The Hunting of the Elementary Conduits

[2718281828]

Maybe someone finds a simple way to get rid of this blinker:

Code: Select all

x = 16, y = 21, rule = LifeHistory
8.D$7.2DB$7.DBD$6.5B$5.6B$4.3D5B$.B.9B$2A11B$2AB.8B$.B3.9B$4.9B2A$5.
8B2A$4.10B$3.10B$3.10B$4.10B$4.3B3C5B$4.3BCBC4B2A$5.BC2BC4B2A$5.C2BC
2B3.B$6.2CB!

As it is at the envelope boundary it might be feasible.

[Freywa]

ElementaryConduits_7December2018.rle.gz

Conduit stamp collection

(134 KiB) Downloaded 764 times

ec-7-12-18.zip

Conduit files + script

(188.76 KiB) Downloaded 729 times

At last, I came! There are some large changes to the conduit collection.

The following new conduits were added:

Code: Select all

HL58Ra
HL58Rb
RR73H
HR71P
HSW-2T21_SW-2T103
HNW31T120_NW31T378
G0NE_CP_semi-Snark
G0NE_CP_semi-cenark
HSW-2T21_SW4T152
HSW-8T89_SW-2T21b
HL98B_eater2
CFx115D
HL135B
HL164R
BLx154H
DSE8T9
DNE-9T149
DNE4T67

These include the dove conduits.

Sphenocorona's idea for pi/QB-to-asymmetric conduits has been implemented, only that I have used * rather than v (which is much inspired by orbifold notation, which Conway popularised). Of the two mirror-image conduits in a pair, I selected the one without x (i.e. not with a flipped output). Thus PL*124R means both PL124R and PRx124R.

I've also shuffled the H-to-G collection a bit. Any H-to-G for which it is possible to get two gliders in the same direction out, possibly including the FNG, I considered as a H-to-2G and moved accordingly. This combines two H-to-Gs into one H-to-G17 and deletes the conduit that is essentially HFx77Hb. Other gliders (excluding the FNG) that can escape are noted in a #C line.

Lastly, I have added repeat times for some of the conduits; these are indicated by a slash and then the repeat time in the name of the conduit.

An interesting note is that with the addition of Ekström's H-to-B we have two conduits with the same input, same output, same orientation and same transit time – I had to add "_eater2" and "_eater3" to distinguish them.

[dvgrn]

A side note about calculating repeat times for elementary conduits: it looks like this came up earlier this year, and nobody seemed to up with a better solution than the instant-appearance recovery time. (Had forgotten I had written all that up in such a nice long boring way.)

There are some large changes to the conduit collection...

Thanks for doing all this! More steps forward for the ECC --

I've also shuffled the H-to-G collection a bit. Any H-to-G for which it is possible to get two gliders in the same direction out, possibly including the FNG, I considered as a H-to-2G and moved accordingly. This combines two H-to-Gs into one H-to-G17 and deletes the conduit that is essentially HFx77Hb. Other gliders (excluding the FNG) that can escape are noted in a #C line.

Looks to me like the HFx77Hb is still there, both when I run the conduit compiler and when I look at the December 7 RLE. And there's no G10 in the H-to-2G series yet. Is there a later version of the ECC hiding somewhere?

I also remember vaguely -- can't offhand seem to find when it was exactly -- that at some point I cavalierly deleted some perfectly good two-digit H-to-Gn converters out of the ECC, on the grounds that anything above one digit should probably just go in the H-to-Gn collection instead.

Looking back, I can see there's an H-to-G21, H-to-G18, and no doubt a bunch of others that could be added, especially if we want to give up on the idea of a separate H-to-Gn collection and move everything back into the ECC. Any votes on that question?

Lastly, I have added repeat times for some of the conduits; these are indicated by a slash and then the repeat time in the name of the conduit.

I had been thinking of adding this information in a separate #C line in each pattern file, but this seems like a perfectly fine alternative.

If you're planning to do any more recovery-time updates, or if you're definitely not planning on doing any more recovery-time updates, could you post something here to that effect? At some point I'd like to contribute ratings for some more conduits, but it's annoying enough work that I want to make sure not to duplicate anyone else's efforts.

[NoLongerBreathedIn]

To a first approximation it's a category, where the objects are things like H and R, and the morphisms are conduits. There is a functor from this category to the monoid of natural numbers (where a conduit is mapped to the delay) and another functor to the automorphism group of Z^2 (which encodes how the object is rotated, reflected and/or translated).

No, actually, the automorphism group of ℤ² is GL(2,ℤ), which is <a,b,c|a²,b⁴,b²c³,(ab)²,(ac)²>.
What you want is ℤ²⋊D₄, where the D₄ acts as the subgroup of GL(2,ℤ) generated by a and b above.
(This is <a,b,c|a²,b⁴,(ab)²,[a,c],[c,cᵇ],(cb²)²>.)
The issue is that GL(2,ℤ) contains things like shears and order-6 rotations, which do not preserve Life rules,
but doesn't contain translations, which do.

[calcyman]

To a first approximation it's a category, where the objects are things like H and R, and the morphisms are conduits. There is a functor from this category to the monoid of natural numbers (where a conduit is mapped to the delay) and another functor to the automorphism group of Z^2 (which encodes how the object is rotated, reflected and/or translated).

No, actually, the automorphism group of ℤ² is GL(2,ℤ), which is <a,b,c|a²,b⁴,b²c³,(ab)²,(ac)²>.
What you want is ℤ²⋊D₄, where the D₄ acts as the subgroup of GL(2,ℤ) generated by a and b above.
(This is <a,b,c|a²,b⁴,(ab)²,[a,c],[c,cᵇ],(cb²)²>.)
The issue is that GL(2,ℤ) contains things like shears and order-6 rotations, which do not preserve Life rules,
but doesn't contain translations, which do.

I meant Z^2 as a metric space rather than as a group; my apologies for the ambiguity. (Your response is entirely correct if I meant Z^2 as a group, certainly, but I was hoping that my intention was clear from context.)

[Freywa]

Looks to me like the HFx77Hb is still there, both when I run the conduit compiler and when I look at the December 7 RLE. And there's no G10 in the H-to-2G series yet. Is there a later version of the ECC hiding somewhere?

I also remember vaguely -- can't offhand seem to find when it was exactly -- that at some point I cavalierly deleted some perfectly good two-digit H-to-Gn converters out of the ECC, on the grounds that anything above one digit should probably just go in the H-to-Gn collection instead.

Looking back, I can see there's an H-to-G21, H-to-G18, and no doubt a bunch of others that could be added, especially if we want to give up on the idea of a separate H-to-Gn collection and move everything back into the ECC. Any votes on that question?

I meant that there were two instances of the HFx77Hb conduit prior to my update: one as a H-to-H and one as a H-to-G. I deleted the one in H-to-G because the H output is more important, and folded the extra glider lane into a #C line.

[Freywa]

A side note about calculating repeat times for elementary conduits: it looks like this came up earlier this year, and nobody seemed to up with a better solution than the instant-appearance recovery time. (Had forgotten I had written all that up in such a nice long boring way.)

Ha, I think I have an idea now. The linked post mentions BFx59H as a standard input connection for a Herschel-input conduit A, and the instant-appearance recovery time of BFx59H + A together is defined as A's recovery time.

I now extend this to more input types and recovery times. For Herschel-input conduits, if the IA time of BFx59H + A is exactly 53 ticks (the IA time of BFx59H itself), we say that A is rate-limited by BFx59H and declare A's recovery time as "<54", because you do need an input connection anyway.

For other types of inputs I propose the following standard inputs:

• B: HFx58Bb if it fits, otherwise RF28Bb
• C: HR160C or HRx160C if either fits, else PL*328C
• D: CFx115D
• G: no connection is necessary in this case
• P: HL75P
• Q: PF31Qb
• R: HLx69R if it fits, else HLx111R
• W: PF35W

Again, if the recovery time of these conduits prepended to the conduit being tested is the same as that of the prepended conduit, we declare that the tested conduit is rate-limited by the prepended conduit.

