ConwayLife.com

Posted: **October 7th, 2022, 4:10 am**

Is there a way to extract the encoded LWSS stream from the p46-based PRNG?

Posted: **October 7th, 2022, 5:44 am**

qqd wrote: October 7th, 2022, 4:10 am Is there a way to extract the encoded LWSS stream from the p46-based PRNG?

Couldn't you just remove the eater at the middle right that deletes the LWSS stream?

Posted: **October 7th, 2022, 8:24 am**

confocaloid wrote: October 7th, 2022, 3:14 amI think this approach can be made to work for stable or periodic X-to-(any number of spaceships and nothing else), as well as factories/keepers/period multipliers that produce stationary objects. But non-spaceship outputs may damage the conduit if nothing is connected to them, so some other ideas are needed.

It would solve most but not all of the weird exceptional cases to add a comment line that gives the canonical name of the elementary conduit. The canonical name plus the canonical (x,y) offset would take care of everything, I think.

The weird exceptional cases include|

1) conduits where the output overlaps the input, so we can't have a script that accepts two-state RLE and a pattern that shows both the input and output patterns;
2) conduits, such as dependent conduits for Herschels, where the input never actually reaches the canonical form, or where the output only converges to a descendant of the canonical form of the output object.

The second type of conduit might not be auto-recognizable even if you switch to a multistate format. But why does it seem like a good idea to re-process and re-recognize conduits, anyway? Seems like we'll eventually want a collection of conduits that has been checked for validity and has all of the relevant information already recorded.

Posted: **October 7th, 2022, 9:33 am**

confocaloid wrote: October 7th, 2022, 3:14 am What could be a way to encode a conduit (i.e. not just timing/lanes/displacements, but the specific conduit itself, including arrangement of catalysts and description of input/output), which is reasonably convenient to use, and hopefully is reasonably compact (ideally short enough to fit on a single line)?

For stable X-to-glider(s), it should be sufficient to provide the two-state RLE with the input given in the preferred canonical form; since all outputs are escaping gliders, it is in principle possible to derive everything else automatically. Example:
Code: Select all
x = 24, y = 27, rule = B3/S23
17bo$15b3o$14bo$14b2o$22b2o$22bo$20bobo$14bo5b2o$14bobo$14b3o$16bo8$
22bo$21bobo$22bo$17b2o$16bo2bo$2b2o13b2o$bobo$bo$2o!
I think this approach can be made to work for stable or periodic X-to-(any number of spaceships and nothing else), as well as factories/keepers/period multipliers that produce stationary objects. But non-spaceship outputs may damage the conduit if nothing is connected to them, so some other ideas are needed.

dvgrn wrote: October 7th, 2022, 8:24 am
confocaloid wrote: October 7th, 2022, 3:14 amI think this approach can be made to work for stable or periodic X-to-(any number of spaceships and nothing else), as well as factories/keepers/period multipliers that produce stationary objects. But non-spaceship outputs may damage the conduit if nothing is connected to them, so some other ideas are needed.
It would solve most but not all of the weird exceptional cases to add a comment line that gives the canonical name of the elementary conduit. The canonical name plus the canonical (x,y) offset would take care of everything, I think.

The weird exceptional cases include|

1) conduits where the output overlaps the input, so we can't have a script that accepts two-state RLE and a pattern that shows both the input and output patterns;
2) conduits, such as dependent conduits for Herschels, where the input never actually reaches the canonical form, or where the output only converges to a descendant of the canonical form of the output object.

The second type of conduit might not be auto-recognizable even if you switch to a multistate format. But why does it seem like a good idea to re-process and re-recognize conduits, anyway? Seems like we'll eventually want a collection of conduits that has been checked for validity and has all of the relevant information already recorded.

Basically, I was wondering whether there is a good way to write down a single-line code that encodes all "important" information about some conduit. That would include ability to recover the canonical name, and also ability to recover the arrangement of catalysts (at least partially, up to replacements of catalysts that do not affect the way how the conduit works).

It would not necessarily be possible to automatically recognize-and-encode a conduit which is given as an input (either as a RLE or in some other format) - the encoding step might still be performed manually, when a conduit is added to the collection. Maybe the "automatic" part would be more applicable in the other direction - that is, given an encoded form, automatically decode it and produce a conduit variant with the same or equivalent encoding (possibly subject to further constraints that limit possibilities for the choices of specific catalysts).

