    xs16_259q453z032         2416.2295    xs16_0g8go8brz23         2416.300     xs16_9fg4czbd            2316.353     xs16_321fgc453           2316.621     xs16_g5r8jdz11           2316.827     xs16_ciaj2ak8zw1         2316.829     xs16_0md1e8z1226         2316.1702    xs16_4a5p68ozx121        2316.1740    xs16_69acga6zx32         2316.3066    xs16_4a9jzx12ego         2316.825     xs16_4alhe8zw65          2216.1846    xs16_25a8c93zw33         2216.2313    xs16_08u16853z32         2216.159     xs16_2egmd1e8            2116.774     xs16_69raa4z32           2116.1084    xs16_31ke12kozw11        2116.1682    xs16_8k9bkk8zw23         2116.1693    xs16_8k8aliczw23         2116.1753    xs16_695q4gozw23         2116.1954    xs16_8kk31e8z065         2116.2096    xs16_wck5b8oz311         2116.2309    xs16_8kk31e8z641         2116.228     xs16_178bp2sg            2016.712     xs16_3pc0qmzw23          2016.723     xs16_i5p64koz11          2016.833     xs16_0mp2sgz1243         2016.872     xs16_2lla8oz065          2016.1073    xs16_3lkaa4z641          2016.1127    xs16_giligoz104a4        2016.1739    xs16_g88r2qkz121         2016.1791    xs16_03lkaa4z3201        2016.1962    xs16_4a9eg8ozw65         2016.2058    xs16_69akg4czx146        2016.2555    xs16_4a9jzxpia4          2016.18      xs16_caarzbd             1916.131     xs16_660uhar             1916.230     xs16_178jd2ko            1916.358     xs16_321fgc2ko           1916.745     xs16_39qb8oz32           1916.801     xs16_08eharz321          1916.1684    xs16_4aab9k8zx32         1916.1694    xs16_4a5p6o8zx121        1916.1881    xs16_259q453zw32         1916.1912    xs16_at16426z32          1916.2050    xs16_6ik8a52z065         1916.2162    xs16_0at16426z32         1916.2200    xs16_06agc93z2521        1916.2307    xs16_6ik8a52z641         1916.2316    xs16_0at16413z32         1916.19      xs16_caarz39c            1816.155     xs16_3pabp46             1816.600     xs16_6421344og84c        1816.665     xs16_699mkiczx1          1816.848     xs16_ca9b8oz0252         1816.914     xs16_8kkja952zx1         1816.926     xs16_3iajc4gozw1         1816.1107    xs16_02egdbz2521         1816.1130    xs16_oe12koz01ac         1816.1558    xs16_3loz1226io          1816.1711    xs16_c8idik8z023         1816.1757    xs16_g8idik8z123         1816.1790    xs16_178cia4z0321        1816.1911    xs16_69q3213z32          1816.1990    xs16_8e1tazx1252         1816.1995    xs16_cik8a52z065         1816.2025    xs16_069q48cz2521        1816.2201    xs16_0ggml96z641         1816.2447    xs16_0g8it248cz23        1816.2480    xs16_3iaczw1139c         1816.15      xs16_178c1f84c           1716.227     xs16_5b8r5426            1716.265     xs16_259m861ac           1716.380     xs16_4a40vh248c          1716.558     xs16_1784c842ak8         1716.616     xs16_i5pajoz11           1716.640     xs16_c9bkkozw32          1716.668     xs16_gbq1daz121          1716.697     xs16_db079ozx32          1716.716     xs16_3pmk46zx23          1716.748     xs16_39ege2z321          1716.799     xs16_c8al56z311          1716.803     xs16_c9bk46z311          1716.843     xs16_4a9liczx56          1716.875     xs16_4a5pa4z2521         