Scratch Your Heads: Glider Synthesis of Bellman One

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Scratch Your Heads: Glider Synthesis of Bellman One

Post by Freywa » June 19th, 2013, 5:09 am

We know that the snark can be synthesised using 49 gliders. However, the synthesis for that was straightforward, and in a sense hinted by all matter of structures on its outer boundary. I will call that Bellman Zero, as it was the first catalyst found using Bellman. Bellman One, shown below, eats a traffic light predecessor if paired with an eater (if you've seen the AK-94 its application should be clear to you):

Code: Select all

x = 8, y = 8, rule = B3/S23
5b2o$2o2bo2bo$obo2b2o$3b2o$4bo$4bob2o$b2obo2bo$b2ob2o!
The question is how to synthesise this. It is a very connected still-life, with no obvious retrosynthesis (borrowing a term from organic chemistry). It could be possible to start with the carrier motif, then work to the beehive and hook and finally the block, but is an explicit construction even possible?
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by codeholic » June 19th, 2013, 8:25 am

Freywa wrote:We know that the snark can be synthesised using 49 gliders.
Actually, 48.
Freywa wrote:It could be possible to start with the carrier motif, then work to the beehive and hook and finally the block, but is an explicit construction even possible?
I see no particular problems for synthesizing this still life. I would probably try to start with one of the following still lifes.

Code: Select all

x = 8, y = 12, rule = B3/S23
2o2b2o$obo2bo$3b2o5$3b2o$4bo$4bob2o$b2obo2bo$b2ob2o!
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Extrementhusiast » June 28th, 2013, 3:43 pm

I did get this far:

Code: Select all

x = 157, y = 25, rule = B3/S23
40bobo43bo$11bo27bo45bo15bobo$12b2o25bo45b3o13b2o$11b2o26bo2bo40bo18bo
$15bo23b3o42bo$14bo18bo48b3o15b2o$14b3o17b2o3bo25bobo32b2o$33b2o5bo4bo
20b2o$38b3o2b2o21bo$19bo24b2o26bo13bo16bo14b2o34b2o$19bobo13bo28b2o5bo
bo7b2o2bobo10b2o2bobo9b2obo2bo13b3o12b2o2bo2bo$11bo7b2o14b2o10b2o14bob
o5b2o8bo3b2o11bo3b2o10bo3b2o13bo3bo11bobo2b2o$12b2o20bobo3b2o4b2o17bo
3b2o11b3o14b3o13b3o19bo14b2o$11b2o28bo6bo21bo13bo16bo15bo18bo16bo$2o
39bob2o25bob2o10bob2o13bob2o12bob2o14bo17bob2o$b2o6b2o27b2obo2bo22b2ob
o2bo7b2obo2bo10b2obo2bo9b2obo2bo29b2obo2bo$o7bobo27b2ob2o24b2ob2o9b2ob
2o12b2ob2o11b2ob2o16bo14b2ob2o$10bo3$8bo$7b2o$3o4bobo$2bo$bo!
All that's left is the final "flourish" step.
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Freywa » June 28th, 2013, 10:46 pm

Extrementhusiast wrote:All that's left is the final "flourish" step.
That was what I was talking about. The whole still-life is "interconnected" - replacing one part by another part almost always destroys stability. Now, can somepony run Glue or gencols or something to complete that last step?
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by codeholic » June 29th, 2013, 3:04 am

Oh, c'mon. If you wanna see something really interconnected, you should take a look at the last step of 60P5H2V0 synthesis.
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by mniemiec » July 1st, 2013, 6:48 pm

Extrementhusiast wrote:I did get this far:
...
All that's left is the final "flourish" step.
I suspect that it will be extremely difficult to find such a step. While it's fairly common to be able to puff the side out of an existing object (e.g., turning a a beehive into a loaf or a loaf into a pond or a hat into a loop), it's usually much harder do the reverse (e.g. turning a pond into a loaf requires first collapsing it into a ship, and then growing the ship into a loaf - something that's not possible if the pond and loaf are attached to something else). The only way the extraneous outside bit can be killed is by over-population, which deprives the internal bits of support, but simultaneously over-populates the internal dead cell where one wants a birth.

Similarly, turning a python into a bookend might be feasible, but going the other way (i.e. removing that third bit) would not. I've also found that pythons in orientations like that, with their ends fairly near other objects, tend to be extremely hard to synthesize. For example, one 20-bit pseudo-object, a beacon between two cis pythons, whose endpoints are just two cells away from each other, is a synthesis that had eluded me for over a decade, and I only just figured out how to make it last year - at a cost of 52 gliders. A similar 21-bit one, substituting a shillelagh for one of the pythons, takes 88! I can post the syntheses if anyone cares, but they are fairly large, and a bit off-topic for this thread.

I suspect that a more fruitful approach might be to start with a beehive instead of a bookend, and then try to peel one side of it open to make the python, while simutaneously turning the other side into the final beehive. Another approach that could work is to start with a tub-with-long-tail and grow the tub into a beehive.