For example, I think it is possible to have an encoding, such that out of these variants of BFx59H, the first four variants all get equivalent encodings, while the last variant gets a non-equivalent encoding:

Code: Select all

x = 325, y = 32, rule = LifeHistory
4D2.5D7.5D2.3D2.D3.D36.4D2.5D7.5D2.3D2.D3.D.D34.4D2.5D7.5D2.3D2.D3.D
36.4D2.5D7.5D2.3D2.D3.D5.D30.4D2.5D7.5D2.3D2.D3.D$D3.D.D11.D5.D3.D.D
3.D36.D3.D.D11.D5.D3.D.D3.D.D34.D3.D.D11.D5.D3.D.D3.D36.D3.D.D11.D5.D
3.D.D3.D5.D30.D3.D.D11.D5.D3.D.D3.D$D3.D.D5.D3.D.D5.D3.D.D3.D2.4D30.D
3.D.D5.D3.D.D5.D3.D.D3.D.4D31.D3.D.D5.D3.D.D5.D3.D.D3.D2.4D30.D3.D.D
5.D3.D.D5.D3.D.D3.D2.4D30.D3.D.D5.D3.D.D5.D3.D.D3.D2.3D$4D2.3D4.D.D3.
3D3.4D.5D.D3.D30.4D2.3D4.D.D3.3D3.4D.5D.D3.D30.4D2.3D4.D.D3.3D3.4D.5D
.D34.4D2.3D4.D.D3.3D3.4D.5D.D3.D30.4D2.3D4.D.D3.3D3.4D.5D.D3.D$D3.D.D
7.D7.D5.D.D3.D.D3.D30.D3.D.D7.D7.D5.D.D3.D.D3.D30.D3.D.D7.D7.D5.D.D3.
D.D34.D3.D.D7.D7.D5.D.D3.D.D3.D30.D3.D.D7.D7.D5.D.D3.D.5D$D3.D.D6.D.D
2.D3.D5.D.D3.D.D3.D30.D3.D.D6.D.D2.D3.D5.D.D3.D.D3.D30.D3.D.D6.D.D2.D
3.D5.D.D3.D.D34.D3.D.D6.D.D2.D3.D5.D.D3.D.D3.D30.D3.D.D6.D.D2.D3.D5.D
.D3.D.D$4D2.D5.D3.D2.3D3.3D2.D3.D2.4D30.4D2.D5.D3.D2.3D3.3D2.D3.D.4D
31.4D2.D5.D3.D2.3D3.3D2.D3.D2.4D30.4D2.D5.D3.D2.3D3.3D2.D3.D2.4D30.4D
2.D5.D3.D2.3D3.3D2.D3.D2.4D10$11.7B.B62.7B.B62.7B.B62.7B.B62.7B.B$11.
13B.B56.13B.B56.13B.B56.13B.B56.13B.B$9.D21B49.D21B49.D21B49.D21B49.D
21B$9.BD21BD47.BD21BD47.BD21BD47.BD21BD47.BD21BD$8.2B2D18B3DB45.2B2D
18B3DB45.2B2D18B3DB45.2B2D18B3DB45.2B2D18B3DB$7.2B2D2B2A15BDBD45.2B2D
2B2A15BDBD45.2B2D2B2A15BDBD45.2B2D2B2A15BDBD45.2B2D2B2A15BDBD$7.2BD3B
2A15BD47.2BD3B2A15BD47.2BD3B2A15BD47.2BD3B2A15BD47.2BD3B2A15BD$9.11B
3.2B2.2B51.11B3.2B2.2B51.11B3.2B2.2B51.11B3.2B2.2B51.11B3.2B2.2B$9.
10B61.10B61.10B61.10B61.10B$10.6B65.6B65.6B65.6B65.6B$11.3B68.3B68.3B
68.3B68.3B$11.B70.B70.B70.B70.B$10.2A69.2A69.2A66.2A.2A68.2A.A$10.A
70.A70.A68.A.A68.A2.2A$11.A70.3A65.A.A68.A.A68.2A$10.2A72.A65.2A70.A!

If either of the first four variants is encoded, and then the encoded form is passed to the automatic decoding algorithm, the algorithm would be allowed to return either of four variants (not necessarily the exact same variant) - but not the fifth variant.