For example, with this scheme, the first conduit listed (BFx157B) has a repeat time of 241 because of the glider passing back through the conduit, straight into the input R of the prepended conduit:

Code: Select all

x = 50, y = 41, rule = LifeHistory
30.2A$5.4B20.A.A$4.6B15.2B2.BA$4.8B11.7B$2.3A9B7.10B$2.A13B3.12B$3.A
2BC10BD12B$4.2B2C10BD10B$4.B2C11B2D7B$4.13B2D10B$4.13BD12B$2.27B$2BA
10B.5B2A7B$BABAB5.4B.4B2A7B4.2A$A2BA7.16B4.B2AB$.2A9.13B7.4B$13.11B7.
4B$14.11B6.3B$15.10B5.5B$15.11B4.5B$12.B.13B2.6B$11.2AB.12B2.6B$11.2A
13B3.8B.B3.B$12.33B$12.33BD$14.31B2D$14.32B2D$14.32BD$14.31BD$12.2AB.
26B$11.A.AB.4B3.19B$11.A5.3B.5B.3B3.4B.4B$10.2A9.2A13.2B.4B$22.A12.BA
2B.4B$19.3A13.A.A3.4B$19.A16.A5.4B$43.4B$44.4B$45.3BA$46.3BA$47.3A!

If you're planning to do any more recovery-time updates, or if you're definitely not planning on doing any more recovery-time updates, could you post something here to that effect? At some point I'd like to contribute ratings for some more conduits, but it's annoying enough work that I want to make sure not to duplicate anyone else's efforts.

I won't be doing any more recovery times, then, because the times would change from what I have already calculated (pure IA, without any prepended conduits).

Looking back, I can see there's an H-to-G21, H-to-G18, and no doubt a bunch of others that could be added, especially if we want to give up on the idea of a separate H-to-Gn collection and move everything back into the ECC. Any votes on that question?

I think we should go ahead there and move H-to-Gn's back into the ECC.

[2718281828]

I now extend this to more input types and recovery times. For Herschel-input conduits, if the IA time of BFx59H + A is exactly 53 ticks (the IA time of BFx59H itself), we say that A is rate-limited by BFx59H and declare A's recovery time as "<54", because you do need an input connection anyway.

For other types of inputs I propose the following standard inputs:

I am not in favour of defining a standard input.

I think we should try to find the minimal feasible repeat time for the corresponding input - independent from a 'standard' input. This might be the standard input or another input, or the input 'constructed' from a glider synthesis.
Of course, then we sometimes do not know the fastest possible way to get the input to the initial position. Therefore we could just consider the fastest known reaction, and define this as (best known) repeat time. As a consequence we need for every conduit, an input reaction. But for a substantial amount the mentioned standard inputs will be sufficient. Still, I guess that in some cases a glider collision for the methuselah will provide better results than all known conduit connections.

[2718281828]

As the dove made it into the conduits collection, I studied a bit natural frequency of methuselahs/induction coils for further potential inputs/outputs.
Based on my post viewtopic.php?f=2&t=3604#p66194 here, I take as id of a methuselah the hash of the (first) maximum population pattern (until time to stability [--> growth pattern are excluded]). The pattern with (first) minimum population before the population maximum is regarded as the starting pattern of the methuselah. This allows to classify pattern as die-hard but also allows similar small pattern that evolve into the same methuselah to be regarded as the methuselah.

Further, I restricted the analysis to pattern that double the population from the starting pattern of the methuselah. [And a bounding box restriction to avoid pattern where e.g. glider hit a very far away blinker and creates a blinker glider mess - but for cluster type pattern this is not relevant]
I don't know the most suitable set of pattern to study this natural, I think polyminos or cluster up to a certain number of cells might be suitable. However, here I decided to go for soups.

I took 1 million 5x5 (Bernoulli) soups, here we have the results.
Here the top 20:

Code: Select all

x = 943, y = 323, rule = LifeHistory
7$171.A$171.3A$172.A$10.3A65.3A$10.A2.A64.A.A$11.2A65.A.A$285.A$284.
2A$283.2A$284.2A220.A103.A.A$505.A103.A$505.A2.A100.A2.A78.2A$506.3A
100.2A78.A.A$368.A.A318.2A$368.A2.A417.A$368.A2.A416.A.A$370.2A419.A$
787.A2.A73.2A$787.3A74.A.A$866.A$865.3A215$820.A$388.2A429.A.A$386.A
3.A427.A$10.2A374.A4.A426.A2.A$86.A.3A80.3A217.A426.2A57.A.A$10.A2.A
72.2A303.A485.A.2A$11.3A158.2A89.A613.A.A$171.2A90.A.A612.A$266.2A$
265.A361.A95.A$544.A81.A.A91.A3.A$543.A81.A2.A90.A4.A$542.A.A80.A93.
2A2.2A$542.A.A80.2A$542.2A!

The frequencies relative to the frequency of the R are:
1.129 1.085 1.000 0.811 0.535 0.359 0.144 0.126 0.126 0.104
0.100 0.098 0.088 0.064 0.062 0.060 0.060 0.052 0.046 0.044

The top 8 (rounded freq.) is:
HF (1.1), pi (1.1), R (1), B (.8), LOM (.5), C(.36), E(.14), Wing(.13)
followed by a couple of methuselah where I don't have a name for.

The honey farm is the most frequent one, but as its life time is short and the reaction envelope is small it is not suitable for conduits. Then pi and R are clearly the next best ones, followed by the B. The LOM is about half as common as the R. We should further investigate it, esp. as an output. Similarly, for the E, even though its frequency is only similar to the wing.

The the 2-glider octomino (0.10) and the herschel (.06) made it into the top20 as well. However, esp. the H is naturally is not very frequent, it usually results from a B in conduits. Still, we have some 'natural' herschels which makes me optimistic to find some other methuselahs as output as well.
For the dove(.033) the situation is even worse it is just top 30 with a frequency of about 3.3% of an R. At the moment we have only one C to dove (and a nice LOM to dove). Obviously, the Q (queen bee, 0.0065) the situation is even worse, it ranks about top 200 and is only about 0.6% as common as the R. Still, next to the pi to Q (which is in D2+1 -> D2+1) we have an H to Q which seems to be like a lucky one.

[Kazyan]

Continuing from my post in the Incomplete Search Patterns thread, here's a solution for a new G-to-X. In this case, the output is a B, but Conduit 1 is attached to show a clean and more accessible Herschel. It's not as tidy or fast as the syringe, but has a different output geometry.

Code: Select all

x = 38, y = 46, rule = LifeHistory
16.2A.A$16.A.2A2$17.5A$12.2A2.A4.A$12.A2.A2.A18.A$13.A.A.2A16.3A$12.
2A.A5.A12.A$15.A4.A.A11.2A$15.2A2.A2.A$20.2A2$9.A$9.3A$12.A$11.2A2$.C
$2.C$3C5$2E$2E3$30.2A$30.2A2$3.2E$4.E29.2A$3.E30.A$3.2E3.2A22.A.A$7.A
.A22.2A$7.A$6.2A8.2A$16.2A$32.2A$32.A.A$34.A$34.2A2$24.2A$24.2A!

Example application: this p369 gun...which is still larger than the current p369 gun, so it's just an example.

Code: Select all

x = 71, y = 46, rule = B3/S23
12b2o$12b2o2$2b2o$3bo$3bobo$4b2o$20b2o$20b2o8b2o$30bo$4b2o22bobo$3bobo
22b2o3b2o16b2o$3bo30bo17bo14b2o$2b2o29bo18bobo12b2o$33b2o18b2o$65b4o$
6b2o56bo3bo$6b2o57bo$63bobo$63b2o$36b2o29b2o$36b2o30bo$68bobo$69b2o5$
31bo$30bobo$25b2o2bo2bo$25bo3b4ob2o$26b3o4bobo34bo$28bobo2bo6b3o25bobo
$29bobobobo3bo3bo25b2o$16b2o13bobo2bo2bob3o$15bo2bo2b2o5bo2bo5bo2b3o$
2b2o11bobo4bo5b3o2bo$3bo12bo5bob2o5b4o$3o16b2obobo5bo5bo9b2o$o18bo2bo
2bo5b6o9bo$16bo4bo2b2o21b3o$16b5o12b2o14bo$33b2o$18b2obo$18bob2o!

