The Hunting of the Elementary Conduits

For discussion of specific patterns or specific families of patterns in Conway's Game of Life, both newly-discovered and well-known.
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Kazyan
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Re: The Hunting of the Elementary Conduits

Post by Kazyan » July 23rd, 2020, 11:18 pm

An old catalyst hit a new(?) vein in the Herschel mines. Usable/salvageable stuff in the top row, interesting sideshow search spaces in the bottom row:

Code: Select all

x = 268, y = 118, rule = B3/S23
175b2o$175bobo2b2o$172bo4bo3bo$172b5ob3o$176bobo73b2o$172b3obobo74bo$
171bo2bob2o75bobo$171b2o81b2o2$69bo113bo64b2o$69b3o110bobo63bo$72bo64b
2o42bo2bo64b3o$71b2o57b2o6bo43b2o67bo$130bo5bo106b2o$20bo110b3obob4o
103bo$20b3o110bobobo2bo103bobo17b2o$23bo112bo108b2o17bobo$22b2o242bo$
10b2o108b2o48b2o94b2o$11bo109bo49bo$11bobo107bobo47bobo$12b2o108b2o48b
2o$143b2o$143b2o100bo$245bobo$245b3o16b2o$247bo16bo$262bobo$12bo49bo
59bo49bo80bo8b2o$12bobo47bobo57bobo47bobo77bobo2bo$12b3o16b2o29b3o16b
2o39b3o16b2o29b3o16b2o60bo3b3o$14bo16bo32bo16bo42bo16bo32bo16bo68bo$
29bobo47bobo57bobo47bobo65b2ob3o$20bo8b2o39bo8b2o49bo8b2o39bo8b2o67b2o
3bo$19bobo2bo44bobo2bo54bobo2bo44bobo2bo71bo4b2o$20bo3b3o43bo3b3o53bo
3b3o43bo3b3o69b5o$27bo49bo59bo49bo72bo$3bo20b2ob3o44b2ob3o54b2ob3o44b
2ob3o68bo$3bobo19b2o3bo44b2o3bo54b2o3bo44b2o3bo67b2o$3b2o18bo4b2o43bo
4b2o53bo4b2o43bo4b2o$23b5o45b5o55b5o45b5o$27bo49bo59bo49bo$25bo49bo59b
o49bo$25b2o48b2o58b2o48b2o30$192b2o$188bo3b2o$187bobo$186bobo$186bo$
65bo118bobo$13b2o50b3o115bobo$13bo54bo54b2obo52b2o3bo$14b3o50b2o54b2ob
3o9b2o39b2o$16bo112bo5bo3bo32b2o$123b2ob2obo5b4o29b2obo2bo$75bo48bob2o
b2o38bobobo$14b2o58bobo47bo10b4o28bo3bob4o$13bo2bo57bobo48b3ob2o3bo3bo
28b4obo3bo$14bobo58bo51bob2o3b2o34bobobo$15bo153bo2bob2o$170b2o81b2o$
252bobo$252b2o$256b2o$256bobo$258bo$258bobo$259b2o$263b2o$119bo52bo59b
o29bobo$119bobo50bobo57bobo27b2o$119b3o16b2o32b3o16b2o39b3o16b2o$121bo
16bo35bo16bo42bo16bo$o59bo75bobo50bobo57bobo$obo57bobo64bo8b2o42bo8b2o
49bo8b2o$3o16b2o39b3o16b2o45bobo2bo47bobo2bo54bobo2bo$2bo16bo42bo16bo
47bo3b3o46bo3b3o53bo3b3o$17bobo57bobo54bo52bo59bo$8bo8b2o49bo8b2o52b2o
b3o47b2ob3o54b2ob3o$7bobo2bo54bobo2bo59b2o3bo47b2o3bo54b2o3bo$8bo3b3o
53bo3b3o55bo4b2o46bo4b2o53bo4b2o$15bo59bo54b5o48b5o55b5o$12b2ob3o54b2o
b3o56bo52bo59bo$13b2o3bo54b2o3bo53bo52bo59bo$11bo4b2o53bo4b2o54b2o51b
2o58b2o$11b5o55b5o$15bo59bo$13bo59bo$13b2o58b2o!
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dvgrn
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Re: The Hunting of the Elementary Conduits

Post by dvgrn » July 24th, 2020, 5:15 am

Kazyan wrote:
July 23rd, 2020, 11:18 pm
An old catalyst hit a new(?) vein in the Herschel mines...
EDIT: It must be new. I don't recognize "NE0T67", which is the systematic name for the H-to-G in your top row:

Code: Select all

x = 40, y = 66, rule = LifeHistory
D3.D.5D2.3D2.5D2.3D2.5D$2D2.D.D5.D3.D3.D3.D9.D$D.D.D.D5.D2.2D3.D3.D8.
D$D2.2D.3D3.D.D.D3.D3.4D4.D$D3.D.D5.2D2.D3.D3.D3.D2.D$D3.D.D5.D3.D3.D
3.D3.D.D$D3.D.5D2.3D4.D4.3D2.D4$.3D2.D3.D8.3D2.5D2.3D4.D$D3.D.D3.D7.D
3.D3.D3.D3.D2.2D$D5.D3.D11.D3.D7.D3.D$.3D2.D.D.D.5D4.D4.D6.D4.D$4.D.D
.D.D9.D5.D5.D5.D$D3.D.2D.2D8.D6.D4.D6.D$.3D2.D3.D7.5D3.D3.5D2.3D6$13.
2A$13.A.A2.2A18.B$10.A4.A3.A17.2B$10.5A.3A17.3B$14.A.A18.4B$10.3ABABA
17.4B$9.A2.AB2A3B14.4B$9.2A2.2B.4B2.B9.4B$16.8B7.4B$16.5BA2B6.4B$16.
4BABA2B4.4B$15.4BA2BA2B3.4B$15.5B2A3B2.4B$16.9B.4B$16.13B$16.12B$17.
10B$17.9B$8.2A7.9B$9.A6.11B$9.A.AB3.12B$10.2AB.15B$12.17B$12.17B$13.
15B$12.15B$10.17B$8.19B$8.2BC15B$7.3BCBC4B.7B$8.2B3C4B.7B4.2A$7.5BC4B
2.6B4.A$6.10B4.4B2.BA.A$5.4B9.A.2B.B2.B2A$4.4B9.A.A.BA.3B$3.4B11.A3.
3AB$2.4B19.A$.4B17.2A.3A$4B19.2A3.A$3B18.A4.2A$2B19.5A$B24.A$23.A$23.
2A!
... I should have recognized the other one, though, the H-to-G0 -- SW-2T103 -- it's even in the doubled-signal toolkit. Should probably update that toolkit now, filling in the missing CP4 category using a Bandersnatch, and maybe put it in its own thread so it's easier to find.