And these two variants of RF48H would receive two non-equivalent encodings:

Code: Select all

x = 100, y = 39, rule = LifeHistory
65.4D2.5D4.D3.3D2.D3.D.D$4D2.5D4.D3.3D2.D3.D36.D3.D.D7.2D2.D3.D.D3.D.
D$D3.D.D7.2D2.D3.D.D3.D36.D3.D.D6.D.D2.D3.D.D3.D.4D$D3.D.D6.D.D2.D3.D
.D3.D2.4D30.4D2.3D3.D2.D3.3D2.5D.D3.D$4D2.3D3.D2.D3.3D2.5D.D3.D30.D2.
D2.D5.5D.D3.D.D3.D.D3.D$D2.D2.D5.5D.D3.D.D3.D.D3.D30.D3.D.D8.D2.D3.D.
D3.D.D3.D$D3.D.D8.D2.D3.D.D3.D.D3.D30.D3.D.D8.D3.3D2.D3.D.4D$D3.D.D8.
D3.3D2.D3.D2.4D9$74.2A$9.4B60.B2AB$8.6B60.2B9.A$8.8B57.4B6.3A$8.10B
54.7B3.A$3.3B.11B4.2B2.2B44.7B3.2A$3.7BD18BD42.7B2.3B$2.8B2D17BDBD40.
10B4.2B2.2B$.8B2D18B3DB37.4BD18BD$2.28B.D37.5B2D17BDBD$3.27B39.4B2D
18B3DB$3.2B2A16B.B43.27BD$3.BA2BA12B49.25B$4.ABA12B50.18B.B$4.BA13B
50.14B$4.16B49.14B$4.16B49.14B$6.13B51.11B.B2A$6.13B52.B2.6B2.BA.A$6.
12B56.2B9.A$13.B61.AB8.2A$74.A.A$74.2A!

Posted: **October 7th, 2022, 10:20 am**

hotdogPi wrote: October 6th, 2022, 11:52 am Take the oscillator 101. Can anything from outside interact with the spark at all? I think I can prove it impossible without touching the stator at all, but given that the stator looks like an eater 1 form, it may be possible for an outside region to hit the spark without destroying the 101 oscillator by having it recover.

If the answer is "no", we can remove it from the "strong sparker" category, which was a bit ridiculous to begin with.

Scorbie answered this in the affirmative on Discord. It remains a sparker.

Code: Select all

x = 47, y = 18, rule = B3/S23
4b2o6b2o$3bobo6bobo$3bo10bo$2obo10bob2o$2obo2bob2obo2bob2o$3bobobo2bob
obo$3bobobo2bobobo$2obo2bob2obo2bob2o$2obo10bob2o$3bo10bo$3bobo6bobo$
4b2o6b2o2$8b3o27b3o$10b5o25b5o$8bo3bo2bo22bo3bo2bo$6b3o7bo19b3o7bo$5bo
29bo!

Posted: **October 8th, 2022, 10:42 am**

Is it possible to stabilize 5 isolated cells in a line from one side? 1, 2, 3, and 4 are all possible, but deduction coils didn't train me well enough for 5:

Code: Select all

x = 40, y = 12, rule = LifeSuper
3.G5.G.G7.G.G.G7.G.G.G.G$2.M.M4.2M.M5.M.3M.M5.M.2M.2M.M$2.HM2H6.M5.M
5.M5.M7.M$3.3H6.2M5.5M5.2M7.2M$4.H16.M4$3.G5.G.G7.G.G.G$.3M3.3M.3M4.M
.2M.3M$M5.M7.M3.M7.M$2M4.2M5.2M2.2M6.2M!

1 is by far the easiest, beings solvable with a tub, boat, loaf, mango, and literally any other tub motif, along with the eater 1's tail
2 is easy, with 2 tails, or a hook motif.
3 is also easy, just do the same as before.
4 just needs 2 hooks, I do not know of any other method of completing 4.
Is 5 possible? Every method I've tried either fails because of b3e or fails again because stabilizing b3e causes s4w or s4k transitions to exist.

Posted: **October 8th, 2022, 11:04 am**

Wyirm wrote: October 8th, 2022, 10:42 am Is it possible to stabilize 5 isolated cells in a line from one side?

This turns out to be a question that JLS can answer without even running any searches. Just the automatic pre-processing produces unsolvable conflicts.

