One Glider Seeds

[MathAndCode]

I've started looking into two-XWSS collisions. Specifically, I've looked at all of the 180° LWSS-LWSS collisions where the two LWSSes have the same parity. Here's a way to collide two LWSSes to make xs14_64lb8ozw11:

Code: Select all

x = 14, y = 6, rule = B3/S23
b4o$o3bo$4bo5bo2bo$o2bo5bo$9bo3bo$9b4o!

The Catalogue page already has a six-glider synthesis of it, but I would argue that mine is better because it allows for two more degrees of freedom. Because I have only gone through a small fraction of all of the possible two-XWSS collisions (It's less than one-twelfth because using the same XWSS and examining 180° collisions each create redundancies due to symmetry.), it's quite possible that one of the collisions creates at least one object that was not previously known to be synthesizable with six or fewer gliders—unless someone else has already examined all of the two-XWSS collisions, in which case I'd like the link for that.

They have, and the XWSS+G collisions.
download/file.php?id=2121

Thank you. I figured that someone had probably done that, but when I saw that what I figured is a better six-glider synthesis is not included on Catalogue, I started to wonder. However, now that I've looked some more, I see that Catalogue apparently doesn't bother optimizing its glider syntheses in any way besides the glider cost. For example, Catalogue's three-glider synthesis of the tub has three degrees of freedom and lasts 64 ticks, but the following three-glider synthesis of the tub has four degrees of freedom and lasts a minimum of 27 ticks:

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x = 9, y = 12, rule = B3/S23
bo5bo$o5bo$3o3b3o7$2bo$b2o$bobo!

I'd argue that if multiple glider syntheses exist for the same object at the minimum glider cost, then the one with the most degrees of freedom should be shown. If that's also a tie, then the next tiebreaker should be the number of ticks from the generation where the gliders start affecting each other to the first generation with the desired object and no sparks, and the tiebreaker after that should be the number of directions that the gliders come from, with 90° syntheses having priority over head-on syntheses. The tiebreakers after that should be the size of the convex hull (or, more likely, some close analog) of the synthesis reaction's bounding envelope, the size of the reaction's bounding envelope itself, the amount of generations for which there are sparks at or near the edge of the bounding envelope, the number of lanes required for the gliders, then the number of half-diagonals occupied by the glider lanes, and hopefully no ties will remain after that. However, my opinion is apparently not universal.

[dvgrn]

I'd argue that if multiple glider syntheses exist for the same object at the minimum glider cost, then the one with the most degrees of freedom should be shown... However, my opinion is apparently not universal.

That opinion is fairly popular, though, I think. That's really the best you can hope for when a legion of Lifenthusiasts is involved.

I'm not so worried about some of those tiebreakers, but it would be really nice if an N-glider recipe with k+1 stages would out-compete an N-glider recipe with only k stages.

Apparently there's a Shinjuku setting that would enable this very easily, so unlike many of the other tiebreaker metrics, there wouldn't be a prohibitive amount of coding to do.

[Ian07]

Apparently there's a Shinjuku setting that would enable this very easily, so unlike many of the other tiebreaker metrics, there wouldn't be a prohibitive amount of coding to do.

I was going to tell you this but then forgot, but calcyman actually flipped that switch a few weeks ago: https://gitlab.com/apgoucher/catagolue/ ... 8b05230413

[MathAndCode]

Apparently there's a Shinjuku setting that would enable this very easily, so unlike many of the other tiebreaker metrics, there wouldn't be a prohibitive amount of coding to do.

I was going to tell you this but then forgot, but calcyman actually flipped that switch a few weeks ago: https://gitlab.com/apgoucher/catagolue/ ... 8b05230413

Apparently, it doesn't change pages that already display glider syntheses with less degrees of freedom. How can this be fixed?

[dvgrn]

Apparently, it doesn't change pages that already display glider syntheses with less degrees of freedom. How can this be fixed?

If the flipped switch is working, then it should be just a matter of submitting recipe with more degrees of freedom than whatever is current for a given object, to the incontrovertibly nonmagical box (bottom of the page).

You don't have to include the synthesis for any intermediate steps that are already known by Catagolue/Shinjuku -- though it doesn't do any harm. So for your tub example, you could try submitting this

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x = 107, y = 12, rule = B3/S23
bo75bo$o75bo$3o30b2o33b2o6b3o$32bo2bo31bo2bo$32bo2bo31bo2bo$33b2o33b2o
4$2bo102bo$b2o101bobo$bobo101bo!

-- or just this:

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x = 9, y = 4, rule = B3/S23
b2o$o2bo3bo$o2bo2bo$b2o3b3o!

[MathAndCode]

Apparently, it doesn't change pages that already display glider syntheses with less degrees of freedom. How can this be fixed?

If the flipped switch is working, then it should be just a matter of submitting recipe with more degrees of freedom than whatever is current for a given object, to the incontrovertibly nonmagical box (bottom of the page).

Thank you. I looked at that page but didn't scroll all the way to the bottom.
Also, for the synthesis of hook on hook with two LWSSes, do you know whether or not it will be recognized as having five degrees of freedom?

Also, here's a three-glider synthesis of a ship with four degrees of freedom due to a pond intermediate:

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x = 13, y = 13, rule = B3/S23
5bo6bo$4bo5b2o$4b3o4b2o8$2o$b2o$o!

The last glider can be moved one tick forward, and the synthesis still works—even though it now interacts with the pond's grandparent.

Code: Select all

x = 13, y = 13, rule = B3/S23
5bo5bo$4bo5bo$4b3o3b3o8$2o$b2o$o!

I suspect that Catalogue will not count the latter as having four degrees of freedom (even though I would), but I'll submit both just in case.



Edit: I found and submitted another six-glider synthesis for hook on hook with five degrees of freedom.

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x = 42, y = 22, rule = B3/S23
25bo$25bobo$25b2o2b3o$29bo$30bo4$39b3o$39bo$40bo$bo$2bo$3o4$11bo$12bo$10b3o2b2o$14bobo$16bo!

Another edit: Here's a similar synthesis:

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x = 42, y = 32, rule = B3/S23
40bo$39bo$39b3o3$25bo$25bobo$25b2o2b3o$29bo$30bo13$11bo$12bo$10b3o2b2o$14bobo$16bo3$3o$2bo$bo!