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Re: The Hunting of the Elementary Conduits

Post by Entity Valkyrie 2 » July 25th, 2020, 8:34 pm

thunk wrote:
December 7th, 2015, 6:33 pm
Reading up on this thread and the Hunting thread, it seems that the primary criterion when picking canonical forms for the conduit collection seems to be a) obtrusiveness, then b) bounding box.

Which leads to the question: what is less obtrusive, an eater tail or a snake? One can be replaced with another, but eater tails are used in almost all conduits where this rock is called for (except for BFx59H).

There are certain situations where snakes are less obtrusive and work where eaters don't:

Code: Select all

x = 84, y = 49, rule = LifeHistory
7$9.2A$10.A$10.A.AB$11.2AB$13.3B$13.4B20.A$14.4B.B17.3A$15.7B8.A9.A$
16.6B6.3A2.A5.2A$16.2B3E2B4.A5.3A3.4B$16.2BE4B4.2A7.A4.2B$16.B3E4B.4B
6.2A.10B$16.11B8.14B.BA$16.12B9.13BA.A$16.12B7.15B.2A$17.11B6.14B$20.
7B3.3B.13B$19.9B.18B6.7B.B$15.34B4.13B.B$13.38BD21B$12.24B3D13BD21BD$
12.26BD13B2D18B3DB$12.24B3D12B2D2B2A15BDBD$10.2AB.37BD3B2A15BD$9.A.AB
3.31B4.11B3.2B2.2B$9.A5.31B5.10B$8.2A6.14B.13B8.6B$17.12B5.9B10.3B$
17.4B.4B2AB5.2B.4B12.B$18.2B3.3B2A5.7B12.2A$17.B2AB2.2B.B6.A.2A15.A$
18.2A6.2C3.3A.A17.A$27.C2.A4.A.A14.2A$26.AD.DA.3A.2A$26.2A2D.A2.A$32.
A.A$33.A!
Yet eaters are considerably more common than snakes, and also spartan. What would be the advice here?
Digging up a post. A solution (yellow eater):

Code: Select all

x = 68, y = 37, rule = LifeHistory
4B$.4B$2.4B$3.4B$4.4B$5.4B20.A$6.4B.B17.3A$7.7B8.A9.A$8.6B6.3A2.A5.2A
$8.2B3C2B4.A5.3A3.4B$8.2BC4B4.2A7.A4.2B$8.B3C4B.4B6.2A.10B$8.11B8.14B
.BA$8.12B9.13BA.A$8.12B7.15B.2A$9.11B6.14B$12.7B3.3B.13B$11.9B.18B6.
7B.B$7.34B4.13B.B$5.60B$4.24B3D12B2D21BD$4.26BD13B2D18B3DB$4.24B3D12B
2D2B2A15BDBD$2.2AB.37BD3B2A15BD$.A.AB3.31B4.11B3.2B2.2B$.A5.31B5.10B$
2A6.14B.13B8.6B$9.12B5.9B10.3B$9.4B.4B2AB5.2B.4B12.B$10.2B3.3B2A5.7B
12.2A$9.B2AB2.2B.B6.A.2A15.A$10.2A6.2E3.3A.A17.A$19.E2.A4.A.A14.2A$
16.3E3.A.3A.2A$16.E6.A2.A$24.A.A$25.A!
Bx222 IS MY WORST ENEMY.

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Scorbie
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Re: The Hunting of the Elementary Conduits

Post by Scorbie » July 27th, 2020, 12:32 am

@EV2
I agree. I'm surprised if nobody pointed this out before. I think I've thought the same before.

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Re: The Hunting of the Elementary Conduits

Post by Entity Valkyrie 2 » July 27th, 2020, 2:05 am

Scorbie wrote:
July 27th, 2020, 12:32 am
@EV2
I agree. I'm surprised if nobody pointed this out before. I think I've thought the same before.
Nobody actually pointed that out.

Both eater tails and eater heads as catalysts can be Spartan, and I think just use the one that is easier to construct (in self-constructing circuitry). For glider synthesis, both using eater tail and eater head are both two gliders.
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Jormungant
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Re: The Hunting of the Elementary Conduits

Post by Jormungant » July 27th, 2020, 5:57 am

pointless variants, 2 rows off the catalyst:

Code: Select all

x = 106, y = 71, rule = LifeHistory
17$22.2A52.2A$22.A.A2.2A47.A.A2.2A$19.A4.A3.A44.A4.A3.A$19.5A.3A45.5A
.3A$23.A.A51.A.A$19.3ABABA47.3ABABA$18.A2.AB2A3B44.A2.AB2A3B$18.2A2.
2B.4B2.B40.2A2.2B.4B2.B$25.7B47.7B$25.5BAB47.5BAB$25.4BABA47.4BABA$
24.4BA2BAB45.4BA2BAB$24.5B2A2B45.5B2A2B$23.11B43.11B$23.12B42.12B$23.
12B42.12B$23.12B42.12B$23.13B41.13B$17.2A4.14B34.2A4.14B$18.A4.13B36.
A4.13B$18.A.AB.13B.2B33.A.AB.13B.2B$19.2AB.16B34.2AB.16B$21.18B36.18B
$21.17B37.17B$22.15B39.15B$21.15B39.15B$19.17B37.17B$17.19B35.19B$17.
B.CB.13B36.B.CB.13B$16.2B.CBC4B.7B36.2B.CBC4B.7B$17.B.3C4B.7B4.2A31.B
.3C4B.7B4.2A$16.5BC4B2.6B4.A31.5BC4B2.6B4.A$15.10B4.4B2.BA.A30.10B4.
4B2.BA.A$14.4B9.A.2B.B2.B2A30.4B9.A.2B.B2.B2A$13.4B9.A.A.BA.3B31.4B9.
A.A.BA.3B$12.4B11.A3.3AB31.4B11.A3.3AB$11.4B19.A30.4B19.A$10.4B17.2A.
3A27.4B17.2A.3A$10.3B14.2A.A.2A3.A26.3B17.A.2A3.A$10.2B15.A.2A4.2A27.
2B17.A5.2A$10.B20.A.2A29.B18.A.4A$31.2A.A49.2A2.A!