With four cells, as you say, JLS comes up with this:

: four-isolated-cells.png (2.49 KiB) Viewed 3714 times

But as soon as you add the fifth cell, the preprocessing says No Way Not Happening Not Even Close:

Posted: **October 8th, 2022, 11:11 am**

dvgrn wrote: October 8th, 2022, 11:04 am
Wyirm wrote: October 8th, 2022, 10:42 am Is it possible to stabilize 5 isolated cells in a line from one side?
But as soon as you add the fifth cell, the preprocessing says No Way Not Happening Not Even Close:

Why would this be the case that 5 is impossible? It's not exactly like the quintic formula and its parity issues, so why is 5 the limit?

Posted: **October 8th, 2022, 11:34 am**

Wyirm wrote: October 8th, 2022, 11:11 am Why would this be the case that 5 is impossible? It's not exactly like the quintic formula and its parity issues, so why is 5 the limit?

So there are three cases to consider for how the center cell is stabilized (with case A also including its mirror as a corollary - just take the entire pattern and flip it horizontally):

Code: Select all

x = 37, y = 9, rule = LifeSuper
2.4H10.3H11.4H$2.H2.H10.H2.H10.H$2.4H10.3H11.H$2.H2.H10.H2.H10.H$2.H
2.H10.3H11.4H3$G.G.G.G.G5.G.G.G.G.G5.G.G.G.G.G$3.2M12.M.M11.3M!

Case A

The second cell from the left needs at least one more neighbor to stabilize it. It can't go here...

Code: Select all

x = 9, y = 2, rule = LifeSuper
G.G.G.G.G$2.3M!

...so it can only go here:

Code: Select all

x = 9, y = 2, rule = LifeSuper
G.G.G.G.G$.M.2M!

But now this cell needs to be suppressed somehow:

Code: Select all

x = 9, y = 2, rule = LifeSuper
GHG.G.G.G$.M.2M!

It's against the rules to stabilize it from above, and we've already established that its southeast neighbor must be off, so this is the only remaining option:

Code: Select all

x = 9, y = 2, rule = LifeSuper
G.G.G.G.G$2M.2M!

But the Coolout Conjecture disproof shows this to be impossible to stabilize.

Case B

We now have these two cells that need to be suppressed:

Code: Select all

x = 9, y = 2, rule = LifeSuper
G.GHGHG.G$3.M.M!

Trying to stabilize them from opposite corners brings us back to that same impossible-to-stabilize shape:

Code: Select all

x = 9, y = 2, rule = LifeSuper
G.G.G.G.G$2.2M.2M!

We could try turning on the center cell, but that would fall under case C.

Case C

There are four subcases to consider for how to stabilize the left cell:

Code: Select all

x = 52, y = 9, rule = LifeSuper
3.2H12.3H11.3H12.H.H$4.H14.H13.H12.H.H$4.H12.3H11.3H12.3H$4.H12.H15.H
14.H$3.3H11.3H11.3H14.H3$G.G.G.G.G5.G.G.G.G.G5.G.G.G.G.G6.G.G.G.G.G$
2M.3M7.2M2.3M7.M.M.3M8.3M.3M!

Cases C1 and C4 both feature that impossible shape, so let's try the other two.

Case C2

The second cell in the pink row needs at least one more neighbor to be stabilized. Putting it above or in the same row is disallowed, so we can only put it in the row below it. Placing it to the southwest leads to the Impossible Shape™, while placing it to the south leads to the cell to the right of it dying due to lack of S4i.

Case C3

We need to suppress this cell somehow.

Code: Select all

x = 10, y = 2, rule = LifeSuper
.GHG.G.G.G$M.M.3M!

Our only options are adding a cell to the southwest (Impossible Shape™) or to the southeast (leads to S4i).

Conclusion

With all possible cases ruled out, it has been proven that it is impossible to stabilize this thing from one direction.

Posted: **October 8th, 2022, 12:46 pm**

Ian07 wrote: October 8th, 2022, 11:34 am
Wyirm wrote: October 8th, 2022, 11:11 am Why would this be the case that 5 is impossible? It's not exactly like the quintic formula and its parity issues, so why is 5 the limit?
Helpful explanation

With all possible cases ruled out, it has been proven that it is impossible to stabilize this thing from one direction.

Thank you!