The biggest problem I've found with both of the above approaches is that the area near the final beehive is unstable until it's actually fully formed. One could start with a pre-block near the tub/beehive instead of at the other end, but moving it would also require a fair it of ingenuity. Or one could have two pre-blocks (one where it's supposed to finally end up, and one stabilizing the tub/beehive), but removing one without affecting the other doesn't seem to be easy either.

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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Freywa » July 2nd, 2013, 2:57 am

mniemiec wrote:Another approach that could work is to start with a tub-with-long-tail and grow the tub into a beehive.

Code: Select all

#C Spin That Record Vinyl Scratch
#C http://youtu.be/3-_x34py8MU
x = 40, y = 8, rule = B3/S23
5bo9b2o9b2o9b2o$2o2bobo3b2o2bo2bo3b2o2bo2bo3b2o2bo2bo$obo2bo4bobo2b2o
4bobo2b2o4bobo2b2o$3b2o8b2o9b2o9b2o$14bo10bo10bo$14bobo3b2o3bob2o7bob
2o$15b2o2bobo2b2ob2o4b2obo2bo$20bo12b2ob2o!
I've pieced together a tentative synthesis plan for Bellman One. The intermediate the boat points to is tentative, as the hypothetical synthesis would require concerted reactions all the way, which is uncharted territory.
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by MikeP » July 2nd, 2013, 5:17 am

Bear in mind that not all the cells of the still life interact; as a result there are many possible patterns that can catalyse the reaction in the same way.

Bellman outputs partial patterns that describe only the catalytic portion of the still life. The partial pattern for the AK-94 catalyst looks like this:

Code: Select all

#P 0 0
.........................
.............???????????.
..............?.**..????.
................*.*.????.
...................*????.
......@.............*???.
.....@.@............*???.
....@...@........**.????.
....@...@........**.????.
....@...@...........????.
.....@.@............????.
......@............?????.
................????????.
...@@..........?????????.
....@.........??????????.
.@@@.....@@..............
.@.......@@..............
.........................
The '?' cells can be either live or dead and the reaction will still work (provided the catalyst is stable). You can also expand the area of '?'s into the empty space away from the reaction if you need to.

This gives you a lot of freedom which you can exploit if you're looking for glider syntheses of these catalysts. The target of your synthesis doesn't have to exactly match the pattern at the start of this thread. Any pattern which agrees with the partial result above will work.

(If anyone has done any work on searching for glider syntheses automatically, it might be interesting to think about feeding it Bellman partial results rather than completed patterns.)

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Bellman 1.5 (or the Reclining Chair)

Post by Freywa » July 2nd, 2013, 10:57 am

MikeP wrote:This gives you a lot of freedom which you can exploit if you're looking for glider syntheses of these catalysts. The target of your synthesis doesn't have to exactly match the pattern at the start of this thread. Any pattern which agrees with the partial result above will work.
Indeed. I have revamped Bellman One to be much more glider-friendly. I hereby introduce Bellman 1.5, aka the Reclining Chair. The reason for the name should be evident in the RLE below.

Code: Select all

x = 35, y = 26, rule = B3/S23
18bobo4bobo4bobo$18b2obob3ob3obob2o$21b2o7b2o$18b2o4b2ob2o4b2o$18bob4o
bobob4obo$20bo11bo$19bo3b2o3b2o3bo$8bo9bo4b2o3b2o4bo$8bo9b2o13b2o$7bob
o$8bo$2b2o4bo$bobo8b2o9bo5bo$bo5b2o4bo9bo5bo$2o5b2o3bo9bobo3bobo$11bo
11bo5bo$6bob4obo9bo5bo$6b2o4b2o4b2o13b2o$9b2o7bo4b2o3b2o4bo$6b3obob2o
5bo3b2o3b2o3bo$6bo4bobo6bo11bo$18bob4obobob4obo$18b2o4b2ob2o4b2o$21b2o
7b2o$18b2obob3ob3obob2o$18bobo4bobo4bobo!
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Extrementhusiast » July 2nd, 2013, 8:18 pm

I actually see that as being harder to construct. How would you go about the constructing process, step by step?

For the original, I have a predecessor that could point us in a good direction:

Code: Select all

x = 9, y = 8, rule = B3/S23
bo4b2o$2bo3bobo$2bo3b2o$o3b2o$5bo$5bob2o$2b2obo2bo$2b2ob2o!
Anybody know how to synthesize the pre-block in that way?

EDIT: An alternative:

Code: Select all

x = 10, y = 8, rule = B3/S23
b2o4b2o$o2bo3bobo$3bo3b2o$5b2o$6bo$6bob2o$3b2obo2bo$3b2ob2o!
Then shorten it using the known method.