[dvgrn]

Apparently, it doesn't change pages that already display glider syntheses with less degrees of freedom. How can this be fixed?

If the flipped switch is working, then it should be just a matter of submitting recipe with more degrees of freedom than whatever is current for a given object, to the incontrovertibly nonmagical box (bottom of the page).

Thank you. I looked at that page but didn't scroll all the way to the bottom.
Also, for the synthesis of hook on hook with two LWSSes, do you know whether or not it will be recognized as having five degrees of freedom?

Well, it's time to do a little experimenting I guess. I can almost see what you mean about five degrees of freedom, but it's a little confusing to me. I'm used to thinking in terms of the number of intermediate stages in a recipe, i.e., the number of times you can stop for an arbitrary length of time before sending more gliders. Your hook-on-hook recipe is a three-stage recipe: build loafnblinker #1, build loafnblinker #2, crash gliders into loafnblinkers simultaneously.

The fourth degree of freedom would be the choice of which loafnblinker to build first, maybe? But the recipe is rotationally symmetrical, so both choices really produce the exact same recipe, from Catagolue's point of view. And what would the fifth degree of freedom be exactly? I'm not seeing it.

Also, I'm not sure that people working on glider syntheses would necessarily consider your recipe to be an improvement over the hook-on-hook recipe that's in Catagolue now, which has two advantages: it takes up a lot less space, and the reaction is complete much more quickly.

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#C [[ GRID MAXGRIDSIZE 14 THEME Catagolue ]]
#CSYNTH xs14_64lb8ozw11 costs 6 gliders (true).
#CLL state-numbering golly
x = 18, y = 12, rule = B3/S23
2bo$3b2o3bo$2b2o4bobo$8b2o6bo$15bo$15b3o$3o$2bo$bo6b2o$7bobo4b2o$
9bo3b2o$15bo!

A spaceship recipe that used the current hook-on-hook recipe as a base would have a significantly lower repeat time than one using your three-stage recipe.

This is what makes Mark Niemiec's database so useful -- it's very often helpful to have multiple known ways to build something, not just the current lowest-cost method. Paste RLE into the "Image" search to look for known recipes. Here's the hook-on-hook recipe collection, which includes the LWSS+LWSS collision you found.

The main idea behind flipping the prefer_long switch in Shinjuku is to make it possible to see the structure of complex syntheses better, when they've been submitted to Catagolue as "continuous" rather than "incremental" syntheses.

Here's a random example. The synthesis of xq4_suuw5b61ruuz1363y11363 currently has four stages:

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x = 196, y = 35, rule = B3/S23
172bo$173bo10bo$171b3o9bo$12bobo152bo15b3o$13b2o153b2o9bo$13bo153b2o10b
obo$179b2o11bo$3bo11bo156bo18bo$bobo11bobo45b2o49b2o48bobo6bo10b2o5b3o
$2b2o11b2o46b2o49b2o49b2o4b3o10b2o$118bo46bo$118bobo$49bo9bo37bo12bo7b
2o60bo$50bo2bo4bobo34bobo11bobo67bobo3b2o4bo$48b3o3b2o3bo36b2o12bo11b
o36bo11bo8bo4bobo2bo$53b2o65b2o38b2o8bobo13bo3b3o$99b2o5bo14b2o36b2o9b
obo3bo$98bobo4bobo63bo3bobo$100bo3bobo56b3o8bobo16b3o$51b3o51bo17b2o31b
2o7bo9bo11bo5bo$53bo69bobo31b2o5bo20b2o7bo$52bo5bo50bo13bo32bo22bo6b2o
$57bobo48bobo56b2o9bobo$58bo50bo58b2o9bo$167bo$171b2o$b2o11b2o46b2o49b
2o55bobo10b2o5b2o$obo11bobo45b2o49b2o57bo10b2o5bobo$2bo11bo175bo$167b
o9b3o$12bo154b2o8bo$12b2o152bobo9bo3b2o$11bobo157b2o9bobo$170bobo9bo$
172bo!

The first stage is really a combination of two separate stages. So theoretically if I pick it apart into these two pieces --

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x = 68, y = 30, rule = B3/S23
62bobo$63b2o$63bo2$53bo11bo$51bobo11bobo$52b2o11b2o12$60bo$59bobo$60bo
3$b2o11b2o48b2o$obo11bobo47b2o$2bo11bo2$12bo$12b2o$11bobo!

-- then the recipe will have five stages instead of four, so it should now be considered to be an improvement on what's in there now. Catagolue doesn't know how to take apart the six-glider synth of two tubnblocks to get the two-stage version, even though it already knows a three-glider recipe for that tubnblock. It's a three-direction recipe, so not quite as useful for adding objects to an existing constellation, but it would work fine in this case.

The addition of the beehive and boat at a later stage could also be split into two stages. To do that we'll just have to make an arbitrary decision about which one to build first; there currently isn't a good way to record the degree of freedom that's implied there.

Anyway, these kinds of patches currently have to be submitted manually. No need to resubmit the entire xq4_suuw5b61ruuz1363y11363 synth, though, just the part that breaks one stage into two stages.

I've submitted the above to Catagolue, so we'll see if anything happens in eight hours. Perhaps clarity will arrive eventually.

[Ian07]

I've submitted the above to Catagolue, so we'll see if anything happens in eight hours. Perhaps clarity will arrive eventually.

The update happened about half an hour ago, but it doesn't look like anything's changed.

[MathAndCode]

Well, it's time to do a little experimenting I guess. I can almost see what you mean about five degrees of freedom, but it's a little confusing to me.

Any glider synthesis always has at least three degrees of freedom:

• The gliders can all be moved the same number of cells left or right
• The gliders can all be moved the same number of cells up or down
• The gliders can all be moved the same number of generations forward or backward

In general, each intermediate brings one additional degree of freedom because all of the gliders after it can be moved by the same number of generations forward or backwards (although if the intermediate step has an oscillator at a certain period, then the number of generations needs to be a multiple of that period). The LWSS-based synthesis of a hook on hook has five degrees of freedom because in addition to the three standard degrees of freedom:

• The three gliders for one LWSS can all be moved any multiple of four cells left or right.
• The three gliders for one LWSS can also be moved any multiple of eight generations forward or backward

[dvgrn]

Well, it's time to do a little experimenting I guess. I can almost see what you mean about five degrees of freedom, but it's a little confusing to me.

