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Thread For Your Bellman Finds

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

Re: Thread For Your Bellman Finds

Postby Kazyan » September 7th, 2017, 11:18 pm

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/S23
8b2o2bo$7bob4o$7bo$5b2ob7o$3bo2bobo6bo$3b2o3bob2o2b2o$7b2ob2o4$8bo$7bo
bo9b2o$7bobo9bo$8bo8bobo$17b2o$9b2o$9bobo$9bo4$7b2o$8bo$5b3o26bo$5bo
26bo2bo$32b5o10b2o$32b3ob2o9b2o$12bo3bo3b3o10b2obo$2o9bo5bo2bo13b2o$2o
9bo9bo$11b2o3bo17b2o$13b3o17b2obo$32b3ob2o9b2o$13b3o16b5o10b2o$11b2o3b
o15bo2bo$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
.
.
..????????????????..
..????????????????..
..????????????????..
..????????????????..
..????????????????..
..????????????????..
..????????????????..
..????????????????..
..????????????????..
..????????????????..
..????????????????..
..????????????????..
..????????????????..
..????????????????..
..????????????????..
..????????????????..
.
.
.........@@
........@..@.......@@
.........@@........@
.................@.@
.........@.......@@
........@@
........@.@
.
.
.............@@
.............@.@
.......@@....@
........@.
.....@@@........@@@
.....@..........@
.................@
....................@@
....................@.@
....................@
.
........................@@
........................@.@
........................@
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Kazyan
 
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Re: Thread For Your Bellman Finds

Postby gmc_nxtman » September 8th, 2017, 1:07 am

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!
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Re: Thread For Your Bellman Finds

Postby Kazyan » September 8th, 2017, 1:27 am

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 = LifeHistory
39.A2.2A$39.4A.A$44.A$37.7A.2A$36.A2.B3.A.A2.A$18.A2.A2.A11.2A2.2A.AB
2.2A$18.7A14.B2AB2A$40.5B$18.7A16.3B$18.A2.A2.A15.2A3B$19.2B.2B15.B2A
B2A$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.B3A6BA3BA3B
A2B5.11BABA$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.2A
3.3BA7B.8BA5B5.2B$9.2BA11B2.3BA4B4.6B$9.8B.9B2A5B.BA6BAB$9.8B.8BAB2A
5B2A6B2A2B$10.B.17B2A3B3A6B3A2B$11.2BABA10BABABA2.2B2A6B2A2B$10.2BA3B
A3BA6B3AB4.BA6BAB$10.B3AB5AB2A2B.2BA2B6.6B$9.3BAB2A4BA5B.4B8.2B$10.3B
2A10B4.B$14.B.6B$16.5B$17.3B$16.2B.2B$15.A2.A2.A$15.7A2$15.7A$15.A2.A
2.A!
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Re: Thread For Your Bellman Finds

Postby chris_c » September 8th, 2017, 5:06 am

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 = LifeHistory
28.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.B2A
2B4.A.A3.A.A2.B8.2A3B82.B2A2B4.A.A3.A.A2.B8.5B$10.4B5.A.4A2.AB2A6.3BA
2B83.4B5.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.2BA5.5BAB2A2BA3B
77.7B6.2A.2BA5.15B19.A2.B3.A.A2.A$7.6B10.3B4.5BA5BA3B78.6B10.3B4.15B
19.2A2.2A.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.B
4.20B2.2B2.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.17B15.2A4.4B
72.B.17B15.2A4.4B18.13B$4.17B15.A5.4B74.17B15.A5.4B17.14B$4.17B12.3A
7.4B73.17B12.3A7.4B16.14B$4.15B.B2A10.A10.4B72.15B.B2A10.A10.4B17.8B
2.2B$4.12B4.BA.A21.4B23.2A46.12B4.BA.A21.4B16.6B5.B$3.11B9.A22.4B22.A
46.11B9.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.B
2A2B50.10B14.3A12.B.3B.4B8.4B7.3A$4.9B18.A10.18B6.4B50.9B18.A10.22B
10.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.7B
9.2A43.5B3.A16.8B.24B4.A.A$8.4B3.2A15.38B6.2B2AB43.4B3.2A15.35B.2A.2A
$2A6.9B14.15B.2B2.20B5.4B3.B32.2A6.9B14.15B.2B2.13B2A2B$.A7.6B14.17B
8.21B.6B2A2B31.A7.6B14.17B8.10BABAB$.A.2A5.6B3.B2.2B2.19B11.26B2A2B
31.A.2A5.6B3.B2.2B2.19B11.7B.2BAB$2.A2.A4.35B12.30B31.A2.A4.35B11.7B
2.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...
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Re: Thread For Your Bellman Finds