Sphenocorona
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Re: The Hunting of the Elementary Conduits

Post by Sphenocorona » July 27th, 2020, 9:31 pm

I've found a couple new H-to-G conduits with the new glider to pre-TL catalyst Kazyan found earlier this month. I feel like there's more potential out there with this, but I personally haven't found anything else after a few days so I'm just going to post what my own investigations have found.

I'm gonna start with the one that I feel is the more unusual finding. It's... an extremely bulky H to FNG:

Code: Select all

x = 43, y = 43, rule = LifeHistory
29.A12.D$28.A.A10.D$27.A.A.A8.D$26.A.A2.3A5.D$26.A.A.A3.A3.D$22.A.2A.
A.A.3A3.D$22.2A.A.A.A.A4.D$26.BA.AB4.D$26.2AB2A3.D$18.2A6.2B.3B.D$19.
A7.5BD$19.A.AB5.4B$20.2AB.3B.2BDB$14.2A6.11B$15.A6.6BD6B$15.A.AB2.16B
$16.2AB.6BD11B$18.20B$18.6BD15B$18.23B$19.3BD18B$19.22B$19.BD21B$19.
24B$18.D24B$17.D2.22B$16.D2.23B$15.D.23B$14.D24B$13.D.2BC21B$12.D.3BC
BC19B$11.D3.2B3C4B.14B$10.D3.5BC4B2.13B$9.D3.10B2.13B$8.D3.4B9.13B$7.
D3.4B9.13B$6.D3.4B10.13B$5.D3.4B10.13B$4.D3.4B10.14B$3.D3.4B11.13B$2.
D3.4B12.13B$.D3.4B13.13B$D3.4B15.11B!
I think the red line illustrates the property that makes this unique among known stable H->X conduits. I've looked for a way to get a left turn conduit of some kind with this same property, but my manual search hasn't turned up anything so far. I really feel there's gotta be something, though.

I've also found a new H-to-G with a new output lane, although I'm not sure how to classify it. I haven't looked into catalysis of the right side as much, so there may be more to find in that regard. I've also added in a few of the failed or useless conduits that I've found in my limited manual search to the right as examples:

Code: Select all

x = 222, y = 48, rule = LifeHistory
194.D$21.A70.A55.A44.3D12.A$20.A.A68.A.A53.A.A42.BDB2D10.A.A$19.A.A.A
66.A.A.A51.A.A.A41.5B9.A.A.A$18.A.A2.3A63.A.A2.3A48.A.A2.3A38.6B8.A.A
2.3A$18.A.A.A3.A62.A.A.A3.A47.A.A.A3.A36.9B6.A.A.A3.A$14.A.2A.A.A.3A
59.A.2A.A.A.3A44.A.2A.A.A.3A37.9B2.A.2A.A.A.3A$14.2A.A.A.A.A61.2A.A.A
.A.A46.2A.A.A.A.A38.9B3.2A.A.A.A.A$18.BA.AB57.2A7.BA.AB42.2A7.BA.AB
39.B2D5B8.BA.AB$18.2AB2A56.B2AB6.2AB2A41.B2AB6.2AB2A39.B2D5B8.2AB2A$
10.2A6.2B.3B56.2B7.2B.3B41.2B7.2B.3B36.11B7.2B.3B$11.A7.5B55.2B2.2B5.
5B40.2B2.2B5.5B36.11B.2B5.5B$11.A.AB5.4B54.8B5.4B39.8B5.4B35.17B4.4B$
12.2AB.3B.4B41.2A10.9B5.4B39.8B5.4B34.19B3.4B$6.2A6.11B41.A10.10B.8B
38.9B.8B33.27B$7.A6.13B39.A.AB7.21B36.20B32.28B$7.A.AB2.15B39.2AB.2B
3.24B34.22B31.13B2D14B$8.2AB.17B40.6B.25B32.24B30.12BDBD15B$10.18B41.
32B32.24B30.14BD15B$10.17B43.33B28.B.26B29.31B$10.17B43.34B26.2E23BD
4B30.13B3D14B$11.16B43.34B26.2E23BDBD2B30.13BD16B$11.19B38.2AB.32B27.
24B3D2B28.2AB.11B2DBD13B$11.20B36.A.AB3.31B26.26BD3B26.A.AB.13B2D14B$
11.20B36.A8.30B29.27B25.A5.29B$11.20B35.2A7.5B2.24B32.24B24.2A5.29B$
12.18B45.BDBDB3.22B34.22B33.B.25B$11.18B47.DBD3.23B33.23B36.24B$9.21B
3.B42.3D.23B33.23B37.23B$7.22B3.2B44.24B32.24B36.24B$7.2BC18B3.3B44.
2BD21B32.2BD21B36.2BD21B$6.3BCBC4B.10B3.4B43.3BDBD19B31.3BDBD19B35.3B
DBD19B$7.2B3C4B2.7B4.4B45.2B3D4B.14B32.2B3D4B.14B36.2B3D4B.14B$6.5BC
4B2.8B2.4B45.5BD4B2.13B31.5BD4B2.13B35.5BD4B2.13B$5.10B2.14B45.10B2.
13B31.10B2.13B35.10B2.13B$4.4B9.13B45.4B9.13B30.4B9.13B34.4B9.13B$4.
3B11.12B2.B41.4B9.13B30.4B9.13B34.4B9.13B$2.4B11.B.11B.B2A39.4B10.13B
29.4B10.13B33.4B10.13B$2.2A12.2B.13B2A38.4B10.13B29.4B10.13B33.4B10.
13B$3.A9.2B.14B.2B38.4B10.14B28.4B10.14B32.4B10.14B$3A9.2A16B40.4B11.
13B29.3B11.13B32.4B11.13B$A11.2A15B40.4B12.13B29.2B12.13B31.4B12.13B$
13.2B.14B38.4B13.13B29.B13.13B30.4B13.13B$17.13B37.4B15.11B45.11B30.
4B15.11B$23.7B36.4B112.4B$24.5B36.4B112.4B$24.5B35.4B112.4B$26.2B35.
4B112.4B!