1716.1097    xs16_ck0ol3z643          1716.1105    xs16_gie0dbz146          1716.1276    xs16_3iakgozw1ac         1716.1373    xs16_32q4goz4a43         1716.1685    xs16_c48n98czx23         1716.1715    xs16_64p784czw23         1716.1722    xs16_4aq32acz032         1716.1758    xs16_4a4o796zw121        1716.1847    xs16_39c8a52z033         1716.1867    xs16_069q453z311         1716.1871    xs16_5bo8ge2z32          1716.1882    xs16_259m453zx23         1716.1905    xs16_8u16853z32          1716.1991    xs16_8e1qbzx1252         1716.2014    xs16_25a8kk8z0253        1716.2018    xs16_25a8c826zw33        1716.2045    xs16_25ao8ge2z032        1716.2132    xs16_0g8it2sgz23         1716.2356    xs16_25icggozx1ac        1716.2467    xs16_0kc3213z34a4        1716.2763    xs16_ol3zw343123         1716.2861    xs16_ol3zw343146         1716.3163    xs16_wo443123zbd         1716.3164    xs16_wo443146zbd         1716.104     xs16_0j5ozj4pz11         1616.115     xs16_0ol3z0mdz32         1616.243     xs16_2egu16426           1616.302     xs16_5b8o642ac           1616.350     xs16_312461tic           1616.360     xs16_2egu16413           1616.593     xs16_3123c48gka4         1616.724     xs16_j5o64koz11          1616.762     xs16_jhke1e8z1           1616.771     xs16_69qb8oz32           1616.772     xs16_3h4e1daz011         1616.810     xs16_ca9la4z311          1616.822     xs16_8ehikozw56          1616.836     xs16_4aajkczx56          1616.838     xs16_ci9b8ozw56          1616.840     xs16_c8idiczw56          1616.856     xs16_kc32acz1252         1616.953     xs16_0cil56z6221         1616.995     xs16_0raik8z643          1616.996     xs16_2lm853z056          1616.1068    xs16_3lo0kcz6421         1616.1080    xs16_3lo0kcz3421         1616.1085    xs16_3h4e12koz011        1616.1304    xs16_0okih3zc8421        1616.1391    xs16_ca168ozc8421        1616.1581    xs16_8o6413zrm           1616.1583    xs16_4a9jzxha6zx11       1616.1675    xs16_xj96z0mdz32         1616.1710    xs16_4a9bk46zx32         1616.1717    xs16_4aajk46zx121        1616.1720    xs16_4a4o79ozx121        1616.1766    xs16_kc321e8z123         1616.1787    xs16_069m4koz311         1616.1796    xs16_0bt06ioz32          1616.1856    xs16_39u06a4z32          1616.1857    xs16_39u0652z32          1616.1864    xs16_31ke1e8z032         1616.1929    xs16_0g5r8b5z121         1616.1959    xs16_4ai31e8zx56         1616.1994    xs16_0g9fgka4z121        1616.2028    xs16_25ao48cz2521        1616.2029    xs16_25ao4a4z2521        1616.2030    xs16_0i5q8a52z121        1616.2060    xs16_69akg4czx56         1616.2124    xs16_0g8jd2koz23         1616.2129    xs16_0g8jt246z23         1616.2190    xs16_032q4goz6413        1616.2204    xs16_0gilla4z641         1616.2214    xs16_0mq0c93z641         1616.2219    xs16_0oe12koz643         1616.2305    xs16_6413ia4z6421        1616.2317    xs16_cik8a52z641         1616.2322    xs16_raak8zx1252         1616.2323    xs16_ra248goz056         1616.2445    xs16_ciligzx254c         1616.2549    xs16_g4c3213zdb          1616.2630    xs16_31e8gzxo9a6         1616.2781    xs16_wj9c826z6221        1616.3032    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:

`x = 14, y = 10, rule = B3/S2312bo\$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?
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

### 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:

`x = 64, y = 41, rule = B3/S2317b2o\$17b2o9\$8b2o\$8b2o2\$59b3o2\$16bo40bo5bo\$15b3o39bo5bo\$15bob2o38bo5bo\$55bo\$8bo45bobo2b3o\$7bobo43b2obo\$7bobo45bo\$8bo\$52b2o3b2o\$51b3o3b2o\$50bobo5bo\$50b2o5b2obo\$2b2o47b2o4b5o\$2ob2o47bo2b3o3bo\$o4bo49b2o\$o3b3o\$b2o4bo\$5bobo\$5b2o2\$10b2o\$10b2o3\$11b2o\$11b2o!`

Goldtiger997

Posts: 515
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

The first reduces to this component reaction:
`x = 11, y = 8, rule = B3/S232obobo2b2o\$5obo2b2o\$2b2obo2\$2bo4b2o\$2b2o3bo\$b3o5bo\$b2o5b2o!`
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

Posts: 1871
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

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

`x = 38, y = 71, rule = B3/S2320bobo2\$19bo3bo\$14bo\$4bob2o14bo11bob2o\$4b2obo4bobobo3bo13b2obo\$2b2o28b2o\$o2bob2o7bo5bo9bo2bob2o\$2o2bo2bo22b2o2bobo\$5b2o\$20bo20\$20bobo2\$19bo3bo\$5b2o7bo\$4bo2bo14bo11bob2o\$4b3o5bobobo3bo13b2obo\$2b2o28b2o\$o2bob2o7bo5bo9bo2bob2o\$2o2bobo23b2o2bobo2\$20bo20\$20bobo2\$19bo3bo\$6b2o6bo\$4bo2bo14bo11bob2o\$4b3o5bobobo3bo13b2obo\$2b2o28b2o\$o2bob2o7bo5bo9bo2bob2o\$2o2bobo23b2o2bobo2\$20bo!`

EDIT:

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

`x = 12, y = 11, rule = LifeHistory10.A\$9.A\$9.3A2\$6.2A\$4.A2.A\$4.3A\$2.2A4.D\$A2.A.2A.D\$2A2.A.A\$8.D!`

Goldtiger997

Posts: 515
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

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

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

`x = 38, y = 71, rule = B3/S2320bobo2\$19bo3bo\$14bo\$4bob2o14bo11bob2o\$4b2obo4bobobo3bo13b2obo\$2b2o28b2o\$o2bob2o7bo5bo9bo2bob2o\$2o2bo2bo22b2o2bobo\$5b2o\$20bo20\$20bobo2\$19bo3bo\$5b2o7bo\$4bo2bo14bo11bob2o\$4b3o5bobobo3bo13b2obo\$2b2o28b2o\$o2bob2o7bo5bo9bo2bob2o\$2o2bobo23b2o2bobo2\$20bo20\$20bobo2\$19bo3bo\$6b2o6bo\$4bo2bo14bo11bob2o\$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.

`x = 136, y = 329, rule = B3/S2313bo4bo13bobo\$7bo6b2o3b2o11b2o\$8b2o3b2o3b2o13bo\$7b2o3\$124bobo\$120b2obob2o\$120bob2o\$124b3o\$31bobo90bo2bo\$31b2o92b2o\$32bo2\$10b2o\$11b2o5b3o\$10bo9bo\$19bo4\$28b3o\$28bo\$21b2o6bo\$22b2o\$21bo60\$17bo39bo\$15bobo38bo\$16b2o38b3o18\$133b3o\$24bobo97bobo\$20b2obob2o93b2obob2o\$20bob2o96bob2o\$24b3o97b3o\$24bo2bo96bo2bo\$25b2o98b2o70\$8bobo\$9b2o\$9bo2\$12bo41bo\$13bo39bo\$11b3o39b3o7\$2bo\$obo\$b2o56bo\$57b2o\$51bo6b2o\$4bo40bobo2bo\$5bo39b2o3b3o\$3b3o40bo3\$34bo\$34bo\$24bobo7bo89bobo\$20b2obob2o93b2obob2o\$20bob2o96bob2o\$24b3o97b2obo\$24bo2bo96bob2o\$25b2o15\$47b2o\$46b2o\$48bo5\$8bo\$8b2o\$7bobo53\$31bobo\$bo29b2o\$2b2o28bo\$b2o5\$2bo\$3b2o\$2b2o3\$2bo\$3bo\$b3o3\$24bobo93b2o2bobo\$20b2obob2o93bo2bob2o\$20bob2o98b2o\$24b2obo96b2obo\$24bob2o96bob2o16\$3bo\$3b2o\$2bobo!`

