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

Goldtiger997 wrote:If a catalyst (most likely found with Bellman) could restore the beehive, this would result in a "one-fifth snark". I've tried using Bellman to find one, but with no success, mostly to do with my lack of experience with the search program. Would anyone else more experienced like to have a go?...

Edit: Or alternatively, a "one-third snark":

Sometimes it's just a matter of knowing where to look, isn't it?

x = 49, y = 38, rule = B3/S238b2o2bo$7bob4o$7bo$5b2ob7o$3bo2bobo6bo$3b2o3bob2o2b2o$7b2ob2o4$8bo$7bobo9b2o$7bobo9bo$8bo8bobo$17b2o$9b2o$9bobo$9bo4$7b2o$8bo$5b3o26bo$5bo26bo2bo$32b5o10b2o$32b3ob2o9b2o$12bo3bo3b3o10b2obo$2o9bo5bo2bo13b2o$2o9bo9bo$11b2o3bo17b2o$13b3o17b2obo$32b3ob2o9b2o$13b3o16b5o10b2o$11b2o3bo15bo2bo$2o9bo22bo$2o9bo5bo$12bo3bo! If you're curious, here's the input file. I was looking for a 1/5. #S max-active 9#S repair-interval 30#S stable-interval 4#S max-live 500#S first-encounter 70#S last-encounter 92#P 0 0....????????????????....????????????????....????????????????....????????????????....????????????????....????????????????....????????????????....????????????????....????????????????....????????????????....????????????????....????????????????....????????????????....????????????????....????????????????....????????????????.............@@........@..@.......@@.........@@........@.................@.@.........@.......@@........@@........@.@...............@@.............@.@.......@@....@........@......@@@........@@@.....@..........@.................@....................@@....................@.@....................@.........................@@........................@.@........................@ Tanner Jacobi Kazyan Posts: 777 Joined: February 6th, 2014, 11:02 pm ### Re: Thread For Your Bellman Finds Kazyan wrote:Sometimes it's just a matter of knowing where to look, isn't it? Very nice! The repeat time is 43, the exact same as the snark... I bet this will reduce a lot of the gun collection. Good work Kazyan! gmc_nxtman Posts: 1146 Joined: May 26th, 2015, 7:20 pm ### Re: Thread For Your Bellman Finds gmc_nxtman wrote:Very nice! The repeat time is 43, the exact same as the snark... I bet this will reduce a lot of the gun collection. Good work Kazyan! I hope so, though signal circuitry is already pretty good--I don't expect a particularly huge wave of improvements. Here's probably the best-case scenario for the...I'm gonna call this a "tremi-snark" for now unless someone has a better idea, because "one-third snark" will be ambiguous in the future whenever someone wants to build something involving three reflectors. Anyway, its best-case scenario is this reduction of the p135 gun from 67*58 (3886) to 49*45 (2205), taking advantage of that gaping unoccupied corner of the p45 gun. x = 49, y = 45, rule = LifeHistory39.A2.2A$39.4A.A$44.A$37.7A.2A$36.A2.B3.A.A2.A$18.A2.A2.A11.2A2.2A.AB2.2A$18.7A14.B2AB2A$40.5B$18.7A16.3B$18.A2.A2.A15.2A3B$19.2B.2B15.B2AB2A$20.3B8.2A6.2ABA4B$19.5B8.A5.9B$18.6B.B6.A.AB3.7B$10.B4.10B2A3B3.2AB.10B$9.4B.5BA4B2ABA3B4.13B$9.2BA2B.2B2AB5AB3AB5.13BA$9.B3A6BA3BA3BA2B5.11BABA$9.ABABA10BABA2B8.8B2.2A$8.B2A17B.B7.A5B5.B$2A.2A4.B2ABA8B.8B5.B2A6B$.A.A.B.4B2A9B.8B4.BABA4.2A$.A.A.6BA3B2.11BA2B3.4B5.A$2A.2A.5BA8B.7BA3B.4B7.3A$.A.A.6BA6B.8BABA6B10.A$.A.A.B.3BABA8B.6BA6B$2A.2A3.3BA7B.8BA5B5.2B$9.2BA11B2.3BA4B4.6B$9.8B.9B2A5B.BA6BAB$9.8B.8BAB2A5B2A6B2A2B$10.B.17B2A3B3A6B3A2B$11.2BABA10BABABA2.2B2A6B2A2B$10.2BA3BA3BA6B3AB4.BA6BAB$10.B3AB5AB2A2B.2BA2B6.6B$9.3BAB2A4BA5B.4B8.2B$10.3B2A10B4.B$14.B.6B$16.5B$17.3B$16.2B.2B$15.A2.A2.A$15.7A2$15.7A$15.A2.A2.A!
Tanner Jacobi

Kazyan

Posts: 777
Joined: February 6th, 2014, 11:02 pm

Kazyan wrote:Sometimes it's just a matter of knowing where to look, isn't it?

Nice! This improvement to the period tripled p436 family improves 14 gun periods:

x = 193, y = 54, rule = LifeHistory28.A11.2A102.A11.2A$27.A.A9.B2AB100.A.A9.B2AB$19.A3.2A2.A.A9.3B93.A3.2A2.A.A9.3B$10.2A6.A.A2.A2.2A.2A9.B.B83.2A6.A.A2.A2.2A.2A9.B.B$9.B2A2B4.A.A3.A.A2.B8.2A3B82.B2A2B4.A.A3.A.A2.B8.5B$10.4B5.A.4A2.AB2A6.3BA2B83.4B5.A.4A2.AB2A6.6B24.A2.2A$8.6B7.A3.A.A.2A4.BAB3A2B81.6B7.A3.A.A.2A4.8B24.4A.A$8.5B7.A2.BA.A2.6B2A5B82.5B7.A2.BA.A2.13B30.A$7.6B6.A.2BA.A5.4BA4BA3B79.6B6.A.2BA.A5.13B21.7A.2A$6.7B6.2A.2BA5.5BAB2A2BA3B77.7B6.2A.2BA5.15B19.A2.B3.A.A2.A$7.6B10.3B4.5BA5BA3B78.6B10.3B4.15B19.2A2.2A.AB2.2A$7.7B10.2B.B.6BAB5A4B77.7B10.2B.B.17B21.B2AB2A$7.6B4.20BA3BAB2AB77.6B4.16B4A9B22.5B$7.7B2.22B3A2B3AB76.7B2.16BA3BA10B22.3B$7.7B2.23B2A2B2A3B75.7B2.16BA4BA10B20.5B$6.9B.27B3.B2A73.9B.17B3A7B3.B2A18.6B$6.36B4.A2.A72.36B4.A2.A9.2A6.8B$.B4.20B2.2B2.B3.6B5.2A.A66.B4.20B2.2B2.B3.6B5.2A.A9.A5.2B2A5B$2AB.19B14.6B7.A65.2AB.19B14.6B7.A9.A.AB3.B2A4B$2A19B14.9B6.2A64.2A19B14.9B6.2A9.2AB.10B$.B.17B15.2A4.4B72.B.17B15.2A4.4B18.13B$4.17B15.A5.4B74.17B15.A5.4B17.14B$4.17B12.3A7.4B73.17B12.3A7.4B16.14B$4.15B.B2A10.A10.4B72.15B.B2A10.A10.4B17.8B2.2B$4.12B4.BA.A21.4B23.2A46.12B4.BA.A21.4B16.6B5.B$3.11B9.A22.4B22.A46.11B9.A22.4B14.9B$2.13B8.2A22.4B18.BA.A45.13B8.2A22.4B12.4B4.2A$3.12B13.A19.4B14.2A.B2A47.12B13.A19.4B10.4B5.A$4.10B14.3A12.B.3B.4B12.B2A2B50.10B14.3A12.B.3B.4B8.4B7.3A$4.9B18.A10.18B6.4B50.9B18.A10.22B10.A$4.9B5.A11.2A3.B5.2B2A16B3.6B50.9B5.A11.2A3.B5.2B2A18B7.A$4.9B3.3A11.8B3.2B2A16B2.6B51.9B3.3A11.8B3.2B2A18B6.A.A$7.5B3.A16.8B.20B.7B9.2A43.5B3.A16.8B.24B4.A.A$8.4B3.2A15.38B6.2B2AB43.4B3.2A15.35B.2A.2A$2A6.9B14.15B.2B2.20B5.4B3.B32.2A6.9B14.15B.2B2.13B2A2B$.A7.6B14.17B8.21B.6B2A2B31.A7.6B14.17B8.10BABAB$.A.2A5.6B3.B2.2B2.19B11.26B2A2B31.A.2A5.6B3.B2.2B2.19B11.7B.2BAB$2.A2.A4.35B12.30B31.A2.A4.35B11.7B2.A3.A$3.2AB3.27B.7B12.31B32.2AB3.27B.7B12.7B3.4A$4.14B2A25B11.30B34.14B2A25B9.2AB.B.3B$5.13B2A26B8.2AB.3B2.22B36.13B2A26B7.A.AB11.2A$6.29B2.8B8.A.AB6.22B37.29B2.8B8.A14.2A$6.17B.B.2B11.6B8.A8.12B3.9B36.17B.B.2B11.6B7.2A$7.15B4.3B10.5B8.2A7.12B5.8BA36.15B4.3B10.5B$7.15B5.A2B.2A7.4B17.9B6.5B3.ABA36.15B5.A2B.2A7.4B$8.13B5.A.A2B.A7.4B15.2AB2.6B6.2A7.2A37.13B5.A.A2B.A7.4B$10.13B2.A.AB2.A9.B.B2A12.A.AB3.B.B9.A8.B39.13B2.A.AB2.A9.B.B2A$9.8B4.2A.A.A3.A12.BA.A11.A7.3B5.3A48.8B4.2A.A.A3.A12.BA.A$9.6B6.2ABA2.4A.A13.A10.2A6.B2AB5.A50.6B6.2ABA2.4A.A13.A$9.5B8.B2.A.A3.A.A12.2A18.2A57.5B8.B2.A.A3.A.A12.2A$9.B.B9.2A.2A2.A2.A.A91.B.B9.2A.2A2.A2.A.A$10.3B9.A.A2.2A3.A93.3B9.A.A2.2A3.A$9.B2AB9.A.A100.B2AB9.A.A$10.2A11.A102.2A11.A! +327 (4158, 'p00436x3_0')+333 (4290, 'p00436x3_1')+339 (4424, 'p00436x3_2')+351 (4698, 'p00436x3_4')+357 (4838, 'p00436x3_5')+375 (5270, 'p00436x3_8')+381 (5418, 'p00436x3_9')+654 (4158, 'p00436x3_0')+666 (4290, 'p00436x3_1')+678 (4424, 'p00436x3_2')+702 (4698, 'p00436x3_4')+714 (4838, 'p00436x3_5')+762 (5418, 'p00436x3_9')+798 (5874, 'p00436x3_12') There will be a few improvements in identical fashion to this, plus now that we no longer need a Herschel to do a period tripling there should be plenty of other possibilities... chris_c Posts: 870 Joined: June 28th, 2014, 7:15 am ### Re: Thread For Your Bellman Finds chris_c wrote:There will be a few improvements in identical fashion to this, plus now that we no longer need a Herschel to do a period tripling there should be plenty of other possibilities... You can say that again. The tremi-Snark even makes small guns like the current period 810 gun look a bit oversized -- the old one was 80x49: #C smaller p810 gun using tremi-Snarksx = 55, y = 48, rule = LifeHistory22.A5B4.B$20.BABA11B$3.B4.3B2AB.B2.B2A3BA10B$.9BABA4B2ABA3BA9B2A$.8B3A4B3A.A3BA7B.B2A$2A6B3A4BA2B2ABABA6B4.B$2AB.5B3A4B2A4BA5B$.B4.4BABA10B$8.3B2AB3.7B$21.4B$22.4B$21.6B$4.2A15.7B$3.B2A2B12.9B$4.4B12.10B13.A$5.4B10.12B10.3A$4.4B10.8B2.4B8.A$4.3AB8.10B3.4B7.2A$3.B3AB8.2A9B3.4B3.5B$3.A3BA7.2B2A.7B4.4B2.3B9.2A$2.A5BA5.2BA3B2A5B5.9B8.A.A$2.BA3BAB4.4B.2B2A.2B.B2A4.8B.B8.A$2.2B3A2B3.4B2.2B6.BA.A4.11B3.B.BA.2A$2.7B2.4B4.2B8.A4.8BA3B.B2A.A.A$2.7B.4B4.B2AB7.2A3.8B2A4B2A.A.A$2.7BA3B6.2A13.5B2A2B2A4B2.A.2A$3.6B2AB20.2AB.2BAB2A2BA3B4A2.A$3.5BABA20.A.AB.3B2ABABAB.BAB2.2A$4.2B.4B13.A6.A5.4B3A6.2A$4.7B13.3A3.2A5.4B.2B7.A$5.6B16.A8.4B9.A$5.5B16.2A7.4B10.2A$4.6B16.5B3.4B$5.5B7.2A9.3B2.4B$4.3BA3B5.A.A8.9B$4.2B3A2B5.A8.B.8B$4.B5AB2.2A.2A.B3.11B$4.ABABABA3.A.A.A2B.A11B$4.2A3B2A3.A.A.2A3BA10B$4.7B2.2A.A2.5B2A8B$5.5B3.A2.4A2BAB2A6B.B2A$5.2BA2B4.2A2.A2B.B2A7B.BA.A$6.ABAB6.2A6.7B5.A$6.ABAB6.A7.2B.4B5.2A$7.A3B7.A9.4B$6.2A2B7.2A10.3BA$5.B2A2B20.3BA$6.2A23.3A!

I'd still like to get the quinti-Snark working, though. It would make a record-setting prime oscillator pattern a whole lot smaller.

-- It wouldn't be a Mersenne prime, though, and primes of the form 5^k-1 are going to be ... um... kind of scarce -- and the same if you mix in semi-Snarks and do 10^k-1 or 10^k+1. But I'm sure something could be found that's 5^k - 2 or some other workable offset.

I might try a speculative catalyst/catfind search over the weekend, just in case a different tool helps turn something up.

Here's a first run at finding likely reductions by period-tripling a gun with a smaller period. The table below doesn't take into account reductions already found this morning -- the numbers were from the current README.

The comparison is between the bounding box of the current period-N/3 gun and the current period-N gun. In general, the bigger the discrepancy between the numbers, the more likely it is that a tremi-Snark will improve things.

Period 132: 1218 < 1849Period 135: 1920 < 3886Period 138: 784 < 1683Period 141: 4248 < 4602Period 180: 1053 < 1320Period 198: 2295 < 3712Period 201: 4968 < 5400Period 216: 1440 < 2960Period 234: 3248 < 3726Period 237: 4160 < 5040Period 243: 3953 < 4760Period 255: 3953 < 5084Period 258: 3843 < 4800Period 261: 3927 < 4730Period 264: 1512 < 2064Period 267: 3127 < 4891Period 270: 1110 < 2162Period 273: 3240 < 5112Period 276: 1320 < 2484Period 279: 3355 < 4425Period 282: 950 < 1976Period 285: 3472 < 4543Period 291: 3591 < 5368Period 294: 3894 < 4779Period 297: 3712 < 5467Period 303: 3835 < 5175Period 309: 3960 < 5580Period 312: 861 < 1848Period 315: 4087 < 4897Period 318: 4410 < 5133Period 321: 4216 < 5766Period 324: 4544 < 4914Period 327: 3510 < 4698Period 333: 3630 < 4840Period 336: 3213 < 4648Period 339: 3752 < 4984Period 342: 3328 < 5060Period 348: 3445 < 4785Period 351: 4002 < 5278Period 354: 3564 < 5225Period 357: 4130 < 5428Period 360: 726 < 1518Period 375: 4526 < 5332Period 378: 4060 < 5644Period 381: 4662 < 5856Period 396: 1849 < 3712Period 399: 5082 < 5200Period 414: 1683 < 3599Period 432: 1155 < 2448Period 435: 4720 < 4830Period 447: 4838 < 6490Period 450: 1575 < 2704Period 462: 4340 < 4355Period 468: 1764 < 3444Period 486: 4661 < 4760Period 489: 5340 < 5609Period 519: 5568 < 7888Period 528: 2024 < 2295Period 534: 3127 < 4189Period 537: 2808 < 5920Period 540: 1320 < 3055Period 543: 5800 < 6580Period 546: 3240 < 5112Period 549: 2915 < 5183Period 552: 1085 < 2430Period 558: 3355 < 4366Period 561: 3024 < 5037Period 564: 1586 < 3192Period 570: 3472 < 4543Period 573: 3135 < 5396Period 582: 3591 < 4543Period 585: 3248 < 4350Period 588: 3894 < 4779Period 594: 3712 < 5396Period 597: 3363 < 5609Period 606: 3835 < 4720Period 609: 3480 < 5530Period 615: 5175 < 5336Period 618: 3960 < 5192Period 621: 3599 < 5986Period 624: 1394 < 2420Period 630: 1375 < 3400Period 633: 3720 < 5460Period 636: 4410 < 5133Period 642: 4216 < 5251Period 645: 3843 < 4662Period 648: 2960 < 4914Period 654: 3510 < 4698Period 657: 3968 < 5795Period 66: 1125 < 2295Period 660: 2610 < 2820Period 666: 3630 < 4840Period 669: 4095 < 6545Period 672: 3213 < 5152Period 678: 3752 < 4984Period 681: 4224 < 4980Period 684: 3328 < 5060Period 69: 2312 < 5390Period 693: 4355 < 5208Period 696: 3445 < 4840Period 702: 3726 < 5278Period 705: 4488 < 5332Period 708: 3564 < 5225Period 711: 5040 < 5063Period 714: 4130 < 5428Period 717: 4623 < 5481Period 72: 1376 < 1440Period 720: 1155 < 1880Period 723: 4050 < 4800Period 726: 4260 < 4757Period 729: 4760 < 5460Period 732: 3364 < 3904Period 738: 1496 < 2992Period 741: 4899 < 5850Period 747: 4316 < 5096Period 753: 5040 < 5655Period 756: 4060 < 5644Period 759: 4452 < 5247Period 762: 4216 < 5856Period 765: 5084 < 6120Period 768: 2401 < 4536Period 771: 4590 < 5400Period 774: 4800 < 5180Period 777: 4130 < 5940Period 783: 4730 < 5555Period 786: 4940 < 5307Period 789: 5041 < 6417Period 792: 2064 < 3944Period 798: 5082 < 5915Period 801: 4891 < 6324Period 804: 4588 < 5112Period 807: 5016 < 5871Period 810: 2162 < 3920Period 813: 5032 < 6762Period 819: 5112 < 6032Period 822: 5175 < 5621Period 825: 4307 < 6624Period 828: 2484 < 4690Period 831: 5310 < 6195Period 834: 4650 < 5760Period 837: 4425 < 5893Period 843: 5460 < 5893Period 846: 1976 < 4608Period 849: 5467 < 6386Period 852: 4320 < 4840Period 855: 4543 < 6527Period 858: 4661 < 5538Period 861: 4543 < 6106Period 864: 2100 < 3740Period 867: 5766 < 6205Period 873: 5368 < 6360Period 879: 5922 < 6776Period 882: 4779 < 4941Period 885: 4602 < 5934Period 891: 5467 < 6364Period 894: 4838 < 6490Period 897: 5106 < 6314Period 900: 1575 < 2754Period 903: 5538 < 6264Period 906: 4897 < 5734Period 909: 5175 < 6396Period 915: 5538 < 6097Period 918: 2550 < 5175Period 921: 5244 < 6478Period 924: 3256 < 4494Period 927: 5580 < 6960Period 933: 5313 < 6560Period 936: 1848 < 3854Period 939: 5642 < 6853Period 942: 5074 < 6205Period 945: 4897 < 6642Period 948: 5605 < 5734Period 951: 5704 < 7140Period 954: 5133 < 5984Period 957: 5530 < 6724Period 963: 5766 < 7138Period 966: 2397 < 3920Period 969: 5680 < 6806Period 972: 4914 < 6004Period 975: 5828 < 6298Period 978: 5340 < 5829Period 981: 4698 < 6888Period 987: 5890 < 7360Period 990: 2352 < 3600Period 999: 4840 < 7381