[dvgrn]

Example application: this p369 gun...which is still larger than the current p369 gun, so it's just an example.

It's too bad the eater3 is so large, in-the-way, and necessary. There don't _quite_ seem to be workable Snark welds before this point (don't take my word for that, though) --

Code: Select all

x = 71, y = 82, rule = LifeHistory
12.2A$11.B2AB$11.3B$2.2A8.B.B$3.A6.5B$3.A.AB2.6B$4.2AB2.11B$6.14B2A$
5.15B2A3B5.2A$6.20B4.A$4.2AB.20BA.A$3.A.AB2.19B2A3.2A16.2A$3.A5.19B6.
A17.A14.2A$2.2A5.19B5.A18.A.AB11.2A$7.21B5.2A18.2AB.B.3B$5.23B6.B20.
7B3.4A$4.2B2A20B6.3B18.7B2.A3.A$4.2B2A21B4.6B16.7B.2BAB$5.25B2.10B11.
10BABAB$5.26B.11B3.2B2.13B2A2B$7.29B2A28B.2A$7.29B2A26B4.A$6.56B6.A.A
$6.56B7.2A$6.28B2A27B$6.22B5.2A12B.4B8.4B$8.19B7.BA5B.B4.4B10.4B$8.
18B9.4B7.4B12.4B$8.9B.7B11.4B5.4B14.4B$6.B2.8B4.6B10.4B3.4B16.4B$5.
12B8.2A11.4B.4B18.4B$3.14B8.A13.7B20.4B$.17B8.3A11.5B22.3B$.17B10.A
11.ABA2B24.B$.16B22.B2A4B$2.14B2A20.3BA.4B$2.3B.2B2.5BA2BA2.2A14.4B3.
4B$2.2A8.2B.ABAB3.A13.4B5.4B$3.A12.A4B.A.2A9.4B7.4B$3A15.B2A.A.A9.4B
9.4B$A17.BAB.A2.A7.4B11.4B$16.A4.A2.2A6.4B13.4B10.2A$16.5A10.4B15.4B
9.A$30.4B17.4B10.A$14.5A10.4B12.2A5.4B5.5A$14.A4.A8.4B14.A5.4B4.A$15.
A2.2A7.4B15.A.AB.7B2.B3A$14.2A2.5B3.4B17.2AB.7B3.2B.A$20.3B2.4B20.12B
4A$10.2A7.9B21.7B2A3BAB2.2A$10.A8.8B22.7B2A2B.B3A2.A$7.2A.A.B3.10B23.
10B3.B.A.2A$7.A2.3AB.2B2A7B22.8B8.A$8.2A2.BA3B2A7B21.9B7.2A$10.4A12B
20.4B2.3B$10.A.2B3.7B.B2A17.4B3.5B$11.3AB2.7B.BA.A15.4B7.2A$14.A4.4B
5.A14.4B8.A$9.5A5.4B5.2A12.4B10.3A$9.A10.4B10.A6.4B13.A$11.A9.4B7.3A
5.4B$10.2A10.4B5.A7.4B$23.4B4.2A5.4B$24.9B4.4B$25.6B5.4B$25.8B2.4B$
23.15B$23.14B$23.13B$21.2AB.10B$20.A.AB3.B2A3B$20.A6.B2A3B$19.2A6.4B$
28.3B$29.2B.BA$28.B2ABA.A$27.BABABA.A$25.A2.A.A.A.A.2A$25.4A.2A2.A2.A
$29.A4.2A$27.A.A$27.2A!

-- which is vaguely competitive but doesn't seem to set records near p220+12N or p330+4N -- bounding box 5822 @ 334, need something smaller than 5394.

Similarly, bootstrapping with the other glider gets p507+8N, also bigger (5270) than the competition (4071):

Code: Select all

x = 85, y = 62, rule = LifeHistory
71.2A$70.B2AB$71.3B$70.B.B8.2A$70.5B6.A$70.6B2.BA.A$65.11B2.B2A$63.2A
14B$53.2A5.3B2A15B$54.A4.20B$54.A.A20B.B2A$32.2A16.2A3.2A19B2.BA.A$
16.2A14.A17.A6.19B5.A$16.2A11.BA.A18.A5.19B5.2A$23.3B.B.B2A18.2A5.21B
$16.4A3.7B20.B6.23B$16.A3.A2.7B18.3B6.20B2A2B$18.BA2B.7B16.6B4.21B2A
2B$18.BABA10B11.10B2.25B$18.2B2A13B2.2B3.11B.26B$16.2A.28B2A29B$16.A
4.26B2A29B$14.A.A6.56B$9.A4.2A7.56B$9.3A10.57B$12.A8.4B8.4B.14B5.22B$
11.2A7.4B10.4B4.B.7B7.19B$11.5B3.4B12.4B7.4B9.18B$13.3B2.4B14.4B5.4B
11.7B.9B$3.2A7.9B16.4B3.4B10.6B4.8B2.B$3.A8.8B18.4B.4B11.2A8.12B$2A.A
.B3.10B20.7B13.A8.14B$A2.3AB.2B2A7B21.5B11.3A8.17B$.2A2.BA3B2A7B21.5B
11.A10.17B$3.4A12B20.7B22.16B$3.A.2B3.7B.B2A17.4B.4B20.2A14B$4.3AB2.
7B.BA.A15.4B3.4B14.2A2.A2BA5B2.2B.3B$7.A4.4B5.A14.4B5.4B13.A3.BABA.2B
8.2A$2.5A5.4B5.2A12.4B7.4B9.2A.A.4BA12.A$2.A10.4B10.A6.4B9.4B9.A.A.2A
B15.3A$4.A9.4B7.3A5.A3B11.4B7.A2.A.BAB17.A$3.2A10.4B5.A7.B2AB13.4B6.
2A2.A4.A$16.4B4.2A5.BABA15.4B10.5A$17.9B4.4B17.4B$18.6B5.4B19.4B10.A$
18.8B2.4B21.4B8.A.A$16.15B23.4B8.A$16.14B25.4B$16.13B27.4B$14.2AB.10B
29.4B$13.A.AB3.B2A3B32.4B$13.A6.B2A3B33.4B$12.2A6.4B36.4B$21.3B37.4B$
22.2B.BA35.4B$21.B2ABA.A35.4B$20.BABABA.A36.4B$18.A2.A.A.A.A.2A34.4B$
18.4A.2A2.A2.A35.4B$22.A4.2A38.3BC$20.A.A45.3BC$20.2A47.3CB!