EDIT: I put together this:

Code: Select all

x = 23, y = 20, rule = B3/S23
13bo$14b2o$obo10b2o5bobo$b2o17b2o$bo19bo$10b2o$11bo$11bobo$12b2o2$17bo
$4bo11bo$4b2o10b3o$3bobo2$9b2o$10b2o$9bo8bo$17b2o$17bobo!
It theoretically combines two of Freywa's steps into one step. However, the extra add-ons get in the way.
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Freywa » July 3rd, 2013, 4:46 am

Code: Select all

#C Bellman 1.5 synthesis
x = 69, y = 21, rule = B3/S23
45b2o9b2o8b2o$44bobo8bobo8b2o$33b2o8bobo8bo8bo$33b2o8b2o9b2obo5b4obo$
56b2o9b2o$31b4o6b4o7b3o8b3o$31bo3bo4bo4bo5bo2bob2o4bo2bob2o$34b2o4b2o
2b2o5b2o2bobo4b2o2bobo4$33b2o$28b2o4bo20b2o10b2o$o2bo24b2o3bo9b2o11bo
5b2o4bo$4bo27bo11bo5b2o3bo6b2o3bo$o3bo23b5obo5bo2bo6bo3bo11bo$b4o23bo
4bobo4b4obo5b4obo4bob4obo$30bo2bobo8b2o9b2o4b2o4b2o$29b2o3bo5b3o8b3o
10b2o$39bo2bob2o4bo2bob2o4b3obob2o$39b2o2bobo4b2o2bobo4bo4bobo!
Oh, this is getting very confusing already...
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Extrementhusiast » July 3rd, 2013, 7:51 pm

Getting closer on one of my ends. I've just found a reaction that will provide the necessary one-bit spark for the eater head transformation:

Code: Select all

x = 18, y = 8, rule = B3/S23
5b2o$2o2bo2bo6bo$obo2b2o8bo$3b2o8b3o$4bo$4bobo$5b2o$15b3o!
All that's left is to get rid of the leftover reaction with another glider or two. However, this creates a new, but fortunately simpler problem: What's an alternate recipe for the other part of the spark? And what's a block recipe that would work to stabilize the pattern?

EDIT: Very close now on another of the ends:

Code: Select all

x = 16, y = 11, rule = B3/S23
10bo$9bo$9b3o$4bo9bo$4bobo6bobo$b2ob2o7b2o$obo8b2o$2bo9bo$12bob2o$9b2o
bo2bo$9b2ob2o!
All that's left is the spark synthesis.

EDIT 2: SCORE!

Code: Select all

x = 23, y = 20, rule = B3/S23
9bo$10b2o$9b2o$20bo$20bobo$20b2o2$15bo$13b2o$14b2o$8bobo$8b2o7b2o$9bo
6bobo$15bobo$15b2o$13b2o$bo12bo$b2o11bob2o$obo8b2obo2bo$11b2ob2o!
Of course, using the usual tactics to get from boat to long ship. Full set of instructions, with proof of functionality:

Code: Select all

x = 160, y = 28, rule = LifeHistory
123.A$124.2A$123.2A$40.A.A60.A30.A$11.A27.A62.A31.A.A$12.2A25.A62.3A
29.2A$11.2A26.A2.A$15.A23.3A30.A29.A26.A$14.A18.A38.A.A26.2A24.2A$14.
3A17.2A3.A32.2A2.2A23.A.A24.2A$33.2A5.A4.A29.2A45.A.A$38.3A2.2A28.D3.
A21.CD21.2A6.DCA24.2C$19.A23.D2A26.C.D23.C.C22.A5.DA.C23.C2.C$19.A.A
13.A6.D.D26.C.C23.C.C24.2D2.DA.C19.2C2.C2.C$11.A7.2A14.2A5.2D3.2A22.
2C24.2C25.D.D2.2C20.C.C2.2C$9.2D.2A20.A.A3.2C4.2A21.2C24.2C30.2C25.2C
$10.D2A28.C6.A21.C25.C18.A12.C26.C$2A8.D.2D27.C.2C25.C.2C22.C.2C15.2A
11.C.2C16.A6.C.2C$.2A4.2DAC2.D24.2C.C2.C22.2C.C2.C19.2C.C2.C14.A.A8.
2C.C2.C14.2A.2A.2C.C2.C$A6.DC.CD26.2C.2C24.2C.2C21.2C.2C27.2C.2C18.A
3.2C.2C$10.A3$8.A141.2A$7.2A141.A$3A4.A.A141.3A$2.A150.A$.A!
Continuous synthesis:

Code: Select all

x = 95, y = 91, rule = B3/S23
9bo$10b2o$9b2o$92bo$92bobo$92b2o2$87bo$85b2o$86b2o$80bobo$80b2o$81bo4$
80bo$79bo$79b3o2$52bo$52bobo$52b2o2$44bo$45b2o8bo14bo$44b2o7bobo14bobo
$54b2o14b2o2$56bo$54b2o$55b2o2$32bo$30bobo3bo$31b2o4b2o25bo$36b2o26bob
o$64b2o3$51bo$52b2o$51b2o$55bo$54bo$54b3o3$59bo$59bobo$51bo7b2o$52b2o$
51b2o$40b2o$41b2o6b2o$40bo7bobo$50bo3$48bo$47b2o$32b3o5b3o4bobo17b2o$
34bo7bo24bobo$33bo7bo25bo6b2o$73b2o$75bo$79bo$78b2o$78bobo20$bo$b2o$ob
o!
It takes 26 gliders, assuming a synthesis from infinity. If it's not from infinity, then it takes one less.
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Freywa » July 3rd, 2013, 11:27 pm

Extrementhusiast wrote:It takes 26 gliders, assuming a synthesis from infinity. If it's not from infinity, then it takes one less.
Well actually 25 gliders. There's a reaction in the Pentadecathlon glider synthesis catalogue that converts the boat into a long ship in one step.

