Binary slow salvos

[chris_c]

By the way, that's not quite a universal set just yet: you also need a mechanism to generate a hand block a sufficient distance from the elbow.

I will try. The code for the first part of the search is up here if anyone wants to try deeper searches . It's based on the elbow searching code from years ago. I'm sure your C++ version is much faster.

I spent a few hours getting good results but no pushes were appearing. When I decided to prune patterns that went too far away from the glider lane things went much quicker.

[calcyman]

By the way, that's not quite a universal set just yet: you also need a mechanism to generate a hand block a sufficient distance from the elbow.

I will try. The code for the first part of the search is up here if anyone wants to try deeper searches . It's based on the elbow searching code from years ago. I'm sure your C++ version is much faster.

I spent a few hours getting good results but no pushes were appearing. When I decided to prune patterns that went too far away from the glider lane things went much quicker.

Progress: this one throws a blinker about 45hd away from the centre of the crystal, which should hopefully be sufficient:

Code: Select all

x = 7680, y = 7683, rule = LifeHistory
2.A$A.A$.2A93$94.A$95.A$93.3A94$190.A$191.A$189.3A94$286.A$287.A$285.
3A95$386.A$384.A.A$385.2A93$478.A$479.A$477.3A95$578.A$576.A.A$577.2A
93$670.A$671.A$669.3A95$770.A$768.A.A$769.2A93$862.A$863.A$861.3A95$
962.A$960.A.A$961.2A93$1054.A$1055.A$1053.3A94$1150.A$1151.A$1149.3A
95$1250.A$1248.A.A$1249.2A93$1342.A$1343.A$1341.3A94$1438.A$1439.A$
1437.3A95$1538.A$1536.A.A$1537.2A93$1630.A$1631.A$1629.3A95$1730.A$
1728.A.A$1729.2A93$1822.A$1823.A$1821.3A94$1918.A$1919.A$1917.3A94$
2014.A$2015.A$2013.3A94$2110.A$2111.A$2109.3A94$2206.A$2207.A$2205.3A
94$2302.A$2303.A$2301.3A94$2398.A$2399.A$2397.3A94$2494.A$2495.A$
2493.3A94$2590.A$2591.A$2589.3A94$2686.A$2687.A$2685.3A94$2782.A$
2783.A$2781.3A95$2882.A$2880.A.A$2881.2A93$2974.A$2975.A$2973.3A94$
3070.A$3071.A$3069.3A94$3166.A$3167.A$3165.3A94$3262.A$3263.A$3261.3A
94$3358.A$3359.A$3357.3A94$3454.A$3455.A$3453.3A94$3550.A$3551.A$
3549.3A94$3646.A$3647.A$3645.3A94$3742.A$3743.A$3741.3A94$3838.A$
3839.A$3837.3A94$3934.A$3935.A$3933.3A94$4030.A$4031.A$4029.3A94$
4126.A$4127.A$4125.3A94$4222.A$4223.A$4221.3A94$4318.A$4319.A$4317.3A
94$4414.A$4415.A$4413.3A95$4514.A$4512.A.A$4513.2A93$4606.A$4607.A$
4605.3A94$4702.A$4703.A$4701.3A95$4802.A$4800.A.A$4801.2A93$4894.A$
4895.A$4893.3A95$4994.A$4992.A.A$4993.2A93$5086.A$5087.A$5085.3A94$
5182.A$5183.A$5181.3A94$5278.A$5279.A$5277.3A94$5374.A$5375.A$5373.3A
94$5470.A$5471.A$5469.3A94$5566.A$5567.A$5565.3A95$5666.A$5664.A.A$
5665.2A93$5758.A$5759.A$5757.3A94$5854.A$5855.A$5853.3A95$5954.A$
5952.A.A$5953.2A93$6046.A$6047.A$6045.3A95$6146.A$6144.A.A$6145.2A93$
6238.A$6239.A$6237.3A95$6338.A$6336.A.A$6337.2A93$6430.A$6431.A$6429.
3A95$6530.A$6528.A.A$6529.2A93$6622.A$6623.A$6621.3A94$6718.A$6719.A$
6717.3A95$6818.A$6816.A.A$6817.2A93$6910.A$6911.A$6909.3A94$7006.A$
7007.A$7005.3A94$7102.A$7103.A$7101.3A94$7198.A$7199.A$7197.3A95$
7298.A$7296.A.A$7297.2A93$7390.A$7391.A$7389.3A253$7649.2A$7648.A2.A$
7649.2A2$7645.A$7644.A.A$7644.A.A$7645.A3$7658.2A$7657.A2.A$7658.2A2$
7654.A$7653.A.A$7653.A.A$7654.A2$7668.2A$7667.A2.A$7668.2A2$7664.A$
7663.A.A$7663.A.A$7664.A3$7677.2A$7676.A2.A$7677.2A2$7673.A$7672.A.A$
7672.A.A$7673.A!

[chris_c]

Progress: this one throws a blinker about 45hd away from the centre of the crystal, which should hopefully be sufficient:

Looks good.

Here is an updated 33 glider RCT that starts off with the sequence A.BA.BA.A that does a 1fd block pull:

Code: Select all

x = 43980, y = 43798, rule = B3/S23
22006bo$22005bo$22005b3o25$288bo$289b2o$288b2o2$21983bobo$21983b2o$
21984bo35$172bo$173b2o$172b2o210$227bobo$228b2o$228bo21$248bo$249b2o$
248b2o2$22323bobo$22323b2o$22324bo11$238bo$239b2o$238b2o21149$123bo$
124b2o$123b2o18$21852bobo$21852b2o$154bo21698bo$155bo$153b3o39$185bo$
183bobo$184b2o17$21914bo$21913bo$21913b3o$214bo$215b2o$214b2o5$21398bo
bo$21399b2o$21399bo96$21952bo$21951bo$21951b3o67$21986b2o$21986bobo$
21986bo32$176bo$176b2o$175bobo$21876b2o$21876bobo$21876bo18$145b3o$
147bo$146bo597$22326b2o$22326bobo$22326bo10$242bo$242b2o$241bobo$
22324b2o$22324bobo$22324bo20785$150b2o$149bobo$151bo61$211bo$211b2o$
210bobo10$21401b3o$21403bo$21402bo$43097b2o$43097bobo$43097bo25$21379b
2o$21380b2o$21379bo67$21949b2o$21948b2o$21950bo$253bo$253b2o$252bobo
25$21971b2o$21971bobo$21971bo25$3o$2bo$bo374$43977b2o$43977bobo$43977b
o!

[Kazyan]

As an observation, the restriction that there be no consecutive "B" gliders strongly resembles phinary rather than binary. I'm not sure if this has mathematical significance aside from more efficient compression of a recipe.

[gameoflifemaniac]

Progress: this one throws a blinker about 45hd away from the centre of the crystal, which should hopefully be sufficient:

Looks good.

Here is an updated 33 glider RCT that starts off with the sequence A.BA.BA.A that does a 1fd block pull:

Code: Select all

x = 43980, y = 43798, rule = B3/S23
22006bo$22005bo$22005b3o25$288bo$289b2o$288b2o2$21983bobo$21983b2o$
21984bo35$172bo$173b2o$172b2o210$227bobo$228b2o$228bo21$248bo$249b2o$
248b2o2$22323bobo$22323b2o$22324bo11$238bo$239b2o$238b2o21149$123bo$
124b2o$123b2o18$21852bobo$21852b2o$154bo21698bo$155bo$153b3o39$185bo$
183bobo$184b2o17$21914bo$21913bo$21913b3o$214bo$215b2o$214b2o5$21398bo
bo$21399b2o$21399bo96$21952bo$21951bo$21951b3o67$21986b2o$21986bobo$
21986bo32$176bo$176b2o$175bobo$21876b2o$21876bobo$21876bo18$145b3o$
147bo$146bo597$22326b2o$22326bobo$22326bo10$242bo$242b2o$241bobo$
22324b2o$22324bobo$22324bo20785$150b2o$149bobo$151bo61$211bo$211b2o$
210bobo10$21401b3o$21403bo$21402bo$43097b2o$43097bobo$43097bo25$21379b
2o$21380b2o$21379bo67$21949b2o$21948b2o$21950bo$253bo$253b2o$252bobo
25$21971b2o$21971bobo$21971bo25$3o$2bo$bo374$43977b2o$43977bobo$43977b
o!

How is this even gonna be cleaned up?

[chris_c]

How is this even gonna be cleaned up?

This old post shows that the debris trails from the glider-producing switch engines can be cleaned up with one glider and 11 Corderships. After that it might "only" take another hundred or so gliders to finish the cleanup. Admittedly this part is not very elegant ;)

[dvgrn]

How is this even gonna be cleaned up?

Seems like this has already been answered fairly thoroughly in response to your last question. If you read that answer, then please be more specific about what is still unclear.

Come to think of it, the Corderfleet + Meteor Shower Seed^2 is probably going to have to be a "Cleanup Gliders + Corderfleet + Meteor Shower Seed^2 + Trigger Glider Seed":

• (Item #4) The last glider produced by the crystal mechanism will trigger an initial seed constellation constructed off to the southwest, the Bait Object Seed^2. This will produce a shower of NE-traveling gliders (or maybe some intersecting synchronized gliders and *WSSes, or whatever -- plenty of ways to do this) that will quickly build junk objects that can cleanly catch all of the incoming GPSEs and the Sakapuffer. "Cleanly catch" just means "stop them without letting any gliders escape"; a scattering of ash objects will be left behind.
  ​
• (Item #5) The last of the incoming GPSEs will hit a piece of junk that produces an output glider, which will trigger a second, much larger seed constellation, the Cleanup Gliders + Corderfleet + Meteor Shower Seed^2 + Trigger Glider Seed, which has also already been constructed off to the southwest somewhere. This seed^2 produces a ridiculously long slow salvo (let's say, because that's the easiest thing for existing tools to generate).
  ​
• (Item #6) This slow salvo builds a Cleanup Gliders + Corderfleet + Meteor Shower Seed constellation, right in the center of the RCT area, the location that all of the GPSEs and the Sakapuffer are aimed at. This area will have to be widened out quite a bit from chris_c's sample pattern, to make room for the huge constellation that will have to be built here. The final glider from the slow salvo will trigger the constellation that was just built. The new constellation will produce three waves of cleanup objects.
  ​
• Item 6a: Wave 1 will be a series of slow gliders that shoots down any remaining junk left over from the GPSE and Sakapuffer crashes. It's equally possible to do this part of the cleanup earlier, by building complicated seed constellations as part of Item #4 above, instead of the minimum junk objects (just a block for each incoming puffer, probably) that will stop them all without releasing any gliders.
  ​
• Item 6b: By this point, the near end of each of the debris chains will all cleaned up. They will all look like many, many copies of the same repetitive unit of debris, plus a blob of junk at the other end, Far Far Away (TM). Wave 2 will be a large Corderfleet aimed at each of these debris chains, which flies past the repetitive junk and cleans it all up. Each Corderfleet will be designed to crash into its Far Far Away blob and stop, without releasing any gliders. The link chris_c just posted shows what this will look like; it's not terribly difficult either to design these Corderfleets or to build a seed constellation to construct them.
  ​
• Item 6c: One of the Corderfleet crashes will release a glider after all. This will be a 180-degree glider that travels all the way back to the RCT area from Far Far Away. Several quintillion bajillion ticks later it will hit the remainder of the seed constellation there, which has now been mostly used up, so it's reduced to a simple Meteor Shower Seed.
  ​
• Item 6d: This final seed produces Wave 3 -- three unidirectional salvos, "meteor showers", maybe about a hundred gliders each as chris_c says. One salvo will be aimed at each of the Far Far Away blobs, and (another quintillion bajillion ticks later) will shoot down every piece of junk out there, leaving nothing at all.
  ​
• Item 6e: One of these meteor showers will produce a return glider, which will return to the RCT area after Yet Another Quintillion Bajillion Ticks, and trigger the seed constellation for the actual object that we wanted to build. In the general case we have to wait until the Far Far Away blobs are gone before building the target object, just because the goal is a clean construction of the object without anything else in the universe.
  