Looking at the first one in the list, tripling the P44 gun, it doesn't look like the tremi-Snark can improve anything. Even an improbably close weld with the old form of the sparker wouldn't improve anything -- and the weld doesn't quite work anyway:

#C Not a smaller p132 gun, and not quite a gun of any kindx = 49, y = 39, rule = LifeHistory23.2A6.2A$21.2B2AB4.B2A2B$21.4B6.4B10.2A$21.5B4.5B8.A.BA$22.5B2.5B8.B2A$22.5B2.5B9.3A$22.12B10.BAB$7.2A12.14B9.2B2A$6.A.A13.12B11.3B$6.A.A.2A3.2A4.14B3.2A5.2A$7.A.A.A2.B2AB2.16B.B2AB4.2B$9.A5.2B4.14B2.4B4.AB$7.2B2AB4.2B3.14B3.2B4.2B$7.2B3A3.8B2A6B2A8B2.3A2B$6.3B3A4B2A4BA2BA4BA2BA4BABA.2B3AB$6.3B3A7B8A2B8A5B3.2B$7.2B3A2.BA6BA2BA4BA2BA3B2ABAB2.2A$7.2B2AB2.BAB2A4B2A6B2A8B3.2B$9.A4.BABAB2.14B3.3B3.BA$7.A.A.A2.B2AB3.13B5.B3.BAB$4.A.A.A.2A3.3B2.14B.B7.B2AB$4.2A2.A12.14B2A7.3A$8.A.4A8.6B.6B.A8.BAB$7.2A.A3.A6.7B.6BA3.2A5.3A$13.2A6.7B2.3B2.A.A2.A3.2A.B$13.5B.9B5.2A2.2A5.2A$4.2A9.4B.A6B6.A3.A$3.A.A8.5BA6B.B6.A4.A$3.A8.B.5B3A6BA4.2A3.2A$2A.AB.B3.BA9B.3B.BA.A$.A.A.2AB.3A9B.B4.BA$.A.A.2A2B2A10B$2A.A2.5BA9B$A2.4A3BA8B.B2A$.2A2.BAB.BA8B.BA.A$3.2A6.7B5.A$3.A7.2B.3BA5.2A$5.A9.3BA$4.2A10.3AB!

The next one in the list is the p135 reduction that Kazyan has already done.

p138 = 3*46 is clearly hopeless...

p141 = 3*47 -- wow, all kinds of room in an empty corner again...

#C smaller p141 gun, same size as the p47 gunx = 72, y = 59, rule = LifeHistory15.A7.2A22.2A7.A$15.3A4.B2AB6.A13.B2AB4.3A$8.2A8.A4.3B4.3A13.3B4.A8.2A$9.A7.2A3.B.B4.A5.2A10.B.B3.2A7.A$9.A.AB4.10B.B2A3.A2.A2.2A3.10B4.BA.A$10.2AB6.3BA8B4.2A2.A.A3.8B6.B2A$12.3B2.6BA5B8.2A.B3.11B2.3B$5.A6.4B2A2BA2B2A4B.2B5.A2.2B.17B6.A$5.3A5.2B3ABABAB3A5B2A.2A.A.20B5.3A$8.A5.2B2A2BA2B2A6B2A.A2.A.2A17B5.A$7.2AB4.3BA5BA9B.A.2A.2A17B4.B2A$7.6B.4B5A6B.2B2.A5.2B.15B.6B$9.10B3A5B4.B.2A8.B2A17B$6.2B.11BA3B.B4.A.A2.2A4.6B.11B2A2B.2B$2.2A.2A17B6.2A2.A2.A3.2AB4.11B2A4B2A.2A$A2.A.2A17B11.2A5.A5.5B2A3BABA4B2A.A2.A$2A.A.20B14.3A5.5BAB2A11B.A.2A$3.A2.2B.17B13.A6.6BABA8B.2B2.A$3.2A.B3.11B2.4B18.4B2.2BA8B3.B.2A$.2A2.A.A3.8B5.4B16.4B5.8B3.A.A2.2A$A2.A2.2A3.10B4.4B14.4B4.10B3.2A2.A2.A$.2A10.B.B3.2A5.4B12.4B5.2A3.B.B10.2A$12.3B4.A7.4B10.4B7.A4.3B$12.B2AB4.3A5.4B8.4B5.3A4.B2AB$13.2A7.A6.3BA6.4B6.A7.2A$30.3BA4.4B$31.3AB2.4B5.2A$32.8B5.A.A$33.7B5.A$34.9B3A$33.9BAB2.2A$32.11B3A2.A$31.12B2.A.2A$16.A13.13B2.A$16.3A10.A13B3.3A7.2A$19.A8.BABA2.7B2A5.3A4.B2AB$18.2A7.2B2A5.4B2A2B7.A4.3B$18.5B3.4B4.5B2.BA2B5.2A3.B.B10.2A$9.2A9.3B2.4B5.2A6.4B4.10B3.2A2.A2.A$8.A.A8.9B7.A7.4B5.8B3.A.A2.2A$8.A8.B.8B5.3A9.4B2.11B3.B.2A$5.2A.AB.B3.11B6.A5.A6.17B.2B2.A$6.A.A.2AB.15B9.3A5.12BA7B.A.2A$6.A.A.2A3B2A9B15.A5.9B2A6B2A.A2.A$5.2A.A2.4B2A9B14.2AB4.B2A15BA.2A$5.A2.4A12B.B2A12.6B.3A10BAB.BA$6.2A2.BAB.10B.BA.A13.5BA12BAB$8.2A6.7B5.A10.2B.4B2A9B.2B3AB$8.A7.2B.4B5.2A5.2A.2A5B2A10B4.B2A$10.A9.4B9.A2.A.2A5BA11B5.A$9.2A10.4B8.2A.A.8B3A2B2A5B5.3A$22.4B10.A2.2B.5B3ABA7B6.A$23.4B9.2A.B3.6B2A3B2.3B$24.4B6.2A2.A.A3.8B6.B2A$25.4B4.A2.A2.2A3.10B4.BA.A$26.4B4.2A10.B.B3.2A7.A$27.3BA14.3B4.A8.2A$28.3BA13.B2AB4.3A$29.3A14.2A7.A!

p180 = 3*60, not much chance, I can only get 49x35=1715...

p198 = 3*66 sneaks in a small improvement...