Postby dvgrn » September 8th, 2017, 4:07 pm

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-Snarks
x = 55, y = 48, rule = LifeHistory
22.A5B4.B$20.BABA11B$3.B4.3B2AB.B2.B2A3BA10B$.9BABA4B2ABA3BA9B2A$.8B
3A4B3A.A3BA7B.B2A$2A6B3A4BA2B2ABABA6B4.B$2AB.5B3A4B2A4BA5B$.B4.4BABA
10B$8.3B2AB3.7B$21.4B$22.4B$21.6B$4.2A15.7B$3.B2A2B12.9B$4.4B12.10B
13.A$5.4B10.12B10.3A$4.4B10.8B2.4B8.A$4.3AB8.10B3.4B7.2A$3.B3AB8.2A9B
3.4B3.5B$3.A3BA7.2B2A.7B4.4B2.3B9.2A$2.A5BA5.2BA3B2A5B5.9B8.A.A$2.BA
3BAB4.4B.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$2.7BA3B
6.2A13.5B2A2B2A4B2.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.A2.4A2BAB2A
6B.B2A$5.2BA2B4.2A2.A2B.B2A7B.BA.A$6.ABAB6.2A6.7B5.A$6.ABAB6.A7.2B.4B
5.2A$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 < 1849
Period 135: 1920 < 3886
Period 138: 784 < 1683
Period 141: 4248 < 4602
Period 180: 1053 < 1320
Period 198: 2295 < 3712
Period 201: 4968 < 5400
Period 216: 1440 < 2960
Period 234: 3248 < 3726
Period 237: 4160 < 5040
Period 243: 3953 < 4760
Period 255: 3953 < 5084
Period 258: 3843 < 4800
Period 261: 3927 < 4730
Period 264: 1512 < 2064
Period 267: 3127 < 4891
Period 270: 1110 < 2162
Period 273: 3240 < 5112
Period 276: 1320 < 2484
Period 279: 3355 < 4425
Period 282: 950 < 1976
Period 285: 3472 < 4543
Period 291: 3591 < 5368
Period 294: 3894 < 4779
Period 297: 3712 < 5467
Period 303: 3835 < 5175
Period 309: 3960 < 5580
Period 312: 861 < 1848
Period 315: 4087 < 4897
Period 318: 4410 < 5133
Period 321: 4216 < 5766
Period 324: 4544 < 4914
Period 327: 3510 < 4698
Period 333: 3630 < 4840
Period 336: 3213 < 4648
Period 339: 3752 < 4984
Period 342: 3328 < 5060
Period 348: 3445 < 4785
Period 351: 4002 < 5278
Period 354: 3564 < 5225
Period 357: 4130 < 5428
Period 360: 726 < 1518
Period 375: 4526 < 5332
Period 378: 4060 < 5644
Period 381: 4662 < 5856
Period 396: 1849 < 3712
Period 399: 5082 < 5200
Period 414: 1683 < 3599
Period 432: 1155 < 2448
Period 435: 4720 < 4830
Period 447: 4838 < 6490
Period 450: 1575 < 2704
Period 462: 4340 < 4355
Period 468: 1764 < 3444
Period 486: 4661 < 4760
Period 489: 5340 < 5609
Period 519: 5568 < 7888
Period 528: 2024 < 2295
Period 534: 3127 < 4189
Period 537: 2808 < 5920
Period 540: 1320 < 3055
Period 543: 5800 < 6580
Period 546: 3240 < 5112
Period 549: 2915 < 5183
Period 552: 1085 < 2430
Period 558: 3355 < 4366
Period 561: 3024 < 5037
Period 564: 1586 < 3192
Period 570: 3472 < 4543
Period 573: 3135 < 5396
Period 582: 3591 < 4543
Period 585: 3248 < 4350
Period 588: 3894 < 4779
Period 594: 3712 < 5396
Period 597: 3363 < 5609
Period 606: 3835 < 4720
Period 609: 3480 < 5530
Period 615: 5175 < 5336
Period 618: 3960 < 5192
Period 621: 3599 < 5986
Period 624: 1394 < 2420
Period 630: 1375 < 3400
Period 633: 3720 < 5460
Period 636: 4410 < 5133
Period 642: 4216 < 5251
Period 645: 3843 < 4662
Period 648: 2960 < 4914
Period 654: 3510 < 4698
Period 657: 3968 < 5795
Period 66: 1125 < 2295
Period 660: 2610 < 2820
Period 666: 3630 < 4840
Period 669: 4095 < 6545
Period 672: 3213 < 5152
Period 678: 3752 < 4984
Period 681: 4224 < 4980
Period 684: 3328 < 5060
Period 69: 2312 < 5390
Period 693: 4355 < 5208
Period 696: 3445 < 4840
Period 702: 3726 < 5278
Period 705: 4488 < 5332
Period 708: 3564 < 5225
Period 711: 5040 < 5063
Period 714: 4130 < 5428
Period 717: 4623 < 5481
Period 72: 1376 < 1440
Period 720: 1155 < 1880
Period 723: 4050 < 4800
Period 726: 4260 < 4757
Period 729: 4760 < 5460
Period 732: 3364 < 3904
Period 738: 1496 < 2992
Period 741: 4899 < 5850
Period 747: 4316 < 5096
Period 753: 5040 < 5655
Period 756: 4060 < 5644
Period 759: 4452 < 5247
Period 762: 4216 < 5856
Period 765: 5084 < 6120
Period 768: 2401 < 4536
Period 771: 4590 < 5400
Period 774: 4800 < 5180
Period 777: 4130 < 5940
Period 783: 4730 < 5555
Period 786: 4940 < 5307
Period 789: 5041 < 6417
Period 792: 2064 < 3944
Period 798: 5082 < 5915
Period 801: 4891 < 6324
Period 804: 4588 < 5112
Period 807: 5016 < 5871
Period 810: 2162 < 3920
Period 813: 5032 < 6762
Period 819: 5112 < 6032
Period 822: 5175 < 5621
Period 825: 4307 < 6624
Period 828: 2484 < 4690
Period 831: 5310 < 6195
Period 834: 4650 < 5760
Period 837: 4425 < 5893
Period 843: 5460 < 5893
Period 846: 1976 < 4608
Period 849: 5467 < 6386
Period 852: 4320 < 4840
Period 855: 4543 < 6527
Period 858: 4661 < 5538
Period 861: 4543 < 6106
Period 864: 2100 < 3740
Period 867: 5766 < 6205
Period 873: 5368 < 6360
Period 879: 5922 < 6776
Period 882: 4779 < 4941
Period 885: 4602 < 5934
Period 891: 5467 < 6364
Period 894: 4838 < 6490
Period 897: 5106 < 6314
Period 900: 1575 < 2754
Period 903: 5538 < 6264
Period 906: 4897 < 5734
Period 909: 5175 < 6396
Period 915: 5538 < 6097
Period 918: 2550 < 5175
Period 921: 5244 < 6478
Period 924: 3256 < 4494
Period 927: 5580 < 6960
Period 933: 5313 < 6560
Period 936: 1848 < 3854
Period 939: 5642 < 6853
Period 942: 5074 < 6205
Period 945: 4897 < 6642
Period 948: 5605 < 5734
Period 951: 5704 < 7140
Period 954: 5133 < 5984
Period 957: 5530 < 6724
Period 963: 5766 < 7138
Period 966: 2397 < 3920
Period 969: 5680 < 6806
Period 972: 4914 < 6004
Period 975: 5828 < 6298
Period 978: 5340 < 5829
Period 981: 4698 < 6888
Period 987: 5890 < 7360
Period 990: 2352 < 3600
Period 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 kind
x = 49, y = 39, rule = LifeHistory
23.2A6.2A$21.2B2AB4.B2A2B$21.4B6.4B10.2A$21.5B4.5B8.A.BA$22.5B2.5B8.B
2A$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$6.3B3A4B2A4BA2BA4B
A2BA4BABA.2B3AB$6.3B3A7B8A2B8A5B3.2B$7.2B3A2.BA6BA2BA4BA2BA3B2ABAB2.
2A$7.2B2AB2.BAB2A4B2A6B2A8B3.2B$9.A4.BABAB2.14B3.3B3.BA$7.A.A.A2.B2AB
3.13B5.B3.BAB$4.A.A.A.2A3.3B2.14B.B7.B2AB$4.2A2.A12.14B2A7.3A$8.A.4A
8.6B.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.2A2B2A
10B$2A.A2.5BA9B$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 gun
x = 72, y = 59, rule = LifeHistory
15.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.B
A.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.A
5.2B2A2BA2B2A6B2A.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.2A17B
11.2A5.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.A3.8B
5.4B16.4B5.8B3.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.B2AB4.3A5.4B
8.4B5.3A4.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$9.2A9.3B2.4B5.2A6.4B
4.10B3.2A2.A2.A$8.A.A8.9B7.A7.4B5.8B3.A.A2.2A$8.A8.B.8B5.3A9.4B2.11B
3.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$8.2A6.7B
5.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 gun
x = 61, y = 60, rule = LifeHistory
51.A2.2A$51.4A.A$56.A$49.7A.2A$48.A2.B3.A.A2.A$48.2A2.2A.AB2.2A$51.B
2AB2A$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$22.4B
3A5B3A2B.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$2A6.3B3.4BA2BA
4B20.4B2.B2.A$.A6.3B.6B2ABA5B6.BA10.4B3.B3.3A$.A.AB2.B3A5BA2B2AB2.2BA
B4.2A.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.B
2A2BA5B3AB2.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.B
14.5B$4.BAB3A3B3.3B6.2A4.5B$4.3AB3A4B.3A6.A4.4B$5.2ABAB2A4B3AB2.BA.A
3.5B$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.BA3BA
5B.BAB6.A$23.A4BA4B2AB2A2.BA.A$22.2BAB3ABA8B.B2A$22.2BABA3BA5B2A3B$
22.3B2A5BA3BABA2B$20.2AB.8BAB3ABA2B$19.A.AB2.2AB2A4BA4BA$19.A6.BAB.5B
A3BAB$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-Snark
x = 51, y = 43, rule = LifeHistory
47.B.AB$41.BABA.5A$16.A10.A12.3ABAB2A.2A$14.3A10.3A10.B.2B.BA.AB$13.A
5.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$14.2A12B
2A2.2B3A3BAB$14.BAB2A5BA5B3.3BABA4B$13.B2A3BA4B2A5B.6BA3B$12.2BA3BA6B
A12BA2B$13.2B3A4B3A10BA5B$15.2A5B2A5B.5BA6B$14.21BABA3B$14.19BA3B3A2B
$15.4B6.2BA3B.BA5BAB$16.2B8.A3B3.A5BA$11.A13.B3A5.6B$11.3A10.4B6.B3AB
3.2A$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!
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Re: Thread For Your Bellman Finds

