Refactoring DRH's cyclotron with stable components?

[pcallahan]

This is clearly not "useful" in light of Herschel technology, but I'm curious if anyone has ever gone back to Dean Hickerson's Cyclotron gun and replaced the p46 shuttles with Snark reflectors? (Assuming spacing makes that possible.) I always liked the way this produced a gun out of seeming chaos, and assuming spacing works, timing should be a lot easier (added: No, as dvgrn points out, snark cannot change glider color so we can't adjust timing as we need; also I am pretty sure spacing fails too, because some output gliders are too close to separate).

Code: Select all

#N Cyclotron
#C An inefficient but amusing period 874 = 46*19 glider gun based on
#C a 3-glider collision that produces 4 blocks, 4 beehives,
#C 8 blinkers, and 13 gliders.  28 p46 shuttles are used to redirect
#C some of the gliders:  1 escapes, 1 is destroyed, 8 are reflected
#C back to delete the debris, and 3 are reflected back to collide
#C again.
#O Dean Hickerson, dean.hickerson@yahoo.com (7/22/92)
x = 310, y = 212, rule = B3/S23
58b2o$59bo175b2o$235bo$73b2o$74bo7$271b4o$53bo3bo213bo2b2o6b2o$54bobo
215bo2b2o6bo$54bobo9b2o5b2o197bo2bo$54bobo9b2obobob2o198b2o$50bo2bo3bo
2bo5bo2bobo2bo$51b3o3b3o6b3o3b3o198b2o$234b3o5b3o27bo2bo$234bo2b2ob2o
2bo10bo16bo2b2o$235b3o3b3o11b2o14bo2b2o$236bo5bo28b4o4$201b2o14b3o8b2o
$201bo17bo9bo$59bo159bo$58b2o158bo16bo$235b2o$74bo143bo$73b2o9b2o8b3o
14b2o106bo$84bo9bo17bo106bo41b2o$94bo122b3o41bo$95bo2$95bo$94bo$94bo$
94b3o5$300b2o$300bo$261bo7bo$260bobo5bobo$263bo3bo$40b2o218bo2bo3bo2bo
$40bo220bobo3bobo$122b3o138b2ob2o$15b2o93b2o8bo4bo57b3o74b2ob2ob2ob2o$
16bo93bo9bo5bo44b2o8bo4bo11b2o60b2o2bobo2b2o$125bo45bo9bo5bo11bo61b3o
3b3o$123b2o61bo75bo5bo$184b2o$123b2o176bo5bo$125bo58b2o114b3o3b3o$120b
o5bo11bo13b2o5b2o25bo74bo37bo3bobo3bo$120bo4bo11b2o14bo5bo21bo5bo73b2o
36bo9bo$9bo5bo106b3o56bo4bo113b3o3b3o$8b3o3b3o48b3o115b3o$7b2obo3bob2o
35b2o8bo4bo$39b3o5b3o3bo9bo5bo129bo$39b3o5b3o18bo128b2o$40b2o5b2o17b2o
130b2o$42bo3bo61bobo$40bo2bobo2bo17b2o41b2o$39bo3bobo3bo18bo40bo35b3o
3b3o5b3o3b3o114bobo$40bo2bobo2bo14bo5bo11bo63bo2bobo2bo5bo2bobo2bo114b
2o$40b3o3b3o14bo4bo11b2o63bo7bo5bo7bo115bo24bo$65b3o239b2o4$48bo$47b2o
2$8bo27bo236b3o$8b2o24bobo236bo$35b2o237bo2$229b2o$230bo2$153bo5bo$
152b2o5b2o7$307b2o$308bo$224b2ob2o$224b2ob2o$224b2ob2o$222bob2ob2obo$
222b3o3b3o$223bo5bo7$300b2o5b2o$299bo2bo3bo2bo$230bo71b2ob2o$229b2o70b
obobobo$301bobobobo$299bo9bo8$308bo$307b2o4$53b2o$53bo2$152b2o5b2o$
153bo5bo7$53bo7bo2$51b3o7b3o$52b2ob2ob2ob2o$53b3o3b3o$54bo5bo$b2o$bo$
112b2o31bo7bo5bo7bo$111bobo31bo2bobo2bo5bo2bobo2bo$23bo89bo31b3o3b3o5b
3o3b3o$23b2o$22bobo2$2bo5bo$b3o3b3o$o2b2ob2o2bo42bo124bob2o$3o5b3o42b
2o69bo47b2o3bo2b2o2b3o$122bo2bo46bo4bo6b2o$122b5o10b2o14bo5bo17b2o3b3o
$42b2o78b3ob2o10bo13b2o5b2o18bo3bo$42bo80b2obo$124b2o53bo3bo$177b2o3b
3o$124b2o51bo6b2o14bo$123b2obo50bo2b2o2b3o12b2o$110bo11b3ob2o50bob2o$
110b2o10b5o$122bo2bo$124bo4$9bo32b3o3b3o$8b2o32b3o3b3o$41bob2o3b2obo
170bo$41bob2o3b2obo169b2o$42b2o5b2o169b2o$43bo5bo171b2o$92b2o2bobo$91b
3obo3bo$90b2o6bo$91bob5o123b2o$92b3o116bo8b2o17bo$211b2o8b2o15b2o$92b
3o127bo$75b2o14bob5o$42bo7bo25bo8bo4b2o6bo14bo$42b2o5b2o34b2o4b3obo3bo
12b2o$92b2o2bobo7$69bo5bo$68b3o3b3o$68bob2ob2obo$39bo30b2ob2o$38b2o15b
2o13b2ob2o$37b2o17bo13b2ob2o$38b2o4$38b2o$28bo8b2o$28b2o8b2o$39bo4$76b
o$75b2o!

This is also the kind of thing I thought would be useful as a challenge problem (as opposed to a research problem, like most of what we do here) that could be posted in a site similar to Project Euler. It would have a series of problems of increasing difficulty "to encourage, challenge, and develop the skills and enjoyment of anyone with an interest" in Life along with badges and so forth to provide a small amount of extrinsic reward.

We now have sophisticated enough software to verify both that the pattern begins with the required components and produces the expected results. So you would just need to define the problem, accept a POST of RLE, e.g. from Golly, and do a short server-side computation to verify that it does what's intended (we can limit the number of steps so it is a decidable problem).

[simsim314]

Dean Hickerson's Cyclotron gun

I was thinking about what is likable about this gun? I think it gives a sense of possibility something like "glider only" gun to be possible. I mean a glider gun which at some point is consistent of gliders only.

Think about a grid of "intersection points" which consists of N gliders in -> M gliders out. And this grid has some sort of communication protocol, i.e. all the interactions in the grid should start and finish in some constant time interval. To build such a grid we only need a good database of interesting glider in -> glider out mechanisms.

Another approach can come from the grey goo theory. Think about random constellation in CGOL bounded by some box, this is what I call grey goo. Now we can ask: what is the most common glider pair to come out of this goo? I think the answer will be distributed somehow not evenelly. Now lets try to generate input glider stream that attack SL which are similar to the distribution of the outputs, and keep those inputs such that the probability to get the output containing them, even for longer random streams in the input is the highest. Let's just evolve the stream glider by glider making sure the chances to get the output for the collective of our inputs is getting higher and higher. If this can be done and I'm not sure it can but I think it worth a trial or at least a post here. At least we will get some competition between the input and the output and we want to evolve the input such that it will code the output with increasing probability. We will consider only soups that code in the output part of the input stream.

could be posted in a site similar to Project Euler.

My question what we need for that? Do you have experience in web? Maybe someone who already done something similar can give us some tips to make such a site? Dave, Adam, Andrew anyone?

[pcallahan]

You may be right about why cyclotron is appealing. The main thing is that the generating power is all in the gliders. This is less interesting if you recirculate them with Herschel-based reflectors that produce tons of extra gliders anyway, but could still be amusing if the pattern is composed of only snarks and gliders at some point in its cycle. I may try to make this myself, but I bet it would be a lot easier for someone else.

My question what we need for [something like Project Euler]? Do you have experience in web? Maybe someone who already done something similar can give us some tips to make such a site? Dave, Adam, Andrew anyone?