Posted: **October 8th, 2022, 4:48 pm**

I was messing around and I found an eater emerge from a natural synthesis.

Code: Select all

x = 93, y = 82, rule = B3/S23
20$72b3o$71bobo$72b2obob2o$74b4o$70b2o3b2o$70bobo2$70bobo$72bo2b2o$69b
3o3bo$70bo3bo$71bo7b3o$70b2ob2o$72b2obo11b2o$75b2o10b2o$75b3o$75b2o$
34b3o12b2o19bo2b3o$33bo15b2o19b5o$33bo3b2o32b3o$31b2o5bo2b3o21b3o8bobo
$30bob3o3bobo2bo5bo14bo2b2o5bo3bo$30bo2b2o2bo2bo2bo4bobo13bo3b2obob2o$
31bo4bo4bo8b2o12b3obo3bo3b2o$46b2ob2o15bobobob2o2b2o$35b3o10b2o15b2ob
2obobo2bo$64bo2b2o3bo2b2o$54bo8b2ob2o5b3o$54bo9bobo8bo4b2o$54bo10bo9bo
3bo2bo$74bobo2bo2bo$75bo4b2o4$65b2o$65b2o12$57b2o$57b2o!

are there any other objects that have been observed to synthesize naturally?

Edit: here's another

Code: Select all

x = 7, y = 7, rule = B3/S23
4b3o$6bo$5b2o2$2o$o$3o!

Posted: **October 8th, 2022, 5:14 pm**

pipsqueek wrote: October 8th, 2022, 4:48 pm I was messing around and I found an eater emerge from a natural synthesis.
Code: Select all
rle
are there any other objects that have been observed to synthesize naturally?

There was a similar question about whether natural LWSSes more commonly form by a glider synthesis or from other predecessors - link to a reply.

Posted: **October 8th, 2022, 8:28 pm**

pipsqueek wrote: October 8th, 2022, 4:48 pmI was messing around and I found an eater emerge from a natural synthesis. ...

Note that the eater in this case forms as a result of a collision of two gliders, rather than by any of the more "natural" eater predecessors. This way is highly anomalous, because with the exception of this two-glider synthesis, eaters occur in random ash with a rarity typical of other objects that need 4 gliders to synthesize.

Posted: **October 8th, 2022, 9:16 pm**

pipsqueek wrote: October 8th, 2022, 4:48 pmI was messing around and I found an eater emerge from a natural synthesis. ...
are there any other objects that have been observed to synthesize naturally?

I can't think of any offhand, though most likely examples could be found of all of the recognizable two-glider collisions, just by running a lot of soups and looking for the ones that have an isolated island off to the side.

The island would be formed by let's say an R/B-heptomino/Herschel producing a first natural glider pointed away from the soup at a corner, which happens to intersect with a 90-degree glider coming from another corner.

It would be hard to find kickback collisions programmatically that way, and two-glider messes would probably make so much mess that they wouldn't show up as isolated islands -- but a lot of the others are probably findable via an overnight search (or thereabouts).

Not sure if it counts as a "natural synthesis", but collisions like this are easy to find by zooming in to the stationary junk in Bill Gosper's novelty experiments.

I definitely don't know of any natural syntheses of objects that require the synchronization of three or more gliders from three different directions. Three gliders from two directions will probably show up, rarely, in a search like the one outlined above -- though the odds are that they won't build anything particularly exciting.

Posted: **October 9th, 2022, 12:12 am**

Does this count as a Bi-block hassler?

Code: Select all

x = 28, y = 32, rule = B3/S23
7bo12bo$5b3o12b3o$4bo18bo$4b2o16b2o2$b2o22b2o$bobo20bobo$2b2o20b2o3$13b
2o$3b3o7b2o7b3o$2bo2bo16bo2bo$bo2b2o7b2o7b2o2bo$2ob2o8b2o8b2ob2o$bobo
3bo12bo3bobo$2bo3bobo10bobo3bo$5b2ob2o8b2ob2o$4b2o2bo10bo2b2o$4bo2bo12b
o2bo$4b3o14b3o4$6b2o12b2o$6bobo10bobo$7b2o10b2o2$4b2o16b2o$5bo16bo$2b
3o18b3o$2bo22bo!