  (Maybe the object is something active, like a Slavic quadratic-growth pattern, and we don't want the Far Far Away blobs messing up the population graphs and the bounding box for multiple quintillion bajillion ticks... Those doomed blobs are guaranteed not to matter at all for the last quintillion bajillion ticks, since no possible constructed pattern can catch the final cleanup gliders. So we could really trigger the target object constellation as part of Item 6d.)
  ​
• And... we're done already (?!?)

The Really Weird Thing
The strange thing about all of this is that we actually know how to do every one of those steps above -- it isn't just hand-waving. In the 35G RCT model, the BLSE cleanup was really a fairly messy detail and we would have had to invent a few new tricks to get it to work. But this stuff is all known technology.

It would be a lot of work to build all of these items, and there's some minor research needed to design the remaining Corderfleets (i.e., for the combined GPSE + Sakapuffer) and then the seeds for those Corderfleets. But there aren't any unsolved technical difficulties that I can see. A specialized Golly algorithm could maybe even run one of these patterns to completion someday.

We could technically completely skip Items 6c and 6d above, and save two quintillion bajillion ticks, by instead sending out very clever tricky slow salvos, part of the Cleanup Gliders stage, all the way out to the Far Far Away blobs, ahead of the Corderfleets. These slow salvos would have to build very complicated "self-destruct circuit" seeds that would be activated by the Corderfleets crashing into them. Those seeds would immediately clean up the blobs, sending back just one glider to the RCT area, same as Item 6e above. But that's a little less like "known technology" and more like "hypothetical future non-trivial original research".

[calcyman]

Progress: this one throws a blinker about 45hd away from the centre of the crystal, which should hopefully be sufficient:

Looks good.

Here is an updated 33 glider RCT that starts off with the sequence A.BA.BA.A that does a 1fd block pull:

I managed to construct the Sakapuffer using 6 gliders instead of 7:

Code: Select all

x = 162, y = 156, rule = B3/S23
2bo$obo$b2o29$60bo$58bobo$59b2o$63bo$62bo$62b3o6$66bo$65b2o$65bobo107$
4b3o$6bo$5bo154bo$159b2o$159bobo!

Now, this produces 3 problematic NE gliders, which ordinarily would invalidate its use in an RCT construction.

However, it's possible for these gliders to be safely and cleanly absorbed by the trail of one of the glider-producing switch engines. Here's a demonstration, which reduces the reverse caber tosser to a nice round power of 2:

Code: Select all

x = 62951, y = 62686, rule = B3/S23
2bo$obo$b2o29$60bo$58bobo$59b2o$42063bo$42062bo$42062b3o460$40978bo$
40976b2o$40977b2o25$868bo$866bobo$867b2o$40955bo$40954bo$40954b3o36$
752bo$750bobo$751b2o19865$703bo$701bobo$702b2o17$42360bo$42359bo$
42359b3o$732bo$733b2o$732b2o39$762bobo$763b2o$763bo17$42422bo$42420b2o
$42421b2o$794bo$792bobo$793b2o4$20442bo$20443bo$20441b3o97$42460bo$
42458b2o$42459b2o19995$40958bo$40957b2o$40957bobo33$754b3o$756bo$755bo
40092bo$40847b2o$40847bobo18$724b2o$725b2o$724bo1365$42066bo$42065b2o$
42065bobo107$4b3o$6bo$5bo42154bo$42159b2o$42159bobo19921$729bo$729b2o$
728bobo62$789b3o$791bo$790bo9$20444b2o$20445b2o$20444bo$62069bo$62068b
2o$62068bobo25$20422b2o$20421bobo$20423bo67$42456b2o$42456bobo$42456bo
2$831b3o$833bo$832bo24$42479bo$42478b2o$42478bobo25$579b2o$580b2o$579b
o374$62949bo$62948b2o$62948bobo!

[dvgrn]

Here's a demonstration, which reduces the reverse caber tosser to a nice round power of 2...

Does this force the first bit returned from the mechanism to be a particular parity? I assume that's okay, as long as any combination of bits after the first one can be returned. But maybe I'm wrong about the first bit also. (?)

[Moosey]

Nice reductions from 329 initially by slightly more than an order of magnitude all the way to 32!

[calcyman]

Here's a demonstration, which reduces the reverse caber tosser to a nice round power of 2...

Does this force the first bit returned from the mechanism to be a particular parity? I assume that's okay, as long as any combination of bits after the first one can be returned. But maybe I'm wrong about the first bit also. (?)

If you run the pattern to generation 80000, there are 3 distinct clusters. You can move each cluster 32 full-diagonals away from the centre to 'increment' the recipe by 1 (and thereby flip the parity of the first bit returned from the Sakapuffer). Specifically, when the gliders first collide, it means that the Sakapuffer is 32 * 12 - 32 * 4 = 256 generations further back than in the original pattern, which means that the rebounding glider is delayed by 128 generations (and therefore has the opposite parity). Try it for yourself...

Not that you'd want to do this in practice, because flipping the first bit means that the shotgun releases two gliders instead of one, irrevocably destroying the target block and leaving the other glider to escape.

EDIT: the example pattern contains the integer 338 as the recipe.

[calcyman]

Here's an RCT where the gliders have been adjusted so that the pattern reaches a minimum population of 128 (at generation 600000):

Code: Select all

x = 563371, y = 563106, rule = B3/S23
2bo$obo$b2o29$60bo$58bobo$59b2o$301971bo$301970bo$301970b3o460$300886b
o$300884b2o$300885b2o25$868bo$866bobo$867b2o$300863bo$300862bo$300862b
3o36$752bo$750bobo$751b2o261913$703bo$701bobo$702b2o17$300732bo$
300731bo$300731b3o$732bo$733b2o$732b2o39$762bobo$763b2o$763bo17$
300794bo$300792b2o$300793b2o$794bo$792bobo$793b2o4$262490bo$262491bo$
262489b3o97$300832bo$300830b2o$300831b2o37855$300866bo$300865b2o$
300865bobo33$754b3o$756bo$755bo300000bo$300755b2o$300755bobo18$724b2o$
725b2o$724bo1365$301974bo$301973b2o$301973bobo107$4b3o$6bo$5bo302062bo
$302067b2o$302067bobo260433$729bo$729b2o$728bobo62$789b3o$791bo$790bo
9$262492b2o$262493b2o$262492bo$562489bo$562488b2o$562488bobo25$262470b
2o$262469bobo$262471bo67$300828b2o$300828bobo$300828bo2$831b3o$833bo$
832bo24$300851bo$300850b2o$300850bobo25$579b2o$580b2o$579bo374$563369b
o$563368b2o$563368bobo!

I wonder whether the lowest-minimum-population oblique spaceship in CGoL is a huge sparse pattern such as this.

[gameoflifemaniac]

I'm not as smart as you guys, and what you do is incomprehensible for me, so I need to ask:
How can merely 32 gliders store so much information about the binary salvo?!

[dvgrn]

I'm not as smart as you guys, and what you do is incomprehensible for me, so I need to ask:
How can merely 32 gliders store so much information about the binary salvo?!

It's a binary encoding, where the billions of bits (well, "billions" is probably a huge underestimate) are encoded in the relative positions of the 32 gliders.

Copy calcyman's pattern, Ctrl+Shift+O in Golly, run it to T=1,125,400 and look at (282017, 281751), and then hit TAB at various step sizes until you see some of the bits coming in.

The key glider is visible at this particular time off to the northwest a little bit, at (281348,281370). That's the glider that bounces back and forth between the Corderpuffer and the reading mechanism, producing bits faster and faster ... until the big crash happens. In calcyman's sample pattern there are enough bits that you can see the crystal starting to be produced, but it doesn't get far enough to start building a target object and shooting gliders at it.

Move the puffer twice as far away from the reading mechanism, and you can add one more bit. Move it 1024 times as far away and you can encode ten more bits, and so on.

[gameoflifemaniac]

I'm not as smart as you guys, and what you do is incomprehensible for me, so I need to ask:
How can merely 32 gliders store so much information about the binary salvo?!

It's a binary encoding, where the billions of bits (well, "billions" is probably a huge underestimate) are encoded in the relative positions of the 32 gliders.

Copy calcyman's pattern, Ctrl+Shift+O in Golly, run it to T=1,125,400 and look at (282017, 281751), and then hit TAB at various step sizes until you see some of the bits coming in.

The key glider is visible at this particular time off to the northwest a little bit, at (281348,281370). That's the glider that bounces back and forth between the Corderpuffer and the reading mechanism, producing bits faster and faster ... until the big crash happens. In calcyman's sample pattern there are enough bits that you can see the crystal starting to be produced, but it doesn't get far enough to start building a target object and shooting gliders at it.

Move the puffer twice as far away from the reading mechanism, and you can add one more bit. Move it 1024 times as far away and you can encode ten more bits, and so on.

I think I get it. Thx!

[MathAndCode]

I managed to construct the Sakapuffer using 6 gliders instead of 7:

Code: Select all

x = 162, y = 156, rule = B3/S23
2bo$obo$b2o29$60bo$58bobo$59b2o$63bo$62bo$62b3o6$66bo$65b2o$65bobo107$
4b3o$6bo$5bo154bo$159b2o$159bobo!

Now, this produces 3 problematic NE gliders, which ordinarily would invalidate its use in an RCT construction.

However, it's possible for these gliders to be safely and cleanly absorbed by the trail of one of the glider-producing switch engines.

Why does the universal constructor use a Sakapuffer instead of a glider-producing switch engine? Not only does it require two fewer gliders to construct, but I believe that it can be more versatile, primarily due to the fact that it already makes gliders, so there are likely multiple ways of preventing the second natural glider from forming. There may even be a way to hit the Herschel or one of its descendants with a glider so that the ash contains a 180° turner sufficiently far out to the side so that it can be accessed by later gliders, which would provide a mechanism for future bit recovery. (I manually searched a few combinations and didn't find anything of that sort, but my search was nowhere near comprehensive; a computer search would be much more practical.) There are more opportunities opened up by a glider-producing switch engine, such as hitting it with a glider in such a way to make it produce Herschels on the other side, which might be useful. Granted, instead of the signal returning as the presence of a glider, the signal returns as the absence of a glider, but I do not think that this will be a problem because if I'm interpreting https://conwaylife.com/forums/viewtopic ... 666#p61666 correctly, the signal is already converted to the absence of a glider (See generation 12810.) before being converted back to the presence of a glider, which is then sent back to the Sakapuffer. The only disadvantage that I see to replacing the Sakapuffer with a glider-producing switch engine is the research gap—you have already researched how to make a universal constructor with a Sakapuffer but have not put in as much research into making a universal constructor with a glider-producing switch engine instead of a Sakapuffer—but this will be only temporary, and I think that the reduced glider count alone would probably be worth it.

Edit: I just had another idea: Even if there's no way to hit a Herschel with a glider so that there's an accessible 180° turner, as long as there's a way to make some ash accessible to gliders traveling the other way, it could provide targets at arbitrarily farther intervals, (Technically, it would be limited by where the glider-producing switch engine started, but if one needs multiple targets, then one is probably trying to build something really complicated, so the glider-producing switch engine would have to start very far back.) which would negate the need for a block-laying switch engine, which would save more gliders. And even if that isn't feasible (although I think that I found at least one example that would demonstrate that it is possible to make glider-accessible ash this way), the fact that it's possible to toggle which side the glider-producing switch engine produces Herschels (and therefore gliders) on might allow a way of telling the gliders to burn through exactly so much of the glider-producing switch engine's ash before getting to the location of the next target—or do something to the same effect by controlling how much ash the gliders must destroy—that would be cheaper than the block-laying switch engine and Sakapuffer.

[calcyman]

I managed to construct the Sakapuffer using 6 gliders instead of 7:

Code: Select all

x = 162, y = 156, rule = B3/S23
2bo$obo$b2o29$60bo$58bobo$59b2o$63bo$62bo$62b3o6$66bo$65b2o$65bobo107$
4b3o$6bo$5bo154bo$159b2o$159bobo!

Now, this produces 3 problematic NE gliders, which ordinarily would invalidate its use in an RCT construction.

However, it's possible for these gliders to be safely and cleanly absorbed by the trail of one of the glider-producing switch engines.

Why does the universal constructor use a Sakapuffer instead of a glider-producing switch engine?

The object needs to be able to reflect gliders at period 192, which means that the mechanism responsible for reflecting the glider must occur at a period which divides 192. This is the case for the Sakapuffer (96 divides 192), but not for the GPSE (384 does not divide 192).