But there are lots of other attachments to try, down to the repeat time which appears to be 270. Maybe a pair of bumpers will fit better.
EDIT2: Even adding just one H-to-2G to get a fixed p451 is still too big, because the darn p443+8N is so compact:

Code: Select all

x = 81, y = 51, rule = LifeHistory
10.2A$9.B2AB$9.3B$2A8.B.B$.A6.5B$.A.AB2.6B$2.2AB2.11B$4.14B2A$3.15B2A
3B5.2A38.A$4.20B4.A39.3A$2.2AB.20BA.A21.A20.A$.A.AB2.19B2A3.2A17.3A9.
A7.2A$.A5.19B6.A20.A8.3A5.4B$2A5.19B5.A20.2A11.A6.4B$5.21B5.2A19.3B9.
2A3.8B$3.23B6.B21.B4.B4.3B.9B$2.2B2A20B6.3B19.B3.3B5.14B$2.2B2A21B4.
6B16.2B.6B3.16B$3.25B2.10B10.5B.7B2.16B$3.26B.11B3.2B2.33B$5.29B2A44B
$5.29B2A44BC$4.51B2A21BCBC$4.51B2A21B.2C$4.75B.B$4.22B5.14B.B5.26B$6.
19B7.7B.B13.B2.19B$6.18B9.4B19.19B$6.9B.7B11.4B6.A10.21B$7.8B4.6B10.
4B5.3A7.9B2.11B$5.10B8.2A11.4B7.A5.4B.5B2.11B$5.10B8.A13.4B5.2A4.4B2.
4B3.9B.B2A$5.11B8.3A11.4B4.9B11.8B.BA.A$.2A2.11B10.A12.4B5.6B12.8B4.A
$.2A2.10B25.4B2.2B2A4B10.9B5.2A$5.9B2A25.6BA2BA5B8.2A3.3B$5.B2.5BA2BA
2.2A21.5B2AB2A4B9.A4.B$4.2A4.2B.ABAB3.A22.5BABA5B6.3A$3.A.A8.A4B.A.2A
20.5BA4B.B2A4.A$.3A.A.A8.B2A.A.A21.8B3.BA.A$A5.2A8.BAB.A2.A22.6B6.A$
2A12.A4.A2.2A24.4B6.2A$14.5A29.3B$45.AB.2B$13.A.3A.A24.A.AB2AB$13.2A.
A.2A24.A.ABABAB$41.2A.A.A.A.A2.A$41.A2.A2.2A.4A$43.2A4.A$49.A.A$50.2A!

EDIT: Ha! 4368 definitely beats 5015 at period 485 (including simeks' improvement):

Code: Select all

x = 78, y = 56, rule = LifeHistory
65.2A$64.B2AB$65.3B$64.B.B8.2A$64.5B6.A$64.6B2.BA.A$59.11B2.B2A$57.2A
14B$47.2A5.3B2A15B$48.A4.20B$48.A.A20B.B2A$26.2A16.2A3.2A19B2.BA.A$
10.2A14.A17.A6.19B5.A$10.2A11.BA.A18.A5.19B5.2A$17.3B.B.B2A18.2A5.21B
$10.4A3.7B20.B6.23B$10.A3.A2.7B18.3B6.20B2A2B$12.BA2B.7B16.6B4.21B2A
2B$12.BABA10B11.10B2.25B$12.2B2A13B2.2B3.11B.26B$10.2A.28B2A29B$10.A
4.26B2A29B$8.A.A6.56B$8.2A7.56B$16.57B$2A13.4B8.4B.14B5.22B$.A12.4B
10.4B4.B.7B7.19B$.A.AB2.B5.4B12.4B7.4B9.18B$2.2AB.3B3.4B14.4B5.4B11.
7B.9B$4.6B.4B16.4B3.4B10.6B4.8B2.B$4.10B18.4B.4B11.2A8.12B$4.2B2A5B
20.7B13.A8.14B$5.A2BA3B22.5B11.3A8.17B$5.BABA4B21.5B11.A10.13B2A2B$6.
BA6B19.7B22.12B2A2B$6.3B2.4B17.4B.4B20.2A14B$6.3B3.4B15.4B3.4B14.2A2.
A2BA5B2.2B.3B$6.B6.4B13.4B5.4B13.A3.BABA.2B4.2A$4.5B5.4B11.4B7.4B9.2A
.A.4BA8.A.A$4.5B6.4B9.4B9.4B9.A.A.2AB8.A.A.3A$3.7A6.4B7.4B11.4B7.A2.A
.BAB8.2A5.A$.3A.3A.3A5.4B5.2A2B13.4B6.2A2.A4.A12.2A$A3.B3AB3.A5.4B3.
2B2A15.4B10.5A$A.3A.A.4A7.4B.2BAB5.A2.2A7.4B$.A3.3B12.7B5.A.A2.A8.4B
7.A.3A.A$3.A.A.A.2A.A8.5B6.A.A.A10.4B6.2A.A.2A$2.2A.ABA.A.2A7.6B5.2A.
A.2A10.4B$3.A.A2.A10.9B.BAB.2A3.A10.4B$3.A2.2A10.5B3A2B.3A2B.2AB.A10.
4B$2.2A15.4BA5B3A2B2A.A.A11.4B$20.3BAB4.3A2B.2ABA13.4B$18.5B6.BAB.2A
18.4B$18.2A11.2A.A.5A13.4B$19.A12.A.A2.A2.A14.3BC$16.3A13.A2.A20.3BC$
16.A16.2A22.3C!

... Bother. Now my gun-building script is out of date again.

[simeks]

Continuing from my post in the Incomplete Search Patterns thread, here's a solution for a new G-to-X.

Nice! Slightly smaller bounding box:

Code: Select all

x = 36, y = 46, rule = LifeHistory
16.2A.A$16.A.2A2$17.5A$12.2A2.A4.A12.2C$12.A2.A2.A9.2C5.C$13.A.A.2A9.
C.C.3C$12.2A.A5.A8.C.C$15.A4.A.A7.2C$15.2A2.A2.A$20.2A$33.2C$9.A23.2C
$9.3A$12.A$11.2A2$.A$2.A$3A5$2A$2A3$30.2A$30.2A2$3.2A$4.A29.2A$3.A30.
A$3.2A3.2A22.A.A$7.A.A22.2A$7.A$6.2A8.2A$16.2A$32.2A$32.A.A$34.A$34.
2A2$24.2A$24.2A!

[calcyman]

Continuing from my post in the Incomplete Search Patterns thread, here's a solution for a new G-to-X. In this case, the output is a B, but Conduit 1 is attached to show a clean and more accessible Herschel. It's not as tidy or fast as the syringe, but has a different output geometry.

Wow! This is exciting! What's the repeat time?

I see that the eater3 interacts twice in quick succession, so cannot be replaced with a loaf reset by a Snark.

This means we now need slow-salvo syntheses of the eater3 in all orientations adding to slmake, to get both this and the rectifier.

I can imagine this being useful in self-constructing circuitry since it's compatible with independent conduits (unlike the syringe) and also allows the FNG to escape.

EDIT: Alternatively, it might be possible to ptbsearch/catgl/catforce your bait reconstruction to obtain a Spartan reflector or G-to-H.

[dvgrn]

Wow! This is exciting! What's the repeat time?...
I can imagine this being useful in self-constructing circuitry since it's compatible with independent conduits (unlike the syringe) and also allows the FNG to escape.

270. So it would have to be the kind of self-constructing circuitry in the switching system of the 0E0P, rather than the single-channel-supporting circuits that every other self-constructing pattern has been made out of lately.

EDIT: Alternatively, it might be possible to ptbsearch/catgl/catforce your bait reconstruction to obtain a Spartan reflector or G-to-H.

Yeah, if CatForce is what found this, then it's worth checking ptbsearch and/or catgl, to see if there's something that gets a glider or some other signal out of that long-running TL+mess, hopefully in a different direction. With three transparent blocks already, might as well try for a few more with ptbsearch.

[Freywa]

The new G-to-H is a G-to-B followed by conduit 1. At first I wanted to call Kazyan's discovery a big syringe, but that abbreviates to BS. So I'll propose the name bronco instead, following the example set by buckaroo and because it outputs a B. The active pattern also looks very wild while it bounces between the catalysts, and the glider seems "kicked back" by the conduit into a B and then H.

[Entity Valkyrie]

It is the Syringe 2 (technically named because this is the second "syringe")

[Freywa]

Defining Orientation and Timing for Glider-Input Conduits

Maybe the most controversial change is that I simplified the names of most of the G(n) input conduits. Without defining which of the two gliders is the "standard" glider that measurements are made from, it's hard to unambiguously define a relative output lane. Recording output timing is similarly difficult because the input is not fixed -- gliders in a tandem pair can come in at many different relative timings.

Even output orientation is hard to define, because gliders can usually come in in either order, and you add or remove the junk still life accordingly. You can mirror G(n)-to-X converters along the input diagonal to switch from one type to the other, and that will change the output orientation.