Short is answer is yes, I have a lot of experience writing web services as part of my job in both Java and Python, though I have never had to obtain a domain and server for personal use. There are cloud solutions out there that I'm not really familiar with but are probably easy to set up (not sure about cost depending on load). This all changes fast and what I do know is probably out of date. I am much less skilled at front-end design (the last web page I wrote is ancient history). The main issue is one of finding time rather than how to do it. I think the basic idea is straightforward if there is interest.

[simsim314]

I may try to make this myself, but I bet it would be a lot easier for someone else.

My question here is why? People see it's a reflector, and we're not gonna change all the patterns done ever to use snarks. I mean we had a project for guns up to P1000, and I think this was a large very tedious projects with some limited benefit.

The main issue is one of finding time rather than how to do it.

I've time - if someone will tell me where to start I can do it. It's something like chess tempo right? Isn't there ready templates for all those things?

[pcallahan]

Well, if nobody else is interested I may work on it in my "copious free time." Just wanted to throw out the idea in case someone else had done it already. Actually, is there any known gun consisting at some point of only gliders and stable snarks?

I've time - if someone will tell me where to start I can do it. It's something like chess tempo right? Isn't there ready templates for all those things?

I'm not aware of templates for a site with challenges and badges, but it would certainly be nice to have that. If it is possible just to plug in an answer verifier to an existing framework, it could be very easy to get this up and running. My thought is to start with really easy challenges before moving to research-level problems (one of my gripes with Project Euler is that the questions start to get very hard fast, and when I was doing it, it was putting more time and effort into it than my paid work.)

[dvgrn]

Well, if nobody else is interested I may work on it in my "copious free time." Just wanted to throw out the idea in case someone else had done it already. Actually, is there any known gun consisting at some point of only gliders and stable snarks?

The closest one I can think of is the 4g-to-5g reaction, and it's not very close at all.

We could probably piece something together by hunting for a seed constellation that produces more gliders than it takes to rebuild it. Especially if the constellation is mostly blocks or honeyfarms or something else that there are a lot of ways to build, that would get rid of some of the difficulties with glider color and mod-8 timing.

Technically we've found constellations that produce more than twice as many gliders as there are blocks in the constellation -- but not for any small or reasonable numbers of blocks. Most likely with constellations with high still life counts, there will turn out to be problems with output gliders getting past the Snarks reflecting gliders onto the input lanes.

The cyclotron is not a really easy case, either. The input gliders are all on one color, and the output gliders are half on that color and half on the other.

So you have to somehow change one glider from one color to the other, and you can't do that with only color-preserving Snarks. Seems like we should have a color-changing Snark by now, but sadly nothing has shown up yet.

We do have syringe-plus-H-to-Gs that don't produce any spare gliders, if that helps.... Unless you use one of those, I think you'll be stuck swapping one glider back and forth between two cyclotrons to get three same-color input gliders for each.

(?)

[Gamedziner]

Universal constructor arguments allow for a gun made purely of gliders.

[pcallahan]

Universal constructor arguments allow for a gun made purely of gliders.

Yes. There is nothing new here. But the same could have been said in 1992 when Dean Hickerson made the original gun, or more than 20 years earlier when Conway had sketched out the principle of a universal constructor.

It's a puzzle and the result is sort of fun to see. That's all. Also, it's an example of the kind of "non-research" challenge that could be collected to drum up interest outside the fairly small Life community as it exists today.

E.g., challenge: submit a design that functions as a glider gun consisting of only gliders and snark reflectors and permitted variants for at least one step in its cycle (snarks must be inactive). You make it using any tools you like, post the RLE to a contest page. The server verifies that your pattern starts with only allowed components and produces the expected output and "rewards" you with badges, rankings, etc. Like Project Euler or TopCoder.

(Do I respond to a top coder challenge with "The Church-Turing thesis allows for code written in any programming language to produce the expected results?" I mean, sorry if I sound testy, but is my point at least clear?)

[pcallahan]

The cyclotron is not a really easy case, either. The input gliders are all on one color, and the output gliders are half on that color and half on the other.

Sorry (says the forever noob), what is the definition of color? Does it refer to the diagonal it's on? I was more worried about odd and even glider phases. I see that both are covered by output gliders.

Given the excess gliders and enough snarks, could a kickback reaction be helpful? I also wonder if the number of cleanup gliders could be reduced.

Unless you use one of those, I think you'll be stuck swapping one glider back and forth between two cyclotrons to get three same-color input gliders for each.

This solution seems acceptable if there is a nice way to do it.

[pcallahan]

Given the excess gliders and enough snarks, could a kickback reaction be helpful? I also wonder if the number of cleanup gliders could be reduced.

OK, now I am beginning to appreciate why this is difficult. There is only one spare glider, destroyed in the original pattern. I can get the cleanup down to 7 gliders (one glider removes 4 blinkers but the opposite blinkers must be cleared away first). That probably doesn't help enough. Now there are just two spare gliders, assuming you can line this up with clearance between reflectors:

Code: Select all

x = 58, y = 49, rule = B3/S23
8bo39bo$6bobo39bobo$7b2o39b2o5$9bo37bo$2o6bobo15bo3bo15bobo6b2o$2o6bob
o15bo3bo15bobo6b2o$9bo16bo3bo16bo$21b3o9b3o18$21b3o9b3o$9bo16bo3bo16bo
$2o6bobo15bo3bo15bobo6b2o$2o6bobo15bo3bo15bobo6b2o$9bo37bo2$18b2o17b2o
$17bobo17bobo$19bo17bo$7b2o39b2o$6bobo39bobo$8bo39bo6$56bo$55b2o$55bob
o!

Maybe some sparks in the cleanup can reflect properly synchronized gliders with a color change. That sort of violates the spirit of refactoring the cyclotron but it would still be all gliders and snarks.

[pcallahan]

Maybe some sparks in the cleanup can reflect properly synchronized gliders with a color change. That sort of violates the spirit of refactoring the cyclotron but it would still be all gliders and snarks.

Yes there some collisions to choose from. I did not look at these carefully for color change or anything else but they all preserve one of the (now valuable) gliders.

Code: Select all

x = 20, y = 11, rule = B3/S23
2bo$obo$b2o12$18bo$9b2o6bobo$9b2o6bobo$18bo5$16b2o$15bobo$17bo$!

Code: Select all

x = 21, y = 11, rule = B3/S23
2bo$obo$b2o11$19bo$10b2o6bobo$10b2o6bobo$19bo5$17b2o$16bobo$18bo$!

Code: Select all

x = 18, y = 11, rule = B3/S23
2bo$obo$b2o16$16bo$7b2o6bobo$7b2o6bobo$16bo5$14b2o$13bobo$15bo$!

Code: Select all

x = 21, y = 11, rule = B3/S23
2bo$obo$b2o13$19bo$10b2o6bobo$10b2o6bobo$19bo5$17b3o$19bo$18bo$!

Code: Select all

x = 17, y = 11, rule = B3/S23
2bo$obo$b2o11$15bo$6b2o6bobo$6b2o6bobo$15bo4$14bo$14b2o$13bobo$!

Code: Select all

x = 22, y = 11, rule = B3/S23
2bo$obo$b2o9$20bo$11b2o6bobo$11b2o6bobo$20bo4$19bo$19b2o$18bobo$!

Here's a combined cleanup/reflection.

Code: Select all

x = 67, y = 49, rule = B3/S23
17bo39bo$15bobo39bobo$16b2o39b2o5$18bo37bo$9b2o6bobo15bo3bo15bobo6b2o$
9b2o6bobo15bo3bo15bobo6b2o$18bo16bo3bo16bo$30b3o9b3o5$2bo$obo$b2o11$
30b3o9b3o$18bo16bo3bo16bo$9b2o6bobo15bo3bo15bobo6b2o$9b2o6bobo15bo3bo
15bobo6b2o$18bo37bo2$27b2o17b2o$26bobo17bobo$28bo17bo$16b2o39b2o$15bob
o39bobo$17bo39bo6$65bo$64b2o$64bobo!

[pcallahan]

Finally, here is a way to clean up the block/hive with no net loss of gliders.

Code: Select all

x = 11, y = 24, rule = B3/S23
8bo$8bobo$8b2o11$9bo$2o6bobo$2o6bobo$9bo5$7b2o$8b2o$7bo!

Surprisingly, this works in the context of the original debris field, so every block/hive can be removed without glider loss provided you can synchronize them.