Any glider synthesis always has at least three degrees of freedom:

• The gliders can all be moved the same number of cells left or right
• The gliders can all be moved the same number of cells up or down
• The gliders can all be moved the same number of generations forward or backward

Ah, I see. It's a bit confusing to mention the three time and space translations as "degrees of freedom", because by traditional definition a "glider synthesis" is still considered to be the same synthesis no matter if you move the target location or rewind the gliders.

A canonical glider synthesis might be the one that puts the target object at (0,0), and has the gliders advanced to the last tick before they start to interact. That gets rid of those three uninteresting degrees of freedom.

[MathAndCode]

Well, it's time to do a little experimenting I guess. I can almost see what you mean about five degrees of freedom, but it's a little confusing to me.

Any glider synthesis always has at least three degrees of freedom:

• The gliders can all be moved the same number of cells left or right
• The gliders can all be moved the same number of cells up or down
• The gliders can all be moved the same number of generations forward or backward

Ah, I see. It's a bit confusing to mention the three time and space translations as "degrees of freedom", because by traditional definition a "glider synthesis" is still considered to be the same synthesis no matter if you move the target location or rewind the gliders.

A canonical glider synthesis might be the one that puts the target object at (0,0), and has the gliders advanced to the last tick before they start to interact. That gets rid of those three uninteresting degrees of freedom.

That's a fair point, so we could simply refer to the number of extra degrees of freedom, which is equal to the number of degrees of freedom minus three. However, the important part is not how to count degrees of freedom; the important part is whether or not Catalogue can reliably tell whether one glider synthesis has more, fewer, or the same number of degrees of freedom as another glider synthesis and choose which glider synthesis to display accordingly.

[MathAndCode]

Getting back on topic, here's a one-glider seed for an edgeshot block.

Code: Select all

x = 8, y = 16, rule = B3/S23
6bo$5bo$5b3o$2o$obo$b2o9$3b2o$3b2o!

It uses the fact that a ship is a one-glider seed for Block and glider then uses another block to suppress the glider's formation.

By the way, why are so many common objects one-glider seeds for ∏-heptominoes even compared to other common methuselahs?

[Entity Valkyrie 2]

By the way, why are so many common objects one-glider seeds for ∏-heptominoes even compared to other common methuselahs?

This is because as long as there's something stabilizing these two cells, then this collision probably results in a pi + something.

Code: Select all

x = 3, y = 5, rule = B3/S23
obo$b2o$bo2$b2o!

[dvgrn]

Getting back on topic, here's a one-glider seed for an edgeshot block.

Code: Select all

x = 8, y = 16, rule = B3/S23
6bo$5bo$5b3o$2o$obo$b2o9$3b2o$3b2o!

It uses the fact that a ship is a one-glider seed for Block and glider then uses another block to suppress the glider's formation.

A boat is also a one-glider seed for block-and-glider; you can just remove one cell from the ship, but you have to move the glider over by one lane:

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x = 45, y = 26, rule = B3/S23
11$24b2o$24bobo$25bo$35b2o$35b2o$23b2o$22bobo$24bo!

And something that I just noticed this morning is that that boat+glider --> block-and-glider can be triggered by gliders coming from two different directions:

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x = 75, y = 30, rule = LifeHistory
3.4B21.4B11.4B21.4B$4.4B19.4B13.4B19.4B$5.4B17.4B15.4B17.4B$6.4B15.4B
17.4B15.4B$7.4B13.4B19.4B13.4B$8.4B12.4B20.4B12.4B$9.4B6.3B.B2C2B21.
4B6.3B.B2C2B$10.4B4.6BCBC2B21.4B4.6BCBC2B$11.4B3.7BCBCB22.4B3.7BCBCB$
12.14BC2B23.14BC2B$13.16B24.16B$14.16B24.16B$14.5B2C8B25.5B2C8B$15.4B
CBC8B25.4BCBC8B$17.3BC9B27.3BC9B$17.12B28.12B$19.10B30.10B$18.4B2.5B
29.4B2.5B$17.4B4.2B32.4B2.2B$16.4B40.4B$15.3CB42.B3C$15.2BC44.C2B$16.
C46.C!

Probably that's been common knowledge for fifty years and I just missed it, or forgot it. This kind of thing might happen fairly often, at least when a glider is hitting something with an axis of symmetry that goes through the middle of a cell. Things like pi-heptominoes created by a glider hitting an even-symmetry domino can't do this kind of trick, I think -- there will tend to be a one-cell difference in location:

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x = 34, y = 12, rule = LifeHistory
6.2C18.2C$6.2C18.2C3$6.D.D17.D.D$6.D.D17.D.D$6.3D17.3D3$3C28.3C$2.C
28.C$.C30.C!
#C [[ STOP 27 ]]

[MathAndCode]

Getting back on topic, here's a one-glider seed for an edgeshot block.

Code: Select all

x = 8, y = 16, rule = B3/S23
6bo$5bo$5b3o$2o$obo$b2o9$3b2o$3b2o!

It uses the fact that a ship is a one-glider seed for Block and glider then uses another block to suppress the glider's formation.

A boat is also a one-glider seed for block-and-glider; you can just remove one cell from the ship, but you have to move the glider over by one lane:
And something that I just noticed this morning is that that boat+glider --> block-and-glider can be triggered by gliders coming from two different directions:

So this means that a ship plus a long boat is also a splitter, although this probably won't be very useful because a clean ship requires three gliders, while there's a two-glider collision that makes a boat.

Also, here is a one-glider seed of a pentadecathlon that can probably be improved.

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x = 20, y = 11, rule = B3/S23
16bo$2bo12bo$bobo11b3o$2bo2$5b2o$o4bobo10bo$o5b2o9bobo$o16bobo$3b2o13bo$3b2o!

It's based on the fact that a queen bee crashing into a blinker can make a pentadecathlon.