So for the collection to be complete with the 2016 naming, it would have been necessary to duplicate most of the converters -- original, and then mirror-image, with different names. It seemed simpler to just record the type of the output, and leave it at that. (Maybe we should go back and rethink pi-input conduit naming, along the same lines.)

14 days in Japan can really wreck your mind (I was there from 11 to 24 December 2018). Nevertheless, I think it's rather easy to resolve the above problems.

We already have a standard orientation and form for the glider, so we can define a standard input position (not lane) for glider-input conduits as the last position A before interacting with the conduit where the glider assumes a form equivalent by rotations and reflections to the standard form (bo$2bo$3o). For tandem glider inputs, the reference glider is the one that produces the output object (the other glider(s) are almost always involved in resetting the conduit). Thus the conduit has a standard orientation where the (reference) glider in position A has the standard orientation. From here output timings can be derived as usual.

Because we have now defined a reference glider for tandem glider inputs, we can now specify whether the second glider is above (+) or below (-) the reference glider when the conduit is in its canonical orientation by adding the minus sign appropriately.

Here are examples demonstrating this new naming scheme:

Code: Select all

x = 420, y = 625, rule = LifeHistory
.3D2.4D10.D6.D3.3D2.4D8.D$D3.D.D3.D8.2D5.2D2.D3.D.D3.D7.D$D5.D3.D.D3.
D3.D4.D.D2.D3.D.D3.D7.4D2.D.2D3.3D2.4D3.4D2.3D$D2.2D.4D3.D.D4.D3.D2.D
3.3D2.4D8.D3.D.2D2.D.D3.D.D3.D.D5.D3.D$D3.D.D3.D3.D5.D3.5D.D3.D.D3.D
7.D3.D.D5.D3.D.D3.D.D5.D3.D$D3.D.D3.D2.D.D4.D6.D2.D3.D.D3.D7.D3.D.D5.
D3.D.D3.D.D5.D3.D$.3D2.4D2.D3.D2.3D5.D3.3D2.4D2.5D.4D2.D6.3D2.D3.D2.
4D2.3D10$42.2A.A$42.A.2A2$43.5A$38.2A2.A4.A12.2A$38.A2.A.BAB8.2A5.A$
39.A.A.2AB8.A.A.3A$38.2A.A.4BA8.A.A$41.A3.BABA.2B3.B2A$41.2A2.A2BA5B
2.2B$46.2A9B2.B$47.12B2A$22.B12.A10.13B2A$21.3B11.3A8.12B.B$21.4B13.A
8.10B$22.4B11.2A8.9B$23.4B10.6B4.8B$24.4B11.7B.9B$25.4B9.18B$26.4B7.
19B$27.4B5.22B$28.3BD26B$29.BD27B$29.2D27B$30.2D25B$31.D25B$33.26B$
34.25B$35.21B2A2B$36.20B2A2B$36.23B$36.21B$36.6BD12B5.2A$36.7BD11B5.A
$34.2A5B3D11B2.BA.A$33.A.A20B.B2A$33.A4.20B$32.2A5.3B2A15B$42.2A14B$
44.11B2.B2A$49.6B2.BA.A$49.5B6.A$49.B.B8.2A$50.3B$49.B2AB$50.2A31$
420D30$120.3D2.D3.D.D3.D2.3D2.5D2.3D3.3D46.2D23.D4.D4.3D3.3D$119.D3.D
.2D2.D.D3.D.D3.D3.D3.D5.D3.D33.D5.D4.D2.D3.D18.D3.2D3.D3.D.D$119.D5.D
.D.D.D3.D.D3.D3.D3.D5.D3.D2.4D7.D.2D3.3D3.4D.5D8.D11.3D2.D.2D4.D5.D3.
D2.2D.D$119.D2.2D.D2.2D.D.D.D2.3D4.D3.4D3.4D.D3.D7.2D2.D.D3.D.D7.D5.D
3.3D5.D3.D3.D.2D2.D3.D5.D3.D.D.D.4D$119.D3.D.D3.D.D.D.D.D3.D3.D3.D3.D
5.D.D3.D7.D5.5D.D7.D5.D4.D6.D3.5D.D7.D5.D3.2D2.D.D3.D$119.D3.D.D3.D.
2D.2D.D3.D3.D3.D3.D5.D.D3.D7.D5.D5.D7.D5.D4.D6.D3.D5.D6.D6.D3.D3.D.D
3.D$120.3D2.D3.D.D3.D2.3D4.D4.3D3.3D3.4D.5D.D6.4D2.4D4.2D3.2D3.D6.2D
3.4D.D6.D5.3D3.3D3.3D2$.3D2.D3.D.5D.5D.5D4.D9.3D20.D8.D5.D3.3D$D3.D.
2D2.D.D9.D3.D5.2D8.D3.D19.D8.D4.2D2.D3.D$D5.D.D.D.D8.D4.D4.D.D8.D5.4D
3.4D.D.2D2.D2.D4.D4.D.D6.D$D2.2D.D2.2D.3D5.D5.D3.D2.D9.3D2.D3.D.D3.D.
2D2.D.D.D5.D3.D2.D4.2D$D3.D.D3.D.D6.D6.D3.5D11.D.D3.D.D3.D.D5.3D5.D3.
5D5.D$D3.D.D3.D.D5.D7.D6.D8.D3.D.D3.D.D3.D.D5.D2.D3.D7.D2.D3.D$.3D2.D
3.D.5D.D7.D6.D2.5D2.3D2.D3.D2.4D.D5.D3.D2.D7.D3.3D2$173.4B$174.4B$
175.4B11.A$170.B5.4B8.3A$169.3B5.4B6.A$169.4B5.4B5.2A$170.4B5.4B2.4B$
171.4B5.4B.2B$30.2B25.B114.4B5.7B$30.3B23.2B115.4B5.6B$30.4B21.3B113.
B2.4B5.5B$31.4B19.4B109.6B2.4B3.8B7.A$32.4B10.A6.4B109.4B2A8B.9B5.3A$
33.4B7.3A5.4B110.3BA2BA18B3.A$34.4B5.A7.4B111.4B2A21B.2A$35.4B4.2A5.
4B113.29B$36.9B4.4B115.26B$37.6B5.4B117.15BD10B$37.4BD3B2.4B119.15BD
8B$35.7BD7B121.12B3D9B$35.5B3D6B122.25B$35.13B124.24B$33.2AB.10B128.
9B2A10B$32.A.AB3.B2A3B135.4B2A11B$32.A6.B2A3B135.17B$31.2A6.4B138.16B
$40.3B139.14B$41.2B.BA136.14B$40.B2ABA.A134.11B$39.BABABA.A135.10B$
37.A2.A.A.A.A.2A133.9B$37.4A.2A2.A2.A135.7B$41.A4.2A141.3B2A$39.A.A
149.A2BA2.2A65.3D9.3D3.3D2.D3.D9.D3.5D.5D3.D4.3D3.3D9.3D2.D3.D9.D4.3D
2.5D2.3D4.D4.3D$39.2A150.ABAB3.A64.D3.D7.D3.D.D3.D.D3.D8.2D3.D7.D4.2D
3.D3.D.D3.D7.D3.D.D3.D8.2D3.D3.D3.D3.D3.D2.2D3.D3.D$192.A4B.A.2A61.D
15.D.D5.D3.D9.D3.D7.D5.D3.D3.D.D3.D7.D5.D3.D9.D7.D3.D7.D3.D3.D3.D$
194.B2A.A.A62.D2.2D.5D4.D3.3D2.D.D.D.5D3.D4.3D4.D5.D4.3D3.4D8.3D2.D.D
.D.5D3.D6.D4.D6.D4.D4.3D$194.BAB.A2.A61.D3.D9.D7.D.D.D.D9.D7.D3.D5.D
3.D3.D5.D11.D.D.D.D9.D5.D5.D5.D5.D3.D3.D$192.A4.A2.2A61.D3.D8.D4.D3.D
.2D.2D9.D3.D3.D3.D5.D3.D3.D5.D7.D3.D.2D.2D9.D4.D6.D4.D6.D3.D3.D$192.
5A67.3D8.5D2.3D2.D3.D8.3D3.3D4.D4.3D3.3D3.3D2.5D2.3D2.D3.D8.3D2.5D3.D
3.5D2.3D3.3D2$194.2A.A$194.A.2A7$296.B$295.3B$295.4B$296.4B$297.4B$
298.4B$299.4B$300.4B$301.4B$302.4B$303.4B$304.4B$305.4B$306.BD2B10.A$
307.BD2B7.3A$306.3D3B5.A$307.6B4.2A$308.11B$309.8B$310.9B$311.8B11.A$
305.A6.8B8.3A$305.3A4.7B8.A$308.A3.8B4.2B.2A$.3D2.D3.D.D3.D2.3D2.5D2.
3D3.3D2.D11.D55.2D3.2D36.D3.3D3.3D3.3D135.2A2.18B$D3.D.2D2.D.D3.D.D3.
D3.D3.D5.D3.D.D11.D20.D33.D2.D3.D17.D18.D2.D3.D.D3.D.D3.D134.3B.16B$D
5.D.D.D.D3.D.D3.D3.D3.D5.D3.D.4D8.4D3.3D3.3D8.D3.D2.D.D8.D.2D3.3D3.D
6.D4.3D3.4D.5D2.3D2.D.2D4.D7.D.D2.2D5.D136.19B$D2.2D.D2.2D.D.D.D2.3D
4.D3.4D3.4D.D3.D7.D3.D.D3.D.D3.D4.D2.D3.D.D.D.D7.2D2.D.D3.D.3D5.D3.D
3.D.D7.D3.D3.D.2D2.D3.D6.D2.D.D.D4.D136.21B$D3.D.D3.D.D.D.D.D3.D3.D3.
D3.D5.D.D3.D7.D3.D.D3.D.D3.D4.D2.D3.D.D.D.D7.D5.5D2.D6.D3.5D.D7.D3.D
3.D.D7.D5.D3.2D2.D3.D136.22B$D3.D.D3.D.2D.2D.D3.D3.D3.D3.D5.D.D3.D7.D
3.D.D3.D.D3.D4.D2.D3.D.D3.D7.D5.D6.D6.D3.D5.D7.D3.D3.D.D6.D5.D4.D3.D
2.D138.22B10.A.2A$.3D2.D3.D.D3.D2.3D4.D4.3D3.3D2.4D2.5D.4D3.3D3.3D5.D
3.4D.D3.D.5D.D6.4D2.D6.2D3.4D2.4D4.2D2.3D2.D6.D4.5D2.3D2.5D136.21B10.
2A.A$72.D2.D233.21B13.A.AB$73.2D238.17B10.2A2.2AB.4B$312.19B9.A5.6B$
313.18B.2B3.BA.A5.9B$313.23B.B2A5.11B$314.24B6.12B$313.25B6.13B3.2A$
313.24B3.16B4.A$313.23B.17B3.BA.A$72.4B231.B3.45B.B2A$73.4B229.2AB.
44B2A2B$74.4B11.A216.2A45BA2BAB$75.4B8.3A217.2B.44B2A2B$70.B5.4B6.A
223.46B$69.3B5.4B5.2A223.43B$69.4B5.4B2.4B224.42B.2B$70.4B5.4B.2B227.
4B2.B.36B.2B$71.4B5.7B228.2B4.38B2A$72.4B5.6B227.BA5.11B.24B.B2A$73.
4B5.5B227.A.A3.26BD11B.B$74.4B3.8B7.A218.2A3.27BD9B$75.4B.9B5.3A224.
24B3D8B$75.15B3.A228.34B$72.2B.17B.2A228.33B$71.2A22B229.22B2A7B$71.
2AB.18B232.7B2.12B2A.5B$72.B.9BD10B230.7B4.12B4.3B$75.9BD8B.B228.7B5.
12B4.2B$76.6B3D11B226.7B6.12B$76.20B225.7B8.11B$77.18B225.7B9.10B$78.
5B2A11B223.7B11.B.7B$78.5B2A12B221.7B15.6B$79.19B219.7B16.3B2A2B$80.
18B218.7B17.2BA2BA$81.17B217.7B20.B2AB$81.18B215.7B21.3B$82.16B215.7B
22.2B$83.16B213.7B24.AB$84.15B.BA209.7B24.A.A$84.16BA.A207.7B25.2A$
85.13B.2BA$86.11B3.B$86.7B$86.8B.2B$86.5B2A3B2A$86.5B2A3B2A$86.9B.B$
85.9B$83.A.2AB.3B$81.3AB2AB.5B$80.A4.B6.2A$81.3A.2A5.A$83.2A2.A5.3A$
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129.9B2.5B2E7.7B$69.4B5.B2E6B.4B3.BE.E129.4B3.2B5.E2BE6.2B3D2B$70.4B
3.8B4.B8.E135.B2EB4.EBEB5.3BD4B$71.4B2.6B15.2E135.2E6.E4B3.2B3D3B$72.
4B.7B161.3B2.8B$73.4B.6B161.4B2.2B2E3B$74.9B163.4B.2B2E5B$75.8B164.
13B$76.8B161.16B$77.7B161.17B$78.5B162.16B$78.2B3D162.15B$79.BDB164.
13B$79.3D$80.B!