Code: Select all

x = 103, y = 99, rule = B3/S23
9bo$10b2o$9b2o$100bo$100bobo$100b2o2$95bo$93b2o$94b2o$88bobo$88b2o$89b
o8$45bo$31bo14b2o$32b2o11b2o$31b2o$56bo$56bobo$56b2o2$48bo$49b2o8bo$
48b2o7bobo$58b2o2$60bo$58b2o$59b2o2$36bo$34bobo3bo$35b2o4b2o25bo$40b2o
26bobo$68b2o3$55bo$56b2o$55b2o$59bo$58bo$58b3o3$63bo$63bobo$55bo7b2o$
56b2o$55b2o$44b2o$45b2o6b2o$44bo7bobo$54bo3$52bo$51b2o$36b3o5b3o4bobo
17b2o12bo$38bo7bo24bobo10b2o$37bo7bo25bo12bobo29$bo$b2o$obo!
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Extrementhusiast » July 4th, 2013, 11:42 am

Slightly compressed:

Code: Select all

x = 101, y = 97, rule = B3/S23
9bo$10b2o$9b2o$98bo$98bobo$98b2o2$93bo$91b2o$92b2o$86bobo$86b2o$87bo
10$40bobo$41b2o12bo$41bo13bobo$55b2o2$47bo$48b2o8bo$47b2o7bobo$57b2o2$
59bo$57b2o$58b2o2$35bo$33bobo3bo$34b2o4b2o25bo$39b2o26bobo$67b2o3$54bo
$55b2o$54b2o$58bo$57bo$57b3o3$62bo$62bobo$54bo7b2o$55b2o$54b2o$43b2o$
44b2o6b2o$43bo7bobo$53bo3$51bo35b2o$50b2o34b2o$35b3o5b3o4bobo17b2o16bo
$37bo7bo24bobo$36bo7bo25bo10$86b2o$85b2o$87bo16$bo$b2o$obo!
Also, I expected at least a little praise.
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by codeholic » July 4th, 2013, 12:23 pm

Congratulations! The long hook synthesis is a very good find. But the mango looks really awkward, so here is a small optimization:

Code: Select all

x = 23, y = 16, rule = B3/S23
$16bobo$16b2o$10bo6bo$10bobo$5bo4b2o$4bo9bo$4b3o6bobo$13b2o3b3o$3o8b2o
5bo$2bo9bo6bo$bo10bob2o$9b2obo2bo$9b2ob2o!
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Tropylium » July 4th, 2013, 12:55 pm

mniemiec wrote:
Extrementhusiast wrote:I did get this far:
...
All that's left is the final "flourish" step.
I suspect that it will be extremely difficult to find such a step. While it's fairly common to be able to puff the side out of an existing object (e.g., turning a a beehive into a loaf or a loaf into a pond or a hat into a loop), it's usually much harder do the reverse (e.g. turning a pond into a loaf requires first collapsing it into a ship, and then growing the ship into a loaf - something that's not possible if the pond and loaf are attached to something else). The only way the extraneous outside bit can be killed is by over-population, which deprives the internal bits of support, but simultaneously over-populates the internal dead cell where one wants a birth.

Similarly, turning a python into a bookend might be feasible, but going the other way (i.e. removing that third bit) would not.
The pond → loaf observations sound sound, but bookend → python does not seem intrinsically impossible at all. Here's a small spark halo that does just the desired conversion:

Code: Select all

x = 11, y = 12, rule = B3/S23
5bo$2bo2b2o$3bo2bo$2bo$2bo5b2o$4b2obo2bo$o3bo3b2o$2o3b3o$7bo$7bob2o$4b
2obo2bo$4b2ob2o!
Whether this translates to any reasonably simple glider synthesis I don't know though; inserting that non-standard preblock might be the real difficulty…

Although this works fully in general, in the current synthesis this is also enormously aided by how the 4th live cell counting from the hook is a "dangling" one — it is actually not required for the object's overall stability.

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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Freywa » July 4th, 2013, 8:53 pm

codeholic wrote:"...here is a small optimization:"
It's no small optimisation. Bellman One is down to 22 gliders, which is good because any synthesis using more than 24 gliders is probably crude.
20-glider synthesis shown below after Niemiec!