Code: Select all

x = 82, y = 76, rule = B3/S23
5$46bo$46bobo$46b2o8$27bo37bo$18b2o6bobo15bo3bo15bobo6b2o$18b2o6bobo
15bo3bo15bobo6b2o$27bo16bo3bo16bo$39b3o9b3o18$39b3o9b3o$27bo16bo3bo16b
o$18b2o6bobo15bo3bo15bobo6b2o$18b2o6bobo15bo3bo15bobo6b2o$27bo37bo25$
5b2o$6b2o$5bo!

[pcallahan]

Two more glider-conserving block/hive cleanups:

Code: Select all

x = 13, y = 10, rule = B3/S23
11bo$2b2o6bobo$2b2o6bobo$11bo3$bo$b2o6b2o$obo6bobo$9bo!

Code: Select all

x = 28, y = 25, rule = B3/S23
$10bo$b2o6bobo$b2o6bobo$10bo3$2bo$2b2o$bobo11$23b2o$23bobo$23bo!

And a reaction where two gliders clean up the block/hive and produce an LWSS.

Code: Select all

x = 12, y = 18, rule = B3/S23
$9bo$2o6bobo$2o6bobo$9bo5$7b3o$9bo$8bo3$9b2o$9bobo$9bo!

This is of questionable utility, since there is no way to reflect the spaceship, but there might be a way to turn the cyclotron into an LWSS-gun.

Here is a glider-conserving 4-blinker cleanup but I think it would be hard to reuse the gliders.

Code: Select all

x = 22, y = 13, rule = B3/S23
$3bo13bo$bobo13bobo$2b2o13b2o5$7b3ob3o$4bo11bo$4bo11bo$4bo11bo!

[dvgrn]

Sorry (says the forever noob), what is the definition of color? Does it refer to the diagonal it's on? I was more worried about odd and even glider phases.

Looks like you've mostly gotten past this question by now, but here's a quick link anyway: Glider#Colour_of_a_glider

Yes, both color and phase are a concern. With known periodic reflectors color is not much of a problem, because both color-changing bouncers and color-preserving bumpers are available. Also you can change the phase of a glider at least to some extent by adding pairs of bumper or bouncer reflectors.

But if you only have Snarks available, no matter how many you add it won't affect the color or mod-8 timing of a glider. Getting the odd/even timing right still leaves three possible relative glider timings that won't work (timing wrong by 2|4|6 mod 8) for every one that will work: if timing is wrong by 0 mod 8, then Snarks can be adjusted to get an exact match.

It might also be worthwhile to look for a way to clean up the debris that creates one or more clean turners -- probably color-changing turners. That way you might get a useful new glider out without adding any new timing dependencies. Many of your proposed cleanups require precise synchronization between two input gliders. For any given choice of two gliders there's only a one in sixteen chance that Snarks alone can do the synchronization, so it's worth avoiding that kind of thing if possible.

[pcallahan]

Looks like you've mostly gotten past this question by now, but here's a quick link anyway: Glider#Colour_of_a_glider

Thanks. I did finally read that. After trying to place the initial snarks, I don't think there is even a way to separate the 8 gliders at the horizontal extremes. Specifically, I can't find a way for them to clear each other's eaters. So this idea is probably DOA barring other thoughts. I also agree that anything involving synchronized collisions is likely to be very difficult.

[simsim314]

Let me jump in and kind of hijack this thread. I was looking similar collisions to wha Jason had found, but with four gliders. Unfortunately without success, but for now I have 4 gliders -> 3 glider clean collision and this is quite rare but existent. Obviously we would like 4->4 examples but for now I've only two 4->3.

Code: Select all

x = 141, y = 189, rule = B3/S23
24$76bo$75b2o$75bobo10bo$67b3o17b2o$69bo17bobo$68bo5$57b2o$56bobo$58bo
126$53b2o$54b2o18b3o$53bo20bo$75bo2$67b3o$69bo7b2o$68bo8bobo$77bo!

I've also posted a stream writing the code for the search using LifeAPI, if someone wants to know how I found these patterns. I was learning lifelib python and understood I need the tiles algorithms which is currently only available in C++ now, and lifelib C++ I still don't know.

[pcallahan]

Here's a 3 to 4 glider reaction that uses a rectifier for cleanup. It is actually based on a 3 to 5 gliders+junk reaction. One glider passes through the rectifier and the other luckily bounces back to remove the junk (loaf and boat). You could argue it is just a catalyzed collision and I could find something smaller. In this case, though, the catalyst (rectified) can be moved arbitrarily far away or substituted with gliders.

Code: Select all

x = 66, y = 98, rule = B3/S23
15bo$16bo$14b3o42$55b2o7b2o$54bobo6b2o$56bo8bo11$18bo$18b3o$21bo$20b2o
6$11bo$11b3o23b2o$14bo21bo2bo$13b2o22b2o8$23b2o$23b2o9$15b2o$10b2o2bo
2bo$10bo4bobo$7b2obo5bo$8bobob2o$7bo2bo2bo$7b2o2bo4bo$12b5o2$11bob2o$
11b2obo!

I am not sure if a gun could be built by adding snarks to it (added: probably not, because the NE glider has to cross the rectifier to get to the collision point) or how interesting that would be anyway. The collision involves a b-heptomino, but only incidentally, and does not extract the Herschel. Anyway, I am just playing around with software I have rarely touched in the last 20 years.

One obvious point to add is that higher period reflectors have the potential to get out of the way of passing gliders some of the time. Stable reflectors do not. In fact, the p46 reflector leaves a lot of space and time for letting things pass, making it ideal for the cyclotron. Trying to do something similar with stable reflectors is much harder than I realized.

[simsim314]

3 to 5 gliders+junk reaction

This is great! I think it breaks some sort of record.

I am not sure if a gun could be built by adding snarks to it

I've posted a video (there are two parts, this is part 1) where I prove mathematically it's impossible regardless of the NE glider.

Trying to do something similar with stable reflectors is much harder than I realized.

Yes it's all scripted already by chris_s and dvgrn. Check out the turing machine script thread, just to have a clue of the complexity available currently with the stable circuitry.

-------------------------

Regardless I was thinking about the benefit of such routing using syringe. I mean if you gave glider duplicator why would you bother to collide glider to generate gliders, and not just use a syringe to duplicate how many you want? This is true for the p46 technology as well, but for the snarks only technology it has benefit value that some point in history, we could think about such designs. I mean there was point in time when there were no syringes and only snarks, and if you time machine friendly - as I'm, you would like to see syringless design, but using the modern stable technology it looks like overkill.

If you want to built a stable circuitry for this gun I can guide you (I know how to build it I'm just more into going back in time to Gosper time, and show how to make self replicator with 20 P30s). I'm also scripting a lot - and it's not the way most people use to think about CGOL. Anyway timing adjustment scripts are all written well by Chris Cain, and I used them for the Turing Machine Simulator script.

EDIT I've also found this during my playing with this interaction. This make clean 4->6 gliders.

Code: Select all

x = 60, y = 61, rule = LifeHistory
11$11.C$12.C$10.3C30$35.2C$34.C2.C$35.C.C2.2C$36.C3.C.C$41.C!

[Hunting]

Off-topic: Can I build a gun with 2-glider mess reaction? It will be messy, but I would like it.

(And probably with some help of a catalyst which could stop the reaction when produced enough gliders.)

[calcyman]

I am not sure if a gun could be built by adding snarks to it (added: probably not, because the NE glider has to cross the rectifier to get to the collision point) or how interesting that would be anyway.