[dvgrn]

Because we have now defined a reference glider for tandem glider inputs, we can now specify whether the second glider is above (+) or below (-) the reference glider when the conduit is in its canonical orientation by adding the minus sign appropriately.

Here are examples demonstrating this new naming scheme...

This looks like a workable convention to me.

It doesn't provide an obvious way to specify an input timing for the second glider in a glider pair, but those are usually adjustable anyway. The timing limitations could be added in a special comment line for Gn conduits, in the RLE file.

The only odd case I thought of is situations where the output timing depends on the second glider instead of the first one (left, below). But that can (almost?) always be disposed of easily by starting with a different form of the conduit (right, below):

Code: Select all

#C example with Paul Callahan's bistable switch
x = 125, y = 80, rule = LifeHistory
49.A$50.A$48.3A33$.A$2.A$3A36.A.2A61.A.2A$39.2A.A61.2A.A2$37.5A60.5A$
36.A2.A2.A58.A2.A2.A$36.2A3.A.A57.2A3.A.A$42.2A63.2A4$58.2A63.2A$58.A
64.A$56.A.A62.A.A$56.2A63.2A9$43.A11.2A63.2A$44.A10.2A63.2A$42.3A3$
43.A$42.A.A$43.2A7$104.A$105.A$31.2A63.2A5.3A$30.A.A62.A.A$30.A64.A$
29.2A63.2A8.2A$104.2A!

If G-to-X conduits are catalogued in this way with the other elementary conduits, then that seems like a good starting point for an Elesrch utility. I'm thinking maybe a good target result for such a utility would be a large pre-computed grid of output locations relative to inputs:

given such-and-such collection of elementary conduits,

if you have a [glider | B-heptomino | Herschel | pi | etc] in canonical form at (0,0),
then we can reach
glider@(X1, Y1, T1, orientation1) with [conduit sequence 1],
glider@(X2, Y2, T2, orientation2) with [conduit sequence 2],
...
Herschel@(X3, Y3, T3, F) with [conduit sequence 3],
Herschel@(X4, Y4, T4, Fx) with [conduit sequence 4],
etc.

There's no reason to extend the tables beyond a certain size. Not sure what the right size will turn out to be, but we only need to cover up to the most distant (X, Y, T) that we _can't_ reach with known conduits. Outside of a certain block of spacetime we can hit any possible target, just by adding a few Snarks, a syringe, and an H-to-whatever converter to something that will already be available in the Glider Outputs table.