[MathAndCode]

Why does the universal constructor use a Sakapuffer instead of a glider-producing switch engine?

The object needs to be able to reflect gliders at period 192, which means that the mechanism responsible for reflecting the glider must occur at a period which divides 192. This is the case for the Sakapuffer (96 divides 192), but not for the GPSE (384 does not divide 192).

But is that really necessary if the timing for the two reflection mechanisms must be different? (I know that the timings must be different because if they weren't, then because the time would be halved after each time that the signal has made a round trip, the period would have to be a factor of 96 the next time, then it would have to be a factor of 48 the time after that, then it would have to be a factor of 24 the time after that, etc… until it can't be an integer.) Or is it that my idea would theoretically work, but in practice, there isn't any pair of ways to hit a glider-producing switch engine with a glider in the same place 192 generations apart that result in a signal being sent back with different timings or on different lanes?

Please keep in mind that I'm new here, so I don't have a lot of experience or prior knowledge (although I have looked as the wiki and forums occasionally for a while before creating an account, and I have even discovered a bunch of interesting patterns and reactions (although must of them are probably independent discoveries)).

[calcyman]

But is that really necessary if the timing for the two reflection mechanisms must be different? (I know that the timings must be different because if they weren't, then because the time would be halved after each time that the signal has made a round trip, the period would have to be a factor of 96 the next time, then it would have to be a factor of 48 the time after that, then it would have to be a factor of 24 the time after that, etc… until it can't be an integer.)

The 'two reflection mechanisms' happen in the fixed circuitry; the approaching Sakapuffer has a single reflection mechanism.

[MathAndCode]

But is that really necessary if the timing for the two reflection mechanisms must be different? (I know that the timings must be different because if they weren't, then because the time would be halved after each time that the signal has made a round trip, the period would have to be a factor of 96 the next time, then it would have to be a factor of 48 the time after that, then it would have to be a factor of 24 the time after that, etc… until it can't be an integer.)

The 'two reflection mechanisms' happen in the fixed circuitry; the approaching Sakapuffer has a single reflection mechanism.

Ah; I think that I understand: So if there are two gliders on the same lane 64 full diagonals apart that would each individually result in the signal being sent back (except if the two return signals are indistinguishable from each other) (with no escaping gliders going backwards or outwards) and each return signal can be converted to a signal sent back to the glider-producing switch engine with the same timing ±some multiple of 256 (I think) ticks without a net increase in glider cost, then my idea will work; otherwise, it won't.

I think that I have some possibilities for the first part. Obviously, none of them will work unless there is a suitable reflection mechanism at the other end that can be constructed cheaply enough to not increase the net cost.
Here are two ways where one glider on a particular lane and timing results in an glider sent back on a lane farther to the outside than the lane for the second natural gliders, and the conjugate signal/glider results in a gap in the stream of second natural gliders, which could be fed into some sort of NOT gate.

Code: Select all

x = 834, y = 788, rule = B3/S23
2o$obo$o9$19bo$17bobo$18b2o51$64b2o$64bobo$64bo62$128b2o$128bobo$128bo62$192b2o$192bobo$192bo62$256b2o$256bobo$256bo9$275bo$273bobo$274b2o51$320b2o$320bobo$320bo62$384b2o$384bobo$384bo62$448b2o$448bobo$448bo62$512b2o$512bobo$512bo62$576b2o$576bobo$576bo9$595bo$593bobo$594b2o12$683bo$683bo$683bo$684b2o$684b3o$684b2o3$694b2o2b3o$694b3o2bo$683bo13bobo$682bobo9b2ob2o$682bo2bo8b3o3$681bo2bo$681b2ob3o$683b2o2bo$684bo2bo$684bobo3$715b2o$715b2o3$704bo$703bobo$703b2o2$723b2o$723b2o3$695b2o$695b2o4$640b2o$640bobo76b3o$640bo76bo4bo7b2o$717bo12bobo$717bo4bo8bo$718bobo$709bo9bobo$708bobo7b2ob2o$708bo2bo6b2o3bo$709b2o5b3obobob2o$702b3o12bo2bobo3bo$698bo3bo15b2o3bobo$699b2obobo19bo$697bobo20bob2o$696b2o3b2o18b2o$696b2o2b4o43b2o$702b2o43b2o$704bo2$736bo$735bobo$699bo2b2o18bo12b2o30b2o$700b3o18bobo42bo2bo$701bo19b2o44b2o4$731bo$730bobo$730b2o3$761bo$760bobo$760bo2bo$761b2o5$731b2o$730bo2bo$731b2o$728bo$728bo$728bo2$730b3o3$733b2o$733b2o9bo$744bo$744bo54b2o$798bo2bo$799b2o2$751b3o2$763bo$762bobo$762b2o2$725b2o$725b2o66bo$792bobo$792bo2bo$793b2o4$721b2o$721b2o40b2o$762bo2bo$763b2o$760bo$760bo$760bo2$762b3o2$731b2o$730bobo32b2o$730b2o33b2o9bo$776bo$776bo54b2o$830bo2bo$831b2o2$783b3o2$795bo$794bobo$794b2o2$757b2o$757b2o66bo$824bobo$824bo2bo$825b2o4$753b2o$753b2o40b2o$794bo2bo$795b2o$792bo$792bo$792bo2$794b3o2$763b2o$762bobo32b2o$762b2o33b2o9bo$808bo$808bo4$815b3o2$827bo$826bobo$826b2o2$789b2o$789b2o7$785b2o$785b2o40b2o$826bo2bo$827b2o$824bo$824bo$824bo2$826b3o2$795b2o$794bobo32b2o$794b2o33b2o!

Code: Select all

x = 538, y = 480, rule = B3/S23
o$b2o$2o24$19b2o$19bobo$19bo62$83b2o$83bobo$83bo36$128bo$129b2o$128b2o24$147b2o$147bobo$147bo62$211b2o$211bobo$211bo62$275b2o$275bobo$275bo27$383bo$383bo$385bo5bo$384bo6bobo$383bo3bo2bo$384bo2bobob2o6b2o$389bob2o7b2o$397bo$397bo7bo$320bo76bo4b3obo$321b2o77bo3b2o$320b2o77bo3b2o$398b4obo$398bobo$399b2o3$392b2o3bo$390b3o4b2o$385b3obo8b2o$389bobo2b5o$390bo3b3o2$419b2o$419b2o3$408bo$407bobo$407b2o2$427b2o$427b2o3$339b2o58b2o$339bobo57b2o$339bo5$415b2o2b2o13b2o$415bo2b3o13bobo$418b3o5bo8bo$412bo4bobo6b2o$412b2o2b3o9bo$407b2o3bo3b3o3b5o$406b3o2bo2bo7bo2b5o$407b2o2bo10b3o3bo$402b3o3b3ob3o$401bo3bo3bo$401bo3bo$401bo3bo$402b3o$451b2o$451b2o2$405b2o$405b2o33bo$439bobo$426bo12b2o30b2o$425bobo42bo2bo$425b2o44b2o4$435bo$434bobo$403b3o28b2o$405bo$404b3o$465bo$464bobo$464bo2bo$465b2o5$435b2o$434bo2bo$435b2o$432bo$432bo$432bo2$434b3o3$437b2o$437b2o9bo$448bo$448bo54b2o$502bo2bo$503b2o2$455b3o2$467bo$466bobo$466b2o2$429b2o$429b2o66bo$496bobo$496bo2bo$497b2o4$425b2o$425b2o40b2o$466bo2bo$467b2o$464bo$464bo$464bo2$466b3o2$435b2o$434bobo32b2o$434b2o33b2o9bo$480bo$480bo54b2o$534bo2bo$535b2o2$487b3o2$499bo$498bobo$498b2o2$461b2o$461b2o66bo$528bobo$528bo2bo$529b2o4$457b2o$457b2o40b2o$498bo2bo$499b2o$496bo$496bo$496bo2$498b3o2$467b2o$466bobo32b2o$466b2o33b2o9bo$512bo$512bo4$519b3o2$531bo$530bobo$530b2o2$493b2o$493b2o!

In each case, the conjugate signal sends a backwards glider, but as long as it's not used as the first signal, the backwards glider can be absorbed by debris from previous signal reflections, so because that restriction already exists, this is not a problem because it will be possible to rephase the shotgun initially in order to switch which signal corresponds to which glider or move the block slightly in order to switch which lane makes crystals if necessary.
Here's a pair of conjugate signals with the same type of returning signal as before so that neither creates a backwards glider that can only be cleaned up with ash from an earlier signal.

Code: Select all

x = 479, y = 420, rule = B3/S23
2bo$obo$b2o95$90b3o$90bo$91bo62$154b3o$154bo$155bo62$218b3o$218bo$219bo22$328bo$327b3o$326b2ob2o$325b2obobo$324b3o2b3o$325bo6bo$326b5obo$327b4ob2o$332bo$331bo8b3o$340b3o3bo$341bo3bobo$346bo$329bo$327b2obo$340b2o$330bo9b2o$327bo2bo$328bo2$333b2o$326b3o5b2o$333b2o$333bo2$360b2o$360b2o3$349bo$348bobo$348b2o2$368b2o$368b2o3$340b2o$340b2o2$282b3o$282bo$283bo2$360b2o13b2o$359bo15bobo$359bo4bo11bo$359b2o5bo$354bo12bo$353bobo5b4o3bo$348b2o3bo2bo6bo4b2ob3o$347bobo4b2o12b2o3bo$346bo2bo14bo2bo$345b2o$343b2o2bo15bobo4bobo$345bo21bob3o$363b2o3b2o$369bo22b2o$366bobo23b2o2$346b2o$345bo2bo32bo$345bobo32bobo$344b2o21bo12b2o30b2o$344bo21bobo42bo2bo$347b2o17b2o44b2o$347b2o$347b2o$344b2obo$345b3o28bo$346bo28bobo$322bo52b2o$320bobo$321b2o$406bo$405bobo$405bo2bo$406b2o5$376b2o$375bo2bo$376b2o$373bo$373bo$373bo2$375b3o3$378b2o$378b2o9bo$389bo$389bo54b2o$443bo2bo$444b2o2$396b3o2$408bo$407bobo$407b2o2$370b2o$370b2o66bo$437bobo$437bo2bo$438b2o4$366b2o$366b2o40b2o$407bo2bo$408b2o$405bo$405bo$405bo2$407b3o2$376b2o$375bobo32b2o$375b2o33b2o9bo$421bo$421bo54b2o$475bo2bo$476b2o2$428b3o2$440bo$439bobo$439b2o2$402b2o$402b2o66bo$469bobo$469bo2bo$470b2o4$398b2o$398b2o40b2o$439bo2bo$440b2o$437bo$437bo$437bo2$439b3o2$408b2o$407bobo32b2o$407b2o33b2o9bo$453bo$453bo4$460b3o2$472bo$471bobo$471b2o2$434b2o$434b2o!

Here is a pair of conjugate signals so that instead of one merely preventing a second natural glider from being formed, it also sends another glider back on a different lane (that is one half-diagonal away from the lane that the signal goes to the glider-producing switch engine on.