Using a cycle of four copies of your reaction, you can engineer the gliders to come from infinity (shown here supported by p1512 guns):

Code: Select all

x = 721, y = 721, rule = B3/S23
636b2ob2obo7bo$610b2o23bobobob2o7b3o$611bo24bo16bo14bo$611bobo38b2o12b
3o$612b2o2b2o47bo$616b2o47b2o3$664b2o$645b2o17b2o$645b2o6$610b2o36b2o$
609bobo16b2o19bo$609bo18bobo16bo$608b2o20bo16b2o$624b2o4b2o19b2o$624bo
2bo24bo$626b2o21b3o$617b2o30bo$617b2o3$608b2o58bo$609bo57bobo$608bo33b
2o24b2o$608b2o33bo$643bobo15b2o5b2o$608b2o34b2o15b2o6bo$608bobo57bo$
609bo58b2o5$627b2o$627bo$625bobo24bo2b2o$625b2o29b2o$655b2o$662b2o$
651b2o2b2o5bobo$657bo6bo$651b4o9b3o$653bo2bo10bo$666b2o$663b2o$28b2ob
2obo16b2o6b2o17b2ob2obo7bo515b2o53bob5o$2b2o23bobobob2o16bo2bo4b2o16bo
bobob2o7b3o513b2o36b2o21bo$3bo24bo19b2obob2o23bo16bo14bo534bobo16b2obo
$3bobo41bobobo42b2o12b3o513b2o19bo18b2ob2o$4b2o2b2o37bo3bob2o52bo516b
2o18b2o$8b2o35b3o2bo2b2o52b2o523b2o18b2o$44bo5b2o557b2ob2o18bo19b2o$
31b2o11b2o564bob2o16bobo$31b2o73b2o500bo21b2o36b2o$87b2o17b2o500b5obo
53b2o$87b2o524b2o$610b2o$610bo$611b3o$110b2o501bo$110bo2bo499bobo$2b2o
52b2o32b2o522b2o$bobo16b2o34b2o11b2o20bo18bo2bo$bo18bobo46bo19bo19bo2b
o538b2o$2o20bo47b3o16b2o18bobo538bobo$16b2o4b2o48bo20b2o15bo539bo$16bo
2bo74bo554b2o$18b2o32b2o37b3o16b2o$9b2o41bo38bo18b2o$9b2o20b2o20b3o$
32bo22bo$29b3o576b2o$2o27bo579bo$bo606bo6b2o15b2o$o607b2o5b2o15bobo$2o
632bo33b2o$608b2o24b2o33bo$2o606bobo57bo$obo606bo58b2o$bo80bo$80b3o$
56bo22bo579b2o$56b3o20b2o20b2o525bo30b2o$20bo38bo41b2o523b3o21b2o$18b
3o37b2o32b2o531bo24bo2bo$17bo74bo2bo529b2o19b2o4b2o$17b2o20bo48b2o4b2o
533b2o16bo20b2o$21b2o16b3o47bo20b2o518bo16bobo18bo$22bo19bo21bobo22bob
o18bo517bo19b2o16bobo$20bo20b2o11b2o8bobo3bo19b2o16bobo517b2o36b2o$20b
2o32b2o7b2o43b2o$64bo$66bobobo$63bo2bob3o$65bo3bo$631b2o$23b2o587b2o
17b2o$4b2o17b2o587b2o$4b2o73b2o$66b2o11b2o$60b2o5bo543b2o47b2o$3b2o52b
2o2bo2b3o35b2o508bo47b2o2b2o$4bo52b2obo3bo37b2o2b2o501b3o12b2o38bobo$b
3o12b2o42bobobo41bobo351b2ob2obo7bo134bo14bo22b4o15bo$bo14bo16bo23b2ob
ob2o44bo325b2o23bobobob2o7b3o148b3o18bo7b2o10b2o$17b3o7b2obobobo16b2o
4bo2bo16b2obo27b2o325bo24bo16bo14bo134bo18bo3b2o2b2o$19bo7bob2ob2o17b
2o6b2o16bob2o354bobo38b2o12b3o154bo2b2o$436b2o2b2o47bo$440b2o47b2o3$
488b2o$469b2o17b2o$469b2o6$434b2o36b2o$433bobo16b2o19bo$433bo18bobo16b
o$432b2o20bo16b2o$448b2o4b2o19b2o$448bo2bo24bo$450b2o21b3o$441b2o30bo$
441b2o41b3o$483bo2bo$483bo3bo$432b2o48b2o2bo5bo$433bo50bo6bobo$432bo
33b2o17b2o5b2o$432b2o33bo17b3o$467bobo15b3o4b2o$432b2o34b2o3b2o18bo$
432bobo40bo16bo$433bo38bobo17b2o146b3o$473bo168bo$641bo3$451b2o$451bo$
449bobo$449b2o2$486b2o$486bobo$488bo$488b3o$491bo$490b2o$487b2o$432b2o
53bob5o$432b2o36b2o21bo$469bobo16b2obo$448b2o19bo18b2ob2o$448b2o18b2o$
456b2o18b2o$433b2ob2o18bo19b2o$434bob2o16bobo$432bo21b2o36b2o$432b5obo
53b2o$437b2o$434b2o$434bo$237b3o195b3o$237bo199bo$238bo198bobo$438b2o
2$475b2o$474bobo$474bo$473b2o4$191b2o$192bo239b2o$192bobo238bo$193b2o
237bo6b2o15b2o$432b2o5b2o15bobo$458bo33b2o$432b2o24b2o33bo41bo$432bobo
57bo40b3o$433bo58b2o38bo$532b2o2$483b2o$452bo30b2o43bo$450b3o21b2o52b
2o$449bo24bo2bo49bobo$449b2o19b2o4b2o$453b2o16bo20b2o$454bo16bobo18bo$
452bo19b2o16bobo$452b2o36b2o6$240bobo212b2o$241b2o193b2o17b2o$241bo
194b2o3$435b2o47b2o$436bo47b2o2b2o$433b3o12b2o38bobo$433bo14bo25bo15bo
$449b3o18b2o2b2ob3o10b2o$451bo18b2o4b4o$474b2o6$137b2ob2obo16b2o6b2o
17b2ob2obo7bo$111b2o23bobobob2o16bo2bo4b2o16bobobob2o7b3o$112bo24bo19b
2obob2o23bo16bo14bo$112bobo41bobobo42b2o12b3o$113b2o2b2o37bo3bob2o52bo
$117b2o35b3o2bo2b2o52b2o$153bo5b2o$140b2o11b2o$140b2o73b2o$196b2o17b2o
$196b2o2$420bo$418b3o$219b2o196bo$219b2o196b2o$111b2o52b2o32b2o$110bob
o16b2o34b2o11b2o20bo$110bo18bobo46bo19bo20b3o$109b2o20bo47b3o16b2o20b
2o170bob2o$125b2o4b2o48bo20b2o13b2o173b2obo$125bo2bo74bo13b3o$127b2o
32b2o37b3o15bobo169b5o$118b2o41bo38bo18b2o169bo4bo2b2o$118b2o20b2o20b
3o228bo2bo2bo$141bo22bo228b2obobo$138b3o249bo5bob2o$109b2o27bo250bobo
4bo$110bo278bo2bo2b2o$109bo280b2o$109b2o2$109b2o$109bobo$110bo80bo$
189b3o$165bo22bo$165b3o20b2o20b2o$129bo38bo41b2o170b2o$127b3o37b2o32b
2o179b2o$126bo59bo14bo2bo$126b2o20bo36bo2bo8b2o4b2o$130b2o16b3o35bobo
9bo20b2o$131bo19bo35bo10bobo18bo$129bo20b2o11b2o34b2o16bobo$129b2o32b
2o52b2o2$368b2o22b2o$367bo2bo21bo$368b2o23b3o$193bo201bo$132b2o59b3o$
113b2o17b2o58bo3bo$113b2o74b3o4bo$175b2o12b3obob2o$169b2o5bo12b2o3bo$
112b2o52b2o2bo2b3o35b2o172b2o$113bo52b2obo3bo37b2o2b2o168bo$110b3o12b
2o42bobobo41bobo75bo92b3o$110bo14bo16bo23b2obob2o44bo74b2o94bo$126b3o
7b2obobobo16b2o4bo2bo16b2obo27b2o73bobo$128bo7bob2ob2o17b2o6b2o16bob2o
12$239b2o$240bo$240bobo$241b2o18$250b2obo$250bob2o2$251b5o$246b2o2bo4b
o20b2o$246bo2bo2bo23bo$247bobob2o21bobo105bo$246b2obo5bo18b2o105bobo$
249bo4bobo72b2o50b2o$249b2o2bo2bo71bobo$254b2o74bo$285b2o93b2o$285bo
93bo2bo$283bobo93bobo$283b2o95bo33bobo$414b2o$265b2o61bo86bo$265b2o60b