Postby Kazyan » September 8th, 2017, 4:40 pm

With some pushing and pulling on the components, the p198 gets even better:

x = 57, y = 52, rule = LifeHistory
37.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$22.7BA
2BA2B2ABA2B3.2A2.2A.AB2.2A$22.2BAB2A2BA2BA7B6.B2AB2A$22.3B2ABAB2A4B2A
B.B2A5.5B$23.5B3A4BA2B2.BA.A5.3B$22.6B2A3B.BAB6.A4.2A3B$19.B2.A5BA2B
3.BAB6.2A2.B2AB2A$9.B7.4B.B2A3B7.B3.2A6.2ABA4B$2A6.3B3.B2A5B2A2B14.A
5.9B$.A6.3A.2BA2BA9B13.A.AB3.7B$.A.AB2.2BA3BA8B2.4B13.2AB.10B$2.2AB.
2BA4BA2BAB2A3B2.4B14.13B$4.5BA2BABAB3A4B3.BABA6.BA5.13BA$4.4B3ABABA2B
A5B4.B2AB4.2A.B4.11BABA$4.3B2ABA2BA4BA2B.B2A3.A3B3.B.2A6.8B2.2A$5.8BA
3BA2B2.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.A
2B6.A4.5B$10.2B2A4BA4BAB2.BA.A3.2A3B$9.2BA2BA11B.B2A3.ABAB$9.2B2AB2A
8BA3B4.3BAB$9.3BA8B2AB2A2B3.4B$7.2AB.11BA2BA2B2.4B$6.A.AB2.BA4BA4B2A
2B2.4B$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$27.2BA
2BA7BABA3B$27.3BABA7BA2BA2B$25.2AB.2B4A5BA2BA2B$24.A.AB2.2B5A4B2A2B$
24.A6.2BA.2A9B$23.2A6.A2B3.9B$32.A7.4B$42.B!