[dvgrn]

Going back to one-glider seeds of the type that started the thread, where one glider creates multiple synchronized signals that then Make Something Happen --

here's a completion of a very old project found in blockish-and-blockic-seeds.rle, upper left corner. Way back in 2004 I had gotten a p256 oscillator recipe down to ten unidirectional gliders... but then didn't have the tools to efficiently make the ten gliders out of one glider.

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x = 155, y = 157, rule = LifeHistory
60.2A34.2A$59.B2A33.B2A$58.6B30.6B$57.8B28.8B$55.2A8B26.2A8B$42.2A10.
B2A8B25.B2A8B$41.B2A10.10B26.10B$39.6B9.11B25.11B$39.6B8.13B23.13B$
39.5B8.4B3.8B21.4B3.8B$39.5B7.4B4.3B2.4B19.4B4.3B2.4B$37.B2A5B5.4B6.
2B3.4B17.4B6.2B3.4B$37.B2A.5B3.4B13.4B15.4B13.4B20.2B$37.3B2.5B.4B15.
4B13.4B5.2A8.4B19.3B$43.8B4.2A11.4B11.4B5.B2A9.4B17.4B$44.6B4.B2A5.2A
5.4B9.4B5.6B8.4B15.6B$41.3B.5B3.5B3.B2A6.4B7.4B5.8B8.4B12.8B$40.11B3.
4B2.4B7.4B5.4B4.2A8B9.4B11.8B$40.18B3.2B9.4B3.4B4.B2A8B10.4B10.9B$31.
2A5.2B2A16B2.2A11.4B.4B5.10B12.4B2.2A5.2A7B$30.B2A5.2B2A18B2AB11.7B6.
11B12.5B2A4.2BA7B$29.4B6.25B.B2A7.5B6.13B12.6B4.2BABA6B$30.2B7.27B2A
7.5B5.4B3.8B12.5B5.2B2A7B$25.2A2.2B8.24B.3B7.7B3.4B4.3B2.4B11.6B4.10B
$24.B2A.4B6.6B2A16B3.B7.4B.4B.4B6.2B3.4B10.7B2A2.9B$24.5B2A3B3.7B2A4B
2A10B10.4B3.7B13.4B7.9B2A.10B$25.B.2B2A19B2A9B10.4B5.5B15.4B5.12B.8BA
2B$28.33B9.4B3.2A.5B16.4B4.12B2.6BABAB$28.24B.9B7.4B3.B2A7B16.4B5.8B
3.8BA4B$24.28B2.9B5.4B3.7B.4B16.4B4.8B2.4B3.7B$24.2A20B2A5B.10B3.4B3.
8B2.4B16.4B2.4B.3B2.4B3.8B$23.B2A5B2A13B2A6B.10B.4B2.2A8B3.4B16.8B6.
4B3.10B$23.8B2A6B.7B3.10B.8B2.B2A8B4.4B3.2B11.6B6.4B4.11B$24.B.11B2.
5B7.9B2.6B3.10B6.5B2A2B11.4B6.4B6.11B$26.10B2.5B9.16B3.11B6.4BABAB10.
6B4.4B8.5B2.4B$26.B2A7B2A4B11.16B.13B6.4B2AB9.8B3.4B8.5B3.4B$26.B2A7B
2A3B13.21B.8B6.7B7.4B2.4B3.3BA8.3B5.4B$25.15B15.11B.7B2.3B2.4B6.7B5.
4B4.8BABAB6.3B6.4B$24.16B15.18B4.2B3.4B5.8B3.4B6.7BA2BA7.B8.4B$23.17B
15.18B10.4B4.14B8.7B2AB17.4B$22.B2A15B15.4B2A13B10.4B4.6B2A4B9.11B17.
4B$21.2B2A15B10.2A3.4B2A9B.4B10.4B2.7BABA2B9.A10B19.4B$20.21B8.B2A2.
15B3.4B10.12B.2AB9.ABA8B21.4B$19.23B7.3B.16B4.4B10.6B.7B9.B2A2B.6B21.
4B2A$18.4B.20B6.8B2.5B2A3B5.4B10.4B4.5B8.4B5.4B21.3BABA$17.4B2.10B2.
9B7.5B2.6B2A3B.B2A2.4B8.6B5.B9.4B6.5B19.4B2A2B$16.4B4.3B.6B.10B2.2A2.
20B2A3.4B6.8B13.4B8.5B17.8B$15.4B10.11B.6B2A5B2A16B5.4B4.4B2.4B11.4B
10.5B15.9B$14.4B12.11B.12B2A15B7.4B2.4B4.4B9.4B12.5B11.11B$13.4B14.
10B2.28B8.8B6.4B7.4B14.5B5.2A2.4B2A6B$12.4B16.10B.23B2A12.6B8.4B5.4B
16.5B2.2B2A2.3BABA5B2.2A$11.4B18.33B2A13.4B10.4B3.4B18.5B.3B4.2B2A8B
2A$10.4B20.19B2.13B.B2A8.6B10.4B.4B20.8B4.7B.6B$9.4B20.20B.4B3.9B2A7.
8B10.7B22.5B6.4B5.5B$6.2A4B17.2A2.24B6.4B.3B7.4B2.4B6.2B2.5B23.5B5.4B
6.6B$5.B2A3B17.B2A.16B.7B8.2B3.B7.4B4.4B4.3B2.5B22.3B2AB4.4B7.7B2A$4.