Code: Select all

x = 715, y = 657, rule = B3/S23
o$b2o$2o245$240b2o$239b2o$241bo62$304b2o$303b2o$305bo62$368b2o$367b2o$369bo62$432b2o$431b2o$433bo7$448bo$449b2o$448b2o13$533bo$530b4o2$547b3o2$533bobo12b2o$534bo13b2o$532b2o14b2o$532bo2bo$531b2ob2o10bo2b3o$546b2ob3o$547bo3b2o2b2o$554bo$551bo2bo3bo$547bo3bobo4bo$547bo3bob2o3bo$554bo9b2o$554b3o7b2o7$572b2o$572b2o3$544b2o$544b2o6$579b2o$579bobo$570b3o7bo$569bo2bo$558bo6b5ob2o$496b2o59bobo8b3o$495b2o60bo2bo$497bo52bo7b2o$548bobo$548b3o4$596b2o$596b2o3$585bo$584bobo$571bo12b2o30b2o$570bobo42bo2bo$570b2o44b2o4$580bo$579bobo$579b2o3$610bo$609bobo$609bo2bo$610b2o5$580b2o$579bo2bo$580b2o2$576b3o2$580bo$580bo$580bo2$582b2o10bob2ob2o3bo$582b2o9bob3o$592bo2bo2bobo4bo$593b2o5b6o42b2o$599bo47bo2bo$648b2o$597b3o3$612bo$611bobo$611b2o2$574b2o$574b2o66bo$641bobo$641bo2bo$642b2o4$570b2o$570b2o40b2o$611bo2bo$612b2o2$608b3o2$612bo$612bo$612bo$580b2o$579bobo32b2o$579b2o33b2o$624b3o$680b2o$679bo2bo$680b2o$633bo$633bo$633bo$644bo$643bobo$643b2o2$606b2o$606b2o66bo$673bobo$673bo2bo$674b2o4$602b2o$602b2o40b2o$643bo2bo$644b2o2$640b3o2$644bo$644bo$644bo$612b2o$611bobo32b2o$611b2o33b2o$656b3o$712b2o$711bo2bo$712b2o$665bo$665bo$665bo$676bo$675bobo$675b2o2$638b2o$638b2o66bo$705bobo$705bo2bo$706b2o4$634b2o$634b2o40b2o$675bo2bo$676b2o2$672b3o2$676bo$676bo$676bo$644b2o$643bobo32b2o$643b2o33b2o$688b3o4$697bo$697bo$697bo$708bo$707bobo$707b2o2$670b2o$670b2o!

Because there are two differences compared to no returned signal instead of one, this might be easier to make the reflecting mechanism react to (although there is still only one difference for the other signal), but it might also make it more difficult to cancel out both differences.
These two signals create extra gliders on different lanes without removing any second natural gliders.

Code: Select all

x = 966, y = 908, rule = B3/S23
o$b2o$2o657$651b3o$651bo$652bo62$715b3o$715bo$716bo39$839bo$838b3o2$838b3o$839b2ob2o$841bo$855b2o$855b2o3$839bo$838bobo$839bo2$838b2o$837bobo$856bo$837b3obobo11bo$841b3o13b2o$841b2o14b2o$858bo$855bo2bo$855bobo$779b3o71b2o$779bo72bo$780bo73bo$843b2o5b4o$843b2o4bo2bo$849bo2bo$850b3o$879b2o$879b2o3$868bo$867bobo$867b2o6$859b2o4bobo20bo$859b2o3bo3bo18b2obobo$863bo4bo17bo4bo$863bo4bo8b2o6bo3bobo$863bo3bo9b2o5bo3bo2b2o$864bo2bo15bo3bo$883bo5b4obo$883bo2bobo4bob2o$884b3o6bo$887bo3b2o$888bo3$863b2o$862bo2bo$863b2o$860bo$860bo$860bo2$862b3o12b2o32b2o$878b2o31b2o$877bo$865b2o$865b2o33bo$899bobo$832bo53bo12b2o30b2o$833b2o50bobo42bo2bo$832b2o51b2o44b2o4$895bo$894bobo$894b2o2$857b2o$857b2o66bo$924bobo$924bo2bo$925b2o$872b3o$872bob2o$868bo3bo2b2o$867b2o4b4o$843b3o5bo7b2o5bobo3bobo20b2o$843bo5bobo6b3o4b2o5b2o20bo2bo$844bo6b2obo6bo4b2o5b2o20b2o$848bo2bo3bobobobo5bo4b3o17bo$848bo7bo3bo31bo$850bo4b2obo33bo$850b2o6bo2bo$859b2o33b3o$860bo2$897b2o$897b2o9bo$908bo$908bo54b2o$962bo2bo$963b2o2$915b3o2$927bo$926bobo$926b2o2$889b2o$889b2o66bo$956bobo$956bo2bo$957b2o4$885b2o$885b2o40b2o$926bo2bo$927b2o$924bo$924bo$924bo2$926b3o2$895b2o$894bobo32b2o$894b2o33b2o9bo$940bo$940bo4$947b3o2$959bo$958bobo$958b2o2$921b2o$921b2o!

Here's another such pair:

Code: Select all

x = 966, y = 927, rule = B3/S23
o$b2o$2o651$646b2o$646bobo$646bo62$710b2o$710bobo$710bo45$836bo$836bo5b3o$835bobo3b2o2bo$836bo3bo5bo$836bo3bo$841bo2b2o$842b2o11b2o$855b2o8$849bo$839b2o9b2o$774b2o62bob3o8b2o$774bobo61bo3bo10bo$774bo64b2obo5b5o6b2o$840bo10bo6bo2bo$857b2ob2o$856bobo$849b2o4b2o$849b2o4bo3bo$856bo2bo$843b2o11b3o$843b2o3$879b2o$845b2o32b2o$847bo$845b3o5b2o$868bo$867bobo$867b2o3$889bo$866b2o20bobo$861b2o3b2o22bo$859b2o2bo22bob2o5b2o$858bob3obo20b2obo6bob2o$857bo2bo3bo33bo$858bo2b2ob2o11b2o10bobo4bobo$859b2o3bo12b2o9bo2bo4b2o$860b3obobo22bobo$865b2o26b2o$893b3o$892bo2bo$892bobo$893bo3$863b2o$862bo2bo17bo$863b2o18b2o$860bo21bobo$860bo$860bo2$862b3o46b2o$911b2o2$865b2o$865b2o33bo$899bobo$832bo53bo12b2o30b2o$833b2o50bobo42bo2bo$832b2o51b2o44b2o4$895bo$894bobo$894b2o2$857b2o$857b2o66bo$924bobo$838b2o84bo2bo$838bobo84b2o$838bo$850b4o9b3o$854bo8bobo$848bo6bo6b2o2b2o$847b3o4bo7b3o30b2o$845bo5bobo6b2o32bo2bo$845bobo3b2o7b4o2bobo26b2o$845bo3b2o13b2obobo5bo16bo$847b3o11bo8bo4bo16bo$861b3o3b4o4bo16bo$865b2ob2o$855b3o2b2obobo28b3o$849b2ob4o2b4o2bo$852b5obo3b2o$857bo39b2o$897b2o9bo$908bo$908bo54b2o$962bo2bo$963b2o2$915b3o2$927bo$926bobo$926b2o2$889b2o$889b2o66bo$956bobo$956bo2bo$957b2o4$885b2o$885b2o40b2o$926bo2bo$927b2o$924bo$924bo$924bo2$926b3o2$895b2o$894bobo32b2o$894b2o33b2o9bo$940bo$940bo4$947b3o2$959bo$958bobo$958b2o2$921b2o$921b2o7$917b2o$917b2o40b2o$958bo2bo$959b2o$956bo$956bo$956bo2$958b3o2$927b2o$926bobo32b2o$926b2o33b2o!

Here's a third such pair where one of the gliders is only one half-diagonal away from the lane that the signal travels to the glider-producing switch engine on:

Code: Select all

x = 774, y = 735, rule = B3/S23
o$b2o$2o457$453bo$452b2o$452bobo62$517bo$516b2o$516bobo46$643b2o$646b2o4bo$643b2ob4o3bo$640b5o4b4o$643b3o6bo$576bo67bo$577b2o64b3o$576b2o72bo12b2o$650bo12b2o8$581bo$580b2o79bo$580bobo76b2obo$645bob2obo9b2ob2o$644bo4b3o9bob2o4b2o$645bo5bo10bobo5b2o$646bo3bo11b3ob3o2bo$647bobo14bob5o$657b2o7b2ob2o$657b2o$666b3o$651b2o13bobo$651b2o10b4obo$663bo2b2o$664b3o$665bo21b2o$687b2o3$676bo$675bobo$675b2o2$669bo$668b2o27bo$667b3o4bo23b2o5b2o$666bob2o4bo20b2ob2o2b2ob3o$665b2obo24b2o2b2o2bo5b2o$665b2obob2o20b3ob2o3b4obo2bo$668bobo22b2o10b2o2b2o$669b2o14b2o12bo5b2ob2o$685b2o11bo2bo$705bo$697b2obo6bo$698b2o3bo2bo2$701b5o$700bo$701b2o2$671b2o19b3o$670bo2bo20bo$671b2o20bo2$667b3o2$671bo$671bo47b2o$671bo47b2o2$673b2o$673b2o33bo$707bobo$694bo12b2o30b2o$693bobo42bo2bo$693b2o44b2o4$703bo$702bobo$702b2o2$665b2o$645bo19b2o66bo$644b2o86bobo$644bobo85bo2bo$662bo70b2o$661bobo$660bo$654b2o4bo2b3o$654bo2bob3o3b2o$653b2o3bo5b5o34b2o$652b2o4bo5b2o2bo33bo2bo$652bo4b2o6bo11b2o24b2o$653bo11bo10bo2b2o$656bo18bo6b3o14b3o$664bo5b3o8bo$664bo4bob3o2b2o2bo22bo$674bo3b2o23bo$670bo4bo27bo$674bo$668bo36b2o$670b3o32b2o$715b3o$771b2o$770bo2bo$771b2o$724bo$724bo$724bo$735bo$734bobo$734b2o2$697b2o$697b2o66bo$764bobo$764bo2bo$765b2o4$693b2o$693b2o40b2o$734bo2bo$735b2o2$731b3o2$735bo$735bo$735bo$703b2o$702bobo32b2o$702b2o33b2o$747b3o4$756bo$756bo$756bo$767bo$766bobo$766b2o2$729b2o$729b2o7$725b2o$725b2o40b2o$766bo2bo$767b2o2$763b3o2$767bo$767bo$767bo$735b2o$734bobo32b2o$734b2o33b2o!

Here is a mechanism where the return signals are gliders on different outer lanes, but a backwards glider from one of the signals leads to the same restriction as with the signal pairs listed at the beginning of this post.

Code: Select all

x = 1414, y = 1375, rule = B3/S23
o$b2o$2o766$768bo$769b2o$768b2o325$1089bo$1088b2o$1088bobo62$1153bo$1152b2o$1152bobo51$1292bo$1278bobo6bo2b4o$1277bo9bob4o$1278bo2bo6b3o3b2o$1216bo63b3o9bo2b2o$1217b2o74bob2o$1216b2o76bo8b2o$1303b2o4$1217bo$1216b2o$1216bobo2$1305bo$1304bobo$1297bo8bo$1283b2o11b2o5b2ob3o$1283b2o11bo3b2o3b2ob2o$1299b3o2b2o2bo$1299bo2bo2b3o$1302bo3bo$1302bo2bo$1298bo2bo3bo$1305bo$1291b2o$1291b2o3$1303bobo2bo18b2o$1304b2o2bo18b2o$1303b2o3bo$1305bo2bo$1308bo7bo$1307bo7bobo$1304bob2o7b2o$1304b3o$1305bo36b3o$1342b2ob2o$1341bobob2o$1330b3o8bobob2o3b2o$1311bo17bo2bo9bobo5b2o$1310bobo16bo3b2o8bo$1310b2o24bo$1325b2o9bo8b2o$1325b2o3b4o11b2o$1334b3o$1336bo3$1341bo$1334b4obo2bo$1334bob2o3bo5bo$1337b2o2bo6b2o$1311b2o26bo7b2o$1310bo2bo$1311b2o2$1307b3o2$1311bo$1311bo47b2o$1311bo47b2o2$1313b2o$1313b2o33bo$1347bobo$1334bo12b2o30b2o$1333bobo42bo2bo$1333b2o44b2o4$1343bo$1281bo60bobo$1280b2o60b2o$1280bobo$1305b2o$1305b2o66bo$1298b2o72bobo$1298bo73bo2bo$1297bo75b2o$1297bo$1297b4o$1296bo3bo$1296bo2bo2bo$1301b2o40b2o$1321b3o18bo2bo$1322bo20b2o$1322bo$1321b3o15b3o2$1343bo$1343bo$1343bo$1311b2o$1310bobo32b2o$1310b2o33b2o$1355b3o$1411b2o$1410bo2bo$1411b2o$1364bo$1364bo$1364bo$1375bo$1374bobo$1374b2o2$1337b2o$1337b2o66bo$1404bobo$1404bo2bo$1405b2o4$1333b2o$1333b2o40b2o$1374bo2bo$1375b2o2$1371b3o2$1375bo$1375bo$1375bo$1343b2o$1342bobo32b2o$1342b2o33b2o$1387b3o4$1396bo$1396bo$1396bo$1407bo$1406bobo$1406b2o2$1369b2o$1369b2o7$1365b2o$1365b2o40b2o$1406bo2bo$1407b2o2$1403b3o2$1407bo$1407bo$1407bo$1375b2o$1374bobo32b2o$1374b2o33b2o!