Further discussion should probably go to the Variable-Speed Firing Squad thread.
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Re: Thread For Your Bellman Finds

Postby Kazyan » September 13th, 2017, 6:52 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/S23
3bo5bo$2bobo3bobo$bo2bo3bo2bo$ob2ob2obo3bo$o4bobob3o$b3o3bobo$3bobobob
o$4b2ob2o2$6bo$5b2o$5bobo!
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Re: Thread For Your Bellman Finds

Postby A for awesome » September 13th, 2017, 7:21 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/S23
3bo5bo$2bobo3bobo$bo2bo3bo2bo$ob2ob2obo3bo$o4bobob3o$b3o3bobo$3bobobob
o$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

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Re: Thread For Your Bellman Finds

Postby Kazyan » October 24th, 2017, 1:18 am

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/S23
17b2o11b2o11b2o11b2o$16bo2bo9bo2bo9bo2bo9bo2bo$16bobo3b2ob2o3bobo9bobo
3b2ob2o3bobo$14b2o2bobo7bobo2b2o5b2o2bobo7bobo2b2o$15bobobo4bo4bobobo
7bobobo4bo4bobobo$14bo2b2o2b7o2b2o2bo5bo2b2o2b7o2b2o2bo$14b2o5bobobobo
5b2o5b2o5bobobobo5b2o$23bobo23bobo$5bo2b2o9b3o5b3o15b3o5b3o9b2o2bo$4bo
bo2bo2bo5bobobo3bobobo13bobobo3bobobo5bo2bo2bobo$4bob2obobobo4b2o2b5o
2b2o13b2o2b5o2b2o4bobobob2obo$3b2obo2bobo2bo45bo2bobo2bob2o$3bo2bob2o
2bo49bo2b2obo2bo$4b3obobo3b3o41b3o3bobob3o$6b2obo5b2o41b2o5bob2o$2bobo
2bobo3bo2bo4bobobo32bo2bo3bobo2bobo$2b2o2b2obob2o2b3o4b3o25b3o4b3o2b2o
bob2o2b2o$8b2obo3b2o6bo26b3o5b2o3bob2o$2b5o4bo39bo11bo4b5o$bo4bob3o17b
2o15b2o17b3obo4bo$bob2obobo6b2o7bo3bobo13bobo11b2o6bobob2obo$2obo2bo6b
4o8bo4bo13bo4bo8b4o6bo2bob2o$bobobobo5b2o2bo5b3o4b2o11b2o3bo8bo2b2o5bo
bobobo$bobob2obo2bo36b3o12bo2bob2obobo$2ob2o2b2o3b4o37b3o3b4o3b2o2b2ob
2o$3bo2b3o2bo2b2o4bo15b2o21b2o2bo2b3o2bo$3bobob2o5bo4bobo8bo5b2o16bo5b
o5b2obobo$2b2obo2b2obo2bo3bo3bo8bo11bo16bo2bob2o2bob2o$4bo3b2o2bo2bo3b
obo7b3o10bo16bo2bo2b2o3bo$4bobo7bo5bo21b3o15bo7bobo$3b2ob2o10b3o33b3o
10b2ob2o$16b7o29b7o$9b2o2bo2b2obob2o2bo2b2o6bo8b2o2bo2b2obob2o2bo2b2o$
9bo4b4o3b4o4bo7bo7bo4b4o3b4o4bo$10b4o11b4o6b3o8b4o11b4o$14b2o7b2o25b2o
7b2o$10b5obo2bo2bob5o3b2o12b5obo2bo2bob5o$9bo6b7o6bo2b2o11bo6b7o6bo$
10b3obo9bob3o17b3obo9bob3o$12b2obob2ob2obob2o21b2obob2ob2obob2o$14b2ob
o3bob2o25b2obo3bob2o$14bo2bo3bo2bo25bo2bo3bo2bo$15b2o5b2o27b2o5b2o2$
48bo$49bo$47b3o4$68b2o$69bo$67bo5b2o$67b2o5bo$74bob2o$67b2o2b2obo2bo$
60bo6b2o3bob2o$61bo10bo$59b3o9b2o$78b2o$78bobo$80bo$80bob2o$77b2obobo$
72b2o3b2obobo$72b2o6bob2o$61b2o14b4o2bo$60bobo14bo3b2o$60bo18b2o$59b2o
19bo$78bo$78b2o8$41b2o$41bo$36b2o5bo$36bo5b2o$33b2obo$33bo2bob2o2b2o$
35b2obo3b2o$38bo$38b2o2$32b2o$32bo$29b2obo$29bo2b3o4b2o$30b2o3bo3b2o$
32b4o$32bo15b2o$33b3o12bobo$36bo13bo$31b5o14b2o$31bo$33bo$32b2o!
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Re: Thread For Your Bellman Finds