Code: Select all

x = 63, y = 52, rule = B3/S23
58bo$58bobo$53bo4b2o$51b2o$22bo29b2o$23b2o21bobo$22b2o22b2o$47bo$40bo$
40bobo$40b2o$25bo$26b2o$25b2o2$23bo$24bo20bo$22b3o18b2o$34bo9b2o$35b2o
$34b2o$38bo$37bo$37b3o3$42bo$42bobo$34bo7b2o$35b2o$34b2o$23b2o$24b2o6b
2o$23bo7bobo$33bo$19bo$19b2o26b2o$18bobo10bo14b2o$30b2o16bo$23b3o4bobo
$25bo$24bo7$61bo$bo58b2o$b2o57bobo$obo!
Last edited by Freywa on July 11th, 2013, 6:04 am, edited 1 time in total.
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by codeholic » July 5th, 2013, 1:32 am

Freywa wrote:Bellman One is down to 22 gliders
I'm still skeptic about this name, because it looks to me like a potential source of confusion with the program itself.

Personally I always, since I saw that pattern, called it 'hanged man' inwardly. But that's just my association, probably not the nicest one. Though there is definitely someone inside that pattern ;)

After all, Mike Playle is the one who has the honor to give the name to the pattern he found.
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Kasuha » July 5th, 2013, 1:57 am

codeholic wrote:I'm still skeptic about this name, because it looks to me like a potential source of confusion with the program itself.
It's an eater, right? Maybe we could call it "Eater B1", then.

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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by codeholic » July 5th, 2013, 8:15 am

Kasuha wrote:It's an eater, right? Maybe we could call it "Eater B1", then.
Strictly speaking, it's not an eater on its own. It is a traffic light predecessor eater only being combined with the eater1 (or another pattern that can eat a blinker).

Code: Select all

x = 9, y = 15, rule = B3/S23
6b2o$b2o2bo2bo$bobo2b2o$4b2o$5bo$5bob2o$2b2obo2bo$2b2ob2o4$2o$o$b3o$3b
o!
But probably, it can eat something else on its own. (I tried gliders and standard spaceships - no result.)
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Extrementhusiast » July 5th, 2013, 12:04 pm

Well, why not call it Catalyst B1, if it's not an eater? Seems to make sense to me.

EDIT: Finished 64-glider synthesis of AK94 gun:

Code: Select all

x = 1011, y = 247, rule = LifeHistory
327.A$325.A.A$326.2A9$187.A25.A$187.A.A21.2A$187.2A17.A5.2A$205.A$29.
A175.3A$30.2A8.A159.A$29.2A7.A.A159.A.A$39.2A159.2A2$191.A$189.2A$
190.2A2$17.A$15.A.A3.A$16.2A4.2A175.A$21.2A176.A.A$199.2A3$36.A$37.2A
321.A175.A7.A$36.2A320.A.A174.A7.A$190.A168.2A17.A.A154.3A5.3A$189.A
189.2A$189.3A187.A3$194.A332.A$194.A.A330.A.A7.A$36.A157.2A331.2A6.2A
$37.2A497.2A$36.2A48$838.A$836.A.A$837.2A5$853.A$844.A6.2A$842.A.A7.
2A5.A.A107.A$464.D7.2D369.2A14.2A109.A$464.3D5.2D386.A107.3A$467.D$
466.2D16.2C$479.2C2.C2.C419.A$479.C.C2.2C418.A.A$482.2C421.2A$454.D
28.C131.D7.2D288.A$454.3D26.C.2C128.3D5.2D58.D7.2D220.A.A$457.D22.2C.
C2.C131.D64.3D5.2D220.2A$91.D7.2D355.2D22.2C.2C132.2D16.2C49.D52.D7.
2D96.D7.2D133.C7.2C$91.3D5.2D529.2C2.C2.C47.2D16.2C34.3D5.2D42.D7.2D
44.3D5.2D47.C7.2D76.3C5.2C$94.D535.C.C2.2C61.2C2.C2.C36.D48.3D5.2D47.
D53.3C5.2D79.C$93.2D16.2D352.3D165.2C63.C.C2.2C36.2D16.2C27.A.A3.D52.
2D16.2C38.C84.2C16.2C$106.2D2.D2.D337.2D.2D8.D3.D9.2D125.D28.C66.2C
51.2C2.C2.C26.2A3.2D16.2C47.2C2.C2.C36.2C16.2C79.2C2.C2.C$106.D.D2.2D
336.D2.D.2D7.D5.D8.D126.3D26.C.2C35.D28.C51.C.C2.2C28.A16.2C2.C2.C46.
C.C2.2C50.2C2.C2.C78.C.C2.2C$109.2D338.2D.D10.D5.D9.3D126.D16.A5.2C.C
2.C35.3D26.C.2C51.2C47.C.C2.2C50.2C52.C.C2.2C82.2C$81.D28.D341.D10.D
5.D11.D125.2D17.A4.2C.2C40.D22.2C.C2.C23.D28.C50.2C24.C28.C55.2C56.C
28.C$81.3D26.D.2D338.2D10.D3.D155.3A48.2D22.2C.2C25.3D26.C.2C19.D28.C
24.3C26.C.2C24.C28.C56.3C26.C.2C$84.D22.2D.D2.D336.2D2.D.D8.3D264.D
22.2C.C2.C19.3D26.C.2C24.C22.2C.C2.C24.3C26.C.2C56.C22.2C.C2.C$83.2D
22.2D.2D337.D2.D2.2D159.3D112.2D22.2C.2C24.D.A20.2C.C2.C23.2C22.2C.2C
29.C22.2C.C2.C55.2C22.2C.2C$450.2D16.2D6.2D124.2C.2C8.D3.D9.2D53.3D
96.2D2.A19.2C.2C82.2C22.2C.2C$468.D7.D123.C2.C.2C7.D5.D8.D40.2C.2C8.D
3.D9.2C86.3A$92.3D367.2D5.3D5.3D120.2C.C10.D5.D9.3D35.C2.C.2C7.D5.D8.
C42.3D103.3D140.3D$78.2D.2D8.D3.D9.2D355.2D7.D7.D123.C10.D5.D6.A4.D
35.2C.C10.D5.D2.A6.3C25.2C.2C8.D3.D9.2C37.3D37.2C.2C8.D3.D9.2C42.3D
69.2C.2C8.D3.D9.2C$76.D2.D.2D7.D5.D8.D497.2C10.D3.D7.2A42.C10.D5.D3.A
7.C23.C2.C.2C7.D5.D8.C24.2C.2C6.A.C3.D9.2C23.C2.C.2C7.D5.D8.C29.2C.2C
8.D3.D9.2C55.C2.C.2C7.D5.D8.C$76.2D.D10.D5.D9.3D492.2C2.C.C8.3D7.A.A
42.2C10.D3.D2.3A31.2C.C10.DA4.D9.3C19.C2.C.2C6.AC5.D8.C24.2C.C10.D5.D
9.3C24.C2.C.2C7.D5.D8.C56.2C.C10.D5.D9.3C$79.D10.D5.D11.D491.C2.C2.2C
61.2C2.C.C8.3D40.C10.D.A3.D11.C19.2C.C10.C5.D9.3C24.C10.D5.D11.C24.2C
.C10.D5.D9.3C56.C10.D5.D11.C$79.2D10.D3.D505.2C16.2D6.2D39.C2.C2.2C
51.2C9.ACA2.D35.C10.D5.D11.C24.2C10.D3.D40.C10.D5.D11.C56.2C10.D3.D$
77.2D2.D.D8.3D524.D7.D41.2C16.2D6.2D28.2C2.C.C8.3D36.2C10.D3.D35.2C2.
C.C8.3D41.2C10.D3.D67.2C2.C.C8.3D$76.D2.D2.2D529.2D5.3D5.3D56.D7.D28.
C2.C2.2C45.2C2.C.C8.3D35.C2.C2.2C50.2C2.C.C8.3D67.C2.C2.2C$77.2D16.2D
6.2D508.2D7.D7.D50.2D5.3D5.3D26.2C16.2D6.2C23.C2.C2.2C47.2C16.2C6.2C
28.C2.C2.2C79.2C16.2C6.2C$95.D7.D577.2D7.D2.A4.D44.D7.C25.2C16.2C6.2C
44.C7.C30.2C16.2C6.2C76.C7.C$89.2D5.3D5.3D586.2A42.2D5.3D5.3C40.C7.C
39.2D5.3C5.3C45.C7.C71.2D5.3C5.3C$89.2D7.D7.D585.A.A42.2D2.A4.D7.C34.
2D5.3C5.3C36.2D7.C7.C39.2D5.3C5.3C68.2D7.C7.C$741.2A46.2D7.C7.C93.2D
7.C7.C$740.A.A9$969.2A$968.A.A$970.A4$968.2A$967.A.A$969.A$1006.2A$
1006.A.A$1006.A36$525.2A$25.2A497.2A$26.2A6.2A331.2A157.A$25.A7.A.A
330.A.A$35.A332.A3$183.A187.3A$182.2A189.A$17.3A5.3A154.A.A17.2A168.A
$19.A7.A174.A.A320.2A$18.A7.A175.A321.2A$526.A3$362.2A$361.A.A176.2A$
363.A175.2A4.2A$541.A3.A.A$545.A$214.2A$.2A211.A.A154.2A$A.A211.A157.
2A$2.A368.A2$522.2A$522.A.A7.2A$522.A8.2A$533.A$580.2A$374.2A203.2A$
373.A.A205.A$375.A$355.2A$354.A.A$356.A11$340.2A$339.A.A$341.A$334.3A
$336.A$328.2A5.A$329.2A$328.A!
EDIT 2: Continuous synthesis:

Code: Select all

x = 402, y = 418, rule = B3/S23
2bo$3bo$b3o19bo$21bobo$22b2o$394bo$394bobo$394b2o4$34bo$32bobo$33b2o5$
369bo$40bo326b2o$38bobo327b2o5bobo$39b2o334b2o$376bo21$348bobo$348b2o$
349bo5$46bo$47bo$45b3o3$349bobo$349b2o$350bo13$64bo$65bo$63b3o3$86bo$
78bo8bo$79bo5b3o$77b3o18$70bo$68bobo$69b2o30$103bo163bo7bo$101bobo162b
o7bo$102b2o17bobo142b3o5b3o$122b2o$122bo3$258bo$258bobo7bo$258b2o6b2o$
267b2o28$222bo25bo$222bobo21b2o$222b2o17bo5b2o$240bo$214bo25b3o$215b2o
8bo9bo$214b2o7bobo9bobo$224b2o9b2o2$226bo$224b2o$225b2o2$202bo$200bobo
3bo$201b2o4b2o25bo$206b2o26bobo$234b2o3$221bo$222b2o$221b2o$225bo$224b
o$224b3o3$229bo$229bobo$221bo7b2o$222b2o$221b2o$210b2o$211b2o6b2o$210b
o7bobo$220bo3$218bo$217b2o$202b3o5b3o4bobo17b2o$204bo7bo24bobo$203bo7b
o25bo9$249b2o$186b2o61bobo$185bobo61bo$187bo56$256b2o$255b2o$110b2o
145bo$109bobo$111bo3$114b3o$116bo$115bo$256b2o$255b2o$257bo3$105b2o$
104bobo164b2o$106bo163b2o4b2o$272bo3bobo$276bo2$114b2o$115b2o$114bo2$
253b2o$253bobo7b2o$253bo8b2o$264bo$311b2o$117b2o191b2o$116bobo193bo$
118bo$98b2o$97bobo$99bo11$83b2o$82bobo$84bo$77b3o$79bo$71b2o5bo$72b2o$
71bo3$88bo$88b2o$87bobo11$80bo$80b2o$79bobo4$66bo$66b2o$65bobo52$2b2o$
bobo$3bo4$b2o$obo$2bo$399b2o$399bobo$399bo!
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Freywa » July 5th, 2013, 9:04 pm

Extrementhusiast wrote:Well, why not call it Catalyst B1, if it's not an eater? Seems to make sense to me.
I'm fine with that. After all, it contains "B1" for Bellman One. Also, the 64-glider construction makes the AK-94 one of the few guns with a known glider synthesis. Congratulations.

When this gun, so small and so efficient, is compared to P94S2... well, you get the idea. The AK47 reaction has prevailed.
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by mniemiec » July 10th, 2013, 10:59 pm

Congratulations on synthesizing the still-life, and the AK94 gun!

The still-life can be reduced further by 2 gliders. First, all the complete syntheses posted use a kick-back reaction to make the LWSS from 4 gliders, rather than 3. I couldn't see any reason for this. But this is also mooted by the fact that a boat can be tied to most snake/eater-type bonding points with only 7 gliders, without any LWSS at all:

Code: Select all

x = 33, y = 24, rule=B3/S23
4bo$5boo$4boo$$10bo$10bobo$10boo$7bo$8boo$7boo$$5bo$6bo8bo$4b3o6boo$
14boo$$31bo$30bobo$30boo$bo6boo18boo$boo6bo7boo10bo$obo6boboo3boo11bob
oo$6boobobbo5bo7boobobbo$6booboo15booboo!

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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Extrementhusiast » July 11th, 2013, 12:44 pm

I chose to use the kickback because I was assuming a synthesis from infinity. In that particular case, one of the gliders making the LWSS would have collided with one of the construction gliders, necessitating the kickback. (If it was being done from a finite but large distance, like with a glider gun salvo, it could be synthesized with just three.) Of course, your seven-glider solution makes the whole thing irrelevant.

Updated continuous synthesis:

Code: Select all

x = 402, y = 418, rule = B3/S23
2bo$3bo$b3o19bo$21bobo$22b2o$394bo$394bobo$394b2o4$34bo$32bobo$33b2o5$
369bo$40bo326b2o$38bobo327b2o5bobo$39b2o334b2o$376bo21$348bobo$348b2o$
349bo5$46bo$47bo$45b3o3$349bobo$349b2o$350bo13$64bo$65bo$63b3o3$86bo$
78bo8bo$79bo5b3o$77b3o18$70bo$68bobo$69b2o29$101bo$102b2o163bo7bobo$
101b2o163bo8b2o$121bobo142b3o7bo$122b2o$122bo3$258bo$258bobo7bo$258b2o
6b2o$267b2o25$251bo$249b2o$244bo5b2o$243bo$243b3o$238bo$206bo31bobo$
207b2o29b2o$206b2o2$230bo$230bobo$230b2o$209bo$210b2o$209b2o2$207bo$
208bo26bo$206b3o24b2o$234b2o3$221bo$222b2o$221b2o$225bo$224bo$224b3o3$
229bo$229bobo$221bo7b2o$222b2o$221b2o$210b2o$211b2o6b2o$210bo7bobo$
220bo3$218bo$203bo13b2o$203b2o5b3o4bobo17b2o$202bobo7bo23b2o$211bo26bo
12$252b2o$183b2o67bobo$182bobo67bo$184bo53$256b2o$255b2o$110b2o145bo$
109bobo$111bo3$114b3o$116bo$115bo$256b2o$255b2o$257bo4$104b2o$105b2o
164b3o$104bo166bo$272bo2$269b2o$268b2o$270bo$108b2o$107bobo$109bo2$
272b2o$271b2o38b2o$273bo36b2o$312bo2$98b2o$97bobo$99bo11$83b2o$82bobo$
84bo$77b3o$79bo$71b2o5bo$72b2o$71bo3$88bo$88b2o$87bobo11$80bo$80b2o$
79bobo4$66bo$66b2o$65bobo52$2b2o$bobo$3bo4$b2o$obo$2bo$399b2o$399bobo$
399bo!
The basic steps remain essentially unchanged, except for the replacement part, which can be directly substituted in.