These are the SLs with synthesis above 30G in my list:

`16.778     xs16_69la8oz321          3416.890     xs16_696ki6zw641         3416.1721    xs16_64kb2acz032         3416.682     xs16_69j0j9czx11         3316.147     xs16_32qjap3             3216.929     xs16_3iaj2ak8zw1         3116.1904    xs16_8u164koz32          31`
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

### 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:

`x = 171, y = 51, rule = B3/S23obo\$b2o\$bo16\$3bo119bo\$bobo120b2o\$2b2o3bo115b2o\$5b2o\$6b2o9bo\$16bo110bo17bo\$16b3o106bobo17bobo\$11b3o112b2o17b2o\$11bo7b3o\$o11bo6bo\$b2o17bo\$2o75bo\$78b2obobo23bo29bo\$77b2o2b2o24bo8bo20bo\$33b2o2bobo23b2o2bobo12bo10b2o2bobo7bo9bo5b2o2bobo7bo25b2o2bobo\$33bo2bob2o23bo2bob2o23bo2bob2o15b3o5bo2bob2o33bo2bob2o\$35b2o28b2o28b2o28b2o22bobo13b2o\$37b3o27b3o27b3o27b3o19b2o16b2obo\$14bo22bo2bo26bo2bo26bo2bo26bo2bo7bo3bo7bo16bob2o\$13b2o23b2o28b2o28b2o19bo8b2o6b2o4bobo\$13bobo101bobo17b2o3b2o\$118b2o\$139bo\$138b2o\$138bobo6\$122b2o\$123b2o\$122bo!`

16.778 in 10 gliders:

`x = 44, y = 58, rule = B3/S2315bo\$16b2o\$15b2o22\$35bobo\$36b2o\$36bo2\$42b2o\$32bo8b2o\$22b2o7b2o10bo\$23b2o6bobo\$22bo4\$37bobo\$37b2o\$38bo\$31b2o\$30bobo6b2o\$32bo5bobo\$40bo2\$3o\$2bo\$bo9\$6b2o\$7b2o\$6bo!`

16.890 in 11 gliders:

`x = 46, y = 22, rule = B3/S2343bobo\$43b2o\$o43bo\$b2o\$2o26bo\$25bo2bobo7bobo\$23bobo2b2o8b2o\$24b2o13bo\$6bo\$4bobo\$5b2o19b3o\$28bo\$7b2o18bo\$8b2o\$7bo4\$28bo\$12b2o13b2o4b2o\$11bobo13bobo3bobo\$13bo19bo!`

EDIT:

16.1721 in 14 gliders:

`x = 48, y = 35, rule = B3/S2345bo\$45bobo\$45b2o\$15bo\$16b2o\$15b2o\$23bo18bobo\$2bo21b2o16b2o\$obo20b2o2bo15bo\$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:

`x = 35, y = 39, rule = B3/S2319bo\$18bo\$18b3o12\$13bobo\$14b2o8bo\$bo12bo8bo\$2bo20b3o\$3o\$14bo\$12bobo\$4b2o7b2ob3o\$5b2o9bo\$4bo12bo5\$10b2o\$10bobo\$10bo6\$33b2o\$32b2o\$34bo!`

EDIT3:

16.147 in 13 gliders:

`x = 41, y = 46, rule = B3/S2339bo\$38bo\$38b3o10\$10bo\$8bobo\$9b2o\$5b3o12bo\$7bo13b2o\$6bo13b2o8bobo\$30b2o\$9b2o20bo\$9bobo\$9bo11bo\$5b2o14bobo\$6b2o13b2o\$5bo4\$9b2o\$10b2o\$9bo8b3o13b2o\$18bo15bobo\$19bo14bo6\$2o\$b2o\$o3\$31b2o\$30b2o\$32bo!`