Postby calcyman » October 24th, 2017, 4:06 am

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/S23
17b2o11b2o11b2o11b2o$16bo2bo9bo2bo9bo2bo9bo2bo$16bobo3b2ob2o3bobo9bobo
3b2ob2o3bobo$14b2o2bobo7bobo2b2o5b2o2bobo7bobo2b2o$15bobobo4bo4bobobo
7bobobo4bo4bobobo$14bo2b2o2b7o2b2o2bo5bo2b2o2b7o2b2o2bo$14b2o5bobobobo
5b2o5b2o5bobobobo5b2o$23bobo23bobo$5bo2b2o9b3o5b3o15b3o5b3o9b2o2bo$4bo
bo2bo2bo5bobobo3bobobo13bobobo3bobobo5bo2bo2bobo$4bob2obobobo4b2o2b5o
2b2o13b2o2b5o2b2o4bobobob2obo$3b2obo2bobo2bo45bo2bobo2bob2o$3bo2bob2o
2bo49bo2b2obo2bo$4b3obobo3b3o41b3o3bobob3o$6b2obo5b2o41b2o5bob2o$2bobo
2bobo3bo2bo4bobobo32bo2bo3bobo2bobo$2b2o2b2obob2o2b3o4b3o25b3o4b3o2b2o
bob2o2b2o$8b2obo3b2o6bo26b3o5b2o3bob2o$2b5o4bo39bo11bo4b5o$bo4bob3o17b
2o15b2o17b3obo4bo$bob2obobo6b2o7bo3bobo13bobo11b2o6bobob2obo$2obo2bo6b
4o8bo4bo13bo4bo8b4o6bo2bob2o$bobobobo5b2o2bo5b3o4b2o11b2o3bo8bo2b2o5bo
bobobo$bobob2obo2bo36b3o12bo2bob2obobo$2ob2o2b2o3b4o37b3o3b4o3b2o2b2ob
2o$3bo2b3o2bo2b2o4bo15b2o21b2o2bo2b3o2bo$3bobob2o5bo4bobo8bo5b2o16bo5b
o5b2obobo$2b2obo2b2obo2bo3bo3bo8bo11bo16bo2bob2o2bob2o$4bo3b2o2bo2bo3b
obo7b3o10bo16bo2bo2b2o3bo$4bobo7bo5bo21b3o15bo7bobo$3b2ob2o10b3o33b3o
10b2ob2o$16b7o29b7o$9b2o2bo2b2obob2o2bo2b2o6bo8b2o2bo2b2obob2o2bo2b2o$
9bo4b4o3b4o4bo7bo7bo4b4o3b4o4bo$10b4o11b4o6b3o8b4o11b4o$14b2o7b2o25b2o
7b2o$10b5obo2bo2bob5o3b2o12b5obo2bo2bob5o$9bo6b7o6bo2b2o11bo6b7o6bo$
10b3obo9bob3o17b3obo9bob3o$12b2obob2ob2obob2o21b2obob2ob2obob2o$14b2ob
o3bob2o25b2obo3bob2o$14bo2bo3bo2bo25bo2bo3bo2bo$15b2o5b2o27b2o5b2o2$
48bo$49bo$47b3o4$68b2o$69bo$67bo5b2o$67b2o5bo$74bob2o$67b2o2b2obo2bo$
60bo6b2o3bob2o$61bo10bo$59b3o9b2o$78b2o$78bobo$80bo$80bob2o$77b2obobo$
72b2o3b2obobo$72b2o6bob2o$61b2o14b4o2bo$60bobo14bo3b2o$60bo18b2o$59b2o
19bo$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/S23
obo$b2o$bo13$15bobo$16b2o$16bo13$30bobo$31b2o$31bo13$45bobo$46b2o$46bo
5$65bo$63b3o$62bo$62b2o5$48b2ob2o7bobo$46bo2bob2o8b2o$46b2o13bo2$51bo
2bo5b2o$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.)
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Re: Thread For Your Bellman Finds

Postby muzik » October 24th, 2017, 4:19 am

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.
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Re: Thread For Your Bellman Finds

Postby calcyman » October 24th, 2017, 4:58 am

The quadri-Snark reduces the area of the p576 gun considerably (54x48 --> 48x45):

x = 48, y = 45, rule = LifeHistory
35.A2.2A$35.4A.A$40.A$33.7A.2A$32.A2.B3.A.A2.A$32.2A2.2A.AB2.2A$27.2A
6.B2AB2A$27.A8.5B$29.A7.3B$25.5A6.5B$25.A9.4BAB$27.B4A3.3BABA2B$27.BA
2.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.AB
A$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$4.3B8.3B
8.4B7.B6.B2A$4.5B4.5B7.5B6.4B4.B2AB$3.2A5B2.5B2A3.8B6.12B$3.2A12B2A.
4BA6B.2B.12B$3.16B.3BABA21B$2.12BA9B3ABA17B$.2A10BAB2A9B3A18B$2.11BAB
A10BA20B$4.10BA3B2.7B2ABA14B$3.16B4.5B3A4B3A5B$3.16B2.14BAB2A6B$4.4B
6.4B.20BA7B$5.2B8.2B2.18B3A7B$20.17BAB3A4B$19.21BABA4B$19.12B.2B.6BA
5B$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.
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Re: Thread For Your Bellman Finds

Postby Saka » October 24th, 2017, 9:18 am

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?
Everyone, please stop posting B/S about CA
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

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Re: Thread For Your Bellman Finds