obo3bo$328b2o2bobo$332bo2bo$333b2o6$303b2o$303b2o2$275bo$274bobo$274bo
bo$275bo3$290b3o14b2o$288bo4bo13b2o$294bo5bo$287bo5bo5b3o$301b2o$291bo
6b3o$289bo2bo4b2obobo$290b2o5bo$298bobobo$297b2obobo$296b2o2b2o$296bo
3bo144bo$297b3o144bobo$298bo145bobo$445bo5$304bo$305b2o142bo$304b2o
142b3o$447b2o2bo$451b2o$446bo3bobo$450b2o$444bo4b2o$442b3o3b2o$444bo4b
2o$436b2o12b2o$268bo166bobo8bo3bobo$267bo167bo15b2o$267b3o164b2o11b2o
2bo$448b3o14b2o$449bo14bo2bo2b2o$464bobo4bo$445b2o18bo5bob2o$444bobo
21b2obobo$444bo23bo2bo2bo$443b2o20bo4bo2b2o$465b5o2$467b2obo$467bob2o
18$478b2o$478bobo$480bo$480b2o12$528b2ob2obo16b2o6b2o20b2obo7bo$502b2o
23bobobob2o16bo2bo4b2o20bob2o7b3o$332bo170bo24bo19b2obob2o40bo14bo$
332b3o168bobo41bobobo42b2o12b3o$335bo168b2o2b2o37bo3bob2o52bo$334b2o
172b2o35b3o2bo2b2o52b2o$526bo3b2o12bo5b2o$524b2obob3o12b2o$524bo4b3o
74b2o$524bo3bo58b2o17b2o$525b3o59b2o$325bo201bo$325b3o23b2o$328bo21bo
2bo$327b2o22b2o2$502b2o52b2o32b2o$501bobo16b2o34b2o11b2o20bo$501bo18bo
bo10bo35bo19bo$304b3o193b2o20bo9bobo35b3o16b2o$306bo209b2o4b2o8bo2bo
36bo20b2o$305bo210bo2bo14bo59bo$337b2o179b2o32b2o37b3o$337b2o170b2o41b
o38bo$509b2o20b2o20b3o$532bo22bo$529b3o$529bo4$610b2o$329b2o280bo$324b
2o2bo2bo278bo$324bo4bobo250bo27b2o$321b2obo5bo249b3o$322bobob2o228bo
22bo$321bo2bo2bo228b3o20b2o20b2o$321b2o2bo4bo169b2o18bo38bo41b2o$326b
5o169b2o16b3o37b2o32b2o$517bo74bo2bo$325bob2o188b2o20bo48b2o4b2o$325b
2obo171b3o18b2o16b3o47bo20b2o$501b2o19bo19bo46bobo18bo$498b2o20bo20b2o
11b2o34b2o16bobo$498b3o19b2o32b2o52b2o$302b2o195bobo$303bo196b2o$300b
3o$300bo2$523b2o$504b2o17b2o$504b2o73b2o$566b2o11b2o$560b2o5bo$503b2o
52b2o2bo2b3o35b2o$504bo52b2obo3bo37b2o2b2o$501b3o12b2o42bobobo41bobo$
501bo14bo40b2obob2o44bo$517b3o7b2obo20b2o4bo2bo16b2obo27b2o$519bo7bob
2o20b2o6b2o16bob2o6$245bo$241b2o2b2ob3o18bo$229b2o10b2o4b4o18b3o$230bo
14b2o25bo14bo$230bobo38b2o12b3o$231b2o2b2o47bo$235b2o47b2o3$283b2o$
264b2o17b2o$264b2o6$229b2o36b2o$228bobo16b2o19bo$228bo18bobo16bo$227b
2o20bo16b2o$243b2o4b2o19b2o$243bo2bo24bo$245b2o21b3o$236b2o30bo$236b2o
2$187b2o$188bo38b2o$185b3o40bo$185bo41bo33b2o$227b2o33bo$262bobo15b2o
5b2o$227b2o34b2o15b2o6bo237b2o$227bobo57bo238bobo$228bo58b2o239bo$528b
2o4$246b2o$246bo$244bobo$244b2o2$281b2o$281bobo$283bo$283b3o$286bo$
285b2o$282b2o$227b2o53bob5o$227b2o36b2o21bo$264bobo16b2obo$243b2o19bo
18b2ob2o$243b2o18b2o$251b2o18b2o$228b2ob2o18bo19b2o$229bob2o16bobo$
227bo21b2o36b2o$227b5obo53b2o$232b2o$229b2o$229bo$230b3o$232bo$232bobo
$233b2o2$270b2o$269bobo$269bo$116bo151b2o$116b2o$115bobo2$247bo$227b2o
17bobo$228bo16bo$227bo18b2o3b2o$227b2o4b3o15bobo$233b3o17bo33b2o$234b
2o17b2o33bo$236bo50bo$234bo2b2o48b2o$233bo3bo$234bo2bo$234b3o41b2o$
247bo30b2o$245b3o21b2o$244bo24bo2bo$244b2o19b2o4b2o$248b2o16bo20b2o$
249bo16bobo18bo$247bo19b2o16bobo$247b2o36b2o6$250b2o$231b2o17b2o$231b
2o3$230b2o47b2o$231bo47b2o2b2o$66b4o158b3o12b2o38bobo351b2ob2obo16b2o
6b2o20b2obo7bo$65bo7b2o18bo134bo14bo41bo325b2o23bobobob2o16bo2bo4b2o
20bob2o7b3o$53b2o10bo3b2o2b2o18b3o148b3o7b2obo27b2o325bo24bo19b2obob2o
40bo14bo$54bo11bo2b2o25bo14bo134bo7bob2o354bobo41bobobo42b2o12b3o$54bo
bo38b2o12b3o501b2o2b2o37bo3bob2o52bo$55b2o2b2o47bo508b2o35b3o2bo2b2o
52b2o$59b2o47b2o543bo5b2o$640b2o11b2o$640b2o73b2o$107b2o587b2o17b2o$
88b2o17b2o587b2o$88b2o$651bo3bo$650b3obo2bo$650bobobo$656bo$611b2o43b
2o7b2o32b2o$53b2o36b2o517bobo16b2o19bo3bobo8b2o11b2o20bo$52bobo16b2o
19bo517bo18bobo22bobo21bo19bo$52bo18bobo16bo518b2o20bo47b3o16b2o$51b2o
20bo16b2o533b2o4b2o48bo20b2o$67b2o4b2o19b2o529bo2bo74bo$67bo2bo24bo
531b2o32b2o37b3o$69b2o21b3o523b2o41bo38bo$60b2o30bo525b2o20b2o20b3o$
60b2o579bo22bo$638b3o$638bo$51b2o$52bo$51bo33b2o$51b2o33bo632b2o$86bob
o15b2o5b2o607bo$51b2o34b2o15b2o6bo606bo$51bobo57bo579bo27b2o$52bo58b2o
576b3o$665bo22bo$665b3o20b2o20b2o$609b2o18bo38bo41b2o$609bo2bo14b3o37b
2o32b2o$70b2o554bo74bo2bo$70bo538bo2bo13b2o20bo48b2o4b2o$68bobo537bo2b
o18b2o16b3o47bo20b2o$68b2o538bobo20bo19bo46bobo18bo$609bo19bo20b2o11b
2o34b2o16bobo$105b2o522b2o32b2o52b2o$105bobo501b2o$107bo501b2o$107b3o$
110bo$109b2o$106b2o524b2o$51b2o53bob5o500b2o17b2o$51b2o36b2o21bo500b2o
73b2o$88bobo16b2obo564b2o11b2o$67b2o19bo18b2ob2o557b2o5bo$67b2o18b2o
523b2o52b2o2bo2b3o35b2o$75b2o18b2o516bo52b2obo3bo37b2o2b2o$52b2ob2o18b
o19b2o513b3o12b2o42bobobo41bobo$53bob2o16bobo534bo14bo40b2obob2o44bo$
51bo21b2o36b2o513b3o7b2obo20b2o4bo2bo16b2obo27b2o$51b5obo53b2o515bo7bo
b2o20b2o6b2o16bob2o$56b2o$53b2o$53bo10bo2bo$54b3o9b4o$56bo6bo$56bobo5b
2o2b2o$57b2o$64b2o$63b2o29b2o$64b2o2bo24bobo$93bo$92b2o5$51b2o$52bo$
51bo6b2o15b2o$51b2o5b2o15bobo$77bo33b2o$77b2o33bo$111bo$111b2o3$102b2o
$71bo30b2o$69b3o21b2o$68bo24bo2bo$68b2o19b2o4b2o$72b2o16bo20b2o$73bo
16bobo18bo$71bo19b2o16bobo$71b2o36b2o6$74b2o$55b2o17b2o$55b2o3$54b2o
47b2o$55bo47b2o2b2o$52b3o12b2o38bobo$52bo14bo41bo$68b3o7b2obo27b2o$70b
o7bob2o!