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Re: The Hunting of the Elementary Conduits

Post by dvgrn » July 27th, 2020, 9:52 pm

Sphenocorona wrote:
July 27th, 2020, 9:31 pm
I've also found a new H-to-G with a new output lane, although I'm not sure how to classify it.
Anyone who wants to classify H-to-Gs can just select one in Golly and run the classifier script. The script produces the LifeHistory version, with a systemic-name label and everything.

This one is "NE21T78" -- a nice find! We didn't have any elementary NE21s. There are a few NEward H-to-Gs with transparent output lanes, but not with so many nearby lanes also transparent. Being able to get the first natural glider out without any conflict with the output lanes is a good thing too.

Code: Select all

x = 42, y = 58, rule = LifeHistory
D3.D.5D2.3D4.D3.5D.5D2.3D$2D2.D.D5.D3.D2.2D5.D7.D.D3.D$D.D.D.D9.D3.D
5.D6.D2.D3.D$D2.2D.3D6.D4.D5.D5.D4.3D$D3.D.D7.D5.D5.D4.D4.D3.D$D3.D.D
6.D6.D5.D3.D5.D3.D$D3.D.5D.5D2.3D4.D3.D6.3D5$21.A$20.A.A$19.A.A.A$18.
A.A2.3A$18.A.A.A3.A$14.A.2A.A.A.3A$14.2A.A.A.A.A$18.BA.AB$18.2AB2A$
10.2A6.2B.3B$11.A7.5B$11.A.AB5.4B$12.2AB.3B.4B$6.2A6.11B$7.A6.13B$7.A
.AB2.15B$8.2AB.17B$10.18B$10.17B$10.17B14.B$11.16B13.2B$11.19B9.3B$
11.20B7.4B$11.20B6.4B$11.20B5.4B$12.18B5.4B$11.18B5.4B$9.21B3.4B$7.
22B3.4B$7.2BC18B3.4B$6.3BCBC4B.10B3.4B$7.2B3C4B2.7B4.4B$6.5BC4B2.8B2.
4B$5.10B2.14B$4.4B9.13B$4.3B11.12B2.B$2.4B11.B.11B.B2A$2.2A12.2B.13B
2A$3.A9.2B.14B.2B$3A9.2A16B$A11.2A15B$13.2B.14B$17.13B$23.7B$24.5B$
24.5B$26.2B!
#C [[ THUMBNAIL THUMBSIZE 2 ]]

Sphenocorona
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Re: The Hunting of the Elementary Conduits

Post by Sphenocorona » July 28th, 2020, 12:43 am

So, I might've posted a bit prematurely, because I've found a working H->LOM->G conduit. If analyzed as a pure H->G it's NW4T282, which appears to be a new lane again. But for me the more exciting bit is the fact that it's a H->LOM (the constituents of which are shown here in white) followed by a LOM->G, and the LOM->G features the catalysis used in the elementary 5c/9 signal injector:

Code: Select all

x = 39, y = 63, rule = LifeHistory
21.C$20.C.C$19.C.C.C$18.C.C2.3C$18.C.C.C3.C$14.C.2C.C.C.3C$14.2C.C.C.
C.C$18.BC.CB$18.2CB2C$10.2C6.2B.3B$11.C7.5B$11.C.CB5.4B$12.2CB.3B.4B$
6.2C6.11B$7.C6.13B$B6.C.CB2.15B$2B6.2CB.17B$3B7.18B$4B6.17B$.4B5.17B$
2.4B5.16B$3.4B4.19B$4.4B3.20B$5.4B2.20B$6.4B.20B$7.4B.18B$8.21B$9.21B
$7.22B$7.2BC18B$6.3BCBC4B.10B3.2C$7.2B3C5B.7B4.B2CB$6.5BC14B4.2B$5.
26B$4.4B8.16B$4.3B10.16B2.B$2.4B11.16B.B2C$2.2C12.2B.16B2C$3.C9.2B.
17B.2B$3C9.2C18B$C11.2C18B$13.2B.16B.BA$17.16BA.A$23.10B.2A$23.9B$24.
4B2D2B$24.3B2D3B$24.2B2D5B$24.11B$24.11B$23.12B$24.9B.B2A$25.7B2.BA.A
$18.2A.2A2.7B5.A$18.2A.A2.A6B6.2A$21.A.2A4B$18.2A.A.AB$18.2A.A2.AB$
21.AB2A2.A$21.A3.3A$22.3A$25.A$24.2A!
Here's a sample glider-activated signal injector using it (terrible repeat time, but it's very compact):