Postby dvgrn » October 24th, 2017, 9:52 am

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 2003
x = 125, y = 72, rule = B3/S23
98bo$90b3o$89bo$89bo3bo$89bobbobo8bo$91bobobbo4b3o$92bo3bo3bo$96bo3boo
$93b3o$98bo$28booboobo7bo54bobo$bboo23boboboboo7b3o53boobboo$3bo24bo
16bo14bo41boo$3bobo38boo12b3o$4boobboo47bo$8boo47boo$40bo80bo$38booboo
77b3o$38bo17boo7boo52bob3o$38bo3bo13boo6bobbo50bo3bo$39b3o23boo50bo3bo
$116b3obo$117b3o$118bo$114bo$113bobo8bo$bboo36boo71boo$bobo16boo19bo
75boo$bo18bobo15b3o76bobo$oo5bobo12bo15bo73boo5bo$7bobbo5boo4boo19boo
67boo5boo$6bo3bo5bobo25bo$7bobbo7bo22b3o$7b3o8boo21bo4$oo$bo$o$oo68boo
$64bo5boo$oo63bo$obo60b3o25boo$bo90boo$91bo3$20bo21boo8b3o$18b3o22bo7b
obbo$17bo25bobo5bo3bo$17boo19boo4boo5bobbo$23bo15bo12bobo5boo$21b3o15b
obo18bo$20bo19boo16bobo$20boo36boo4$74boo$74boobboo$20b3o55bobo$4boo
13bo3bo55bo$4boo17bo59bo$19booboo52boo4bobo$21bo55bo3bo3bo$3boo47boo
20b3o5bo3bo$4bo47boobboo16bo8bo3bo$b3o12boo38bobo25bo3bo$bo14bo16bo24b
o26bobo22bo$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/S23
74bo26bo$74boo18bo$73boobo16bobo$72bobb3o14bo3bo$62bo8bobobo6boo9bo3bo
8bo$62b3o5bobobo6bobbo9bo3bo5b3o$65bobb3obbo8boo11bo3bo3bo$64boo3boboo
23bobo4boo$70boo25bo$67bo3bo29bo$66bobo31bobo$62boobboo33boobboo$31bo
23b4o3boo41boo$29b3o11bo6boo7bo$3boo23bo14b3o4boobboo3bo$4bo23boo16bo
7boobbo10bo$4bobo38boo20bobo$5boobboo57boo$9boo25boo3bo$27bo3boo3boo3b
o$25boobob3o5bobbo$25bo4b3o4boo10b3o$25bo3bo5bobo11bobbo$26b3o6b4obo7b
o4bo$28bo6b3obo11bo11boo$5boo56bobo$5bobobobo37boo14bo$8booboo36bobo
13boo$9boboo36bobo$3boo3b5o28boo38bo53b3o$bbobo3b5o8boo19bo37bobo34b3o
15b3o$bbo4boobbo9bobo16bo39bobbo3bo29bo17b3o$boo5b3o12bo16boo39boo4bo
30bo13b3o$9bo7boo4boo19boo41bo44b3o$17bobbo24bo86b3o$19boo21b3o11bo26b
3o$10boo30bo14bo71bo9bo$10boo43b3o70bobo$80boo46boo$81bo50boo$60boo16b
3o51bobo$60bobo15bo48boo5bo$62bo64boo5boo$62boo$oo$bo51b3o$bobo48bobbo
$bboo48bo4bo$52bo$58bo$53bo$21bo28boo5bo$9bobo7b3o21boo4boobooboo$8bo
bbo6bo24bobbo3bo4bo$8bobbo6boo19boo4boo4bobbo$7bo3bo10boo16bo10boo8boo
$8bobo12bo16bobo18bo$9bo11bo19boo16bobo41boo$21boo36boo42boobboo$107bo
bo$45boo61bo$45boo$44bobbo57boo4boo$41bobboboo58bo4boobo$22boo16bobbo
59b3o9bo$5boo14bobbo16bobo59bo8bo$5boo14b3o89boboo$22boo91boo22bo$137b
obo$4boo47boo83boo$5bo47boobboo$bb3o12boo38bobo$bbo14bo16boo23bo$18b3o
14bo23boo$20bo11b3o$32bo!