I wonder how big the precomputed tables would be, say with all possible glider output orientations and a glider input, to cover the whole block of "Not Universally Reachable" spacetime locations? Before the Snark and syringe came along, this was a ridiculously large block of spacetime, but it's clearly shrunk a lot in the last few years.

[gmc_nxtman]

Partial BF107B:

Code: Select all

x = 43, y = 44, rule = LifeHistory
11.4B20.4B$12.4B18.4B$13.4B16.4B$14.4B11.B2.4B$15.4B8.8B$16.4B5.9B$
17.4B4.8B$18.4B2.8B$19.14B$20.12B$21.10B$22.9B$21.12B$8.2A11.12B$8.A
12.14B$2A3.2A.A13.14BD$A4.A.A14.15BD$.3A.A15.16B2D$3.A.2A2.5B6.16B2D$
3.13B3.17BD$4.2B.10B2.13B$5.13B.12B$4.14B.13B$4.28B4.4B$4.29B3.5B$4.
37B$5.28B2D7B$5.27BD2BD7B$6.27B2D5B2DB$5.35B2D$4.C31B$2.3BC29B$.4B2C
28B$.3B2C28B$2.2BC15B.13B$2.32B$4.16B.12B$7.2B2A20B$9.2A2B3.12B$11.B
4.13B$16.14B$17.12B2A$17.10B.B2A$18.8B3.B!

The main problems are the resulting FNG, and the fact that there isn't much room for catalysis. However it has both a forward and backward extra glider, which could be very valuable in a working conduit.

EDIT:

...Could be a problem for Bellman, maybe?

I was thinking Bellman, or maybe CatForce if there's a lucky transparent catalyst or something. I haven't been able to get CatForce to work though.

[dvgrn]

Partial BF107B...
The main problems are the resulting FNG, and the fact that there isn't much room for catalysis. However it has both a forward and backward extra glider, which could be very valuable in a working conduit.

I was just looking at this on Discord. Drat and bother -- it looks like the most likely trick would be to catalyze the extra block so that it affects the beehive as it's forming, since catalysts can't quite reach the pre-beehive directly. Could be a problem for Bellman, maybe?

A second glider four steps above the FNG would solve the problem nicely, and a glider five steps below _almost_ solves the problem:

Code: Select all

x = 73, y = 52, rule = LifeHistory
57.A$57.3A.A$60.2A$54.A2.2A$54.4A.5A$59.B4.A$54.5ABABA.A$54.A2.A.2A.
2A$11.4B20.4B7.2A7.6B$12.4B18.4B9.A8.5B$13.4B16.4B10.A.AB3.7B$14.4B
11.B2.4B12.2AB.8B$15.4B8.8B15.12B$16.4B5.9B8.2A6.13B$17.4B4.8B10.A6.
13B8.2A$18.4B2.8B11.A.AB5.11B8.A$19.14B11.2AB.3B2.11B4.BA.A$20.12B14.
21B.B2A$21.10B15.19B2A2B$22.9B16.18BA.AB$21.12B13.15B5.2A$8.2A11.12B
11.17B$8.A12.14B7.19B$2A3.2A.A13.14BD5.2BD15B$A4.A.A14.15BD3.3BDBD12B
$.3A.A15.16B2D3.2B3D4B2.6B$3.A.2A2.5B6.16B2D3.5BD4B3.6B$3.13B3.17BD3.
10B6.4B$4.2B.10B2.13B7.4B.4B7.B2A2B$5.13B.12B7.4B.4B9.2A.B2A$4.14B.
13B5.4B.4B13.BA.A$4.28B4.4B.4B17.A$4.29B2.9B18.2A$4.39B$5.28BD8B$5.
27BD10B$6.27BD6B2DB$5.35B2D$4.C33B$2.3BC31B$.4B2C29B$.3B2C28B$2.2BC
15B.13B$2.32B$4.16B.12B$7.2B2A20B$9.2A2B3.12B$11.B4.13B$16.14B$17.12B
2A$17.10B.B2A$18.8B3.B!

But that final extra beehive can't be cleaned up by the normal block catalyst, unfortunately. And anyway as soon as an extra glider is needed, the conduit will inevitably end up too big to be very useful.

[2718281828]

I noticed this post viewtopic.php?f=2&t=1599&p=16608#p16608 which is a few years old.
It contains the pattern shown on the right, in the conduit collection we have the pattern on the left:

Code: Select all

x = 100, y = 42, rule = LifeHistory
5$37.4B$36.4B45.4B$35.4B45.4B$34.4B45.4B$16.A16.4B45.4B$16.3A13.4B28.
A16.4B$19.A11.4B29.3A13.4B$18.2A10.4B33.A11.4B$18.4B7.4B33.2A10.4B$
20.2B6.4B34.4B7.4B$19.5B3.4B37.2B6.4B$17.8B.4B37.5B3.4B$15.14B36.8B.
4B$14.14B35.14B$13.16B33.14B$14.17B30.16B$14.17B11.2A18.17B$13.18B12.
A18.17B$14.19B7.3A18.18B$15.18B7.A21.19B$15.5B3E17B23.18B$16.3BE2BE
18B22.5B3E15B$16.2BE2BE20B22.3BE2BE18B$17.2B2E22B21.2BE2BE20B$17.26B
22.2B2E21B$18.4B.2B6.12B22.23B.B2A$19.2B10.10B25.4B.2B6.9B.BA.A$32.6B
29.2B11.3B9.A$34.3B44.4B7.2A$83.2A$83.A$84.3A$86.A!

I think we should add this one from Extrementhusiast even though the output is the same but it has clearly different cleaning and spacing of some eaters.

Moreover, I found this lom-to-B

Code: Select all

x = 29, y = 27, rule = LifeHistory
4$21.A$19.3A$18.A$18.2A$9.2B4.5B$8.10B$6.D12B$5.D7B3E3B$4.2D7BE2B2EB$
5.2D6B2E2BEB$6.D8B3E$10.2B2.B.4B$18.2A$18.A$19.3A$21.A!

It goes together with this dove-to-lom which makes it technically at the moment to a dove-to-B:

Code: Select all

x = 36, y = 34, rule = LifeHistory
5$22.A$21.A.A$22.2A$19.A$19.5A2.A$23.4A$5.2A12.3A$6.A12.A2.5A$6.A.A8.
A.A2.A4.A$7.2A8.2A5.BAB.A$13.3D8.B2A.A2.A$13.DBD6.A4B.A.A.A$12.D2BDB
4.ABAB3.A2.A$12.DBD2B4.A2BA2.2A$12.3D7B2A$12.B3E6B$12.E2BE6B$11.E2B2E
5B$11.EBE9B$12.E5B.B.2A$21.A$11.D2B2D6.3A$12.3D9.A$13.D!

However, at the moment we only have a single C-to-Dove in the conduit collection, adding this one yields

Code: Select all

x = 49, y = 66, rule = LifeHistory
6$27.A$26.A.A$27.2A$24.A$24.5A2.A$28.4A$10.2A12.3A$11.A12.A2.5A$11.A.
A8.A.A2.A4.A$12.2A8.2A5.BAB.A$18.3D8.B2A.A2.A$18.DBD6.A4B.A.A.A$17.D
2BDB4.ABAB3.A2.A$17.DBD2B4.A2BA2.2A$11.2B2.2B3D7B2A$10.8B3D6B$10.7BD
2BD6B$10.6BD2B2D5B$9.7BDBD9B$9.8BD5B.B.2A$10.10B6.A$10.6BD2B2D6.3A$
10.7B3D9.A$11.7BD$11.9B$11.9B$11.11B$11.12B$8.B2.12B$7.16B$6.17B$6.
17B.BA$6.3B2E13BA.A$5.4BEB2E9B.2BA$5.7BE10B.B$4.6B3E9B$5.15B.3B$5.14B
3.2A$5.14B3.A$5.10B8.3A$5.10B10.A$6.9B$8.2B.5B$14.2A.A$14.2AB3A$15.B
4.A$14.2A.3A$15.A.A$15.A.A$16.A!

so not really pleasant position for the B. But it might be useful if we find another x-to-dove

Edit1:
more on the LOM. A LOM-to-2B which can be made to a LOM-to-2G:

Code: Select all

x = 35, y = 30, rule = LifeHistory
11.4B$12.4B$9.A3.4B$7.3A4.4B$6.A8.4B$6.2A8.4B$4.4B9.4B$3.2AB4.2A6.5B$
3.A.AB2.B2AB6.5B$4.2AB2.4B5.6B$4.3B.17B9.A$5.7BD13B6.3A$5.6B2D14B4.A$
4.6B2D3B3C10B.B.2A$4.7BD3BC2B2C2BD10B$2.10BD2B2C2BC3BD7B$2.2A.B.10B3C
3B2D6B$3.A4.14B2D6B$3A6.13BD7B$A9.17B.3B$11.6B5.4B2.B2A$11.5B6.B2AB2.
BA.A$12.5B6.2A4.B2A$14.4B9.4B$15.4B8.2A$16.4B8.A$17.4B4.3A$18.4B3.A$
19.4B$20.4B!