For the options where one of the return signals is only the absence of a glider, if suitable mechanisms can be found to reflect the signals back to the glider-producing switch engine, then instead of having to add another glider as the initial signal, one can time the gliders from the glider-producing switch engine to reach the signal reflection mechanism a little bit late so that it's interpreted as the return of the signal where a glider prevented a second natural glider from forming, which would decrease the glider cost further by one. This would possible even if that signal could not be first because one could also delay the construction glider that the "signal" was supposed to let through, although it would not be as efficient time-wise.

Admittedly, the ash will make cleanup more difficult, but if your goal is reducing the glider count, then this will be worth it.







By the way, this seems like an efficient way of burning through some of the glider-producing switch engine's Herschel ash.

Code: Select all

x = 581, y = 546, rule = B3/S23
obo$b2o$bo19$23bo$24bo$22b3o233$258bo$259bo$257b3o100$421bo$420b3o15bo$419b2ob2o14bo$418b2o3bo7b4o3bo$419bobobobo5bo3bo$420b2obo2bo4b2o3bo$423b2obo7b3o$424b2o10b2obo$437b3o$438bo10$426b2o$426b2o3$462b2o$462b2o2$373b2o9bobo$373bobo9b2o64bo$373bo11bo64bobo$450b2o3$469bo$468b3o$469b2o$442b2o$442b2o22b2o$464b2o5bo$464bo5bo$464b2o$466bo3bo$467bo2bo$468bo8b2o$477bobo$478bo3$407bo$408bo37b2o$406b3o36bo2bo$446b2o$443bo$443bo$443bo2$445b3o46b2o$494b2o2$448b2o$448b2o33bo$482bobo$469bo12b2o30b2o$468bobo42bo2bo$468b2o44b2o2$450bo$450b2o$449bobo26bo$477bobo$477b2o2$440b2o$441bo66bo$507bobo$507bo2bo$508b2o$442b2obo$443b2o$444bo2$446bo31b2o$442b2ob2o30bo2bo$443b3o32b2o$444bo30bo$475bo$475bo2$477b3o3$480b2o$480b2o9bo$491bo$491bo54b2o$545bo2bo$546b2o2$498b3o2$510bo$509bobo$509b2o2$472b2o$472b2o66bo$539bobo$539bo2bo$540b2o4$468b2o$468b2o40b2o$509bo2bo$510b2o$507bo$507bo$507bo2$509b3o2$478b2o$477bobo32b2o$477b2o33b2o9bo$523bo$523bo54b2o$577bo2bo$578b2o2$530b3o2$542bo$541bobo$541b2o2$504b2o$504b2o66bo$571bobo$571bo2bo$572b2o4$500b2o$500b2o40b2o$541bo2bo$542b2o$539bo$539bo$539bo2$541b3o2$510b2o$509bobo32b2o$509b2o33b2o9bo$555bo$555bo4$562b3o2$574bo$573bobo$573b2o2$536b2o$536b2o7$532b2o$532b2o40b2o$573bo2bo$574b2o$571bo$571bo$571bo2$573b3o2$542b2o$541bobo32b2o$541b2o33b2o!

Unfortunately, the blocks that the ships leave behind when serving as turners are inaccessible as targets—although just barely.

[MathAndCode]

Here is a way where one glider on a particular lane and timing results in an glider sent back on a lane farther to the outside than the lane for the second natural gliders, and the conjugate signal/glider results in a gap in the stream of second natural gliders, which could be fed into some sort of NOT gate, so that neither creates a backwards glider that can only be cleaned up with ash from an earlier signal.

Code: Select all

x = 479, y = 420, rule = B3/S23
2bo$obo$b2o95$90b3o$90bo$91bo62$154b3o$154bo$155bo62$218b3o$218bo$219bo22$328bo$327b3o$326b2ob2o$325b2obobo$324b3o2b3o$325bo6bo$326b5obo$327b4ob2o$332bo$331bo8b3o$340b3o3bo$341bo3bobo$346bo$329bo$327b2obo$340b2o$330bo9b2o$327bo2bo$328bo2$333b2o$326b3o5b2o$333b2o$333bo2$360b2o$360b2o3$349bo$348bobo$348b2o2$368b2o$368b2o3$340b2o$340b2o2$282b3o$282bo$283bo2$360b2o13b2o$359bo15bobo$359bo4bo11bo$359b2o5bo$354bo12bo$353bobo5b4o3bo$348b2o3bo2bo6bo4b2ob3o$347bobo4b2o12b2o3bo$346bo2bo14bo2bo$345b2o$343b2o2bo15bobo4bobo$345bo21bob3o$363b2o3b2o$369bo22b2o$366bobo23b2o2$346b2o$345bo2bo32bo$345bobo32bobo$344b2o21bo12b2o30b2o$344bo21bobo42bo2bo$347b2o17b2o44b2o$347b2o$347b2o$344b2obo$345b3o28bo$346bo28bobo$322bo52b2o$320bobo$321b2o$406bo$405bobo$405bo2bo$406b2o5$376b2o$375bo2bo$376b2o$373bo$373bo$373bo2$375b3o3$378b2o$378b2o9bo$389bo$389bo54b2o$443bo2bo$444b2o2$396b3o2$408bo$407bobo$407b2o2$370b2o$370b2o66bo$437bobo$437bo2bo$438b2o4$366b2o$366b2o40b2o$407bo2bo$408b2o$405bo$405bo$405bo2$407b3o2$376b2o$375bobo32b2o$375b2o33b2o9bo$421bo$421bo54b2o$475bo2bo$476b2o2$428b3o2$440bo$439bobo$439b2o2$402b2o$402b2o66bo$469bobo$469bo2bo$470b2o4$398b2o$398b2o40b2o$439bo2bo$440b2o$437bo$437bo$437bo2$439b3o2$408b2o$407bobo32b2o$407b2o33b2o9bo$453bo$453bo4$460b3o2$472bo$471bobo$471b2o2$434b2o$434b2o!

I think that I have figured out a way to made this work. I chose the third pair because it doesn't create any backwards gliders, and one of the signals is a gap in the second natural glider stream, which could be exploited into sending the initial signal to GPSE A without needing an extra glider by delaying when GPSE A's gliders reach the fixed circuitry so that the circuitry interprets this as a returning signal in the form of the absence of a second natural glider and sends a glider "back" to GPSE A. This would also let a construction glider from GPSE B through, but if you don't want that, you can simply make the gliders from GPSE B arrive late by the same amount of time. (There are more tricks along this line that could save some time at the beginning, but I won't bother describing them fully because they're straightforward.)
I have prepared a color-coded diagram of how the setup will work:

Universal constructor circuitry.png (101.29 KiB) Viewed 10570 times

When there are no returning signals, glider stream A₀ (the stream of second natural gliders from GPSE A) will collide with the gliders from GPSE B, creating a reaction that also destroys the gliders from glider stream C. (One possibility is that a kickback reaction will occur that reflects glider stream B back the way it came, causing it to mutually annihilate glider stream C.) In addition, glider streams D and E will destroy each other.
When a signal is returned in the form of a gap in glider stream A₀, a construction glider from glider stream B will be let through, and a glider from glider stream C will be sent to GPSE A.
When a signal is returned in the form of a glider on glider lane A₁, it will collide with a glider from glider stream D, preventing it from destroying a construction glider from glider stream E. The collision between gliders A₁ and D will, with the help of catalyst X, create a glider (notated D′) that will interact with the collision between glides A₀ and B in a way that prevents it from destroying glider C.

My design requires five GPSEs, which will cost twenty gliders (unless one uses a trick that I will explain later in this paragraph). Creating the target will cost two gliders, but one of them can be from GPSE B or E, so the target will only cost one additional glider. I'm not sure what the best catalyst would be, so I'm going to guess that it would cost three additional gliders with an uncertainty of two (i.e. anywhere from 1 to 5) for a total of 24±2 gliders. We might be able to decrease this by fixing an inefficiency in creating the GPSEs. Specifically, there are two pairs of GPSEs that are near each other, so it's possible that there's a four-glider collision that will create a GPSE and an escaping glider that can be used in the synthesis of the other GPSE. (There might be a way to synthesize two GPSEs with the right relative orientation and position with six gliders, but that's unlikely.) We might be able to synthesize zero, one, or both pairs of GPSEs with only seven gliders, reducing the total glider cost to 23±3.

As soon as I know what the best catalyst is and the separation and relative parity of glider streams B and E, I'll download Golly and put the GPSEs, catalyst, and target together, make sure that it works, and then put together a demonstration with the glider syntheses. Who knows what the best catalyst is and the relative timing and orientation of gliders A₁ and D necessary for it to work?



Edit: I just realized that the light blue line (for glider D′) should be dotted, not solid.



Another edit: I assembled some of the circuitry (specifically the extra target-creating glider and GPSEs A, B, and C) with LifeViewer.