Code: Select all

x = 91, y = 84, rule = LifeHistory
73.A$72.A.A$71.A.A.A$70.A.A2.3A$70.A.A.A3.A$66.A.2A.A.A.3A$66.2A.A.A.
A.A$70.BA.AB$70.2AB2A$62.2A6.2B.3B$63.A7.5B$63.A.AB5.4B$64.2AB.3B.4B$
58.2A6.11B$37.A21.A6.13B$37.3A19.A.AB2.15B$40.A19.2AB.17B$39.2A4.2B
15.18B$4.A30.B3.8B15.17B$2.ABAB27.4B4.7B14.17B$3.2A2B25.6B.9B9.B5.16B
$4.4B10.A13.6B.10B8.AB4.19B$5.4B7.3A12.19B7.3A3.20B$6.4B5.A14.19B8.3B
A2.20B$7.4B4.2A13.17B11.B2AB.20B$2A6.9B14.15B13.4B.18B$.A7.6B14.17B
14.21B$.A.2A5.6B3.B2.2B2.22B13.21B$2.A2.A4.19BD21B3.2B2.23B$3.2AB3.6B
D13BDBD4B.24BD18B$4.9BDBD2B2A9B3D4B2.23BDBD4B.10B3.2A$5.9B2D2B2A11BD
4B2.23B3D5B.7B4.B2AB$6.29B4.24BD14B4.2B$6.17B.4B10.45B$7.15B3.2B12.
16B.4B8.16B$7.15B3.3B11.12B5.3B10.16B2.B$8.13B5.A2B.2A7.9B6.4B11.16B.
B2A$10.13B2.A.A2B.A6.11B5.2A12.2B.16B2A$9.8B4.2A.A.AB2.A8.7B.B2A5.A9.
2B.17B.2B$9.6B6.2ABA4.A11.4B2.BA.A.3A9.2A18B$9.5B8.B2.5A.A8.B2A2B5.A.
A11.2A18B$9.B.B5.2A.A.2A.A4.A.A8.2A7.2A13.2B.16B.BA$10.3B4.A.2A.A2.A.
2A2.A37.16BA.A$9.B2AB11.2A.A.2A44.10B.2A$10.2A63.9B$76.4B2D2B$76.3B2D
3B$76.2B2D5B$76.11B$76.11B$69.2A4.12B$69.A.A4.9B.B2A$71.A5.7B2.BA.A$
71.A.2A2.7B5.A$64.2A3.A.A.A2.A6B6.2A$63.A2.A.A.2A.A.2A4B$63.2A.A.A4.A
.AB$66.A.A.2A.A2.AB$66.A2.A.A.AB2A2.A$63.2A.A4.A.A3.3A$63.A2.2A2.2AB
4A$65.A3.A2.B.B.A.2A$62.A3.3A.5A.A2.A$62.4A2.A.A.B2.A.2A$59.A6.ABA.B.
AB.A$59.5AB.A.4A.A.A$57.2A5.ABA2B4.A.2A$56.A.A.2A.A2.A.4A.A$56.A2.A.A
.AB2A.A2.A.A$53.2A.A4.A.A3.A2.A2.2A$53.A2.2A2.2AB4A4.2A$55.A3.A2.B.B.
A.A3.A$52.A3.3A.5A.A.4A$52.4A2.A.A.B2.A.A$56.ABA.B.AB.A3.A$52.2AB.A.
4A.A.A2.2A$51.A2.ABA2B4.A.2A$50.A2.A2.A.4A.A$50.2A.AB2A.A2.A.A$51.A.A
3.A2.A2.2A$51.A2.3A4.2A$52.A.A7.A$53.A6.A$60.2A!
I think there's a possibility that other LOM conduits may exist that can hook up to this H->LOM. The fact that the output is oriented the way it is, but still edgy enough to catalyze the inwards-facing half with a boat makes this seem much more promising for new connections than prior LOM sources.

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Re: The Hunting of the Elementary Conduits

Post by Scorbie » July 28th, 2020, 5:50 am

HYPE! This should reduce the 2c/3 transmitter by an order of magnitude.

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Re: The Hunting of the Elementary Conduits

Post by dvgrn » July 28th, 2020, 6:15 am

Scorbie wrote:
July 28th, 2020, 5:50 am
HYPE! This should reduce the 2c/3 transmitter by an order of magnitude.
Not sure about that... The 2c/3 transmitter is definitely overdue for a rebuild, unless someone has rebuilt this 2017 effort and I missed collecting it at the top of the Stable signal circuitry thread.

However... someday maybe someone will find a way to extract a signal out of the other end of a 5c/9 wire, but at the moment that's still just a dead end for signals as far as I know.

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Re: The Hunting of the Elementary Conduits

Post by apg » July 28th, 2020, 7:43 am

dvgrn wrote:
July 28th, 2020, 6:15 am
Scorbie wrote:
July 28th, 2020, 5:50 am
HYPE! This should reduce the 2c/3 transmitter by an order of magnitude.
Not sure about that... The 2c/3 transmitter is definitely overdue for a rebuild, unless someone has rebuilt this 2017 effort and I missed collecting it at the top of the Stable signal circuitry thread.
You missed this, yes: viewtopic.php?f=2&t=2817&start=200#p100406
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Re: The Hunting of the Elementary Conduits

Post by apg » August 11th, 2020, 8:17 am

Kazyan wrote:
January 19th, 2016, 7:46 pm
EDIT: Here's something delightfully weird and spartan. I haven't found a good way to cleanly extract one of the B outputs, but I'm sure there's something that doesn't require resorting to Bellman:

Code: Select all

x = 34, y = 35, rule = B3/S23
$10b2o$10bobo7bo$12bo5b3o$12b2o3bo$17b2o4$30b2o$9bo20b2o$10bo$10b2o14b
o$9b2o14bobo$9bo14bo2bo$25b2o16$20bo$19bobo$19b2o!
It's possible to get a glider output:

Code: Select all

x = 46, y = 39, rule = LifeHistory
3B$4B$.4B$2.4B$3.4B$4.4B$5.4B15.2A$6.4B14.A.A7.A$7.4B15.A5.3A$8.4B14.
2A3.A$9.6B7.2A3.B3.2A$10.6B5.B2AB.3B.3B5.B$10.8B4.3B2.4B5.5B$10.10B3.
B2.16B2.B$10.10B2.20B.B2A$10.2BC10BD20B2A$10.2B2C10BD17B.2B$10.B2C11B
2D14BAB$10.13B2D14BABA$11.12BD14BA2BA$12.B2.24B2AB$15.2B3.21B$16.AB3.
19B$15.A.A4.16B$15.2A5.16B$22.17B$22.17B$22.17B$22.16B$22.14B$20.17B$
20.17B$20.17B$18.2AB.15B$17.A.AB3.2B2.8B$17.A14.3B$16.2A16.AB$33.A.A$
33.2A!

EDIT:
It looks as though this is already in the elementary conduit collection.
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Re: The Hunting of the Elementary Conduits

Post by Kazyan » August 26th, 2020, 9:19 pm

New Pi-to-G, shown with the one conduit it connects to:

Code: Select all

x = 104, y = 109, rule = B3/S23
62b2o$62b2o2$60b4o$47b2o3b2o6bo2bo$48bo4bo$48bob3o$45b2obobo10b2o$45bo
2bo11bo2bo$47b2o12bobo$62bo6$56b3o$56bobo9b2o$44b2o10bobo7bo2bo$45bo
20b3o$42b3o$42bo23b2obob2o$67bob2obo$67bo$66b2o38$26b2o54b2o$26b2o54b
2o2$24b4o54b4o$11b2o3b2o6bo2bo54bo2bo6b2o3b2o$12bo4bo74bo4bo$12bob3o
76b3obo$9b2obobo10b2o56b2o10bobob2o$9bo2bo11bo2bo54bo2bo11bo2bo$11b2o
12bobo54bobo12b2o$26bo56bo7$32b2o39b2ob2o$8b2o20bo2bo40bobo2bo20b2o$9b
o20b3o40bo3b3o20bo$6b3o64bob2o24b3o$6bo23b2obob2o37bobob2o23bo$31bob2o
bo39bobo$31bo43bo2bo$7b2o21b2o39b2obob2o$8bo60bo2bobo$8bobo58b2o3bob2o
$9b2o17b2ob2obo38bo2b2o17b2ob2obo$28b2obob2o38b2o20b2obob2o6$9bo66bo$
9bobo18b2o44bobo18b2o$9b3o18b2o44b3o18b2o$11bo66bo5$2b2o65b2o$3bo19b2o
45bo19b2o$3o20bo43b3o20bo$o23b3o40bo23b3o$26bo66bo!
It also probably connects to HF95P in one orientation if there's a Bellmant catalyse to replace the block-and-eater in that conduit in a nice way, but whatever.
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Re: The Hunting of the Elementary Conduits