#C smaller p198 gunx = 61, y = 60, rule = LifeHistory51.A2.2A$51.4A.A$56.A$49.7A.2A$48.A2.B3.A.A2.A$48.2A2.2A.AB2.2A$51.B2AB2A$52.5B$53.3B$37.B14.2A3B$27.B7.2BAB12.B2AB2A$18.2A6.3B3.5B2A2B2.2A6.2ABA4B$19.A6.3B.7B3AB3.A5.9B$19.A.AB2.2BA6B2A4B4.A.AB3.7B$20.2AB.2B3A5B3A4B4.2AB.10B$22.3BA2BA5B3A4B6.13B$22.4B3A5BA2BA3B6.13BA$22.4B3A5B3A2B.B2A4.11BABA$23.4B2A6BA2B2.BA.A5.8B2.2A$22.B3A7B.3B6.A5.6B5.B$19.B2.2B2A5B3.3B6.2A3.9B$9.B7.2B2A.3BA2B7.B11.6B2.2A$2A6.3B3.4BA2BA4B20.4B2.B2.A$.A6.3B.6B2ABA5B6.BA10.4B3.B3.3A$.A.AB2.B3A5BA2B2AB2.2BAB4.2A.B8.4B10.A$2.2AB.2BABA4BA7B2.2B2A3.B.2A7.3AB$4.3BA3BA3BA3BA3B3.2A2B3.AB7.3BA$4.3BA3BA3BA3BA3B4.5B9.3BA$4.7BA4BABA2B.B2A3.5B7.4B$5.B2A2BA5B3AB2.BA.A3.3B2A5.4B$4.BAB2A6B.3B6.A4.2BABA3.4B$4.BA2BA4B3.3B6.2A3.4BAB.4B$6.2A2B7.B13.9B$7.B23.6B2A$31.B3ABABA$7.B24.2BA3B$6.3AB7.B14.5B$4.BAB3A3B3.3B6.2A4.5B$4.3AB3A4B.3A6.A4.4B$5.2ABAB2A4B3AB2.BA.A3.5B$4.B2ABABA6BA3B.B2A3.4B$4.2BA4BABA4B2A3B4.2A2B$4.3B2A4BABA4BA2B3.ABAB$2.2AB.3BA6BABAB2AB2.3BA$.A.AB2.B3A4B2ABAB2A2.4B$.A6.3A.4B3AB3A4B$2A6.3B3.3B3ABA4B$9.B7.B3A.2B2A2B7.B$19.B2.BA2B2A3B3.3B6.2A$22.BA3BA5B.BAB6.A$23.A4BA4B2AB2A2.BA.A$22.2BAB3ABA8B.B2A$22.2BABA3BA5B2A3B$22.3B2A5BA3BABA2B$20.2AB.8BAB3ABA2B$19.A.AB2.2AB2A4BA4BA$19.A6.BAB.5BA3BAB$18.2A6.3B3.3B2A2BAB$27.B7.2B2A$37.B! p201 = 3*67, no, the geometry is terrible and alternate glider outputs don't work... p216 = 3*72 -- yup, definitely improvable. #C smaller p216 gun using a tremi-Snarkx = 51, y = 43, rule = LifeHistory47.B.AB$41.BABA.5A$16.A10.A12.3ABAB2A.2A$14.3A10.3A10.B.2B.BA.AB$13.A5.A4.A5.A7.BA.AB.2B.B$12.A.6A4.6A.A5.2A.2ABAB3A$12.A.A14.A.A5.5A.ABAB$11.2A2.A2B2A4.2A2BA2.2A4.BA.B$13.AB2A2BA4.A2B2ABA6.2B$13.A.A3B6.3BA.A5.2B4.2A2.B$14.A2B10.2BA5.4B2.B4ABAB$15.B12.B6.B3A3BA.A2B3A$15.B2A8.3B5.6B6.B.B$15.3A2B4.5B5.A5BA4.B2A$14.BA5B2.5B2A3.BA5BAB4.AB$14.2A12B2A2.2B3A3BAB$14.BAB2A5BA5B3.3BABA4B$13.B2A3BA4B2A5B.6BA3B$12.2BA3BA6BA12BA2B$13.2B3A4B3A10BA5B$15.2A5B2A5B.5BA6B$14.21BABA3B$14.19BA3B3A2B$15.4B6.2BA3B.BA5BAB$16.2B8.A3B3.A5BA$11.A13.B3A5.6B$11.3A10.4B6.B3AB3.2A$14.A8.4B3.2A2.8B2AB$13.2A7.4B3.B2A2B2.3B.4B$13.5B3.4B5.2A2B6.3B$4.2A9.3B2.4B7.A2B6.B3A3.B$3.A.A8.9B3.B3.ABAB7.2A.A.B2A$3.A8.B.8B3.3A.A.AB10.2A2B2A$2A.AB.B3.BA9B4.4ABA12.2A3B$.A.A.2AB.3A10B4.3BAB13.4B$.A.A.2A2B2A10B5.4B$2A.A2.5BA9B$A2.4A3BA8B.B2A$.2A2.BAB.BA8B.BA.A$3.2A6.7B5.A$3.A7.2B.3BA5.2A$5.A9.3BA$4.2A10.3AB! (And there goes my lunch hour.) That's a 50% success rate so far, for the periods on this list -- not bad! dvgrn Moderator Posts: 5229 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI ### Re: Thread For Your Bellman Finds With some pushing and pulling on the components, the p198 gets even better: x = 57, y = 52, rule = LifeHistory37.B$27.B7.4B8.A2.2A$18.2A6.BAB3.2BA4BAB6.4A.A$19.A6.BAB.3B2A6B11.A$19.A.AB2.2BA4B3A5B5.7A.2A$20.2AB.B2A4B2ABAB2A3B3.A2.B3.A.A2.A$22.7BA2BA2B2ABA2B3.2A2.2A.AB2.2A$22.2BAB2A2BA2BA7B6.B2AB2A$22.3B2ABAB2A4B2AB.B2A5.5B$23.5B3A4BA2B2.BA.A5.3B$22.6B2A3B.BAB6.A4.2A3B$19.B2.A5BA2B3.BAB6.2A2.B2AB2A$9.B7.4B.B2A3B7.B3.2A6.2ABA4B$2A6.3B3.B2A5B2A2B14.A5.9B$.A6.3A.2BA2BA9B13.A.AB3.7B$.A.AB2.2BA3BA8B2.4B13.2AB.10B$2.2AB.2BA4BA2BAB2A3B2.4B14.13B$4.5BA2BABAB3A4B3.BABA6.BA5.13BA$4.4B3ABABA2BA5B4.B2AB4.2A.B4.11BABA$4.3B2ABA2BA4BA2B.B2A3.A3B3.B.2A6.8B2.2A$5.8BA3BA2B2.BA.A3.4B3.AB7.6B5.B$4.5BA2BA2B.3A6.A3.6B9.9B$4.6B2AB3.3B6.2A3.3BA2B7.6B2.2A$6.4B7.B14.2B2AB5.4B2.B2.A$7.B25.2A3B3.4B3.B3.3A$33.6B.4B10.A$34.5B3AB$12.B21.7BA$11.4B7.B11.6BAB$9.9B3.BAB6.2A3.6B$9.9BAB.A2B6.A4.5B$10.2B2A4BA4BAB2.BA.A3.2A3B$9.2BA2BA11B.B2A3.ABAB$9.2B2AB2A8BA3B4.3BAB$9.3BA8B2AB2A2B3.4B$7.2AB.11BA2BA2B2.4B$6.A.AB2.BA4BA4B2A2B2.4B$6.A6.2BA.BA9B3AB$5.2A6.BAB3.11BA$14.B7.4B.2BA3B7.A$24.B2.9B3.2BA6.2A$27.9B2A.A2B6.A$28.2B2A4B5A2B2.BA.A$27.2BA2BA5B4A2B.B2A$27.2BA2BA7BABA3B$27.3BABA7BA2BA2B$25.2AB.2B4A5BA2BA2B$24.A.AB2.2B5A4B2A2B$24.A6.2BA.2A9B$23.2A6.A2B3.9B$32.A7.4B$42.B!

Tanner Jacobi

Kazyan

Posts: 777
Joined: February 6th, 2014, 11:02 pm

While this thread is up here, this catalyst is rather general. It's a glider eater, but that's the last of what it can do, judging from two quick tests.

x = 13, y = 12, rule = B3/S233bo5bo$2bobo3bobo$bo2bo3bo2bo$ob2ob2obo3bo$o4bobob3o$b3o3bobo$3bobobobo$4b2ob2o2$6bo$5b2o$5bobo!
Tanner Jacobi

Kazyan

Posts: 777
Joined: February 6th, 2014, 11:02 pm

Kazyan wrote:While this thread is up here, this catalyst is rather general. It's a glider eater, but that's the last of what it can do, judging from two quick tests.

x = 13, y = 12, rule = B3/S233bo5bo$2bobo3bobo$bo2bo3bo2bo$ob2ob2obo3bo$o4bobob3o$b3o3bobo$3bobobobo$4b2ob2o2$6bo$5b2o$5bobo!