The input position is not great (not even constructable with 2 gliders.). It should also work with this B-to-R:

Code: Select all

x = 22, y = 28, rule = LifeHistory
4$11.D$8.2B3D$7.D2BD5B$5.3BD7B$5.3B2D6B$4.3B2D6B$5.2BD7B$5.7B.3B$7.B.
B3.B2A$7.B2AB2.BA.A$8.2A4.B2A$12.4B$12.2A$13.A$10.3A$10.A!

Edit2:
And this one is close to a lom-to-E:

Code: Select all

x = 35, y = 28, rule = LifeHistory
4$15.5B$11.D3.7B$10.3D2.8B$7.B.BDBD11B$5.4B2D13B$4.2D19B$4.2D19B$5.
19B$5.8B3C7B$5.2D6BC2B2C7B$5.2D6B2C2BC8B$5.10B3C8B$4.21B$4.22B$4.23B$
5.10B.3B2.5B$6.7B4.B5.2B$6.6B10.A.A.A$6.4B10.3A.2A.A$7.2B10.A7.A$19.
2A6.2A!

but there are the two lom-blocks remaining on one side. And I don't know how to remove them, I get only one removed:

Code: Select all

x = 34, y = 28, rule = LifeHistory
3$17.5B$13.D3.7B$12.3D2.8B$9.B.BDBD11B$7.4B2D13B$4.B.21B$3.2A22B$3.2A
B.19B$4.B2.8B3C7B$7.2D6BC2B2C7B$7.2D6B2C2BC8B$7.10B3C8B$6.21B$6.22B$
6.23B$7.10B.3B2.5B$8.7B4.B5.2B$8.6B10.A.A.A$8.4B10.3A.2A.A$9.2B10.A7.
A$21.2A6.2A!

[Extrementhusiast]

Let's make things confusing, shall we?

Code: Select all

x = 73, y = 26, rule = LifeHistory
11.2A54.2A$12.A55.A$10.A55.A$10.5A51.5A$14.A55.A$10.2A54.2A$9.A.A53.A
.A$9.2A54.2A$13.2A54.2A$13.A.A53.A.A$.2D12.A39.2D14.A$2D13.2A37.2D15.
2A$.2D52.2D$2.D53.D8$.3C53.3C7.2A$2.C8.2A45.C8.A.A$2.3C6.A46.3C8.A$
12.3A54.2A$14.A!

[Freywa]

Let's make things confusing, shall we?

Code: Select all

x = 73, y = 26, rule = LifeHistory
11.2A54.2A$12.A55.A$10.A55.A$10.5A51.5A$14.A55.A$10.2A54.2A$9.A.A53.A
.A$9.2A54.2A$13.2A54.2A$13.A.A53.A.A$.2D12.A39.2D14.A$2D13.2A37.2D15.
2A$.2D52.2D$2.D53.D8$.3C53.3C7.2A$2.C8.2A45.C8.A.A$2.3C6.A46.3C8.A$
12.3A54.2A$14.A!

The first conduit is a mere stator variation of HR44Bc, but it saves one cell so I've replaced it with your version. The second conduit is a more substantial variant of HR48B and has been added as such:

Code: Select all

x = 83, y = 40, rule = LifeHistory
D3.D.4D5.D5.D2.4D20.D3.D.4D5.D3.3D2.4D2.D$D3.D.D3.D3.2D4.2D2.D3.D19.D
3.D.D3.D3.2D2.D3.D.D3.D.D$D3.D.D3.D2.D.D3.D.D2.D3.D2.4D13.D3.D.D3.D2.
D.D2.D3.D.D3.D.4D$5D.4D2.D2.D2.D2.D2.4D2.D17.5D.4D2.D2.D3.3D2.4D2.D3.
D$D3.D.D2.D2.5D.5D.D3.D.D17.D3.D.D2.D2.5D.D3.D.D3.D.D3.D$D3.D.D3.D4.D
5.D2.D3.D.D17.D3.D.D3.D4.D2.D3.D.D3.D.D3.D$D3.D.D3.D4.D5.D2.4D3.4D13.
D3.D.D3.D4.D3.3D2.4D2.4D10$22.A46.A$22.3A44.3A$8.2A15.A3.2A25.A15.A3.
2A$9.A14.2A4.A25.3A12.2A4.A$9.A.AB11.5B.A.2A25.A11.5B.A.2A$10.2AB.3B
9.B2A.A2.A24.2A3.B9.B2A.A2.A$12.7B6.BA.A.2A26.8B6.BA.A.2A$12.9B.4B2A
32.8B.4B2A$13.15B32.15B$12.15B32.15B$10.17B30.17B$8.18B29.18B$8.2BD
15B29.2BD15B$7.3BDBD4B.7B29.3BDBD4B.7B$8.2B3D4B2.B2DBDB30.2B3D4B2.6B$
7.5BD4B4.3D30.5BD4B2.6B$6.10B6.D30.10B4.2D2BD$5.4B43.4B12.3D$5.3B43.
4B14.D$3.4B43.4B$3.2A46.2B$4.A$.3A$.A!

[Gamedziner]

Let's make things confusing, shall we?

Code: Select all

x = 73, y = 26, rule = LifeHistory
11.2A54.2A$12.A55.A$10.A55.A$10.5A51.5A$14.A55.A$10.2A54.2A$9.A.A53.A
.A$9.2A54.2A$13.2A54.2A$13.A.A53.A.A$.2D12.A39.2D14.A$2D13.2A37.2D15.
2A$.2D52.2D$2.D53.D8$.3C53.3C7.2A$2.C8.2A45.C8.A.A$2.3C6.A46.3C8.A$
12.3A54.2A$14.A!

The first one fails, as a glider destroys an eater.

[Moosey]

Let's make things confusing, shall we?

Code: Select all

x = 73, y = 26, rule = LifeHistory
11.2A54.2A$12.A55.A$10.A55.A$10.5A51.5A$14.A55.A$10.2A54.2A$9.A.A53.A
.A$9.2A54.2A$13.2A54.2A$13.A.A53.A.A$.2D12.A39.2D14.A$2D13.2A37.2D15.
2A$.2D52.2D$2.D53.D8$.3C53.3C7.2A$2.C8.2A45.C8.A.A$2.3C6.A46.3C8.A$
12.3A54.2A$14.A!

The first one fails, as a glider destroys an eater.

Not really; the syringe on its own is destroyed by its Herschel. It works. So does the first one.

A good way to show this is that the conduit can be chained up to other conduits, e.g. BRx46B:

Code: Select all

x = 27, y = 29, rule = LifeHistory
21.2A$22.A$20.A$20.5A$2A22.A$2A7.2A9.2A$9.2A8.A.A$19.2A$23.2A$.A21.A.
A$A.A8.2D12.A$A.A7.2D13.2A$.A9.2D$12.D8$11.3C$12.C8.2A$12.3C6.A$22.3A
$24.A$3.2D.D$4.3D$5.D!