6B18.7B2A19B7.B2A9.A4B6.4B3.11B2.2A17.3B2AB3.4B6.9B2A$4.5B20.B.4B2A
18B7.2B2A5.B2.ABA2B8.13B.5B2A19.2B4.4B6.12B$3.6B23.15B.8B7.2B5.4B2A2B
10.B2A8B3.6B24.4B7.12B$2.2A5B24.2B2.10B2.8B12.8B11.B2A7B5.5B23.4B10.
8B$.B2A7B21.B2A2.11B2A8B11.7B12.11B4.6B21.4B11.8B$12B19.2B2A2.3B2A.5B
2A.8B9.2A5B14.10B4.7B2A17.4B11.4B.3B$12B20.2B3.3B2A2.6B2.8B7.BABA6B
14.3B2A3B2.9B2A16.4B11.4B$2.8B29.2B4.6B2.8B6.2BA7B15.2B2A2B2.12B15.4B
11.4B$2.8B35.7B2.8B4.11B16.3B4.12B14.4B11.4B$3.3B.4B34.7B2A.8B4.11B2.
2A12.2B6.8B15.4B11.4B$8.4B31.9B2A2.8B2.7B2.5B2A17.3B.7B14.4B11.4B$9.
4B29.13B2.15B4.6B17.10B14.4B11.4B$10.4B28.14B2.10B9.5B16.9B15.4B11.4B
$11.4B29.8B.4B2.8B10.6B15.7B2AB13.4B11.4B$12.4B28.8B2.4B2.8B9.7B2A13.
5BA2BAB11.4B11.4B$13.4B26.4B.3B4.4B2.8B6.9B2A12.6BABAB11.4B11.4B$14.
4B24.4B10.14B4.12B11.BA5B.A2B10.4B11.4B$15.4B22.B2AB12.14B3.12B10.BAB
A8B9.4B11.4B$16.4B20.BA2BA13.4B2.8B4.8B11.2BABA2.4B10.4B11.4B$17.4B
18.3B2A13.6B2.8B3.8B10.4BA2.4B5.2B3.4B11.4B$18.4B13.2B.5B13.8B2.8B.4B
.3B10.5B3.4B4.3B2.4B11.4B$19.4B10.8B14.4B2.4B2.11B14.4B6.4B3.8B11.4B$
20.4B6.2B.8B8.2B3.4B4.4B2.9B14.4B8.13B11.4B$21.4B4.3B.8B.2B4.3B2.4B6.
4B2.8B13.4B10.B2A8B11.4B$22.4B3.4B.5B2A4B3.8B8.4B2.8B11.4B11.B2A7B11.
4B$23.15BA2BA13B10.4B.9B9.4B12.11B9.4B$24.B2A11BA.A3B2A8B12.14B7.4B
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5B2.8B3.4B19.2B2A2B7.4B$25.10B.5B3.10B10.2A7B2.8B.4B21.3B8.4B$27.3B2A
3B2.B2.2A4.3B2A3B9.B2A3B.4B2.11B23.2B7.4B$28.2B2A2B4.2B2A5.2B2A2B9.6B
3.4B2.9B32.4B$29.3B6.3B7.3B11.5B5.14B31.4B$30.2B2.7B8.2B10.6B6.B2A11B
29.4B$34.2A3B21.2A5B6.B2A12B27.4B$33.B2A4B19.B2A7B4.16B25.4B$33.8B17.
12B4.16B23.4B$34.8B16.12B6.3B2A10B21.4B$34.2B2.5B17.8B9.2B2A2B.8B19.
4B$39.5B16.8B10.3B4.8B17.4B$40.5B16.3B.4B10.2B5.8B15.4B$41.5B20.4B17.
8B13.4B$42.5B20.4B17.8B11.4B$43.5B20.4B17.8B9.4B$44.5B20.4B17.8B7.4B$
45.5B20.4B17.8B5.4B$46.5B20.4B17.8B3.4B$47.5B20.4B17.3B2A3B.4B$48.5B
20.4B17.BABA7B$49.5B20.4B15.2B2A7B$50.5B20.4B13.12B$51.5B20.4B6.2B3.
14B8.3B$52.5B20.4B4.3B2.4B2.10B6.2B2A$53.5B20.4B3.8B3.6BA4B5.2BABA$
54.5B20.13B4.5BABA4B3.4BAB$55.5B20.B2A8B5.5B2A6B.7B$56.5B19.B2A7B5.
21B$57.5B18.11B4.7B.13B$58.5B18.10B3.8B2.12B$59.5B19.3B2A3B2.4B2.B5.
11B$60.5B19.2B2A2B2.4B9.2B2A7B$61.5B19.3B3.4B10.2BABA5B$62.5B19.2B2.
4B11.2B.2A2B$63.5B21.4B12.A7B$64.5B19.4B12.ABA7B$65.5B2.2B13.4B12.BAB
A3B.4B$66.5B2A2B11.4B13.2BA3B3.4B2.2A$67.4BABAB10.4B14.6B4.5B2A$68.4B
2AB9.4B15.6B5.6B$69.7B7.4B17.4B2A5.5B$70.7B5.4B19.2BABA.3B.6B$70.8B3.
4B19.2BABA13B2A$70.14B20.3BA14B2A$71.6B2A4B20.21B$70.7BABA2B21.21B$
69.9B2AB23.9B2A7B$68.4B.8B24.7BABA7B$67.4B4.7B23.8BA7B$69.B7.B.4B21.
12B$80.4B20.12B$81.4B19.10B$82.4B19.3B3.4B$83.4B23.4B$84.4B21.4B$85.
4B19.4B$86.4B17.4B$87.4B15.4B$88.4B13.4B$89.4B3.2B6.4B$90.4B2.3B4.4B$
91.8B3.4B$92.13B$93.10B2A$94.9B2A$93.11B$93.10B$93.5B2AB$94.4B2A$46.
3A47.3B$48.A47.2B$47.A!