This assembly might be completable using Snarks. (If not, multiple copies of this could be.)

[pcallahan]

3 to 5 gliders+junk reaction

This is great! I think it breaks some sort of record.

Hasn't anyone done a complete survey of 3-glider collisions yet? Maybe they are just not looking for this outcome.

I found it using my 1994 gencols code to set up a long, but not exhaustive, list of 3-glider collisions. (It looks like I wrote in sloppy K&R C, making it tough to compile now, and it seems buggy when I use it generate over long periods on my Mac laptop--added: ouch! am I maybe limited to a 2^16x2^16 grid?) I ran the output through "safestable", an ANSI C program I wrote while visiting Nick Gotts in 1997-1998 to find population and gliders after stabilizing (more reliable I hope). I used awk to filter for small populations and some gliders. Here's a variation that leaves a loaf and a blinker. (I'd be happy to hear how to do this with state of the art tools.)

Code: Select all

x = 60, y = 49, rule = B3/S23
2$bobo$2b2o$2bo42$44b2o7b2o$43bobo6b2o$45bo8bo!

I could not find a way to remove the extra part using one glider. Here are the ways I found to remove the loaf and boat combination. Maybe one of them is more useful than the one that shows up fortuitously with the rectifier.

Code: Select all

x = 9, y = 9, rule = B3/S23
b2o$o2bo$bobo2b2o$2bo3bobo$7bo5$5b2o$4bobo$6bo$!

Code: Select all

x = 17, y = 8, rule = B3/S23
9b2o$8bo2bo$9bobo2b2o$10bo3bobo$b2o12bo$obo$2bo$!

Code: Select all

x = 17, y = 9, rule = B3/S23
b2o$o2bo$bobo2b2o$2bo3bobo$7bo$14b2o$14bobo$14bo$!

Code: Select all

x = 14, y = 9, rule = B3/S23
2bo$obo$b2o5$6b2o$5bo2bo$6bobo2b2o$7bo3bobo$12bo$!

Code: Select all

x = 17, y = 9, rule = B3/S23
2bo$obo$b2o$9b2o$8bo2bo$9bobo2b2o$10bo3bobo$15bo$!

Using a cycle of four copies of your reaction, you can engineer the gliders to come from infinity (shown here supported by p1512 guns):

Thanks! I will need to take a closer look. I had briefly thought about using one of the close-spaced gliders to remove the junk with 2 copies of the reaction rotated 180 degrees, but I couldn't get it to work. I remember a lot of frustration in the past when I was trying to set up reactions with stable components (pre-Herschel technology) and didn't want to get drawn in too far.

[calcyman]

This assembly might be completable using Snarks. (If not, multiple copies of this could be.)

I've managed to remove four of the guns using Snarks:

Code: Select all

x = 721, y = 721, rule = B3/S23
636b2ob2obo7bo$610b2o23bobobob2o7b3o$611bo24bo16bo14bo$611bobo38b2o12b
3o$612b2o2b2o47bo$616b2o47b2o3$664b2o$645b2o17b2o$645b2o6$610b2o36b2o$
609bobo16b2o19bo$609bo18bobo16bo$608b2o20bo16b2o$624b2o4b2o19b2o$624bo
2bo24bo$626b2o21b3o$617b2o30bo$617b2o3$608b2o58bo$609bo57bobo$608bo33b
2o24b2o$608b2o33bo$643bobo15b2o5b2o$608b2o34b2o15b2o6bo$608bobo57bo$
506b2o101bo58b2o$506bobo$508bo4b2o$504b4ob2o2bo2bo$504bo2bobobobob2o$
507bobobobo113b2o$508b2obobo113bo$512bo112bobo$625b2o$498b2o$499bo7b2o
153b2o$499bobo5b2o153bobo$500b2o162bo$664b3o$667bo$666b2o$663b2o$28b2o
b2obo16b2o6b2o17b2ob2obo7bo515b2o53bob5o$2b2o23bobobob2o16bo2bo4b2o16b
obobob2o7b3o513b2o36b2o21bo$3bo24bo19b2obob2o23bo16bo14bo399b2o133bobo
16b2obo$3bobo41bobobo42b2o12b3o399bo113b2o19bo18b2ob2o$4b2o2b2o37bo3bo
b2o52bo403b3o110b2o18b2o$8b2o35b3o2bo2b2o52b2o404bo118b2o18b2o$44bo5b
2o557b2ob2o18bo19b2o$31b2o11b2o564bob2o16bobo$31b2o73b2o500bo21b2o36b
2o$87b2o17b2o500b5obo53b2o$87b2o524b2o$610b2o$610bo$611b3o$110b2o501bo
$110b2o501bobo$2b2o52b2o32b2o522b2o$bobo16b2o34b2o11b2o20bo395b2o$bo
18bobo46bo19bo21b2o373bobo162b2o$2o20bo47b3o16b2o18bob2o375bo161bobo$
10b2o4b2o4b2o48bo20b2o14bo540bo$10b2o4bo2bo74bo14bo539b2o$10b2o6b2o32b
2o37b3o15bo2bo$52bo38bo18b2o$6b2o2bo20b2o20b3o$7b3o22bo22bo$8bo20b3o
576b2o58bo$2o27bo579bo57bobo$bo606bo6b2o15b2o34b2o$o607b2o5b2o15bobo$
2o632bo33b2o$608b2o24b2o33bo$608bobo57bo$609bo58b2o$82bo$80b3o$56bo22b
o579b2o$56b3o20b2o20b2o525bo30b2o$20bo38bo41b2o523b3o21b2o$18b3o37b2o
32b2o531bo24bo2bo$17bo74bo2bo529b2o19b2o4b2o$17b2o20bo48b2o4b2o533b2o
16bo20b2o$21b2o16b3o47bo20b2o518bo16bobo18bo$22bo19bo46bobo18bo517bo
19b2o16bobo$20bo20b2o11b2o34b2o16bobo517b2o36b2o$20b2o32b2o52b2o467bo$
575b3o$574bo$574b2o$628b3o$628b3obo$23b2o557b2o28b2o19bo$4b2o17b2o558b
o28b2o19b2o$4b2o73b2o502bob2o45b2o$66b2o11b2o494b2o4b3o2bo45bo$60b2o5b
o507b2o3bo3b2o25b2o47b2o$3b2o52b2o2bo2b3o35b2o476b4o28bo47b2o2b2o$4bo
52b2obo3bo37b2o2b2o458b2o15bo25b3o12b2o21bobo14bobo$b3o12b2o42bobobo
41bobo456bobo12b3o26bo14bo25bo15bo$bo14bo40b2obob2o44bo456bo13bo45b3o
18bo4bo2b2o10b2o$17b3o7b2obo20b2o4bo2bo16b2obo27b2o454b2o14b5o42bo18b
2obo2bob2o$19bo7bob2o20b2o6b2o16bob2o503bo65b2o$582bo$582b2o20$104b2o$
104bobo$106bo4b2o$102b4ob2o2bo2bo$102bo2bobobobob2o$105bobobobo$106b2o
bobo$110bo2$96b2o$97bo7b2o$97bobo5b2o$98b2o4$181bo$182b2o$181b2o$108b
2o$108bo$109b3o$111bo29$191b2o$192bo$192bobo$193b2o3$535bo$533b3o$532b
o$532b2o10$37b2o$38bo$36bo$36b5o14b2o$41bo13bo322b2o$38b3o12bobo322bob
o$37bo15b2o325bo4b2o$37b4o335b4ob2o2bo2bo$35b2o3bo3b2o330bo2bobobobob
2o$34bo2b3o4b2o333bobobobo$34b2obo342b2obobo$37bo346bo$37b2o$370b2o$
371bo7b2o$45b2o324bobo5b2o$46bo325b2o$43b3o$43bo5$382b2o$382bo$383b3o$
385bo3$368b2o$367bobo$369bo4$420bo$418b3o$417bo$417b2o4$392bob2o$392b
2obo2$390b5o$390bo4bo2b2o$393bo2bo2bo$393b2obobo$390bo5bob2o$389bobo4b
o$389bo2bo2b2o$390b2o$468b2o$469b2o$468bo5$325b2o$326bo55b2o$324bo57b
2o$324b5o14b2o$329bo13bo$326b3o12bobo$325bo15b2o$325b4o$323b2o3bo3b2o$
322bo2b3o4b2o$322b2obo42b2o22b2o$325bo41bo2bo21bo82bo$325b2o41b2o23b3o
77b2o$395bo78b2o2$333b2o$334bo$331b3o$331bo$385b2o$385bo$386b3o$388bo
14$239b2o$240bo$240bobo$241b2o18$250b2obo$250bob2o192b2o$446bobo$251b
5o192bo4b2o$246b2o2bo4bo20b2o166b4ob2o2bo2bo$163b2o81bo2bo2bo23bo167bo
2bobobobob2o$163bobo81bobob2o21bobo105bo14bo49bobobobo$163bo82b2obo5bo
18b2o105bobo11bobo50b2obobo$249bo4bobo124b2o13b2o54bo$249b2o2bo2bo$
254b2o182b2o$211b2o72b2o93b2o57bo7b2o$212bo72bo93bo2bo56bobo5b2o$210bo
72bobo93bobo58b2o$210b5o14b2o52b2o95bo$215bo13bo$212b3o12bobo35b2o$
211bo15b2o36b2o$211b4o89bo3bobo$209b2o3bo3b2o82bobo3b2o$208bo2b3o4b2o
83b2o4bo140b2o$208b2obo238bo$211bo239b3o$211b2o240bo3$219b2o$220bo$
217b3o$217bo57bo$274bobo$274bobo$275bo10$425bo$426bo$424b3o2$445bo$
444bobo$444bobo$445bo57bo$501b3o$500bo$500b2o3$267bo240b2o$267b3o239bo
$270bo238bob2o$269b2o78b2o35b2o113b2o4b3o2bo$348b2o35bo2bo112b2o3bo3b
2o$350bo35bobo2b2o113b4o$387bo3bobo60b2o36b2o15bo$392bo61b2o35bobo12b
3o$491bo13bo$436b2o52b2o14b5o$279b2o154bobo72bo$272b2o5bobo153bo72bo$
272b2o7bo152b2o72b2o$281b2o182b2o$464bo2bo2b2o$268bo195bobo4bo$267bobo
b2o172b2o18bo5bob2o$267bobobobo170bobo21b2obobo$264b2obobobobo2bo167bo
23bo2bo2bo$264bo2bo2b2ob4o166b2o20bo4bo2b2o$266b2o4bo192b5o$272bobo$
273b2o192b2obo$467bob2o18$361bo116b2o$361b2o115bobo$360bobo117bo$480b
2o14$332bo$332b3o$335bo$334b2o$389bo$387b3o$386bo$386b2o2$325bo$325b3o
23b2o41b2o$328bo21bo2bo41bo$327b2o22b2o42bob2o$387b2o4b3o2bo$387b2o3bo
3b2o$392b4o$378b2o15bo$377bobo12b3o$377bo13bo$376b2o14b5o$337b2o57bo$
337b2o55bo$394b2o5$421bo$421bobo$421b2o$329b2o$324b2o2bo2bo$324bo4bobo
$321b2obo5bo$322bobob2o$321bo2bo2bo$321b2o2bo4bo$326b5o2$325bob2o$325b
2obo4$302b2o$303bo$300b3o$300bo9$335bo$335b3o$338bo$337b2o5$677bo$675b
3o$347b2o325bo$340b2o5bobo324b2o$340b2o7bo$349b2o$682b2o$336bo346bo$
335bobob2o342bob2o$335bobobobo333b2o4b3o2bo$332b2obobobobo2bo330b2o3bo
3b2o$332bo2bo2b2ob4o335b4o$245b2o87b2o4bo325b2o15bo$244bobo93bobo322bo
bo12b3o$246bo94b2o322bo13bo$664b2o14b5o$684bo$682bo$682b2o10$187b2o$
188bo$185b3o$185bo3$526b2o$526bobo$528bo$528b2o29$609bo$609b3o$612bo$
611b2o$605b2o$605bobo$605bo4$621b2o$614b2o5bobo$614b2o7bo$623b2o2$610b
o$609bobob2o$609bobobobo$606b2obobobobo2bo$606bo2bo2b2ob4o$608b2o4bo$
614bobo$615b2o20$137b2o$66bobo69bo$69bo66bo500b2ob2obo16b2o6b2o17b2ob
2obo7bo$65bo4bo2b2o18bo42b5o14b2o454b2o23bobobob2o16bo2bo4b2o16bobobob
2o7b3o$53b2o10b2obo2bob2o18b3o45bo13bo456bo24bo19b2obob2o23bo16bo14bo$
54bo14b2o25bo14bo26b3o12bobo456bobo41bobobo42b2o12b3o$54bobo38b2o12b3o
25bo15b2o458b2o2b2o37bo3bob2o52bo$55b2o2b2o47bo28b4o476b2o35b3o2bo2b2o
52b2o$59b2o47b2o25b2o3bo3b2o507bo5b2o$88bo45bo2b3o4b2o494b2o11b2o$87b
2o45b2obo502b2o73b2o$86b2o19b2o28bo558b2o17b2o$87bo19b2o28b2o557b2o$
88bob3o$90b3o$145b2o$146bo$143b3o$143bo467b2o52b2o32b2o$53b2o36b2o517b
obo16b2o34b2o11b2o20bo$52bobo16b2o19bo517bo18bobo46bo19bo$52bo18bobo
16bo518b2o20bo47b3o16b2o$51b2o20bo16b2o533b2o4b2o48bo20b2o$67b2o4b2o
19b2o529bo2bo74bo$67bo2bo24bo531b2o32b2o37b3o$69b2o21b3o523b2o41bo38bo
$60b2o30bo525b2o20b2o20b3o$60b2o579bo22bo$638b3o$638bo80bo$51b2o665bob
o$52bo666b2o$51bo33b2o$51b2o33bo632b2o$86bobo15b2o5b2o607bo$87b2o15b2o
6bo606bo$111bo579bo27b2o$111b2o576b3o20bo$665bo22bo22b3o$665b3o20b2o
20bo2b2o$609b2o18bo38bo$609b2o16b3o37b2o32b2o6b2o$70b2o554bo74bo2bo4b
2o$70bo555b2o20bo48b2o4b2o4b2o$68bobo539b2o18b2o16b3o47bo20b2o$68b2o
538bob2o19bo19bo46bobo18bo$608bo20bo20b2o11b2o34b2o16bobo$105b2o501bo
20b2o32b2o52b2o$105bobo500bo2bo$107bo501b2o$107b3o$110bo$109b2o$106b2o
524b2o$51b2o53bob5o500b2o17b2o$51b2o36b2o21bo500b2o73b2o$88bobo16b2obo
564b2o11b2o$67b2o19bo18b2ob2o557b2o5bo$67b2o18b2o118bo404b2o52b2o2bo2b
3o35b2o$75b2o18b2o110b3o403bo52b2obo3bo37b2o2b2o$52b2ob2o18bo19b2o113b
o399b3o12b2o42bobobo41bobo$53bob2o16bobo133b2o399bo14bo40b2obob2o44bo$
51bo21b2o36b2o513b3o7b2obo20b2o4bo2bo16b2obo27b2o$51b5obo53b2o515bo7bo
b2o20b2o6b2o16bob2o$56b2o$53b2o$53bo$54b3o$56bo162b2o$56bobo153b2o5bob
o$57b2o153b2o7bo$221b2o$94b2o$93bobo112bo$93bo113bobob2o$92b2o113bobob
obo$204b2obobobobo2bo$204bo2bo2b2ob4o$206b2o4bo$212bobo$51b2o160b2o$
52bo$51bo6b2o15b2o$51b2o5b2o15bobo$77bo33b2o$77b2o33bo$111bo$111b2o3$
102b2o$71bo30b2o$69b3o21b2o$68bo24bo2bo$68b2o19b2o4b2o$72b2o16bo20b2o$
73bo16bobo18bo$71bo19b2o16bobo$71b2o36b2o6$74b2o$55b2o17b2o$55b2o3$54b
2o47b2o$55bo47b2o2b2o$52b3o12b2o38bobo$52bo14bo41bo$68b3o7b2obo27b2o$
70bo7bob2o!