EDIT: Minimal, if not close-to-minimal, continuous synthesis:

Code: Select all

x = 186, y = 207, rule = B3/S23
10bo$11b2o$10b2o$185bo$183b2o$184b2o2$18bobo$19b2o$19bo$obo$b2o$bo160b
o$22bobo137bobo$23b2o137b2o$23bo144bo$167bo$162bobo2b3o$162b2o$163bo5$
10bo$11bo$9b3o3$163bobo$163b2o$164bo2$34bo$25bo9bo$26b2o5b3o$20bo4b2o$
21bo$19b3o6$8bo$6bobo$7b2o12$125bobo$42bo82b2o$40bobo83bo$26bo14b2o$
27bo101bo$25b3o101bobo$118bo10b2o$116b2o8bo$117b2o6bo$125b3o$133bo$
133bobo$128bo4b2o$126b2o$99bo27b2o$100b2o19bobo$99b2o20b2o$122bo$115bo
$115bobo$115b2o$102bo$103b2o$102b2o2$100bo$101bo18bo$99b3o8bo7b2o$111b
2o6b2o$110b2o$114bo$113bo$113b3o3$118bo$118bobo$110bo7b2o$111b2o$110b
2o$99b2o$100b2o6b2o$99bo7bobo$96bo12bo$96b2o24b2o$95bobo23b2o$107bo15b
o$106b2o$99b3o4bobo$101bo$100bo6$136bo$78bo56b2o$78b2o55bobo$77bobo29$
114b3o$114bo$29b2o84bo$30b2o$29bo2$34bo$34b2o$33bobo2$114b3o$28b3o83bo
11bo$30bo84bo9b2o$29bo95bobo3$122b3o$122bo$123bo$32b2o$33b2o116b2o$32b
o117b2o$152bo$125b3o$26b2o97bo$25bobo98bo$27bo$21b2o13bo$20bobo13b2o$
22bo12bobo$15b3o$17bo$9b2o5bo$10b2o$9bo4$22bo$22b2o$21bobo$27b3o$29bo$
28bo6$b2o$2b2o$bo4$2o$b2o$o$178b2o$177b2o$179bo!
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Re: Scratch Your Heads: Glider Synthesis of Bellman One

Post by Extrementhusiast » July 20th, 2013, 5:20 pm

I only just realized how similar Catalyst B1 and one of the eaters are!

Code: Select all

x = 33, y = 15, rule = B3/S23
10b2o18b2o$5b2o2bo2bo12b2o2bo2bo$5bobo2b2o13bobo2b2o$8b2o18b2o$9bo19bo
$2bo6bob2o9bo3bo2bob2o$2ob2ob2obo2bo10bobobobo2bo$2bo3b2ob2o10b3o2b2ob
2o4$4b2o$4bo$5b3o$7bo!
Here is a 21-glider synthesis of that eater:

Code: Select all

x = 108, y = 32, rule = LifeHistory
38.A$39.2A$38.2A2$44.A$44.A.A$44.2A$41.A$15.A26.2A$16.2A23.2A$15.2A$
19.A19.A39.A.A$18.A21.A8.A29.2A$18.3A17.3A6.2A24.A6.A$48.2A23.A.A$A.A
65.A4.2A$.2A20.A43.A9.C27.2C$.A21.A.A41.3A6.C.C21.2C2.C2.C$15.A7.2A
51.2C3.3A16.C.C2.2C$13.2D.2A17.A6.2C19.3A8.2C5.A21.2C$14.D2A18.2A6.C
7.2A12.A9.C6.A21.C$11.D2.D.2D16.A.A3.C2.C.2C3.2A12.A7.C2.C.2C18.A3.C
2.C.2C$4.3A3.D.DAC2.D21.C.C.C2.C5.A18.C.C.C2.C19.A.C.C.C2.C$6.A4.DC.C
D24.2C.2C27.2C.2C19.3A2.2C.2C$5.A8.A3$12.A$11.2A$4.3A4.A.A$6.A$5.A!
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