Posted: **October 9th, 2022, 12:16 am**

confocaloid wrote: October 8th, 2022, 5:14 pm
pipsqueek wrote: October 8th, 2022, 4:48 pm I was messing around and I found an eater emerge from a natural synthesis.
Code: Select all
rle
are there any other objects that have been observed to synthesize naturally?
There was a similar question about whether natural LWSSes more commonly form by a glider synthesis or from other predecessors - link to a reply.

The LWSS can appear like this:

Code: Select all

x = 13, y = 7, rule = B3/S23
o$b2o$2o$10b2o$11b2o$10b2o$10bo!

Posted: **October 9th, 2022, 5:21 am**

Roughly how many "promising" oscillator partials are known (in total and/or in average per period and/or for some specific periods), for some definition of "promising", probably including but not limited to those posted in Oscillator Discussion Thread?

Posted: **October 9th, 2022, 9:27 am**

confocaloid wrote: October 9th, 2022, 5:21 am Roughly how many "promising" oscillator partials are known (in total and/or in average per period and/or for some specific periods), for some definition of "promising", probably including but not limited to those posted in Oscillator Discussion Thread?

One hundred thirty-seven. You might think it would be more, but a lot of them aren't particularly "promising" because they don't have much hope of being completed in a way that supplies any kind of interesting sparks or other interactions at the edges.

Posted: **October 9th, 2022, 2:42 pm**

Is there hope of a p19 oscillator? Have we spent so long trying to prove omniperiodicity that we should instead be trying to disprove it?

Posted: **October 9th, 2022, 2:52 pm**

Wyirm wrote: October 9th, 2022, 2:42 pm Is there hope of a p19 oscillator? Have we spent so long trying to prove omniperiodicity that we should instead be trying to disprove it?

Have you forgotten that two of the four missing periods were discovered this year?

Posted: **October 9th, 2022, 10:02 pm**

Wyirm wrote: October 9th, 2022, 2:42 pm Is there hope of a p19 oscillator? Have we spent so long trying to prove omniperiodicity that we should instead be trying to disprove it?

Where there's Life, there's hope, as the saying goes. The idea of disproving omniperiodicity has been discussed plenty of times before, and it really just doesn't seem like there's any mathematically viable way to even start working on such a proof.

We'd have to successfully rule out hundreds or thousands ... or maybe millions, I'm not sure ... of individual potentially viable mechanisms -- and we haven't been successful at ruling out any of them definitively yet.

Posted: **October 11th, 2022, 6:06 pm**

dvgrn wrote: September 20th, 2022, 4:59 pm

... Well, that's not quite true. Maybe we should look at re-implementing the SQ / B2D unit using the reactions from Kiho Park's 2D memory unit, but with Snarks and syringes and such as needed.

There's barely any description on how it works. Could you tell me how it works?

Posted: **October 11th, 2022, 7:01 pm**

AlbertArmStain wrote: October 11th, 2022, 6:06 pm There's barely any description on how it works. Could you tell me how it works?

I don't know how it works any more than you do. It would be an interesting reverse-engineering job.

It definitely _would_ be nice to have some kind of technical summary of the various mechanisms in Kiho Park's memory unit.

One way or another, it seems likely that a new self-constructible SQ / B2D unit could be designed, with no size increase over the current one ... even with the circuitry all being slmake-compatible.

Nobody has done anything self-constructing that's anywhere near that big since the Gemini, though. Generally the focus has been on reducing the hardware to an absolute minimum size and putting all the complexity in the software.

Side note: there's no harm in putting new posts on Kiho Park's thread if the posts contain new details that someone has figured out. People sometimes apologize for double-posting or necroposting in cases where it makes perfect sense to add a new post.

Posted: **October 13th, 2022, 7:23 am**

is searching for conduits that output a given methuselah harder than finding ones that have it as an input?

Posted: **October 13th, 2022, 8:54 am**

C28 wrote: October 13th, 2022, 7:23 am is searching for conduits that output a given methuselah harder than finding ones that have it as an input?

Much harder. Not even comparable.

Searches for conduit outputs happen the same way as searches for specific medium-sized oscillator periods: basically you just build things and see what you get.

There's no known way to bias a search effectively to aim for any specific output, so the only option is to find enough conduits that some of them will have the type of output you're looking for.

Conversely, if you want a given active reaction as input, you can just start a conduit search (with ptbsearch, catgl, manual search, etc.) and if anything turns up, well, there it is.

ConwayLife.com

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