[dvgrn]

This assembly might be completable using Snarks. (If not, multiple copies of this could be.)

I've managed to remove four of the guns using Snarks...

The remaining spare glider outputs can't be connected to the inputs with Snarks, because the color is wrong. There might be a chance if bistable switches are allowed as well as Snarks, though. Are those allowable?

Code: Select all

x = 90, y = 85, rule = LifeHistory
59.2A$59.A.A$61.A4.2A$57.4A.2A2.A2.A$57.A2.A.A.A.A.2A$59.BABABA.A$60.
B2ABA.A$61.2B.BA$60.3B$51.2A6.4B$22.A29.A6.B2A3B$22.3A27.A.AB3.B2A3B$
25.A27.2AB.10B13.A$24.2AB28.13B10.3A$24.4B5.2B20.14B8.A$25.4B3.4B2A
17.15B7.2A$26.4B.5B2AB18.8B2.4B3.5B$27.13B8.B8.6B5.4B2.3B$28.12B7.3B
6.9B4.9B7.2A$16.2A11.11B7.3B5.4B4.2A5.8B8.A$15.B2AB10.11B6.5B3.4B5.A
7.10B3.B.A.2A$16.2B12.11B3.8B.4B7.3A4.7B2A2B.B3A2.A$15.2B8.31B10.A4.
7B2A3BAB2.2A$14.BA2B.3B.33B15.12B4A$14.A.A39B13.2AB.7B3.2B.A$15.A.41B
10.A.AB.7B2.B3A$12.3A3.40B10.A5.4B4.A$12.A5.40B9.2A5.4B5.5A$18.40B15.
4B10.A$17.40B15.4B9.A$17.40B14.4B10.2A$16.39B2A13.4B$14.41B2A12.4B$
13.22B2.19B12.4B$13.21B4.18B11.4B$11.22B6.17B10.4B$10.22B8.2B2.11B10.
4B$11.20B14.9B10.4B$12.18B14.10B9.4B$13.17B13.4B5.2A8.4B$14.17B11.4B
6.A8.4B$14.17B10.4B8.3A4.4B$16.16B8.4B11.A3.4B$17.2B2.6B.5B6.4B15.4B$
20.6B4.4B4.4B15.4B$19.6B6.4B2.4B15.4B$18.6B8.2B4.2B15.4B$17.8B10.2B
17.4B$16.4B.2B2AB8.4B15.4B$3.2A10.4B4.2A8.6B13.4B$4.A9.4B14.8B11.4B$
2.A10.4B14.4B2.4B9.4B$2.5A5.4B5.2A7.4B4.4B7.4B$7.A4.4B5.A7.4B6.4B5.4B
$4.3AB2.7B.BA.A6.4B8.4B3.4B$3.A.2B3.7B.B2A6.4B10.4B.4B$3.4A12B7.4B12.
7B$.2A2.BA3B2A7B6.4B14.5B$A2.3AB.2B2A7B5.4B15.5B$2A.A.B3.10B4.4B15.7B
$3.A8.8B2.4B15.4B.4B$3.2A7.13B15.4B3.4B$13.3B2.6B4.A10.4B5.4B$11.5B3.
4B5.3A7.4B7.4B$11.2A5.6B7.A5.4B9.4B$12.A4.8B5.2A4.4B11.4B$9.3A4.4B2.
4B4.9B13.4B$9.A5.4B4.4B5.6B15.4B$14.4B6.4B2.8B16.4B$13.4B8.15B15.4B$
12.4B10.14B16.4B$11.4B12.13B17.4B$10.3AB14.10B.B2A16.4B$12.A17.3B2AB
3.BA.A16.4B$11.A18.3B2AB6.A17.4B$32.4B6.2A17.4B$32.3B$29.AB.2B$28.A.A
B2AB$28.A.ABABAB$25.2A.A.A.A.A2.A$25.A2.A2.2A.4A$27.2A4.A$33.A.A$34.
2A!
#C [[ THUMBNAIL THUMBSIZE 2 ZOOM 5 ]]

I suppose they're kind of suspect, since in this form they produce an extra glider output, just like Herschel-based solutions would.

[pcallahan]

There might be a chance if bistable switches are allowed as well as Snarks, though. Are those allowable?

It's an admittedly artificial constraint. Components should be stable and not capable of producing gliders by themselves (but this is a slippery constraint that could be changed just by finding a new catalyst). Abstractly, components have no phase constraints (because they're stable), a specific transformation from 1 glider to 1 glider, a specific recovery time, and they block some diagonals. A solution that really just used snarks or similar reflectors if found would be ideal.

It is interesting (and I assume true) that nobody has ever found a snark-sized object that shifts the glider without changing direction. That seems like the kind of failed result that would come up when looking. But anyway, such an object could be allowed.

A solution (if possible) that created a free b-heptomino and kept it going with a glider wave long enough to harvest and recirculate an excess would violate the spirit of the challenge even if it existed only as snarks and gliders for some periods. As would anything based on universal constructors.

If a pure snark solution is found it could be called a "snarklotron." (Just one of those things that popped into my head on my commute.)

Update: I don't know how I missed this last night (I was sure I looked for it; gencols seems to have run into some code rot). You can get another glider when destroying the loaf and boat.

Code: Select all

x = 19, y = 16, rule = B3/S23
$5bobo$6b2o$6bo4$5b2o$4bo2bo$5bobo2b2o$6bo3bobo$11bo!

Combined into a 4 to 6 glider collision:

Code: Select all

x = 132, y = 110, rule = B3/S23
$obo$b2o$bo60$81bo$82bo$80b3o42$121b2o7b2o$120bobo6b2o$122bo8bo!

This also may provide some flexibility with timing.

Update: I think gencols is failing because it's the first time I used it on a 64 bit machine. With this change to defs.h, it can find the turner collision:

Code: Select all

< typedef unsigned long cellseg;
---
> typedef unsigned int cellseg;

There are a bunch of things I hate about this code, not least the silly bit-parallel algorithm, but it might be worth spending a couple hours porting it to ANSI C and fixing problems like the above.

Update: Since the first two gliders produce a b-heptomino, there are variations on this collision. For one additional glider, you can construct an eater and collide that with another glider. Since the extra "junk" is really a turner, you still have a net gain 5 to 6 collision:

Code: Select all

x = 140, y = 96, rule = B3/S23
15$25bo$23bobo$24b2o16$60bo$61bo$59b3o36$102bo$100bobo$101b2o$118bo$
118bobo$108bo9b2o$109b2o$108b2o!

[pcallahan]

Starting a new post since I updated the last one several times. This is a complete snark-assisted 3-to-5 glider collision.

Code: Select all

x = 152, y = 147, rule = B3/S23
bo$2bo$3o12$86b2o3b2o$84b3obo2b2o$83bo4bo$83bo2b2ob4o$82b2obobobo2bo$
83bobobobo$83bobob2o$84bo2$97b2o$88b2o7bo$88b2o5bobo$95b2o7$85b2o$86bo
$83b3o$83bo15$44bo$44b3o$47bo$46b2o3$35b2ob2o$35b2obo$38bo$38b3o4b2o$
36b2o3bo3b2o$35bo2b4o$35b2obo15b2o$36bo2b3o12bobo$36bo5bo13bo$37b5o14b
2o$39bo3$140bo$122b2o14b5o$123bo13bo5bo$123bobo12b3o2bo$124b2o15bob2o$
138b4o2bo$133b2o3bo3b2o$133b2o4b3o$141bo$141bob2o$140b2ob2o3$132b2o$
132bo$133b3o$135bo25$86bo$84b3o$83bo$83b2o7$73b2o$72bobo5b2o$72bo7b2o$
71b2o2$85bo$81b2obobo$80bobobobo$77bo2bobobob2o$77b4ob2o2bo$81bo4bo$
77b2o2bob3o$77b2o3b2o11$41b2o107b2o$40bobo106b2o$42bo108bo!

The 3 input gliders can enter from infinity. The southeast output glider is recirculated to hit the collision junk in a turner reaction, and exits northeast.

Unfortunately, the paired northeast and southwest gliders are on diagonals too close to separate with snarks. However, they could be used to clean up other 3-to-5 glider reactions either with a turner or vanish reaction.