#C p1368 (72*19)
x = 114, y = 97, rule = B3/S23
oo6boo$bob3ob3o13bo10bo$bobboobobbo10b3o10b3o$3bobboboobbo7bo5bo4bo5bo
$4b3ob3obo6bob6o4b6obo$4boo6boo5bobo14bobo$18boo3boboo4boobo3boo$20bo
4boo4boo4bo$4bo15bobboo8boobbo$bbo3b4o11boo12boo$bbo3bo5b3o$bbo$5bo4bo
$3boo5b3obb3o3b3o11boo$11bobooboo17boo$10boobboo8boo5boo$11boo8b3obbo
6bo18bo$20boo8bobo9boo7bobo$21boobo6boo8bobbo5bo3bo$15boo6bo18boo7bo3b
o8bo$12boobboo34bo3bo5b3o$10booboobo36bo3bo3bo$10b3obb3o36bobo4boo$17b
o37bo$59bo$7boo4b3o42bobo$7boo10boo38boobboo$7boo9bobo42boo$8bo8b3o$7b
obo7boo$bb3obobo9bobo$bb4obo11bobobboo$6bo13bobbobo7bo$21b4o6bobo$22b
oo8boo8$41bo3b3o$40bobo$40bobbo$41boo3$43b3o12$109b3o$109b3o$109b3o$
93b3o10b3o$93bo12b3o$94bo11b3o$$103bo$102bobo$102boo$106boo$106bobo$
101boo5bo$101boo5boo13$79boo$79boobboo$83bobo$84bo$$81boo4boo$82bo4boo
bo$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, 7/28/2006
x = 116, y = 89, rule = B3/S23
6bo34boobo$5bobo14bo18boboo$5bobo13bobo$4booboo12bobo$22bo8$3bo5bo$bb
3o3b3o$booboobooboo$3o7b3o24bo7bo$36bobo5bobo16boo$bbo7bo10boo13bobo5b
obo16bobo$20bobo14bo7bo19bo$22bo42boo$40boo$39bobbo$9bo30boo$8b3o$8bo
bbo$7bobobo42bo$8b3o9boo31bobo$bboo5bo10boo31bobo$bboo50bo$$49boo$48bo
bbo$49boo$14bo5bo$13b3o3b3o42bo$12boobbobobboo40bobo$12bo3bobo3bo40bob
o$12boboo3boobo41bo$12boo7boo$59boo$58bobbo$59boo43boobo$85boo12b3obb
oobbo$72boo11boo13boo6bo$72boo27b3o3b4o$102bo3bo3b3o$86bo5bo20bo$71boo
13bo5bo9bo3bo3b3o$70bobo28b3o3b4o$70boo10boo11boo3boo6bo$99b3obboobbo$
86bo5bo11boobo$86bo5bo$13boo5boo$13boo5boo91boo$113boo$$106boo$89boo
14booboo4boo$89boo15bobbo4boo$106bobbo$107boo$18boo68boo$18boo66b4o17b
oo$29bo23boo30bobbobo15bobbo$27bobbo22boo29bo21bobbo4boo$17boo8b5o10b
oo41boo18booboo4boo$17boo8b3oboo9boo42b3o17boo$28boobo43b3o9boo$29boo
42bo4bo9bo24boo$73bo5bo33boo$29boo35bobobo7bo$28boobo32b7o5boo$17boo8b
3oboo30bo$17boo8b5o32b7o5boo$27bobbo17boo16bobobo7bo$29bo18boo23bo5bo
10boo$18boo53bo4bo11boo$18boo55b3o$$56boo$56bo$57b3o$59bo$$46boo$47bo
24bo$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 1996
x = 215, y = 249, rule = B3/S23
29b2o$29b2o15b2o26b2o$46b2o26b2o2$5b2o$5b2o39b3o$46b3o3$74b3o$44b2o3b
2o22bo3bo$28b3o14b5o$27bo3bo14b3o23bo5bo$26bo5bo14bo24b2o3b2o$4b3o20bo
3bo$3bo3bo20b3o$2bo5bo19b3o44bo$2bo5bo65bob2o$5bo68bo16b2o$3bo3bo66bo
3bo10bo3bo$4b3o41bo26bo2bo4b2o3bo5bo13b2o$5bo24b3o16b2o24b5o3b2o2b2obo
3bo13b2o4b3o$25bo3b2ob2o14b2o25b5o8bo5bo10b2o6b5o$23b2o4b2ob2o40b2o3b
2o8bo3bo10b3o5bo3bobo$2b3o19b2o3b5o41b5o11b2o12b2o6bo3b2o$2b3o23b2o3b
2o21bo11bobo5b3o17bobo9b2o$bo3bo49bobo10b2o7bo18b2o10b2o$9bobo30b2o3b
2o20bo27bo$2o3b2o3b2o8b2o22b3o$10bo9b2o21bo3bo$29b2o13bobo9bo$45bo8b2o
$55bo$17bo38b2o16b2o8b2o$16bo14b2o24bo17bo8b2o$18bo12b2o11b2o26b3o$15b
o2bo25b2o26bo$89b3o$2b2o11b2o43b2o13b2o12bo2b2o$2b2o31bo24b2o12bobo16b
o$35b3o36bo16bobo$38bo16bo17b2o$37b2o15bobo2$101b2o9b2o$100b2o9bobo$
20b2o73bo6bo7b3o4b2o$20bo34b2o37bobo12b3o4bo2b4o$21b3o14b2o16bo35b2o3b
o12b3o4b2ob3o$23bo5bo7bobo13b3o31b2o3b2o3bo13bobo$27bob2o6bobo13bo33b
2o3b2o3bo14b2o$28bobo5bo57bobo$39bo55bo$36bo3bo$28bob2o5b4o$27bob2o9bo
$28b2o21b2o$52bo$51bo$51b2o43bo49bo$94b3o34b2o11b3o$37b2o31bo22bo26bo
10bo11bo26bo$38bo21bo9b3o20b2o25b3o9bo10b2o25b3o$38bobo17b2o13bo49bo7b
2o40bo23b2o$39b2o18b2o11b2o48b2o48b2o23bo$195bobo$103bo49bo37b2o2b2o$
103b3o47b3o35b2o$106bo49bo$81bo23b2o11b2o35b2o11b2o$79b3o36b2o48b2o$
62b2o15bobo$62b2o15bo2$47b2o$46bobo$46bo$45b2o$59b2o32b2o48b2o52b2o$
59bo20b2o11b2o35b2o11b2o34b2o16bobo$60bo20bo49bo46bobo18bo13b2o$59b2o
17b3o47b3o47bo20b2o12bo$78bo49bo48b2o4b2o26bobo$182bobo26b2o$97b2o48b