Post by MathAndCode » October 28th, 2020, 1:10 pm

Here's a clean R−H→C.

Code: Select all

x = 13, y = 15, rule = LifeHistory
2A8.2A$.A8.2A$.A.A$2.2A2$9.A$9.3A$10.A4$11.D$11.2D$10.2D$10.D!
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Re: The Hunting of the Elementary Conduits

Post by dvgrn » October 28th, 2020, 3:55 pm

MathAndCode wrote:
October 28th, 2020, 1:10 pm
Here's a clean R−H→C.

Code: Select all

x = 13, y = 15, rule = LifeHistory
2A8.2A$.A8.2A$.A.A$2.2A2$9.A$9.3A$10.A4$11.D$11.2D$10.2D$10.D!
Along the same lines as the new candidate conduit in the Periodic Herschel Conduits thread, this will only get added to the Elementary Conduits Collection if there's an X-to-R conduit that can connect with this one. I haven't gone through and checked, but it looks like the R is facing the wrong way.

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Re: The Hunting of the Elementary Conduits

Post by MathAndCode » October 28th, 2020, 7:08 pm

dvgrn wrote:
October 28th, 2020, 3:55 pm
Along the same lines as the new candidate conduit in the Periodic Herschel Conduits thread, this will only get added to the Elementary Conduits Collection if there's an X-to-R conduit that can connect with this one. I haven't gone through and checked, but it looks like the R is facing the wrong way.
The R-sequence often starts from b3o$o3bo$5bo, which is commonly edgeshot, such as from a Herschel.

Code: Select all

x = 32, y = 42, rule = B3/S23
b2o8b2o$2bo8b2o$2bobo$3b2o10$30bo$29b2o$28b2o$29b2o7$3b2o$2bobo16b2o$2bo17bo2bo2b2o$b2o17bobo4bo2bo$21bo5bobobo$24b2obo2bo$24bo2bo$21bo4bo$21b5o2$23bo$22bobo$3bob2o5b2o9bo$b3ob2o5bobo$o13bo$b3ob2o7b2o$3bobo$3bobo$4bo!
This particular method of generating the R-sequence makes extracting the century very difficult if not impossible, but the R-pentomino has about 270 degrees of empty space stretching indefinitely far around it, and this is about 315 degrees for the century, so it seems that it should be possible to connect the conduit that I found to other conduits.
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Re: The Hunting of the Elementary Conduits

Post by Scorbie » October 29th, 2020, 9:40 pm

MathAndCode wrote:
October 28th, 2020, 7:08 pm
The R-sequence often starts from b3o$o3bo$5bo, which is commonly edgeshot, such as from a Herschel.
This. That "Backwards R" seems very interesting, although I don't have a way to tame it.
Are there any other contexts of this pattern other than the Herschel?
(IMHO Even if there are none, that Herschel source makes it worth exploration.)

IMHO not worth in the Conduit collection just yet, but it may be soon.

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Re: The Hunting of the Elementary Conduits

Post by MathAndCode » October 29th, 2020, 10:02 pm

Scorbie wrote:
October 29th, 2020, 9:40 pm
MathAndCode wrote:
October 28th, 2020, 7:08 pm
The R-sequence often starts from b3o$o3bo$5bo, which is commonly edgeshot, such as from a Herschel.
This. That "Backwards R" seems very interesting, although I don't have a way to tame it.
Are there any other contexts of this pattern other than the Herschel?
(IMHO Even if there are none, that Herschel source makes it worth exploration.)
I'm fairly sure that I've seen it form in another way at least once, but I can't remember the specific occurrence. The pattern looks easily edgeshootable, though, and this post states that there are plenty of conduits that create backwards-facing Rs.



Edit: Here are a couple that produce Rs from alternative directions, including one from that easily edgeshot sexaplet.
MathAndCode wrote:
October 16th, 2020, 10:40 am
Luckily, it can be modified, but the block is put back in the wrong place.

Code: Select all

x = 25, y = 28, rule = LifeHistory
13.D$12.3D$12.D.2D8$23.2C$23.2C4$2.2A$.A.A13.A$.A11.3A$2A10.4A$11.2A5.D$11.2A4.3D$12.2A3.D3$9.2A$10.A$7.3A$7.A!
Here's another modification with an extra blinker.

Code: Select all

x = 28, y = 28, rule = LifeHistory
13.D$12.3D$12.D.2D5$26.2A$26.A$24.A.A$24.2A5$2.2A$.A.A13.A$.A11.3A$2A10.4A$11.2A$11.2A7.2D$12.2A5.2D$20.D2$9.2A$10.A$7.3A$7.A!


Another edit: While looking for other converters, I found 30bo$29b2o$2o26b2o$bo27b2o$bobo$2b2o5$3b2o$2bobo16b2o$2bo18bobo$b2o20bo$17b2o4b2o$17bobo$19bo$10b2o7b2o$10b2o. Is there any way to extract both B-heptominoes? Conduit 1 only works on the bottom B-heptomino.
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Re: The Hunting of the Elementary Conduits

Post by Scorbie » October 30th, 2020, 3:13 am

@MathAndCode I see, thanks for the info.
(Note: I personally use @ for messages not worth pinging another user immediately. I don't mind being pingged though.)
MathAndCode wrote:
October 29th, 2020, 10:02 pm
Another edit: While looking for other converters, I found

Code: Select all

30bo$29b2o$2o26b2o$bo27b2o$bobo$2b2o5$3b2o$2bobo16b2o$2bo18bobo$b2o20bo$17b2o4b2o$17bobo$19bo$10b2o7b2o$10b2o
.
Is there any way to extract both B-heptominoes? Conduit 1 only works on the bottom B-heptomino.
The PI at gen 87 (the heptaplet at the center, just in case; It's pretty common too) seems very hard to clean, but one never knows.