I could certainly have completed this extremely inefficiently in 2004, as I did with the Blockic star recipe on the right side of the same pattern. There weren't a whole lot of one-time splitters known at the time, or at least no well-organized collections of them. My idea back then was that it was going to be much simpler to come up with a provably universal toolkit that could build anything glider-constructible, if all the one-time turners were just made out of blocks. That way we'd only have to collect slow-salvo recipes that split one block into two, and moved blocks around.

Now we have the Honeysearch database in slsparse, so it was really pretty silly of me to bother finishing the p256 oscillator seed, especially with modern OTTs. If I'm going to burn up eaters just to turn gliders, I might as well allow eaters in the base pattern as well... Someone could easily make a much smaller version of this, by just inserting a Herschel into a p256 Herschel loop that already had three out of the four eaters in place.

In fact, now that I think about it again, there's probably a way to get that Herschel in there using a chain of one-time turners, with all four of the eaters already place. Anyone want to give that a try? I should have done it that way, but I had this ancient half-finished project that kept me from thinking properly until I was almost done connecting everything up. I'm just not very clever sometimes.

Classified splitters from the 12x12 project
The whole thing was really just an excuse to work on classifying the 2G splitters from the 12x12 constellation enumeration project. I'll post the various stamp collections somewhere, probably on a new thread, when everything is sorted out.

It would be nice to have each of the output gliders classified in the same way that the turners are classified, but first I'd have to figure out a better classification system for the 0-degree and 180-degree turners. So in the meantime, I ran all the 2G splitters through the script that classifies gliders for the glider-pair construction toolkit.

So once we have this new toolkit sorted out, we'll be able to do the same kind of manual or automated stringing-together of one-time circuitry, as we currently do with permanent glider synchronization circuits, using the same classification system.

It might take a while to get all the bugs out of the system, though. A subset of the output gliders from the 2G OTTs turned out not to be classifiable by the script, for reasons that I'm not at all clear on yet. If someone wanted to write a better classifier script from the ground up, with all the math sorted out properly and no weird hacks, I'd be most grateful.

[MathAndCode]

Going back to one-glider seeds of the type that started the thread, where one glider creates multiple synchronized signals that then Make Something Happen --

In fact, now that I think about it again, there's probably a way to get that Herschel in there using a chain of one-time turners, with all four of the eaters already place. Anyone want to give that a try? I should have done it that way, but I had this ancient half-finished project that kept me from thinking properly until I was almost done connecting everything up. I'm just not very clever sometimes.

I'm currently searching for a simple one-glider Herschel seed. I haven't found one yet, but I did find this.

Code: Select all

x = 17, y = 8, rule = B3/S23
obo5bobo$b2o6b2o$bo7bo5$6b3o5b3o!

There's probably a relatively simple splitter that allows this.

Edit: Here are the Herschel-creating collisions that I've found so far.

Code: Select all

x = 7, y = 9, rule = B3/S23
obo$b2o$bo4$4b2o$3bo2bo$4b2o!

Code: Select all

x = 8, y = 9, rule = B3/S23
obo$b2o$bo4$5b2o$4bo2bo$5b2o!

Code: Select all

x = 10, y = 7, rule = B3/S23
obo$b2o$bo2$7b2o$6bo2bo$7b2o!

Code: Select all

x = 10, y = 7, rule = B3/S23
obo$b2o$bo$8bo$7bobo$6bo2bo$7b2o!

Code: Select all

x = 15, y = 9, rule = B3/S23
obo$b2o$bo3$12bo$11bobo$11bo2bo$12b2o!

Code: Select all

x = 9, y = 11, rule = B3/S23
obo$b2o$bo5$6bo$5bobo$5bo2bo$6b2o!

I'm sure that at least one of these could be made into a working one-glider seed with some splitters to create cleanup gliders, but there's probably something better, so I'll keep looking.

Another edit: I got a clean B-heptomino!

Code: Select all

x = 10, y = 7, rule = B3/S23
obo$b2o$bo2$7b2o$7bobo$8bo!

I'll keep searching for a clean Herschel.

Yet another edit: This could be useful.

Code: Select all

x = 10, y = 12, rule = B3/S23
obo$b2o$bo3$8b2o$7bobo$8bo3$2o$2o!

Fourth edit: Here is a clean one-glider seed for a Herschel.

Code: Select all

x = 16, y = 14, rule = B3/S23
obo$b2o$bo7$b2o$b2o$14b2o$13bobo$14bo!

There might be a way to place the block closer that also works, but besides that, I'm done.

Fifth edit: Here are one-glider seeds for a clean Herschel that are slightly more compact in certain ways.

Code: Select all

x = 16, y = 14, rule = B3/S23
obo$b2o$bo9$b2o11b2o$o2bo9bobo$b2o11bo!

Code: Select all

x = 16, y = 19, rule = TripleB3S23
G.G$.2G$.G9$14.2G$13.G.G$14.G2$5.G$4.G.G$4.BEF$5.B!

Code: Select all

x = 16, y = 19, rule = TripleB3S23
G.G$.2G$.G9$14.2G$13.G.G$14.G3$5.G$4.G.G$4.BEF$5.B!

[dvgrn]

Here is a clean one-glider seed for a Herschel...
There might be a way to place the block closer that also works, but besids that, I'm done...
Here are one-glider seeds for a clean Herschel that are slightly more compact in certain ways.

The Python3 find-octohash script turns out to be a good tool for this kind of thing. it found a hundred and seventy-odd clean Herschel descendant seeds, and I only had to look as far as the eighth constellation to find one that allowed a glider to sneak in from outside:

Code: Select all

x = 49, y = 58, rule = B3/S23
13bo17b2o$13b3o15b2o5b2o$16bo21b2o$15b2o$22bo$7b2o12bobo12b2o$7b2o11bo
bo13b2o$20b2o20b2o$42b2o$b2o$b2o18b2o$5b2o13bo2bo$5b2o13bobo$21bo25b2o
$47bo$45bobo$2o43b2o$2o3$7b2o$7b2o4$3b2o$3b2o5$47b2o$2b2o43b2o$bobo$bo
$2o$42b2o$42b2o$46b2o$46b2o$5b2o$5b2o$11b2o27b2o$11b2o27b2o2$32b2o$9b
2o21bo$9b2o5b2o15b3o$16b2o17bo7$35b3o$35bo$36bo!

Here's the full output, in case anyone wants to look for one where the glider comes in directly from outside, instead of needing a 90-degree one-time turner. There might also be a solution that permits the four eaters to move back in to their closest possible positions, where they are in the incredibly archaic seed I posted above.