Code: Select all

x = 4385, y = 4261, rule = B3/S23
43b2o$43b2o2$6b2o$5bobo$6bo$17bo$17bo$17bo4$24b3o$35b2o33b2o$35b2o32bobo$69b2o$38bo$38bo$38bo2$40b3o2$37b2o$36bo2bo$37b2o40b2o$79b2o4$7b2o$6bo2bo$7bobo$8bo66b2o$75b2o2$38b2o$37bobo$38bo$49bo$49bo$49bo$b2o$o2bo$b2o$56b3o$67b2o33b2o$67b2o32bobo$101b2o$70bo$70bo$70bo2$72b3o2$69b2o$68bo2bo$69b2o40b2o$111b2o4$39b2o$38bo2bo$39bobo$40bo66b2o$107b2o2$70b2o$69bobo$70bo$81bo$81bo$81bo$33b2o$32bo2bo$33b2o$88b3o$99b2o33b2o$99b2o32bobo$133b2o$102bo$102bo$102bo2$104b3o2$101b2o$100bo2bo$101b2o40b2o$143b2o4$71b2o$70bo2bo$71bobo$72bo66b2o$139b2o2$102b2o$101bobo$102bo$113bo$113bo$113bo$65b2o$64bo2bo$65b2o$120b3o$131b2o33b2o$131b2o32bobo$165b2o$134bo$134bo$134bo2$136b3o2$133b2o$132bo2bo$133b2o40b2o$175b2o4$103b2o$102bo2bo$103bobo$104bo66b2o$171b2o2$134b2o$133bobo$134bo$145bo$145bo$145bo$97b2o$96bo2bo$97b2o$152b3o$163b2o33b2o$163b2o32bobo$197b2o$166bo$166bo$166bo2$168b3o2$165b2o$164bo2bo$165b2o40b2o$207b2o4$135b2o$134bo2bo$135bobo$136bo66b2o$203b2o2$166b2o$165bobo$166bo$177bo$177bo3875bo$177bo3874bobo$129b2o3921bobo$128bo2bo3921bo59b2o$129b2o3973bo8b2o$184b3o3904bo11bobo4bo$195b2o33b2o3833bo24bobo10bobo4bo$195b2o32bobo3832bobo24b2o11bo5bo$229b2o3832bo2bo$198bo3865b2o40b3o$198bo$198bo2$200b3o2$197b2o$196bo2bo3888bo$197b2o40b2o3847bo$239b2o3847bo4$167b2o$166bo2bo$167bobo$168bo66b2o3845b3o$235b2o2$198b2o$197bobo$198bo$209bo$209bo3811bo$209bo3810bobo$161b2o3857bobo$160bo2bo3857bo59b2o$161b2o3909bo8b2o$216b3o3840bo11bobo4bo33b2o$227b2o33b2o3769bo24bobo10bobo4bo33bobo$227b2o32bobo3768bobo24b2o11bo5bo34b2o$261b2o3768bo2bo$230bo3801b2o40b3o$230bo$230bo3863b2o$4094b2o$232b3o2$229b2o3871b2o$228bo2bo3824bo45b2o$229b2o40b2o3783bo$271b2o3783bo4$199b2o$198bo2bo$199bobo$200bo66b2o3781b3o$267b2o2$230b2o$229bobo$230bo$241bo$241bo3747bo$241bo3746bobo$193b2o3793bobo$192bo2bo3793bo59b2o$193b2o3845bo8b2o$248b3o3776bo11bobo4bo33b2o$259b2o33b2o3705bo24bobo10bobo4bo33bobo$259b2o32bobo3704bobo24b2o11bo5bo34b2o$293b2o3704bo2bo$262bo3737b2o40b3o$262bo$262bo3799b2o$4062b2o$264b3o2$261b2o3807b2o$260bo2bo3760bo45b2o$261b2o40b2o3719bo$303b2o3719bo3$3982b2o$231b2o3749b2o$230bo2bo$231bobo$232bo66b2o3680b2o35b3o$299b2o3661b3o15bobo$3958b3o21bo$262b2o3694b3o$261bobo3694b3o$262bo3697bo4b3o$3961b3ob4o$3968b2o17bo$3963bo4bo17bobo$225b2o44b2o3694bo19b2o$224bo2bo42bobo3690bo53b2o$225b2o30b2o12bo3736bo8b2o$256bobo75bo3617b2o11b2o28bo11bobo4bo33b2o$257bo33b2o42b2o3613b2o3bo38bobo10bobo4bo33bobo$250b2o39b2o41b2o3614bo4bo8bo2bo27b2o11bo5bo34b2o$250bobo3697b2o12bob2o3b2o$252b2o40bo3658bob2o14bobo36b3o$250bobo41bo3658bob2o4bo10bo$250b2o42bo3659bo4bo3bo66b2o$3958bo2b3o66b2o$296b3o3659bob3o$3957b2o30bo$293b2o3662bo2bo27bobo47b2o$292bo2bo3662b3o28b2o47b2o$256bo36b2o3667b2o$255bob2o3703b3o$254bo10bo3696b2o$254b2o3bo4bobo$252b2obo3bo4b2o3684b2o$254b2o2b2o3690b2o3$251bo12bo$251b2o9b3o$251bo10b2o3bo$254b3o5b2o4b2o24b2o$254b3o7bob2o2bo4bo17bobo$254b2o10bo2b3o3bo18bo$266b2obo3bo2bo$267b2o4b2o3680bo$267bobo3b2o3679bobo$251b2o13bo2bo2b2o29b2o3650b2o$251b2o14bo2b3o29bobo3680b2o$269b2o2bo15b2o12bo3672bo8b2o$262b2o8bo15bobo3647bo24bo11bobo4bo33b2o$260b2o2bo4b2obo16bo3647bobo22bobo10bobo4bo33bobo$260b2o3bo3671b2o24b2o11bo5bo34b2o$261b2obo$263bo13b2o3699b3o$277b2o$3998b2o$263bobo3732b2o$264bo48b2o3611b2o$313b2o3611b2o12b2o15bo$306b2o3632b2o14bobo47b2o$306b2o3649b2o47b2o2$3944b2o$302b2o6bo3611b3o19b2o$302b2o4b6o3611bo5bobo$294bo13b2o2b2o7b2o3597b2obobo9bobo$293bobo25b2o3597b2o3b2o10bo$294b2o16bo3607b2ob3o5bo3bobo$308b2o2bo3609b4o5bob2o$308b2o3bo3608b2o22b2o$312bo3633b2o$310bobo$311bo2$309bo$309b2o13b3o$310b2o11bo2b2o$301b2o7b2o3626b2o$301b2o7b3o13bo3600bo10b2o$306bo16bo2bo3595b5o$310bo12bo3594b3obo2bobo$310bobo10bobo72bo3518bo6bo$322bo3bo72b2o3516bo4b2o3bo$322bo2b2o71b2o3517bo4bo3bobo$322b3o2bo3590b3o6bo$309b2o15bobo$309b2o15b2o3661bo$324bo3663bo$324bo2bo3660b3o$325b3o56$462bo$463b2o$462b2o3$3925bo$3924bo$3924b3o57$526bo$527b2o$526b2o3$3861bo$3860bo$3860b3o57$590bo$591b2o$590b2o3$3797bo$3796bo$3796b3o57$654bo$655b2o$654b2o3$3733bo$3732bo$3732b3o57$718bo$719b2o$718b2o3$3669bo$3668bo$3668b3o57$782bo$783b2o$782b2o3$3605bo$3604bo$3604b3o57$846bo$847b2o$846b2o3$3541bo$3540bo$3540b3o57$910bo$911b2o$910b2o3$3477bo$3476bo$3476b3o57$974bo$975b2o$974b2o3$3413bo$3412bo$3412b3o57$1038bo$1039b2o$1038b2o3$3349bo$3348bo$3348b3o57$1102bo$1103b2o$1102b2o3$3285bo$3284bo$3284b3o57$1166bo$1167b2o$1166b2o3$3221bo$3220bo$3220b3o57$1230bo$1231b2o$1230b2o3$3157bo$3156bo$3156b3o57$1294bo$1295b2o$1294b2o3$3093bo$3092bo$3092b3o57$1358bo$1359b2o$1358b2o3$3029bo$3028bo$3028b3o57$1422bo$1423b2o$1422b2o3$2965bo$2964bo$2964b3o57$1486bo$1487b2o$1486b2o3$2901bo$2900bo$2900b3o57$1550bo$1551b2o$1550b2o3$2837bo$2836bo$2836b3o57$1614bo$1615b2o$1614b2o3$2773bo$2772bo$2772b3o57$1678bo$1679b2o$1678b2o3$2709bo$2708bo$2708b3o57$1742bo$1743b2o$1742b2o3$2645bo$2644bo$2644b3o57$1806bo$1807b2o$1806b2o3$2581bo$2580bo$2580b3o57$1870bo$1871b2o$1870b2o3$2517bo$2516bo$2516b3o57$1934bo$1935b2o$1934b2o3$2453bo$2452bo$2452b3o57$1998bo$1999b2o$1998b2o3$2389bo$2388bo$2388b3o57$2062bo$2063b2o$2062b2o3$2325bo$2324bo$2324b3o57$2126bo$2127b2o$2126b2o3$2261bo$2260bo$2260b3o57$2190bo$2191b2o$2190b2o3$2197bo$2196bo$2196b3o67$2258bo$2257b2o$2257bobo62$2322bo$2321b2o$2321bobo62$2386bo$2385b2o$2385bobo62$2450bo$2449b2o$2449bobo62$2514bo$2513b2o$2513bobo62$2578bo$2577b2o$2577bobo62$2642bo$2641b2o$2641bobo62$2196bo509bo$2195b2o508b2o$2195bobo507bobo62$2770bo$2769b2o$2769bobo62$2834bo$2833b2o$2833bobo62$2898bo$2897b2o$2897bobo62$2962bo$2961b2o$2961bobo62$3026bo$3025b2o$3025bobo62$3090bo$3089b2o$3089bobo62$3154bo$3153b2o$3153bobo62$3218bo$3217b2o$3217bobo62$3282bo$3281b2o$3281bobo62$3346bo$3345b2o$3345bobo62$3410bo$3409b2o$3409bobo62$3474bo$3473b2o$3473bobo62$3538bo$3537b2o$3537bobo62$3602bo$3601b2o$3601bobo62$3666bo$3665b2o$3665bobo62$3730bo$3729b2o$3729bobo62$3794bo$3793b2o$3793bobo62$3858bo$3857b2o$3857bobo62$3922bo$3921b2o$3921bobo56$4058bo$4057bobo$4056b2ob2o$4056b2o16b2o$4062b2o9bo2bo$4056b3o2bo12bo2bo$3986bo73bob2o$3985b2o71bo2bo$3985bobo73bo11bo$4059b2o11b2o3bo$4073bo3b2o$4059bo13bobob2o3b2o$4057b2ob2o11bo3b2o3b2o$4060bo13b3o$4057bo16b3o$4059bo3$4073bo$4072b3o$4075bo$4072b2ob2o$4071b2ob2o13b2o$4062b2o7b2ob2o13bobo$4062b2o8bo2bo14bo$4073b3o5b2o$4073b2o6b2o3$4077b2o$4077b2o$4070b2o$4070b2o$4119b3o$4119bobo$4106b2o$4106b2o$4120bo2bo$4114bo5b2obo$4095bo18bo6bobo$4094bobo15b2obo6bo$4081bo12b2o15b2o$4080bobo28b3o2bo15b2o$4080b2o34b2o14b2o$4115bo$4109b3ob4o$4109b2ob3obo$4090bo17b2o4b2obo12bo$4089bobo25b4o5b2ob4o$4089b2o24bob5o3bo4b4o$4119bo2bo2bo3bo3b2o$4119b3o7bo3b2o$4119b2o11bo$4127bo2$4125bobo2b2o$4119b2o5bo2b3o$4118bobo6bo2b2o$4119bo7bobo$4127b3o$4090b2o$4089bo2bo$4090b2o2$4086b3o2$4090bo42b2o$4090bo42b2o$4090bo41bo$4133b2o$4050bo41b2o39b2o$4049b2o41b2o33bo$4049bobo74bobo$4113bo12b2o30b2o$4112bobo42bo2bo$4112b2o44b2o4$4122bo$4121bobo$4121b2o2$4084b2o$4084b2o66bo$4151bobo$4151bo2bo$4152b2o4$4080b2o$4080b2o40b2o$4121bo2bo$4122b2o2$4118b3o2$4122bo$4122bo$4122bo$4090b2o$4089bobo32b2o$4089b2o33b2o$4134b3o$4190b2o$4189bo2bo$4190b2o$4143bo$4143bo$4143bo$4154bo$4153bobo$4153b2o2$4116b2o$4116b2o66bo$4183bobo$4183bo2bo$4184b2o4$4112b2o$4112b2o40b2o$4153bo2bo$4154b2o2$4150b3o2$4154bo$4154bo$4154bo$4122b2o$4121bobo32b2o$4121b2o33b2o$4166b3o$4222b2o$4221bo2bo$4222b2o$4175bo$4175bo$4175bo$4186bo$4185bobo$4185b2o2$4148b2o$4148b2o66bo$4215bobo$4215bo2bo$4216b2o4$4144b2o$4144b2o40b2o$4185bo2bo$4186b2o2$4182b3o2$4186bo$4186bo$4186bo$4154b2o$4153bobo32b2o$4153b2o33b2o$4198b3o$4254b2o$4253bo2bo$4254b2o$4207bo$4207bo$4207bo$4218bo$4217bobo$4217b2o2$4180b2o$4180b2o66bo$4247bobo$4247bo2bo$4248b2o4$4176b2o$4176b2o40b2o$4217bo2bo$4218b2o2$4214b3o2$4218bo$4218bo$4218bo$4186b2o$4185bobo32b2o$4185b2o33b2o$4230b3o$4286b2o$4285bo2bo$4286b2o$4239bo$4239bo$4239bo$4250bo$4249bobo$4249b2o2$4212b2o$4212b2o66bo$4279bobo$4279bo2bo$4280b2o4$4208b2o$4208b2o40b2o$4249bo2bo$4250b2o2$4246b3o2$4250bo$4250bo$4250bo$4218b2o$4217bobo32b2o$4217b2o33b2o$4262b3o$4318b2o$4317bo2bo$4318b2o$4271bo$4271bo$4271bo$4282bo$4281bobo$4281b2o2$4244b2o$4244b2o66bo$4311bobo$4311bo2bo$4312b2o4$4240b2o$4240b2o40b2o$4281bo2bo$4282b2o2$4278b3o2$4282bo$4282bo$4282bo$4250b2o$4249bobo32b2o$4249b2o33b2o$4294b3o$4350b2o$4349bo2bo$4350b2o$4303bo$4303bo$4303bo$4314bo$4313bobo$4313b2o2$4276b2o$4276b2o66bo$4343bobo$4343bo2bo$4344b2o4$4272b2o$4272b2o40b2o$4313bo2bo$4314b2o2$4310b3o2$4314bo$4314bo$4314bo$4282b2o$4281bobo32b2o$4281b2o33b2o$4326b3o$4382b2o$4381bo2bo$4382b2o$4335bo$4335bo$4335bo$4346bo$4345bobo$4345b2o2$4308b2o$4308b2o66bo$4375bobo$4375bo2bo$4376b2o4$4304b2o$4304b2o40b2o$4345bo2bo$4346b2o2$4342b3o2$4346bo$4346bo$4346bo$4314b2o$4313bobo32b2o$4313b2o33b2o$4358b3o4$4367bo$4367bo$4367bo$4378bo$4377bobo$4377b2o2$4340b2o$4340b2o!