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Re: The Hunting of the Elementary Conduits

Post by MathAndCode » October 30th, 2020, 10:15 am

Scorbie wrote:
October 30th, 2020, 3:13 am
(Note: I personally use @ for messages not worth pinging another user immediately. I don't mind being pingged though.)
Ah; thank you for explaining.
Scorbie wrote:
October 30th, 2020, 3:13 am
The PI at gen 87 (the heptaplet at the center, just in case; It's pretty common too) seems very hard to clean, but one never knows.
I also noticed it, but I don't think that there is enough room for conduits for there to be hope of extracting the ∏. Consequently, something, whether an eater or a catalyst in a conduit, has to interact with the B-heptomino relatively early, before its trailing dust contributes to the ∏'s formation.
By the way, here is another output that is probably useless.

Code: Select all

x = 30, y = 30, rule = B3/S23
15b2o$15bo$13bobo$13b2o9$29bo$28b2o$27b2o$28b2o7$2b2o$bobo16b2o$bo18bobo$2o20bo$5b2o15b2o$6bo$3b3o$3bo!


Edit: There probably isn't a catalyst that works in this case, but this is how easy it is to edgeshoot that R-sexaplet.

Code: Select all

x = 30, y = 28, rule = B3/S23
14bo$12b3o$11bo$11b2o10$29bo$28b2o$27b2o$28b2o7$2b2o$bobo16b2o$bo18bobo$2o20bo$22b2o!
#C [[ T 90 PAUSE 1 ]]


Another edit: I'm trying to find a stable version of Lx73. I haven't found one yet, but I did notice something else.

Code: Select all

x = 31, y = 26, rule = B3/S23
5bo9bo$5b3o5b3o$8bo3bo$7b2o3b2o$b2o$2bo$2bobo$3b2o$30bo$29b2o$2o26b2o$bo27b2o$bobo$2b2o5$3b2o$2bobo16b2o$2bo18bobo$b2o20bo$15b2o6b2o$15bobo$17bo$17b2o!
At generation 114, an octaplet is edgeshot and follows an evolutionary sequence that eventually becomes diagonally symmetric (or at least would if there weren't fishhooks in its way). I'm pretty sure that I've seen that sequence at least twice before in the last few days, it looks edgeshootable, and it has at least 28 three-glider syntheses, all of which suggest that it should be fairly common. Combined with the fact that there are similarly edgeshootable clusters, some with only seven cells, and the fact that there is a simple way to make it from an R-pentomino, I think that it would be a good cluster to look for conduits accepting. I'll do that after I finish looking for a stable Lx73 unless someone has told me otherwise.



Yet another edit: Here is a way to turn it into a B-heptomino.

Code: Select all

x = 16, y = 10, rule = B3/S23
9bo$7b3o$8bo2$2b2o$bobo$bo10b2o$2o10bobo$14bo$14b2o!
Unfortunately, this particular pair will likely be difficult to hook up to other conduits.



Fourth edit: Why does this not work with an eater 2?

Code: Select all

x = 9, y = 21, rule = B3/S23
6bo$4b3o$3bo$3b2o5$6b2o$6b2o2$2bo$3o$bo4$5b2o$5bobo$7bo$7b2o!
#C [[ PASTEMODE XOR ]]
#C [[ RLE tub bo$obo$bo! ]]
#C [[ PASTET 55 ]]
#C [[ PASTE tub 4 0 ]]


Fifth edit: Is it possible to replace a block with a catalyst that does not get destroyed?

Code: Select all

x = 6, y = 6, rule = B3/S23
4b2o$4b2o2$b2o$2o$bo!
I tried replacing it with a fishhook, and that resulted in another partial R conduit. One can also use a boat or a ship.

Code: Select all

x = 8, y = 8, rule = TripleB3S23
6.2D$5.CE$4.G.G$4.2G2$.2G$2G$.G!


Sixth edit: One can seemingly use anything where the cell closest to the R-pentomino have two neighbors instead of three.

Code: Select all

x = 8, y = 8, rule = TripleB3S23
4.2D$5.D2A$4.G.BC$4.2G.B2$.2G$2G$.G!


Seventh edit: Here is another partial conduit where the block can probably be replaced by a catalyst.

Code: Select all

x = 5, y = 7, rule = B3/S23
b2o$2o$bo3$3b2o$3b2o!


Eighth edit: Apparently, no one here has thought of a BFx10 before, so now I have another partial conduit that would be new if completed.
MathAndCode wrote:
October 23rd, 2020, 5:27 pm

Code: Select all

x = 62, y = 13, rule = B3/S23
2o8b2o8b2o8b2o8b2o8b2o8b2o$2o8b2o8b2o8b2o8b2o8b2o8b2o3$60bo$59b2o$58b2o$59b2o4$5b2o8b2o8b2o8b2o8b2o8b2o$5b2o8b2o8b2o8b2o8b2o8b2o!


Ninth edit: Could this be salvageable?

Code: Select all

x = 31, y = 27, rule = DoubleB3S23
28.C$26.3C$25.C$25.2C6$2C27.2A$.C27.2A$.C.C$2.2C23.2B$27.B$15.2C11.3B$14.2C6.2C6.B$15.C6.C.C$4.2C18.C$5.C18.2C$2.3C$2.C11.2C$14.2C2$17.2C$17.C$18.3C$20.C!


Tenth edit: This partial RF57 looks so promising that I'm already demonstrating that it can be connected to other conduits.

Code: Select all

x = 89, y = 55, rule = LifeHistory
79.2A.A$70.A.2A6.3A$70.2A.A7.A2$79.2A$79.2A16$47.2A$47.A$48.A$47.2A$56.2A$55.A.A$56.A3$44.2A$44.2A$23.2A35.2D21.2A.2A$23.2A34.2D23.A.A$60.D21.A.A.A.A$82.2A3.2A2$57.2D$56.2D$38.A.2A15.D24.A$36.3A.2A40.3A$35.A49.A$36.3A.2A6.2A34.2A$2A36.A.A8.A$2A36.A.A5.3A31.2A$39.A6.A19.2A12.A.A$54.A11.2A14.A$14.2A37.A.A26.2A$14.A38.2A$15.3A$17.A$4.2A$5.A$2.3A$2.A!