I posted this a while back as a result of a dr search. It's been used in at least one conduit so far, but I don't have time to search for it.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

A for awesome

Posts: 1695
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

At the cost of 5 more ticks of repeat time, this catalyst increments the tremi-snark multiplier by one. It also works for the original snark, which turns it into a color-preserving version of the semi-snark. It doesn't work for augmenting the color-changing semi into a color-changing tremi, though.

x = 84, y = 102, rule = B3/S2317b2o11b2o11b2o11b2o$16bo2bo9bo2bo9bo2bo9bo2bo$16bobo3b2ob2o3bobo9bobo3b2ob2o3bobo$14b2o2bobo7bobo2b2o5b2o2bobo7bobo2b2o$15bobobo4bo4bobobo7bobobo4bo4bobobo$14bo2b2o2b7o2b2o2bo5bo2b2o2b7o2b2o2bo$14b2o5bobobobo5b2o5b2o5bobobobo5b2o$23bobo23bobo$5bo2b2o9b3o5b3o15b3o5b3o9b2o2bo$4bobo2bo2bo5bobobo3bobobo13bobobo3bobobo5bo2bo2bobo$4bob2obobobo4b2o2b5o2b2o13b2o2b5o2b2o4bobobob2obo$3b2obo2bobo2bo45bo2bobo2bob2o$3bo2bob2o2bo49bo2b2obo2bo$4b3obobo3b3o41b3o3bobob3o$6b2obo5b2o41b2o5bob2o$2bobo2bobo3bo2bo4bobobo32bo2bo3bobo2bobo$2b2o2b2obob2o2b3o4b3o25b3o4b3o2b2obob2o2b2o$8b2obo3b2o6bo26b3o5b2o3bob2o$2b5o4bo39bo11bo4b5o$bo4bob3o17b2o15b2o17b3obo4bo$bob2obobo6b2o7bo3bobo13bobo11b2o6bobob2obo$2obo2bo6b4o8bo4bo13bo4bo8b4o6bo2bob2o$bobobobo5b2o2bo5b3o4b2o11b2o3bo8bo2b2o5bobobobo$bobob2obo2bo36b3o12bo2bob2obobo$2ob2o2b2o3b4o37b3o3b4o3b2o2b2ob2o$3bo2b3o2bo2b2o4bo15b2o21b2o2bo2b3o2bo$3bobob2o5bo4bobo8bo5b2o16bo5bo5b2obobo$2b2obo2b2obo2bo3bo3bo8bo11bo16bo2bob2o2bob2o$4bo3b2o2bo2bo3bobo7b3o10bo16bo2bo2b2o3bo$4bobo7bo5bo21b3o15bo7bobo$3b2ob2o10b3o33b3o10b2ob2o$16b7o29b7o$9b2o2bo2b2obob2o2bo2b2o6bo8b2o2bo2b2obob2o2bo2b2o$9bo4b4o3b4o4bo7bo7bo4b4o3b4o4bo$10b4o11b4o6b3o8b4o11b4o$14b2o7b2o25b2o7b2o$10b5obo2bo2bob5o3b2o12b5obo2bo2bob5o$9bo6b7o6bo2b2o11bo6b7o6bo$10b3obo9bob3o17b3obo9bob3o$12b2obob2ob2obob2o21b2obob2ob2obob2o$14b2obo3bob2o25b2obo3bob2o$14bo2bo3bo2bo25bo2bo3bo2bo$15b2o5b2o27b2o5b2o2$48bo$49bo$47b3o4$68b2o$69bo$67bo5b2o$67b2o5bo$74bob2o$67b2o2b2obo2bo$60bo6b2o3bob2o$61bo10bo$59b3o9b2o$78b2o$78bobo$80bo$80bob2o$77b2obobo$72b2o3b2obobo$72b2o6bob2o$61b2o14b4o2bo$60bobo14bo3b2o$60bo18b2o$59b2o19bo$78bo$78b2o8$41b2o$41bo$36b2o5bo$36bo5b2o$33b2obo$33bo2bob2o2b2o$35b2obo3b2o$38bo$38b2o2$32b2o$32bo$29b2obo$29bo2b3o4b2o$30b2o3bo3b2o$32b4o$32bo15b2o$33b3o12bobo$36bo13bo$31b5o14b2o$31bo$33bo$32b2o! Tanner Jacobi Kazyan Posts: 777 Joined: February 6th, 2014, 11:02 pm ### Re: Thread For Your Bellman Finds Kazyan wrote:At the cost of 5 more ticks of repeat time, this catalyst increments the tremi-snark multiplier by one. It also works for the original snark, which turns it into a color-preserving version of the semi-snark. It doesn't work for augmenting the color-changing semi into a color-changing tremi, though. x = 84, y = 102, rule = B3/S2317b2o11b2o11b2o11b2o$16bo2bo9bo2bo9bo2bo9bo2bo$16bobo3b2ob2o3bobo9bobo3b2ob2o3bobo$14b2o2bobo7bobo2b2o5b2o2bobo7bobo2b2o$15bobobo4bo4bobobo7bobobo4bo4bobobo$14bo2b2o2b7o2b2o2bo5bo2b2o2b7o2b2o2bo$14b2o5bobobobo5b2o5b2o5bobobobo5b2o$23bobo23bobo$5bo2b2o9b3o5b3o15b3o5b3o9b2o2bo$4bobo2bo2bo5bobobo3bobobo13bobobo3bobobo5bo2bo2bobo$4bob2obobobo4b2o2b5o2b2o13b2o2b5o2b2o4bobobob2obo$3b2obo2bobo2bo45bo2bobo2bob2o$3bo2bob2o2bo49bo2b2obo2bo$4b3obobo3b3o41b3o3bobob3o$6b2obo5b2o41b2o5bob2o$2bobo2bobo3bo2bo4bobobo32bo2bo3bobo2bobo$2b2o2b2obob2o2b3o4b3o25b3o4b3o2b2obob2o2b2o$8b2obo3b2o6bo26b3o5b2o3bob2o$2b5o4bo39bo11bo4b5o$bo4bob3o17b2o15b2o17b3obo4bo$bob2obobo6b2o7bo3bobo13bobo11b2o6bobob2obo$2obo2bo6b4o8bo4bo13bo4bo8b4o6bo2bob2o$bobobobo5b2o2bo5b3o4b2o11b2o3bo8bo2b2o5bobobobo$bobob2obo2bo36b3o12bo2bob2obobo$2ob2o2b2o3b4o37b3o3b4o3b2o2b2ob2o$3bo2b3o2bo2b2o4bo15b2o21b2o2bo2b3o2bo$3bobob2o5bo4bobo8bo5b2o16bo5bo5b2obobo$2b2obo2b2obo2bo3bo3bo8bo11bo16bo2bob2o2bob2o$4bo3b2o2bo2bo3bobo7b3o10bo16bo2bo2b2o3bo$4bobo7bo5bo21b3o15bo7bobo$3b2ob2o10b3o33b3o10b2ob2o$16b7o29b7o$9b2o2bo2b2obob2o2bo2b2o6bo8b2o2bo2b2obob2o2bo2b2o$9bo4b4o3b4o4bo7bo7bo4b4o3b4o4bo$10b4o11b4o6b3o8b4o11b4o$14b2o7b2o25b2o7b2o$10b5obo2bo2bob5o3b2o12b5obo2bo2bob5o$9bo6b7o6bo2b2o11bo6b7o6bo$10b3obo9bob3o17b3obo9bob3o$12b2obob2ob2obob2o21b2obob2ob2obob2o$14b2obo3bob2o25b2obo3bob2o$14bo2bo3bo2bo25bo2bo3bo2bo$15b2o5b2o27b2o5b2o2$48bo$49bo$47b3o4$68b2o$69bo$67bo5b2o$67b2o5bo$74bob2o$67b2o2b2obo2bo$60bo6b2o3bob2o$61bo10bo$59b3o9b2o$78b2o$78bobo$80bo$80bob2o$77b2obobo$72b2o3b2obobo$72b2o6bob2o$61b2o14b4o2bo$60bobo14bo3b2o$60bo18b2o$59b2o19bo$78bo$78b2o8$41b2o$41bo$36b2o5bo$36bo5b2o$33b2obo$33bo2bob2o2b2o$35b2obo3b2o$38bo$38b2o2$32b2o$32bo$29b2obo$29bo2b3o4b2o$30b2o3bo3b2o$32b4o$32bo15b2o$33b3o12bobo$36bo13bo$31b5o14b2o$31bo$33bo$32b2o!

So now we have 1x, 2x, 3x and 4x variants of the Snark. If the quinti-Snark from the previous page were to be completed, we would have both 5x and 6x variants as well:

x = 66, y = 71, rule = B3/S23obo$b2o$bo13$15bobo$16b2o$16bo13$30bobo$31b2o$31bo13$45bobo$46b2o$46bo5$65bo$63b3o$62bo$62b2o5$48b2ob2o7bobo$46bo2bob2o8b2o$46b2o13bo2$51bo2bo5b2o$51b4o4bo2bo$48bo11b2o$48b5o$52bo$50bo$50b2o! (Incidentally, whence did you get that p48 gun? The modern way is to filter a p24 gun using Rich's p16.) What do you do with ill crystallographers? Take them to the mono-clinic! calcyman Posts: 1907 Joined: June 1st, 2009, 4:32 pm ### Re: Thread For Your Bellman Finds Could there be a way to engineer any n-snark? I would assume such a thing would work by pulling an object like a block from the end to the beginning through some repetitive contraption, where the block would be regenerated at the end again. Then again, I know nothing about this kind of stuff. Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace! muzik Posts: 3218 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Thread For Your Bellman Finds The quadri-Snark reduces the area of the p576 gun considerably (54x48 --> 48x45): x = 48, y = 45, rule = LifeHistory35.A2.2A$35.4A.A$40.A$33.7A.2A$32.A2.B3.A.A2.A$32.2A2.2A.AB2.2A$27.2A6.B2AB2A$27.A8.5B$29.A7.3B$25.5A6.5B$25.A9.4BAB$27.B4A3.3BABA2B$27.BA2.A2.4BABA2B$27.4B4.4BA2B$23.2A3.15B$23.A2.A.2A14B$5.A19.2A.2A3BA11B$3.3A23.B.BABA11B$2.A5.A23.BA7B2.4B$.A.6A23.7B5.3BA$.A.A18.2AB7.9B4.ABA$2A2.A2B2A8.B2.2B3A6.4B4.2A5.2A$2.2A2BABA7.2A2BA2BABA4.4B5.A7.B$2.A.A3B8.2A2B2A2B2A3.4B7.3A$3.A2B11.3B2A2.B3.4B10.A$4.B12.3B7.4B$4.3B8.3B8.4B7.B6.B2A$4.5B4.5B7.5B6.4B4.B2AB$3.2A5B2.5B2A3.8B6.12B$3.2A12B2A.4BA6B.2B.12B$3.16B.3BABA21B$2.12BA9B3ABA17B$.2A10BAB2A9B3A18B$2.11BABA10BA20B$4.10BA3B2.7B2ABA14B$3.16B4.5B3A4B3A5B$3.16B2.14BAB2A6B$4.4B6.4B.20BA7B$5.2B8.2B2.18B3A7B$20.17BAB3A4B$19.21BABA4B$19.12B.2B.6BA5B$18.12B6.12B$18.B2AB4.4B6.4B4.B2AB$19.2AB6.B8.B6.B2A! The guns particularly worth targeting with this contraption are those with periods divisible by 64. What do you do with ill crystallographers? Take them to the mono-clinic! calcyman Posts: 1907 Joined: June 1st, 2009, 4:32 pm ### Re: Thread For Your Bellman Finds I'm not sure where else to put this, but I have some Bellman questions: 1. At what point do filters start at? What is the origin? The center of the search space, top left, bottom left? 1.5 Can someone elaborate what #P does? 2. What setup could I use to find unusual glider eaters? If you're the person that uploaded to Sakagolue illegally, please PM me. x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

Saka

Posts: 2734
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

muzik wrote:Could there be a way to engineer any n-snark? I would assume such a thing would work by pulling an object like a block from the end to the beginning through some repetitive contraption, where the block would be regenerated at the end again.

There isn't a really simple object that can support an arbitrary number of "pull" operations using just a single glider on a single lane. However, we do have a nice small H->G10 converter, which means we can do a 3fd block pull with just one input signal, or a 6fd pull if you double the input signal first as is done in the current draft HashLife-friendly metacell.

So I guess you might say that the ladder circuit in that metacell is the closest thing we have right now to an engineered (1/n)-Snark. It would have to be rebuilt from the ground up to produce an output for every n inputs -- the output signal would be split and sent to rebuild the block in its starting position, but more importantly an output glider might be created with every pull operation, with a bank of n-1 eaters to stop each output until the count gets high enough.

That's all just speculation -- there's probably some reasonable way to do it, but I think it's safe to say there's no known really compact mechanism, and it won't be able to accept input signals at anywhere near 48-tick repeat time.

For any given multiplier and input stream, there will probably be a custom solution that's smaller than a general (1/n)-Snark. Just to give an idea, here's a custom period septupler from a long time ago:

#C p784 gun made from a p112 with self-intersecting output#C Herschel factory is capped off by a beehive#C Dave Greene 7 May 2003x = 125, y = 72, rule = B3/S2398bo$90b3o$89bo$89bo3bo$89bobbobo8bo$91bobobbo4b3o$92bo3bo3bo$96bo3boo$93b3o$98bo$28booboobo7bo54bobo$bboo23boboboboo7b3o53boobboo$3bo24bo16bo14bo41boo$3bobo38boo12b3o$4boobboo47bo$8boo47boo$40bo80bo$38booboo77b3o$38bo17boo7boo52bob3o$38bo3bo13boo6bobbo50bo3bo$39b3o23boo50bo3bo$116b3obo$117b3o$118bo$114bo$113bobo8bo$bboo36boo71boo$bobo16boo19bo75boo$bo18bobo15b3o76bobo$oo5bobo12bo15bo73boo5bo$7bobbo5boo4boo19boo67boo5boo$6bo3bo5bobo25bo$7bobbo7bo22b3o$7b3o8boo21bo4$oo$bo$o$oo68boo$64bo5boo$oo63bo$obo60b3o25boo$bo90boo$91bo3$20bo21boo8b3o$18b3o22bo7bobbo$17bo25bobo5bo3bo$17boo19boo4boo5bobbo$23bo15bo12bobo5boo$21b3o15bobo18bo$20bo19boo16bobo$20boo36boo4$74boo$74boobboo$20b3o55bobo$4boo13bo3bo55bo$4boo17bo59bo$19booboo52boo4bobo$21bo55bo3bo3bo$3boo47boo20b3o5bo3bo$4bo47boobboo16bo8bo3bo$b3o12boo38bobo25bo3bo$bo14bo16bo24bo26bobo22bo$17b3o7boobobobo23boo26bo24bo$19bo7bobooboo75b3o! Jason Summers responded with a few other high-multiplier mechanisms: Jason Summers wrote:Here are a couple of variations of this that result in multipliers that aren't a multiple of 7. There are probably a lot of other variations of this. These reactions are somewhat sporadic, and I don't know if they are much use in general. #C p1088 (64*17)x = 140, y = 76, rule = B3/S2374bo26bo$74boo18bo$73boobo16bobo$72bobb3o14bo3bo$62bo8bobobo6boo9bo3bo8bo$62b3o5bobobo6bobbo9bo3bo5b3o$65bobb3obbo8boo11bo3bo3bo$64boo3boboo23bobo4boo$70boo25bo$67bo3bo29bo$66bobo31bobo$62boobboo33boobboo$31bo23b4o3boo41boo$29b3o11bo6boo7bo$3boo23bo14b3o4boobboo3bo$4bo23boo16bo7boobbo10bo$4bobo38boo20bobo$5boobboo57boo$9boo25boo3bo$27bo3boo3boo3bo$25boobob3o5bobbo$25bo4b3o4boo10b3o$25bo3bo5bobo11bobbo$26b3o6b4obo7bo4bo$28bo6b3obo11bo11boo$5boo56bobo$5bobobobo37boo14bo$8booboo36bobo13boo$9boboo36bobo$3boo3b5o28boo38bo53b3o$bbobo3b5o8boo19bo37bobo34b3o15b3o$bbo4boobbo9bobo16bo39bobbo3bo29bo17b3o$boo5b3o12bo16boo39boo4bo30bo13b3o$9bo7boo4boo19boo41bo44b3o$17bobbo24bo86b3o$19boo21b3o11bo26b3o$10boo30bo14bo71bo9bo$10boo43b3o70bobo$80boo46boo$81bo50boo$60boo16b3o51bobo$60bobo15bo48boo5bo$62bo64boo5boo$62boo$oo$bo51b3o$bobo48bobbo$bboo48bo4bo$52bo$58bo$53bo$21bo28boo5bo$9bobo7b3o21boo4boobooboo$8bobbo6bo24bobbo3bo4bo$8bobbo6boo19boo4boo4bobbo$7bo3bo10boo16bo10boo8boo$8bobo12bo16bobo18bo$9bo11bo19boo16bobo41boo$21boo36boo42boobboo$107bobo$45boo61bo$45boo$44bobbo57boo4boo$41bobboboo58bo4boobo$22boo16bobbo59b3o9bo$5boo14bobbo16bobo59bo8bo$5boo14b3o89boboo$22boo91boo22bo$137bobo$4boo47boo83boo$5bo47boobboo$bb3o12boo38bobo$bbo14bo16boo23bo$18b3o14bo23boo$20bo11b3o$32bo!

#C p1368 (72*19)x = 114, y = 97, rule = B3/S23oo6boo$bob3ob3o13bo10bo$bobboobobbo10b3o10b3o$3bobboboobbo7bo5bo4bo5bo$4b3ob3obo6bob6o4b6obo$4boo6boo5bobo14bobo$18boo3boboo4boobo3boo$20bo4boo4boo4bo$4bo15bobboo8boobbo$bbo3b4o11boo12boo$bbo3bo5b3o$bbo$5bo4bo$3boo5b3obb3o3b3o11boo$11bobooboo17boo$10boobboo8boo5boo$11boo8b3obbo6bo18bo$20boo8bobo9boo7bobo$21boobo6boo8bobbo5bo3bo$15boo6bo18boo7bo3bo8bo$12boobboo34bo3bo5b3o$10booboobo36bo3bo3bo$10b3obb3o36bobo4boo$17bo37bo$59bo$7boo4b3o42bobo$7boo10boo38boobboo$7boo9bobo42boo$8bo8b3o$7bobo7boo$bb3obobo9bobo$bb4obo11bobobboo$6bo13bobbobo7bo$21b4o6bobo$22boo8boo8$41bo3b3o$40bobo$40bobbo$41boo3$43b3o12$109b3o$109b3o$109b3o$93b3o10b3o$93bo12b3o$94bo11b3o$$103bo102bobo102boo106boo106bobo101boo5bo101boo5boo1379boo79boobboo83bobo84bo$$81boo4boo$82bo4boobo$79b3o9bo$79bo8bo24bo$89boboo18bobo$91boo19boo!