EDIT4:

16.929 in 9 gliders:

`x = 29, y = 33, rule = B3/S23bo\$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:

`x = 114, y = 38, rule = B3/S2361bo\$62bo\$60b3o4\$73bobo\$74b2o\$74bo\$81bobo\$81b2o\$8bo73bo\$6bobo100b2o\$7b2o100bobo\$10bo100bo\$10bobo36b2o15bo13bo8b2o20b2o\$10b2o36bo2bo12b2o13b2o7bo2bo21bo\$49b2o14b2o12bobo7b2o16bob4o\$107b2obo\$77b2o\$76bobo\$78bo\$64bo\$64b2o\$bobo59bobo\$b2o38bo39bo\$2bo37bobo37bobo\$40b2o38b2o\$3o\$2bo\$bo51b2o\$52bobo\$54bo3\$97bo\$96b2o\$96bobo!`

Now all 16-bit still-lifes cost less than 30 gliders!

Goldtiger997

Posts: 515
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:

`x = 108, y = 45, rule = B3/S238bo\$6bobo\$7b2o14\$9bo5bo\$10bo4bobo\$8b3o4b2o2\$9bo60bo\$9b2o59bobo\$2bo5bobo14bo44b2o\$obo20b2o19bob2o13bo4bo7bob2o26bob2o\$b2o21b2o18b2obo11bobo5b2o5b2obo26b2obo\$60b2o4b2o\$42b5o16bo8b5o23bob5o\$40bo2bo2bo16b2o5bo2bo2bo23b2obo2bo\$40b2o20bobo5b2o2\$66b3o\$68bo\$9bo57bo\$9b2o\$8bobo8\$b3o\$3bo\$2bo!`

Goldtiger997

Posts: 515
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)

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.

`x = 129, y = 226, rule = B3/S2310bo\$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\$21bobobo95bob2o\$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:

`x = 126, y = 138, rule = B3/S2332bo\$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\$bobo\$2b2o24bo\$28bobo\$28b2o2\$obo\$b2o\$bo4\$5bobo\$6b2o\$6bo5\$18bo2bo99bo\$18b6o95b5o\$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:

`x = 89, y = 24, rule = LifeHistory43.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:

`16.151     xs16_64kr2pm             2816.278     xs16_32qj43146           2816.349     xs16_35s26z39c           2816.628     xs16_kc32qkz0113         2816.731     xs16_3iajkcz23           2816.786     xs16_3pa3ia4zw11         2816.1979    xs16_4ap30ga6zw121       2716.3227    xs16_31e8gzy012ego       2716.1077    xs16_69m88cz6221         2616.1691    xs16_4a9l6o8zx121        2616.1703    xs16_4a9la8ozx121        2616.623     xs16_o5r8jdz01           2516.828     xs16_4alhe8z0641         2516.834     xs16_8u15a4z1226         2516.930     xs16_3iaj21e8zw1         2516.1139    xs16_kq23z124871         2516.1398    xs16_g88c93zc952         2516.706     xs16_39s0qmz023          2416.713     xs16_o8bap3z23           2416.1034    xs16_3lkaa4z065          2416.1064    xs16_39m88cz6221         2416.1323    xs16_031e8gzc9311        2416.1880    xs16_259q453z032         2416.2295    xs16_0g8go8brz23         2416.300     xs16_9fg4czbd            2316.353     xs16_321fgc453           2316.354     xs16_35s26zbd            2316.621     xs16_g5r8jdz11           2316.829     xs16_0md1e8z1226         2316.1702    xs16_4a5p68ozx121        2316.1740    xs16_69acga6zx32         2316.3066    xs16_4a9jzx12ego         2316.825     xs16_4alhe8zw65          2216.1846    xs16_25a8c93zw33         2216.2313    xs16_08u16853z32         2216.159     xs16_2egmd1e8            2116.218     xs16_3pajc48c            2116.774     xs16_69raa4z32           2116.1084    xs16_31ke12kozw11        2116.1682    xs16_8k9bkk8zw23         2116.1693    xs16_8k8aliczw23         2116.1753    xs16_695q4gozw23         2116.1954    xs16_8kk31e8z065         2116.2096    xs16_wck5b8oz311         2116.2309    xs16_8kk31e8z641         2116.217     xs16_3146pajo            2016.228     xs16_178bp2sg            2016.712     xs16_3pc0qmzw23          2016.723     xs16_i5p64koz11          2016.833     xs16_0mp2sgz1243         2016.872     xs16_2lla8oz065          2016.1073    xs16_3lkaa4z641          2016.1127    xs16_giligoz104a4        2016.1739    xs16_g88r2qkz121         2016.1791    xs16_03lkaa4z3201        2016.1962    xs16_4a9eg8ozw65         2016.2058    xs16_69akg4czx146        2016.2555    xs16_4a9jzxpia4          20`