[calcyman]

I think that I have figured out a way to made this work.

This looks good!

In terms of cheap catalysts, there's a logic gate (discovered by Dave Greene and/or Chris Cain and used in the current RCT) with two perpendicular inputs (A, B) and three outputs (A AND NOT B, B AND NOT A, A AND B) which costs exactly one glider (which needs to arrive the first time A and B are both present).

Code: Select all

x = 564, y = 313, rule = LifeHistory
238.4B8.4B55.4B$239.4B8.4B53.4B$240.4B8.4B51.4B$241.4B8.4B49.4B$242.
4B8.4B47.4B$243.4B8.4B45.4B$244.4B8.4B43.4B$245.4B8.4B41.4B$246.4B8.
4B39.4B$247.4B8.4B37.4B$248.4B8.4B35.4B$249.4B8.4B33.4B$250.4B8.4B31.
4B$251.4B8.4B29.4B$252.4B8.4B27.4B$253.4B8.4B25.4B$254.4B8.4B23.4B$
255.4B8.4B21.4B$256.4B8.4B19.4B$257.4B8.4B17.4B$258.4B8.4B15.4B$259.
4B8.4B13.4B$260.4B8.4B4.B6.4B$261.4B8.4B2.3B4.4B$262.4B8.10B.4B$263.
4B8.13B$264.4B8.11B$265.4B8.9B$266.4B7.8B$267.4B7.6B$268.4B6.6B$269.
4B5.7B$270.4B3.9B$271.4B.11B$272.16B$273.16B$273.11B2.4B$272.12B3.4B$
271.14B3.4B$270.4B.9B5.4B$269.4B2.9B6.4B$268.5B.B.8B7.4B$267.16B9.4B$
266.17B10.4B$265.8B2.7B12.4B$264.8B5.5B13.4B$263.8B6.B2DB15.4B$262.8B
8.2D17.4B$261.8B29.4B$260.8B31.4B$259.8B33.4B$258.8B35.4B$257.8B37.4B
$256.8B39.4B$255.8B41.4B$254.8B43.4B$253.8B45.4B$252.8B47.4B$251.8B
49.4B$250.8B51.4B$249.8B53.4B$248.8B55.4B$247.8B57.4B$246.8B59.4B$
245.8B61.4B$244.8B63.4B$243.8B65.4B$242.8B67.4B$241.8B69.4B$240.8B71.
4B$239.8B73.4B$238.8B75.4B$237.8B77.4B$236.8B79.4B$235.8B81.4B$234.8B
83.4B$233.8B85.4B$232.8B87.4B$231.8B89.4B$230.8B91.4B$229.8B93.4B$
228.8B95.4B$227.8B97.4B$226.8B99.4B$225.8B101.4B$224.8B103.4B$223.8B
105.4B$222.8B107.4B$221.8B109.4B$220.8B111.4B$219.8B113.4B$218.8B115.
4B$217.8B117.4B$216.8B119.4B$215.8B121.4B$214.8B123.4B$213.8B125.4B$
212.8B127.4B$211.8B129.4B$210.8B131.4B$209.8B133.4B$208.8B135.4B$207.
8B137.4B$206.8B139.4B$205.8B141.4B$204.8B143.4B$203.8B145.4B$202.8B
147.4B$201.8B149.4B$200.8B151.4B$199.8B153.4B$198.8B155.4B$197.8B157.
4B$196.8B159.4B$195.8B161.4B$194.8B163.4B$193.8B165.4B$192.2A6B167.4B
$191.2B2A4B169.2B2A$190.2BA5B171.2A2B$189.8B173.BA2B$188.8B175.4B$
187.8B177.4B$186.8B179.4B$185.8B181.4B$184.8B183.4B$183.8B185.4B$182.
8B187.4B$181.8B189.4B$180.8B191.4B$179.8B193.4B$178.8B195.4B$177.8B
197.4B$176.8B199.4B$175.8B201.4B$174.8B203.4B$173.8B205.4B$172.8B207.
4B$171.8B209.4B$170.8B211.4B$169.8B213.4B$168.8B215.4B$167.8B217.4B$
166.8B219.4B$165.4B3CB221.4B$164.4B.2BC223.4B$163.4B3.C225.4B$162.4B
231.4B$161.4B233.4B$160.4B235.4B$159.4B237.4B$158.4B239.4B$157.4B241.
4B$156.4B243.4B$155.4B245.4B$154.4B247.4B$153.4B249.4B$152.4B251.4B$
151.4B253.4B$150.4B255.4B$149.4B257.4B$148.4B259.4B$147.4B261.4B$146.
4B263.4B$145.4B265.4B$144.4B267.4B$143.4B269.4B$142.4B271.4B$141.4B
273.4B$140.4B275.4B$139.4B277.4B$138.4B279.4B$137.4B281.4B$136.4B283.
4B$135.4B285.4B$134.4B287.4B$133.4B289.4B$132.4B291.4B$131.4B293.4B$
130.4B295.4B$129.4B297.4B$128.4B299.4B$127.4B301.2B2A$126.4B303.2A2B$
125.4B305.BA2B$124.4B307.4B$123.4B309.4B$122.4B311.4B$121.4B313.4B$
120.4B315.4B$119.4B317.4B$118.4B319.4B$117.4B321.4B$116.4B323.4B$115.
4B325.4B$114.4B327.4B$113.4B329.4B$112.4B331.4B$111.4B333.4B$110.4B
335.4B$109.4B337.4B$108.4B339.4B$107.4B341.4B$106.4B343.4B$105.4B345.
4B$104.4B347.4B$103.4B349.4B$102.4B351.4B$101.4B353.4B$100.4B355.4B$
99.4B357.4B$98.4B359.4B$97.4B361.4B$96.4B363.4B$95.4B365.4B$94.4B367.
4B$93.4B369.4B$92.4B371.4B$91.4B373.4B$90.4B375.4B$89.4B377.4B$88.4B
379.4B$87.4B381.4B$86.4B383.4B$85.4B385.4B$84.4B387.4B$83.4B389.4B$
82.4B391.4B$81.4B393.4B$80.4B395.4B$79.4B397.4B$78.4B399.4B$77.4B401.
4B$76.4B403.4B$75.4B405.4B$74.4B407.4B$73.4B409.4B$72.4B411.4B$71.4B
413.4B$70.4B415.4B$69.4B417.4B$68.4B419.4B$67.4B421.4B$66.4B423.4B$
65.4B425.4B$64.2A2B427.4B$63.2B2A429.4B$62.2BAB431.4B$61.4B433.4B$60.
4B435.4B$59.4B437.4B$58.4B439.4B$57.4B441.4B$56.4B443.4B$55.4B445.4B$
54.4B447.4B$53.4B449.4B$52.4B451.4B$51.4B453.4B$50.4B455.4B$49.4B457.
4B$48.4B459.4B$47.4B461.4B$46.4B463.4B$45.4B465.4B$44.4B467.4B$43.4B
469.4B$42.4B471.4B$41.4B473.4B$40.4B475.4B$39.4B477.4B$38.4B479.4B$
37.4B481.4B$36.4B483.4B$35.4B485.4B$34.4B487.4B$33.4B489.4B$32.4B491.
4B$31.4B493.4B$30.4B495.4B$29.4B497.4B$28.4B499.4B$27.4B501.4B$26.4B
503.4B$25.4B505.4B$24.4B507.4B$23.4B509.4B$22.4B511.4B$21.4B513.4B$
20.4B515.4B$19.4B517.4B$18.4B519.4B$17.4B521.4B$16.4B523.4B$15.4B525.
4B$14.4B527.4B$13.4B529.4B$12.4B531.4B$11.4B533.4B$10.4B535.4B$9.4B
537.4B$8.4B539.4B$7.4B541.4B$6.4B543.4B$5.4B545.4B$4.4B547.4B$3.4B
549.4B$2.4B551.4B$.4B553.4B$2A2B555.4B$B2A557.2B2A$AB559.2AB$562.BA!

This isn't a drop-in replacement for Catalyst X, because the inputs need to be perpendicular, but it might be possible to rearrange your design to use this instead of Catalyst X?

[MathAndCode]

This isn't a drop-in replacement for Catalyst X, because the inputs need to be perpendicular, but it might be possible to rearrange your design to use this instead of Catalyst X?

Unless there's a Spartan way to modify this to send a signal back in the direction that one of the gliders came from, rearranging only that part seems unlikely to work because a perpendicular collision between gliders A₁ and D would mandate that either GPSE D would crowd out GPSEs B and E or glider stream D would pass close enough to the target to potentially interfere with it. However, I'm thinking that if glider stream B comes from the A₁ side instead of the A₀ side, along with other changes, there might be a way to make the entire circuitry work. I'll think about it.

Edit: Actually, if we put one of GPSEs B, D, and E far enough behind the other two but synthesize it much earlier so that the timing is correct, we might be able to make it work. Regardless, I suspect that having the construction gliders come from the A₁ will be easier because the information has to travel from the A₁ side to the A₀ side. With construction gliders coming from the A₁ side, this might be possible with only four GPSEs, athough we'll need to use the logic gate to shift one of the construction gliders in order to make it work.

Another edit: Actually, we don't need the logic gate if we are allowed to let A₀ gliders through in the event of an A₁ signal. I thought of this earlier today but dismissed it because it would allow escaping gliders. However, I just realized that there's probably a four-glider collision that would both make GPSE C and ash that could absorb these A₀ gliders without emitting more gliders, so if there's four-GPSE circuitry that works without anything extra (which is probably the biggest if), and we manage to synthesize the two construction GPSEs with only seven gliders, then the total glider cost will only be sixteen. (We might be able to make the target by colliding a combination of gliders that wouldn't occur in the circuitry once all four glider streams have arrived, but that seems pretty unlikely to me.)

Yet another edit: Here is a partial demonstration of a possible 4-GPSE circuitry mechanism. The GPSEs included are A and B, and the lone gliders are C and E (the latter of which shall be renamed to D as soon as we ensure that we only need four GPSEs). The timing of glider C isn't correct, but it's on the right lane and an even number of full diagonals from where it should be, which I think means that this can be corrected by making glider B collide with glider A₀ slightly sooner in the same way. I plan to correct it, but in case something goes wrong, I'm posting this now so I don't lose it.