There are very high period guns based on a crystal build-then-collapse multiplier mechanism:

#C p8832 gun based on p4416, doubled using a p46 pulse divider#C Dave Greene, 7/28/2006x = 116, y = 89, rule = B3/S236bo34boobo$5bobo14bo18boboo$5bobo13bobo$4booboo12bobo$22bo8$3bo5bo$bb3o3b3o$booboobooboo$3o7b3o24bo7bo$36bobo5bobo16boo$bbo7bo10boo13bobo5bobo16bobo$20bobo14bo7bo19bo$22bo42boo$40boo$39bobbo$9bo30boo$8b3o$8bobbo$7bobobo42bo$8b3o9boo31bobo$bboo5bo10boo31bobo$bboo50bo$$49boo48bobbo49boo14bo5bo13b3o3b3o42bo12boobbobobboo40bobo12bo3bobo3bo40bobo12boboo3boobo41bo12boo7boo59boo58bobbo59boo43boobo85boo12b3obboobbo72boo11boo13boo6bo72boo27b3o3b4o102bo3bo3b3o86bo5bo20bo71boo13bo5bo9bo3bo3b3o70bobo28b3o3b4o70boo10boo11boo3boo6bo99b3obboobbo86bo5bo11boobo86bo5bo13boo5boo13boo5boo91boo113boo$$106boo$89boo14booboo4boo$89boo15bobbo4boo$106bobbo$107boo$18boo68boo$18boo66b4o17boo$29bo23boo30bobbobo15bobbo$27bobbo22boo29bo21bobbo4boo$17boo8b5o10boo41boo18booboo4boo$17boo8b3oboo9boo42b3o17boo$28boobo43b3o9boo$29boo42bo4bo9bo24boo$73bo5bo33boo$29boo35bobobo7bo$28boobo32b7o5boo$17boo8b3oboo30bo$17boo8b5o32b7o5boo$27bobbo17boo16bobobo7bo$29bo18boo23bo5bo10boo$18boo53bo4bo11boo$18boo55b3o$$56boo56bo57b3o59bo$$46boo$47bo24bo$44b3o26bo$44bo26b3o! It's also possible to have a Herschel send gliders backward into a circuit it has just passed by, or forward in some cases I think, to create boat-bits that block some number of following Herschels. The available multipliers get complicated quickly when you have multiple boat-bits fed by multiple glider outputs -- I seem to recall it's pretty easy to produce Fibonacci numbers, for example. #C period 750*13=9750 gun#C Dean Hickerson, 21 Nov 1996x = 215, y = 249, rule = B3/S2329b2o$29b2o15b2o26b2o$46b2o26b2o2$5b2o$5b2o39b3o$46b3o3$74b3o$44b2o3b2o22bo3bo$28b3o14b5o$27bo3bo14b3o23bo5bo$26bo5bo14bo24b2o3b2o$4b3o20bo3bo$3bo3bo20b3o$2bo5bo19b3o44bo$2bo5bo65bob2o$5bo68bo16b2o$3bo3bo66bo3bo10bo3bo$4b3o41bo26bo2bo4b2o3bo5bo13b2o$5bo24b3o16b2o24b5o3b2o2b2obo3bo13b2o4b3o$25bo3b2ob2o14b2o25b5o8bo5bo10b2o6b5o$23b2o4b2ob2o40b2o3b2o8bo3bo10b3o5bo3bobo$2b3o19b2o3b5o41b5o11b2o12b2o6bo3b2o$2b3o23b2o3b2o21bo11bobo5b3o17bobo9b2o$bo3bo49bobo10b2o7bo18b2o10b2o$9bobo30b2o3b2o20bo27bo$2o3b2o3b2o8b2o22b3o$10bo9b2o21bo3bo$29b2o13bobo9bo$45bo8b2o$55bo$17bo38b2o16b2o8b2o$16bo14b2o24bo17bo8b2o$18bo12b2o11b2o26b3o$15bo2bo25b2o26bo$89b3o$2b2o11b2o43b2o13b2o12bo2b2o$2b2o31bo24b2o12bobo16bo$35b3o36bo16bobo$38bo16bo17b2o$37b2o15bobo2$101b2o9b2o$100b2o9bobo$20b2o73bo6bo7b3o4b2o$20bo34b2o37bobo12b3o4bo2b4o$21b3o14b2o16bo35b2o3bo12b3o4b2ob3o$23bo5bo7bobo13b3o31b2o3b2o3bo13bobo$27bob2o6bobo13bo33b2o3b2o3bo14b2o$28bobo5bo57bobo$39bo55bo$36bo3bo$28bob2o5b4o$27bob2o9bo$28b2o21b2o$52bo$51bo$51b2o43bo49bo$94b3o34b2o11b3o$37b2o31bo22bo26bo10bo11bo26bo$38bo21bo9b3o20b2o25b3o9bo10b2o25b3o$38bobo17b2o13bo49bo7b2o40bo23b2o$39b2o18b2o11b2o48b2o48b2o23bo$195bobo$103bo49bo37b2o2b2o$103b3o47b3o35b2o$106bo49bo$81bo23b2o11b2o35b2o11b2o$79b3o36b2o48b2o$62b2o15bobo$62b2o15bo2$47b2o$46bobo$46bo$45b2o$59b2o32b2o48b2o52b2o$59bo20b2o11b2o35b2o11b2o34b2o16bobo$60bo20bo49bo46bobo18bo13b2o$59b2o17b3o47b3o47bo20b2o12bo$78bo49bo48b2o4b2o26bobo$182bobo26b2o$97b2o48b2o33bo$98bo49bo32b2o7b2o$95b3o20b2o25b3o20b2o20b2o$95bo22bo26bo22bo$119b3o47b3o$121bo49bo$78bo$78b3o11b2o$54bo26bo11bo$52b3o25b2o10bo$26b2o23bo40b2o$27bo23b2o$27bobo$28b2o2b2o37bo49bo$32b2o35b3o47b3o17b2o$68bo49bo20bo$55b2o11b2o35b2o11b2o20bo11bo27bo$55b2o48b2o32b2o9b3o27b3o$149bo33bo$149b2o10b2o19b2o$161bo15bo$159bobo15b3o$159b2o19bo$136b2o41b2o$136b2o$26b2o52b2o$25bobo16b2o34b2o11b2o$10b2o13bo18bobo46bo$11bo12b2o20bo47b3o$11bobo26b2o4b2o48bo79b2o$12b2o26bobo133b2o17b2o$42bo33b2o48b2o67b2o$33b2o7b2o32bo49bo18b2o$33b2o20b2o20b3o25b2o20b3o16bo$56bo22bo26bo22bo13b3o50b2o$53b3o47b3o37bo52bo$53bo49bo79b2o12b3o$146bo20b2o15bo14bo$131b2o11b3o20bobo11b3o$131bo11bo25bo11bo$132bo10b2o24bobo$131b2o37b2o25b2o$197bo$195bobo$103bo49bo37b2o2b2o$84b2o17b3o47b3o35b2o$85bo20bo49bo$44bo27bo11bo20b2o11b2o35b2o11b2o$42b3o27b3o9b2o32b2o48b2o$41bo33bo$41b2o19b2o10b2o$47bo15bo$45b3o15bobo$44bo19b2o$44b2o41b2o$87b2o$143b2o52b2o$130b2o11b2o34b2o16bobo$131bo46bobo18bo13b2o$128b3o47bo20b2o12bo$47b2o79bo48b2o4b2o26bobo$28b2o17b2o133bobo26b2o$28b2o67b2o48b2o33bo$78b2o18bo49bo32b2o7b2o$78bo16b3o20b2o25b3o20b2o20b2o$27b2o50b3o13bo22bo26bo22bo$28bo52bo37b3o47b3o$25b3o12b2o79bo49bo$25bo14bo15b2o20bo$41b3o11bobo20b3o11b2o$43bo11bo25bo11bo$53bobo24b2o10bo$26b2o25b2o37b2o$27bo$27bobo$28b2o2b2o37bo49bo$32b2o35b3o47b3o17b2o$68bo49bo20bo$55b2o11b2o35b2o11b2o20bo11bo27bo$55b2o48b2o32b2o9b3o27b3o$149bo33bo$149b2o10b2o19b2o$161bo15bo$159bobo15b3o$159b2o19bo$136b2o41b2o$136b2o$26b2o52b2o$25bobo16b2o34b2o11b2o$10b2o13bo18bobo46bo$11bo12b2o20bo47b3o$11bobo26b2o4b2o48bo79b2o$12b2o26bobo133b2o17b2o$42bo33b2o48b2o67b2o$33b2o7b2o32bo49bo18b2o$33b2o20b2o20b3o25b2o20b3o16bo$56bo22bo26bo22bo13b3o50b2o$53b3o47b3o37bo52bo$53bo49bo79b2o12b3o$146bo20b2o15bo14bo$131b2o11b3o20bobo11b3o$131bo11bo25bo11bo$132bo10b2o24bobo$131b2o37b2o25b2o$197bo$195bobo$103bo49bo37b2o2b2o$84b2o17b3o47b3o35b2o$85bo20bo49bo$44bo27bo11bo20b2o11b2o35b2o11b2o$42b3o27b3o9b2o32b2o48b2o$41bo33bo$41b2o19b2o10b2o$47bo15bo$45b3o15bobo$44bo19b2o$44b2o41b2o$87b2o$143b2o52b2o$130b2o11b2o34b2o16bobo$131bo46bobo18bo$128b3o47bo20b2o$47b2o79bo48b2o4b2o$28b2o17b2o133bobo$28b2o67b2o48b2o33bo$78b2o18bo49bo32b2o7b2o$78bo16b3o20b2o25b3o20b2o20b2o$27b2o50b3o13bo22bo26bo22bo$28bo52bo37b3o47b3o$25b3o12b2o79bo49bo$25bo14bo16b2o$41b3o14bo$43bo11b3o$55bo4$121bo$119b3o17b2o$118bo20bo$105b2o11b2o20bo11bo27bo$105b2o32b2o9b3o27b3o$149bo33bo$149b2o10b2o19b2o$161bo15bo$85b2o72bobo15b3o$85b2o72b2o19bo$136b2o41b2o$136b2o4$89b2o$89b2o85b2o$176b2o17b2o$126b2o67b2o$126bo18b2o$105b2o20b3o16bo$106bo22bo13b3o50b2o$103b3o37bo52bo$103bo79b2o12b3o$166b2o16bo14bo$166bo14b3o$167b3o11bo$169bo!