Eleventh edit: Here's a quick way to turn an LoM predecessor into a ∏-heptomino.

Code: Select all

x = 11, y = 9, rule = DoubleB3S23
B9.A$3B5.3A$3.B3.A$2.2B3.2A2$4.3C$3.C3.C$3.C$4.C!
It looks like it is probably not compatible with most catalysts, but there might be one or two pairs that work.
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EvinZL
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Re: The Hunting of the Elementary Conduits

Post by EvinZL » November 1st, 2020, 4:58 pm

MathAndCode wrote:
October 30th, 2020, 10:15 am
Fifth edit: Is it possible to replace a block with a catalyst that does not get destroyed?

Code: Select all

x = 6, y = 6, rule = B3/S23
4b2o$4b2o2$b2o$2o$bo!
This has already been completed by Kazyan:

Code: Select all

x = 26, y = 21, rule = LifeHistory
A24.A$3A20.3A$3.A18.A$2.2AB2.2B8.2B2.B2A$2.8B6.8B$4.18B$4.15B2AB$3.
16B2A2B$3.5BACA5BD3BA2B$3.5BCDC4B3D3A2B$4.4BC8BDB2AB$4.13BABA2B$4.B2A
11BA3B$5.2A5B2.7B$7.4B4.4B$7.3B6.3B$7.2AB6.B2A$6.A.A8.A.A$4.3A.A.A4.A
.A.3A$3.A5.2A4.2A5.A$3.2A16.2A!
Partial RF57

Code: Select all

x = 89, y = 55, rule = LifeHistory
79.2A.A$70.A.2A6.3A$70.2A.A7.A2$79.2A$79.2A16$47.2A$47.A$48.A$47.2A$56.2A$55.A.A$56.A3$44.2A$44.2A$23.2A35.2D21.2A.2A$23.2A34.2D23.A.A$60.D21.A.A.A.A$82.2A3.2A2$57.2D$56.2D$38.A.2A15.D24.A$36.3A.2A40.3A$35.A49.A$36.3A.2A6.2A34.2A$2A36.A.A8.A$2A36.A.A5.3A31.2A$39.A6.A19.2A12.A.A$54.A11.2A14.A$14.2A37.A.A26.2A$14.A38.2A$15.3A$17.A$4.2A$5.A$2.3A$2.A!

Code: Select all

x = 23, y = 16, rule = LifeHistory
11.2B3.2B.2D$8.B.4B.3B2DB$6.13BD2B$5.17B$4.19B$4.12B2C4B$4.11B2C5B$2.
2AB.10BC4B$.A.AB4.10B$.A5.3B2.7B$2A5.2A3.7B$8.A3.7B$5.3A6.4B$5.A9.2B$
14.B2AB$15.2A!
In general check the ECC first

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Re: The Hunting of the Elementary Conduits

Post by bubblegum » November 1st, 2020, 5:15 pm

MathAndCode wrote:
October 30th, 2020, 10:15 am
Fourth edit: Why does this not work with an eater 2?

Code: Select all

x = 9, y = 21, rule = B3/S23
6bo$4b3o$3bo$3b2o5$6b2o$6b2o2$2bo$3o$bo4$5b2o$5bobo$7bo$7b2o!
#C [[ PASTEMODE XOR ]]
#C [[ RLE tub bo$obo$bo! ]]
#C [[ PASTET 55 ]]
#C [[ PASTE tub 4 0 ]]
The eater is given 4 ticks to recover. An eater 2 takes 6.
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July 2nd, 2020, 8:33 pm
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MathAndCode
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Re: The Hunting of the Elementary Conduits

Post by MathAndCode » November 1st, 2020, 5:45 pm

EvinZL wrote:
November 1st, 2020, 4:58 pm

Code: Select all

x = 23, y = 16, rule = LifeHistory
11.2B3.2B.2D$8.B.4B.3B2DB$6.13BD2B$5.17B$4.19B$4.12B2C4B$4.11B2C5B$2.
2AB.10BC4B$.A.AB4.10B$.A5.3B2.7B$2A5.2A3.7B$8.A3.7B$5.3A6.4B$5.A9.2B$
14.B2AB$15.2A!
In general check the ECC first
I'm sorry; I remember being told by another user that searching the forums for the name would be sufficient.
bubblegum wrote:
November 1st, 2020, 5:15 pm
The eater is given 4 ticks to recover. An eater 2 takes 6.
It actually only requires five ticks, which I thought was the minimum for an eater 2 because that's how long it takes to recover from eating a glider. However, now that I checked, I realize that a spark from the glider allows the eater 2 to recover one generation more quickly than usual (and this only occurs for two out of four glider lanes that it can eat).



Edit: I made an R−B through a method besides simply deleting the B-sequence from an R-sequence.

Code: Select all

x = 23, y = 34, rule = B3/S23
21bo$20bo$20b3o10$6b2o$6b2o8b2o$16b2o5$2bo$bobo$2bo6$9bo$8b3o$8bo$2b2o$3bo$3o$o!
The sacrificial fishhook probably makes it not useful for anything, but it's the first time that I've ever seen an alternative formation.
For reference, here is the R→W that I was trying to clean up when I found it.

Code: Select all

x = 10, y = 18, rule = LifeHistory
5.2A$5.2A2D$6.D2.D$6.D.D$6.2D3$.A$A.A$2A6$8.C$7.3C$7.C!
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MathAndCode
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Re: The Hunting of the Elementary Conduits

Post by MathAndCode » November 2nd, 2020, 6:40 pm

HL58R only requires one catalyst to clean up everything besides the first natural glider. It even cleans up the Herschel's first block.

Code: Select all

x = 23, y = 31, rule = LifeHistory
12.D$10.3D$11.D7$2.C$3C$C.C$C12$16.2A.A$16.2A.3A$22.A$16.2A.3A$17.A.A$17.A.A$18.A!


Edit: I think that this partial would be a new conduit if completed.

Code: Select all

x = 10, y = 12, rule = LifeHistory
2.C$3C4.2D$.C6.2D$7.2D$7.D4$6.2A$6.A.A$8.A$8.2A!
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