(*) in reality it was brute force...
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

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

This should drop 16.151 to about 18G:
`x = 95, y = 72, rule = B3/S2393bo\$92bo\$92b3o18\$36bo\$34bobo\$35b2o\$54bo\$54bobo\$54b2o3\$26bo\$25bobo\$25bobo\$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]

Posts: 1871
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

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

`x = 95, y = 72, rule = B3/S2393bo\$92bo\$92b3o18\$36bo\$34bobo\$35b2o\$54bo\$54bobo\$54b2o3\$26bo\$25bobo\$25bobo\$26bo2\$30b2o\$29bo2bo\$30b2o2\$26bo8b3o\$25bobo9bo25b3o\$25bobo8bo\$26bo\$48bo\$46b3o\$46bobo9bo\$46bo10b2o\$57bobo2\$54bo\$54b2o\$53bobo20\$2o\$b2o\$o!`

16.151 in 15 gliders:

`x = 112, y = 97, rule = B3/S23110bo\$109bo\$109b3o18\$37bo\$35bobo\$36b2o\$71bo\$71bobo\$71b2o8\$21bo\$22b2o\$21b2o3\$34bo\$35b2o\$34b2o2\$33bo\$33b2o\$32bobo15bo16bo\$48bobo16bobo\$49b2o16b2o2\$66bo\$48bo18bo\$49b2o14b3o\$48b2o2\$36b3o\$38bo\$37bo2\$73bo\$72b2o\$72bobo3\$49bo\$49b2o\$48bobo21\$b2o\$2b2o\$bo7\$2o\$b2o\$o!`

EDIT:

16.278 in 12 gliders:

`x = 79, y = 99, rule = B3/S2377bo\$76bo\$76b3o5\$55bo\$54bo\$54b3o20\$27bo\$25b2o\$26b2o2\$36bobo\$16b2o7b2o9b2o\$17b2o5b2o11bo\$16bo9bo3\$22bo\$23b2o\$22b2o2\$21bo\$20b2o\$20bobo5\$34bo\$33bo\$33b3o2\$34bo\$33b2o\$33bobo3b3o\$39bo\$40bo38\$2o\$b2o\$o!`

Got stuck on 16.349...

Goldtiger997

Posts: 515
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)

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.

`x = 23, y = 27, rule = B3/S234bo\$2bobo5bobo\$3b2o5b2o\$11bo2\$2bo14bo\$obo6bo6b3o\$b2o4bobo6bo\$8b2o\$4b2o\$3bobo12bo\$5bo12bobo\$18b2o7\$21b2o\$15b2o3b2o\$14b2o6bo\$16bo2\$9b2o\$10b2o\$9bo!`
chris_c

Posts: 892
Joined: June 28th, 2014, 7:15 am

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

16.628:
`x = 51, y = 30, rule = B3/S2321bo28bo\$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]