The idea is for each boat-bit to be placed so that it kills off the previous Herschel in the chain before it can produce the glider that would otherwise create the previous boat-bit.

It might be interesting to see how much smaller this kind of structure could be made now, with syringes and such -- there may well be an algorithm for chaining boat-bit suppressors that will produce any arbitrarily-chosen multipler. It will be a lot easier to experiment now that we have Snarks (and the various multiplier-Snarks, maybe!) to help get gliders onto the right lanes.

The only other case I remember offhand is a custom count-to-19 mechanism made for the Infinite Conduit.

dvgrn
Moderator

Posts: 5229
Joined: May 17th, 2009, 11:00 pm

I am not trying to win the compactness contest here, but this is a 5-snark (with non-trivial periodicity constraints):

x = 181, y = 145, rule = LifeHistory14$120.2A11.A$119.B2AB9.A.A$120.3B9.A.A2.2A3.A$119.B.B9.2A.2A2.A2.A.A$119.5B8.B2.A.A3.A.A$119.6B6.2ABA2.4A.A$119.8B4.2A.A.A3.A$120.13B2.A.AB2.A15.2A$118.13B5.A.A2B.A14.A$117.15B5.A2B.2A11.BA.A$117.15B4.3B12.2A.B2A$116.17B.B.2B12.B2A2B$116.29B6.4B$115.13B2A16B3.6B$114.14B2A16B2.6B$113.2AB3.27B.7B$112.A2.A4.35B$101.A9.A.2A5.6B3.B2.2B2.20B$100.A.A3.2A3.A7.6B14.17B$99.A2.A3.A3.2A6.9B14.15B$99.A.A.2A.A10.4B4.2A15.15B$98.2A.A.A.A10.4B5.A15.16B3.2A$96.A2.A.2A2B10.4B7.3A12.16B3.A$96.2A2.4B10.4B10.A10.2AB.15BA.A$100.7B6.4B21.A.AB2.12B2.2A$101.8B3.4B22.A4.13B$102.8B.4B3.2A17.2A3.15B$43.2A57.12B4.A22.17B$30.A11.B2AB53.2B.11B2.BA.A21.4B3.11B$30.3A3.2A5.2B6.2A45.2A14B.B2A10.A10.4B4.11B$33.A.B2AB3.B.2B5.A46.2A4BA11B12.3A7.4B7.7B.B2A$32.2A2.2B3.6B.BA.A47.2B.B3A10B15.A5.4B9.6B.BA.A$32.3B.B3.7B.B2A51.BABA3B3A3B15.2A4.4B4.A6.4B5.A$32.17B50.AB.7B2A5B14.9B4.A.A3.5B6.2A$31.18B49.A4B2A13B14.6B5.A2.A2.2A$31.18B49.2AB.3BA15B2.2B2.B3.6B5.2A.2A3.A$31.17B51.B2.A34B4.A2.A2.3A$33.14B55.4BA3B.27B3.B2A2.A$34.12B56.BA2BA2B2.16B2A14B4.A$33.4B2.8B55.2B3A2B2.16B2A13B4.2A$32.4B4.7B55.7B3.29B$31.4B2.11B51.AB.6B11.2B.B.17B$30.4B2.12B50.A.A7B10.3B4.15B$29.4B3.12B51.A8B6.2A.2BA5.15B$28.4B4.11B53.B.6B6.A.2BA.A5.13B$27.4B5.B3D4B.4B54.5B7.A2.BA.A2.13B$26.4B6.2BD4B4.2A53.6B8.A3.A.A.2A4.8B$25.4B7.2B3D2B4.A53.5B.B2A4.A.4A2.AB2A6.6B$24.4B8.6B6.3A49.4B3.BA.A3.2A3.A.A2.B8.5B$23.4B8.7B8.A48.4B7.A6.A.A.2A.2A9.B.B$22.4B8.8B56.4B8.2A2.3A.A3.A.A9.3B$21.4B8.8B38.4B14.4B13.A2.A4.A.A9.B2AB$20.4B8.9B37.4B14.4B15.2A6.A11.2A$19.4B8.4B.6B35.4B14.BD2B$18.4B8.12B34.4B4.2C8.2D2B$17.4B8.12B27.2C5.4B4.B2CB6.2B2D$16.4B8.13B19.2C5.B2C2B2.4B6.2B6.4B$15.4B8.15B19.C6.4B.4B6.2B6.4B$14.4B8.18B17.C.CB.10B5.5B3.5B$13.4B8.20B17.2CB.9B2.B2.7B2.4B$12.4B6.B.22B18.4B3D16B.4B$11.4B5.26B18.4BD4B2D16B$10.4B6.26B18.4B3D2B2D15B$9.4B6.27B18.26B$8.4B7.25B.B2A15.12B.14B$7.4B8.24B2.BA.A14.14B.12B$6.4B7.2AB.21B6.A14.26B$5.4B7.A.AB.8B5.8B6.2A13.15B2C2B3D4B$4.4B8.A5.8B4.3B2.4B19.16B2C4BD4B$3.4B8.2A6.7B5.3B2.4B10.A6.4B.16B3D4B$2.4B14.11B4.B2A3.4B7.3A5.4B2.7B2.B2.9B.B2C$.4B14.11B6.A5.4B5.A7.5B3.5B5.10B.BC.C$4B6.2A7.11B7.3A3.4B4.2A5.4B6.2B6.4B.4B6.C$3B6.A2.A2.2A2.11B9.A4.9B4.4B6.2B6.4B2.2B2CB5.2C$2B8.2A2.A.A2.B3D4B2.B2A13.6B5.4B6.B2CB4.4B5.2C$B11.2A.B3.2BD4B3.BA.A12.8B2.4B8.2C4.4B$12.A2.2B2.2B3D2B6.A10.15B14.4B$9.2A.A.BA2B.6B7.2A9.14B14.4B$9.A.2A.A.A8B18.13B14.4B$13.A.A.8B16.2AB.10B14.4B$10.2A2.A.8B16.A.AB3.B2A4B14.4B$8.3A.2A.9B16.A6.B2A3B14.4B$7.A4.B.4B.6B14.2A6.5B7.A6.4B$8.3AB2A3B.7B22.4B2.B3.3A5.4B$10.A.2A10B22.5B.BAB.A7.4B$11.13B21.4B2ABA.AB.A5.4B$10.10B2A3B19.4BABABABAB2A4.4B$14.6B2A2B5.2A12.2BAB.A.A.A.ABA.2B.4B$14.10B5.A12.3B4A.2A2.A.A.6B$13.11B2.BA.A11.4B4.A4.2A3.4B$13.9BD2B.B2A11.4B3.A.A8.4B$12.9B2D4B20.2A8.5B$11.10BDBD3B29.4B$8.2B.16B28.4B$7.2A18B27.4B$7.2AB.17B25.4B$8.B.4B.8B2.4B23.4B$15.7B4.4B21.4B$16.6B5.4B19.4B$18.4B6.4B6.A10.4B$20.3BA5.4B5.3A7.4B$21.BA.A5.4B7.A5.4B$22.A.A6.4B5.2A4.4B$23.A8.4B4.9B$24.3A6.4B5.7B$26.A7.4B2.9B$35.15B.B$36.15B2A.2A$37.14B2A.A2.A$38.15B3.2A$39.2BA4B4.4B$38.2BABA4B2.A2.AB$38.2BABA3B3.4AB$40.BA4B9.A$40.5B6.5A$41.3B7.A$40.5B8.A$40.2AB2AB6.2A$36.2A2.BA.2A2.2A$36.A2.A.A3.B2.A$38.2A.7A$40.A$40.A.4A$41.2A2.A!

it can be altered to make all 2^a3^b(2^c3^d +1), which covers many, but not all, primes. To get to 11 or 23, you can feed into the input a gliders to get 12-1 or 24-1. These constructions are large though.
Jormungant

Posts: 78
Joined: May 27th, 2016, 1:01 am

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