2o33bo$98bo49bo32b2o7b2o$95b3o20b2o25b3o20b2o20b2o$95bo22bo26bo22bo$
119b3o47b3o$121bo49bo$78bo$78b3o11b2o$54bo26bo11bo$52b3o25b2o10bo$26b
2o23bo40b2o$27bo23b2o$27bobo$28b2o2b2o37bo49bo$32b2o35b3o47b3o17b2o$
68bo49bo20bo$55b2o11b2o35b2o11b2o20bo11bo27bo$55b2o48b2o32b2o9b3o27b3o
$149bo33bo$149b2o10b2o19b2o$161bo15bo$159bobo15b3o$159b2o19bo$136b2o
41b2o$136b2o$26b2o52b2o$25bobo16b2o34b2o11b2o$10b2o13bo18bobo46bo$11bo
12b2o20bo47b3o$11bobo26b2o4b2o48bo79b2o$12b2o26bobo133b2o17b2o$42bo33b
2o48b2o67b2o$33b2o7b2o32bo49bo18b2o$33b2o20b2o20b3o25b2o20b3o16bo$56bo
22bo26bo22bo13b3o50b2o$53b3o47b3o37bo52bo$53bo49bo79b2o12b3o$146bo20b
2o15bo14bo$131b2o11b3o20bobo11b3o$131bo11bo25bo11bo$132bo10b2o24bobo$
131b2o37b2o25b2o$197bo$195bobo$103bo49bo37b2o2b2o$84b2o17b3o47b3o35b2o
$85bo20bo49bo$44bo27bo11bo20b2o11b2o35b2o11b2o$42b3o27b3o9b2o32b2o48b
2o$41bo33bo$41b2o19b2o10b2o$47bo15bo$45b3o15bobo$44bo19b2o$44b2o41b2o$
87b2o$143b2o52b2o$130b2o11b2o34b2o16bobo$131bo46bobo18bo13b2o$128b3o
47bo20b2o12bo$47b2o79bo48b2o4b2o26bobo$28b2o17b2o133bobo26b2o$28b2o67b
2o48b2o33bo$78b2o18bo49bo32b2o7b2o$78bo16b3o20b2o25b3o20b2o20b2o$27b2o
50b3o13bo22bo26bo22bo$28bo52bo37b3o47b3o$25b3o12b2o79bo49bo$25bo14bo
15b2o20bo$41b3o11bobo20b3o11b2o$43bo11bo25bo11bo$53bobo24b2o10bo$26b2o
25b2o37b2o$27bo$27bobo$28b2o2b2o37bo49bo$32b2o35b3o47b3o17b2o$68bo49bo
20bo$55b2o11b2o35b2o11b2o20bo11bo27bo$55b2o48b2o32b2o9b3o27b3o$149bo
33bo$149b2o10b2o19b2o$161bo15bo$159bobo15b3o$159b2o19bo$136b2o41b2o$
136b2o$26b2o52b2o$25bobo16b2o34b2o11b2o$10b2o13bo18bobo46bo$11bo12b2o
20bo47b3o$11bobo26b2o4b2o48bo79b2o$12b2o26bobo133b2o17b2o$42bo33b2o48b
2o67b2o$33b2o7b2o32bo49bo18b2o$33b2o20b2o20b3o25b2o20b3o16bo$56bo22bo
26bo22bo13b3o50b2o$53b3o47b3o37bo52bo$53bo49bo79b2o12b3o$146bo20b2o15b
o14bo$131b2o11b3o20bobo11b3o$131bo11bo25bo11bo$132bo10b2o24bobo$131b2o
37b2o25b2o$197bo$195bobo$103bo49bo37b2o2b2o$84b2o17b3o47b3o35b2o$85bo
20bo49bo$44bo27bo11bo20b2o11b2o35b2o11b2o$42b3o27b3o9b2o32b2o48b2o$41b
o33bo$41b2o19b2o10b2o$47bo15bo$45b3o15bobo$44bo19b2o$44b2o41b2o$87b2o$
143b2o52b2o$130b2o11b2o34b2o16bobo$131bo46bobo18bo$128b3o47bo20b2o$47b
2o79bo48b2o4b2o$28b2o17b2o133bobo$28b2o67b2o48b2o33bo$78b2o18bo49bo32b
2o7b2o$78bo16b3o20b2o25b3o20b2o20b2o$27b2o50b3o13bo22bo26bo22bo$28bo
52bo37b3o47b3o$25b3o12b2o79bo49bo$25bo14bo16b2o$41b3o14bo$43bo11b3o$
55bo4$121bo$119b3o17b2o$118bo20bo$105b2o11b2o20bo11bo27bo$105b2o32b2o
9b3o27b3o$149bo33bo$149b2o10b2o19b2o$161bo15bo$85b2o72bobo15b3o$85b2o
72b2o19bo$136b2o41b2o$136b2o4$89b2o$89b2o85b2o$176b2o17b2o$126b2o67b2o
$126bo18b2o$105b2o20b3o16bo$106bo22bo13b3o50b2o$103b3o37bo52bo$103bo
79b2o12b3o$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
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Re: Thread For Your Bellman Finds

Postby Jormungant » October 24th, 2017, 7:12 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 = LifeHistory
14$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$114.14B2A16B
2.6B$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.B3A
10B15.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$28.4B
4.11B53.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.A
2.A4.A.A9.B2AB$20.4B8.9B37.4B14.4B15.2A6.A11.2A$19.4B8.4B.6B35.4B14.B
D2B$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$14.4B8.18B
17.C.CB.10B5.5B3.5B$13.4B8.20B17.2CB.9B2.B2.7B2.4B$12.4B6.B.22B18.4B
3D16B.4B$11.4B5.26B18.4BD4B2D16B$10.4B6.26B18.4B3D2B2D15B$9.4B6.27B
18.26B$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.A5.8B4.3B2.4B
19.16B2C4BD4B$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.
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