Code: Select all

x = 5514, y = 20, rule = LifeHistory
255.A.A.A.A.A.A.A.A2$253.A17.A2$.4C36.C23.2C30.2C30.2C30.C31.C32.2C
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2C33.2C29.C60.2C2.2C29.2C27.2C35.C28.3C27.2C37.2C59.C67.C24.2C31.2C
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2.C29.C.C63.C68.C29.2C34.C29.C29.3C23.C2.C35.C26.2C38.C23.C.C37.C27.
3C23.C.C$5.3C31.2C92.C.C33.C.C30.C.C24.C23.A12.C.C2.A20.C38.C57.C31.C
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2C29.2C29.C2.C29.C.C28.3C2.2C29.C27.2C2.2C27.C3.C.C24.C.C31.C2.C28.C
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2C3.C.C23.2C65.C31.C.C27.C.C3.C25.C.C29.C.C28.C2.C2.2C24.C.C30.C32.C
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3C63.C.C87.3C3.C25.C.C2.2C25.C33.C2.2C59.C61.3C3.C26.C$6.C27.C4.C.C
91.C35.C32.C63.C26.C38.C116.C.C29.C35.C32.2C29.C64.C32.C.C32.C23.C32.
C65.C33.C30.C.C30.C.C30.C24.2C4.C25.2C32.C5.C87.C37.C.C27.C.C29.C36.C
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C.C89.C36.C29.C.C29.C.C24.2C34.2C26.2C30.2C29.2C2.C27.2C2.3C25.C.C29.
C.C29.C.C29.C.C29.C.C29.C.C32.C29.C.C29.2C30.C31.C2.C28.C.C29.C.C.3C
24.C2.C2.2C27.C29.C.C28.C.C29.C2.C28.C2.C29.C.C28.2C3.C26.C32.C.C61.
3C29.C30.2C2.C.C26.2C30.C.C30.C.C3.C25.2C29.C4.2C26.C.C27.C2.C29.C.C
29.C3.2C28.C3.C29.C29.2C60.C33.2C30.2C29.C3.2C26.C3.3C27.C28.C3.C.C
26.3C28.C.C28.C.C32.C36.C27.C.C94.2C28.2C31.C29.C5.C25.C2.3C26.C30.2C
3.C.C24.2C29.2C2.3C27.2C28.2C2.3C29.C.C28.C2.C28.C.C3.C23.3C31.C28.C.
C29.C.C35.C30.2C31.2C28.3C25.2C30.2C30.C2.C2.C.C23.C.C2.2C57.3C30.C
67.C28.C61.C35.C65.C96.C25.C3.C.C24.C31.C.C2.C.C127.C27.3C$33.C.C36.
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2C31.C35.2C26.2C95.2C30.C2.3C26.C2.C27.2C2.2C27.2C30.C30.C31.2C30.2C
31.C2.3C24.2C30.2C32.2C2.2C57.C128.C32.2C29.C.C28.2C3.C.C26.2C28.2C
31.C2.3C24.2C3.C.C26.2C65.C160.C.C29.C91.C31.2C28.2C2.2C28.2C64.C96.
2C126.C126.C63.C32.C30.2C29.2C30.C30.2C29.C30.2C133.C89.2C30.C2.2C91.
C33.3C32.C60.3C26.2C30.3C2.C191.C26.C31.2C3.C28.2C127.C$34.C.C34.C2.C
28.C2.C538.C.C89.C.C70.C.C277.C.C355.C58.C170.C18.2C515.C223.C.C59.C
97.C32.C32.C189.C95.2C91.2C61.C97.2C33.C94.C31.C154.2C64.C35.C32.C28.
2C126.C.C220.C32.2C64.C26.2C64.C33.C63.C256.2C28.C33.C31.2C126.C60.2C
62.C63.2C30.C31.2C318.C128.C$35.2C34.C.C29.C.C2.3C144.A.A.A.A.A.A.A.A
540.C279.C.C604.C.C543.2C28.2C63.2C31.2C65.C60.2C61.C36.C93.C126.C34.
C96.C90.C.C59.2C160.C67.C185.C.C62.2C97.C.C125.C221.2C32.C.C90.C.C62.
2C128.2C29.C96.C28.2C31.2C34.C.C26.2C32.2C220.C.C62.C62.C.C30.C30.C.C
314.3C$72.C31.C3.C982.C605.C545.C.C27.C.C62.C.C30.C.C125.C.C59.2C129.
2C125.2C222.C61.C.C158.2C253.C64.C.C96.C349.C.C31.C92.C64.C.C127.C.C
27.2C95.2C28.C.C30.C.C33.C28.C.C31.C.C219.C127.C63.C316.C$109.C2133.C
29.C64.C32.C189.C.C128.C.C124.C.C444.C.C1088.C29.C.C94.C.C27.C32.C$
70.2C1017.2C$70.C.C1016.C.C$70.C1018.C!

For example, this Herschel-descendant seed should let the eaters move in at least one cell closer:

Code: Select all

x = 16, y = 14, rule = LifeHistory
3$5.C$4.C.C3.2C$3.C2.C2.C2.C$4.2C4.C.C$11.C$6.3C$6.C$7.C!

EDIT: Couldn't resist checking as far as the 24th constellation, and found one that has the right clearance for the minimum eater placements:

Code: Select all

x = 49, y = 55, rule = LifeHistory
31.2A$31.2A5.2A$38.2A3$7.2A8.2A17.2A$7.2A9.A17.2A$18.A.A21.2A$19.2A
21.2A$.2A$.2A$5.2A21.2C$5.2A20.C2.C$28.C.C$23.2C4.C$24.C$2A19.3C$2A
19.C21.A$41.3A$40.A$40.2A7$14.2A$7.2A5.2A$8.A$5.3A$5.A41.2A$10.2A35.
2A$10.2A3$42.2A$42.2A$46.2A$46.2A$5.2A21.2A$5.2A21.A.A$11.2A17.A9.2A$
11.2A17.2A8.2A3$9.2A$9.2A5.2A$16.2A4$32.3A$32.A$33.A!

There still might be one out there that doesn't need an additional 90-degree one-time turner, though.

The next useful piece of code to add to the octohash search will be some kind of template pattern. All the matching glider+constellation combinations should get pasted into the template in the same orientation, probably with history cells showing which cells had to turn on to get the output pattern. Then it should be easy to scan through the list and see which reactions actually fit the intended purpose.

[MathAndCode]

I haven't found a combination of splitter and two turners that is compatible with synthesizing a pentadecathlon from two blinkers.

Code: Select all

x = 17, y = 8, rule = B3/S23
obo5bobo$b2o6b2o$bo7bo5$6b3o5b3o!

Code: Select all

x = 24, y = 8, rule = B3/S23
obo18bobo$b2o18b2o$bo20bo5$6b3o6b3o!

Code: Select all

x = 18, y = 15, rule = B3/S23
obo$b2o$bo4$15b3o2$7b3o4$9bo$9b2o$8bobo!

Edit: I improved the one-glider seed from this post, so now what I was trying to find is not as necessary.

Code: Select all

x = 20, y = 10, rule = B3/S23
3b2o11bo$2bobo10bo$3bo11b3o3$5b2o$o4bobo10bo$o5b2o9bobo$o16bobo$18bo!

[Entity Valkyrie 2]

"Trivial" herschel seeds:

Code: Select all

x = 16, y = 49, rule = B3/S23
8b2o$8b2o$4bo$5b2o$4b2o4$o12b2o$3o9bobo$2bo9bo$2bo8b2o17$4bo$5b2o$4b2o
5$13b2o$13bobo$14bo2$2b2o$2b2o6$11b3o$11bo$10b2o!

A non-trivial example, but it contains an aircraft carrier:

Code: Select all

x = 27, y = 17, rule = B3/S23
16b2o$16b2o4$13bo$14b2o$13b2o4$25b2o$o22bo2bo$3o20b2o$2bo$2bo!

[MathAndCode]

I improved the one-glider seed from this post, so now what I was trying to find is not as necessary.

Code: Select all

x = 20, y = 10, rule = B3/S23
3b2o11bo$2bobo10bo$3bo11b3o3$5b2o$o4bobo10bo$o5b2o9bobo$o16bobo$18bo!

A block would probably be easier to construct than a beehive.

Code: Select all

x = 18, y = 9, rule = B3/S23
3b2o11bo$2bobo10bo$3bo11b3o3$5b2o$o4bobo$o5b2o8b2o$o15b2o!

A blinker might be easier to construct than a boat.

Code: Select all

x = 18, y = 9, rule = B3/S23
16bo$3b3o9bo$15b3o3$5b2o$o4bobo$o5b2o8b2o$o15b2o!

[dvgrn]

A block would probably be easier to construct than a beehive.
A blinker might be easier to construct than a boat.

It had completely failed to occur to me to check the new octohash database for pentadecathla, until now. There's exactly one match:

Code: Select all

x = 17, y = 8, rule = B3/S23
15bo$14bo$14b3o$2o$obo$2bo5bo$2b2o3bobo$7b2o!

Makes me wonder what other surprises might be lurking in that database.

[MathAndCode]

It had completely failed to occur to me to check the new octohash database for pentadecathla, until now. There's exactly one match

Thank you. I figured there was probably a more efficient way if one didn't rely on any single reaction. Also, each still-life can be created with only two gliders (in either order), which is better than my ship.

Makes me wonder what other surprises might be lurking in that database.

The patterns that I can think of that both could reasonably have small one-glider seeds and would be the most useful to have one-glider seeds for are the three XWSSes. Finding small one-glider seeds for an Eater 2 or Eater 5 would also be nice and seem plausible, but stationary objects probably don't need one-glider seeds as badly.
Disclaimer: For all I know, all five of those patterns could already have small one-glider seeds.

[dvgrn]

Disclaimer: For all I know, all five of those patterns could already have small one-glider seeds.

Most of those aren't quite likely enough to be in the octohash database, which just shows all possible collisions with two common objects that fit inside 12x12.

There are three ways to make a tub-with-tail that I didn't know about --

Code: Select all

x = 127, y = 35, rule = LifeHistory
9$13.A37.2A34.A27.A$12.A.A30.2A5.A24.2A7.A.A24.3A$13.A.A30.A5.A.A23.A
6.A.A24.A$15.A30.A.A4.2A23.A.A4.2A25.2A$15.2A30.2A30.2A2$110.2A$109.A
2.A$110.2A$56.A31.A$55.2A30.2A$55.A.A29.A.A$118.2A$118.A.A$118.A!

-- but none of them allow you to put a block nearby to make an eater5 in one step. Maybe a database of say three objects inside 12x12, or four objects inside 16x16, would be big enough to include something like that, but that would need dozens of gigabytes for the database, and weeks to run to build it.

There's only one LWSS seed in the octohash database, and it needs a blinker:

Code: Select all

x = 12, y = 13, rule = B3/S23
3bo$3bo$3bo3$2b2o$2bo$obo$2o2$9b3o$9bo$10bo!

No MWSSes or HWSSes, unfortunately. I think lots of three-object seeds can be found for those, but two objects doesn't seem to be enough (unless maybe a larger bounding box might help, but I think 12x12 is probably big enough to include most of the good stuff.) There's an old "Blockic seeds" thread by knightlife that contains good blocks-only converters, glider --> LWSS or MWSS --> glider.

Eater2s are quite a bit rarer. They seem to need five or six objects, generally, though there are probably some four-object seeds and maybe a rare three-object one.

[MathAndCode]

There's only one LWSS seed in the octohash database, and it needs a blinker:

Code: Select all

x = 12, y = 13, rule = B3/S23
3bo$3bo$3bo3$2b2o$2bo$obo$2o2$9b3o$9bo$10bo!

No MWSSes or HWSSes, unfortunately.

I figured that since I know that there are at least two one-glider seeds for a B-heptomino with or without additional ash, there would be more one-glider seeds for XWSSes. Is the only problem that the bounding box is too small, or are there not any known ways to stabilize a B-heptomino that has already formed into an XWSS?

Eater2s are quite a bit rarer. They seem to need five or six objects, generally, though there are probably some four-object seeds and maybe a rare three-object one.

I figured that an Eater 2 would have a decent chance of forming from a two-glider seed for two reasons:

1. It's symmetric.
2. It's an eater, which carries two advantages.
   1. It will still form even if it initially forms with a spark instead of a block for certain sparks.
   2. If the seed generates an Eater 2 and something else that would destroy most objects, the Eater 2 could still survive. (I think that I saw a synthesis of some fishhook-tie where the fishhook eats something about five generations after being formed.)

I figured that the second reason would also help make an Eater 5 likely.



Edit: The fishhook forms in its eating phase but doesn't do its next catalysis until about fifteen generations later, not five generations later.