Code: Select all

x = 4449, y = 2535, rule = B3/S23
325$2180bo$2178bobo$2179b2o7$2179bo$2179bo$2178bobo2bo$2181bo$2181bo2$2179b2o$2174b2o3b2o$2175b2o$2174bo39$2129b2o97b3o$2130b2o96bo$2129bo99bo62$2065b2o225b3o$2066b2o224bo$2065bo227bo62$2001b2o353b3o$2002b2o352bo$2001bo355bo62$1937b2o481b3o$1938b2o480bo$1937bo483bo62$1873b2o609b3o$1874b2o608bo$1873bo611bo62$1809b2o737b3o$1810b2o736bo$1809bo739bo62$1745b2o865b3o$1746b2o864bo$1745bo867bo62$1681b2o993b3o$1682b2o992bo$1681bo995bo62$1617b2o1121b3o$1618b2o1120bo$1617bo1123bo62$1553b2o1249b3o$1554b2o1248bo$1553bo1251bo62$1489b2o1377b3o$1490b2o1376bo$1489bo1379bo62$1425b2o1505b3o$1426b2o1504bo$1425bo1507bo62$1361b2o1633b3o$1362b2o1632bo$1361bo1635bo62$1297b2o1761b3o$1298b2o1760bo$1297bo1763bo62$1233b2o1889b3o$1234b2o1888bo$1233bo1891bo62$1169b2o2017b3o$1170b2o2016bo$1169bo2019bo62$1105b2o2145b3o$1106b2o2144bo$1105bo2147bo62$1041b2o2273b3o$1042b2o2272bo$1041bo2275bo62$977b2o2401b3o$978b2o2400bo$977bo2403bo62$913b2o2529b3o$914b2o2528bo$913bo2531bo62$849b2o2657b3o$850b2o2656bo$849bo2659bo62$785b2o2785b3o$786b2o2784bo$785bo2787bo62$721b2o2913b3o$722b2o2912bo$721bo2915bo62$657b2o3041b3o$658b2o3040bo$657bo3043bo62$593b2o3169b3o$594b2o3168bo$593bo3171bo62$529b2o3297b3o$530b2o3296bo$529bo3299bo62$465b2o3425b3o$466b2o3424bo$465bo3427bo21$3989b3o$3993bo$3993b2o13bo$3993bo2bo11bo$3994bobo11bo$3994bo$3993b2o14bo$3992bobo13bobo$3994b2o11bo$3991b2o14bo2bo$3993bo12b2o7bo$4005b3o2b2o3bo$4006b2obobo3bo$4006bo2bo2bo$4007b6o4b3o$4008b3obo$4015bo8b2o$4015bo8b2o$4015bo$4002bo$4001bo$4002bo3$4032b2o$4032b2o3$4004b2o$4004b2o4$4008b2o2$4011bo14b2o11b2o$4011bo13bo2bo10bobo$4007bo2bo19b2o8bo$4006bo20b2ob3o$4006b2o10bo7b2o2bobo$4006b2o9bobo5b3o$401b2o3553b3o48b2o8bo2bo6bo$402b2o3552bo50b2obo7b2o$401bo3555bo51b2o5$4056b2o$4056b2o3$4045bo$4044bobo$460bo3570bo12b2o30b2o$459bobo3568bobo42bo2bo$4030b2o44b2o$458bo2bo$458b2o$458bo$443b2o3595bo$443b2o3594bobo$4039b2o2$460b2o$459bo3610bo$459b2o3608bobo$459b3o3607bo2bo$435b2o23b2o3608b2o$435b2o21bob3o$457bo3bo$456bo2bo$457b3o$457b2o3581b2o$429bo10b2o2b3o3592bo2bo$428b3o11bobobo3593b2o$427bob3o4bobo7bo3590bo$436bobo3598bo$435bo4b2o3595bo$431bo5b4o$430b2o5b3o15b2o3582b3o$430bo24b2o$432bo3624b2o$432bo3609b2o12b3o$4042b2o10b2ob2o$4054bobo3b6o$367b2o47b2o3636bo2bo3b5o42b2o$367b2o47bobo14b2o3620bo5b2o44bo2bo$417bo15b2o12b2o3609b3o47b2o$447b2o3609b3o$375b2o$375b2o$395bo3676bo$395bo3675bobo$395bo3675b2o$356b2o40bo11b2o24b2o$356bobo32b3o3bobo10bobo22bobo3596b2o$357b2o38bobo11bo24bo3597b2o66bo$388b2o8bo3702bobo$388b2o3711bo2bo$418b2o3682b2o$418bobo$419bo2$4030b2o$4030b2o40b2o$4071bo2bo$4072b2o$4069bo$4069bo$4069bo2$423b2o3646b3o$423b2o$4040b2o$4039bobo32b2o$4039b2o33b2o9bo$4085bo$335b2o47b2o3699bo54b2o$335b2o47bobo3752bo2bo$385bo3754b2o2$343b2o3747b3o$343b2o48b3o$363bo30b2o3708bo$363bo3739bobo$363bo27bo4bo25bo3680b2o$324b2o40bo11b2o17bobo21bobo$324bobo32b3o3bobo10bobo18bo21bobo3642b2o$325b2o38bobo11bo14bo4bo14b2o6bo3643b2o66bo$356b2o8bo27bo3bo15b2o3717bobo$356b2o37b3o3735bo2bo$4134b2o3$411b3o$398b2o11bob2o3647b2o$398b2o12bo3bo3645b2o40b2o$412bobo2bo3685bo2bo$412b3o2bo3686b2o$355bo3745bo$355bo3745bo$355bo3745bo2$4103b3o2$4072b2o$4071bobo32b2o$4071b2o33b2o9bo$349b3o3765bo$303b2o3812bo54b2o$303b2o3866bo2bo$4172b2o2$311b2o3811b3o$311b2o$331bo3804bo$331bo41b2o3760bobo$331bo40bo2bo3759b2o$292b2o40bo11b2o24bobo$292bobo32b3o3bobo10bobo24bo3724b2o$293b2o38bobo11bo3750b2o66bo$324b2o8bo3830bobo$324b2o59bo3779bo2bo$384bobo3779b2o$384bobo$385bo2$4094b2o$4094b2o40b2o$4135bo2bo$4136b2o$323bo3809bo$323bo3809bo$323bo3809bo2$4135b3o2$4104b2o$4103bobo32b2o$4103b2o33b2o9bo$317b3o3829bo$271b2o3876bo54b2o$271b2o3930bo2bo$4204b2o2$279b2o3875b3o$279b2o$299bo3868bo$299bo41b2o3824bobo$299bo40bo2bo3823b2o$260b2o40bo11b2o24bobo$260bobo32b3o3bobo10bobo24bo3788b2o$261b2o38bobo11bo3814b2o66bo$292b2o8bo3894bobo$292b2o59bo3843bo2bo$352bobo3843b2o$352bobo$353bo2$4126b2o$4126b2o40b2o$4167bo2bo$4168b2o$291bo3873bo$291bo3873bo$291bo3873bo2$4167b3o2$4136b2o$4135bobo32b2o$4135b2o33b2o9bo$285b3o3893bo$4181bo54b2o$4235bo2bo$4236b2o2$4188b3o2$267bo3932bo$267bo41b2o3888bobo$267bo40bo2bo3887b2o$270bo11b2o24bobo$263b3o3bobo10bobo24bo3852b2o$269bobo11bo3878b2o66bo$260b2o8bo3958bobo$260b2o59bo3907bo2bo$320bobo3907b2o$320bobo$321bo2$4158b2o$4158b2o40b2o$4199bo2bo$4200b2o$4197bo$4197bo$4197bo2$4199b3o2$4168b2o$4167bobo32b2o$4167b2o33b2o9bo$4213bo$4213bo54b2o$4267bo2bo$4268b2o2$4220b3o2$4232bo$4231bobo$4231b2o2$4194b2o$4194b2o66bo$4261bobo$4261bo2bo$4262b2o4$4190b2o$4190b2o40b2o$4231bo2bo$4232b2o$4229bo$4229bo$4229bo2$4231b3o2$4200b2o$4199bobo32b2o$4199b2o33b2o9bo$4245bo$4245bo54b2o$4299bo2bo$4300b2o2$4252b3o2$4264bo$4263bobo$4263b2o2$4226b2o$4226b2o66bo$4293bobo$4293bo2bo$4294b2o4$4222b2o$4222b2o40b2o$4263bo2bo$4264b2o$4261bo$4261bo$4261bo2$4263b3o2$4232b2o$4231bobo32b2o$4231b2o33b2o9bo$4277bo$4277bo54b2o$4331bo2bo$4332b2o2$4284b3o2$4296bo$4295bobo$4295b2o2$4258b2o$4258b2o66bo$4325bobo$4325bo2bo$4326b2o4$4254b2o$4254b2o40b2o$4295bo2bo$4296b2o$4293bo$4293bo$4293bo2$4295b3o2$4264b2o$4263bobo32b2o$4263b2o33b2o9bo$4309bo$4309bo4$4316b3o2$4328bo$4327bobo$4327b2o2$4290b2o$4290b2o!

Fourth edit: Here's the mechanism with all four GPSEs.

Code: Select all

x = 4191, y = 4198, rule = B3/S23
42bo$41bobo$41bobo$42bo2$4bo$3bobo24bo$3b2o24bobo$29bo2bo$30b2o7$7bo$7bo$7bo7$11b3o7$74bo$73bobo$73bobo$13b2o59bo$13b2o8bo$17bo4bobo11bo$17bo4bobo10bobo24bo$17bo5bo11b2o24bobo$61bo2bo$19b3o40b2o2$2o$2o4$39bo$39bo$39bo7$43b3o7$106bo$105bobo$105bobo$45b2o59bo$45b2o8bo$14b2o33bo4bobo11bo$13bobo33bo4bobo10bobo24bo$13b2o34bo5bo11b2o24bobo$93bo2bo$51b3o40b2o2$32b2o$32b2o3$24b2o$24b2o45bo$71bo$71bo7$75b3o7$138bo$137bobo$137bobo$77b2o59bo$77b2o8bo$46b2o33bo4bobo11bo$45bobo33bo4bobo10bobo24bo$45b2o34bo5bo11b2o24bobo$125bo2bo$83b3o40b2o2$64b2o$64b2o3$56b2o$56b2o45bo$103bo$103bo7$107b3o7$170bo$169bobo$169bobo$109b2o59bo$109b2o8bo$78b2o33bo4bobo11bo$77bobo33bo4bobo10bobo24bo$77b2o34bo5bo11b2o24bobo$157bo2bo$115b3o40b2o2$96b2o$96b2o3$88b2o$88b2o45bo$135bo$135bo7$139b3o7$202bo$201bobo$201bobo$141b2o59bo$141b2o8bo$110b2o33bo4bobo11bo$109bobo33bo4bobo10bobo24bo$109b2o34bo5bo11b2o24bobo$189bo2bo$147b3o40b2o2$128b2o$128b2o3$120b2o$120b2o45bo$167bo$167bo7$171b3o7$234bo$233bobo$233bobo$173b2o59bo$173b2o8bo$142b2o33bo4bobo11bo$141bobo33bo4bobo10bobo24bo$141b2o34bo5bo11b2o24bobo$221bo2bo$179b3o40b2o2$160b2o$160b2o3$152b2o$152b2o45bo$199bo$199bo7$203b3o7$266bo$265bobo$265bobo$205b2o59bo$205b2o8bo$174b2o33bo4bobo11bo$173bobo33bo4bobo10bobo24bo$173b2o34bo5bo11b2o24bobo$253bo2bo$211b3o40b2o2$192b2o$192b2o3$184b2o$184b2o45bo$231bo$231bo7$235b3o7$298bo$297bobo$297bobo$237b2o59bo$237b2o8bo$206b2o33bo4bobo11bo$205bobo33bo4bobo10bobo24bo$205b2o34bo5bo11b2o24bobo$285bo2bo$243b3o40b2o2$224b2o$224b2o3$216b2o$216b2o45bo$263bo$263bo3$321bo$321bo$321bo2$267b3o52b2o$294bo25b2o2bo$292b2ob2o21b2o4b2o3b2o$292bo4bo14bo5bo6bo3b2o$311bobo3bo7bo$303bo7bobo2bo3bo3bo$293b2ob2o6b2o6bo4b3ob3o$295bo$302bo$302bo11bo$269b2o42bobo$269b2o8bo33bo21b2o$238b2o33bo4bobo11bo23bo10b3o5b2o$237bobo33bo4bobo10bobo23bo9bo3b2o$237b2o34bo5bo11b2o18b2o3bo9bo6bo$309b2o3b2o9bo2b2o3bo$275b3o31bo2b2o12b2o7bo$309b3o18bob4o$256b2o72b3o$256b2o2$298bo$248b2o47bobo$248b2o47b2o5$336b2o$336b2o10$332bo$331bobo$331b2o$301b2o$301b2o8bo$270b2o33bo4bobo11bo24bo$269bobo33bo4bobo10bobo22bobo$269b2o34bo5bo11b2o24b2o2$307b3o2$288b2o$288b2o$360b2o$330bo15b2o12b2o$280b2o47bobo14b2o$280b2o47b2o23b2o$353b2obo$353bo2bo$348b3ob2ob2o$351b2o2bo$342bo5bo5bo13b2o$342b4o4bo2bo14b2o$341bob4o4b2o$342b2o12b3o$342b2obo9bo3bo$344bo$360bo$355b5o$356bo3$370bob3o$348b2o19bob3obo$348b2o7b2o9bo2bo3bo$356b3o13bo$355bo3bo9bo4bo$354bo2b3o10b4o$355bo3bo$356b3o14bo$372bobo$371bo3bo$372bobo$373bo11$310bo$308bobo$309b2o62$374bo$372bobo$373b2o62$438bo$436bobo$437b2o62$502bo$500bobo$501b2o62$566bo$564bobo$565b2o62$630bo$628bobo$629b2o62$694bo$692bobo$693b2o62$758bo$756bobo$757b2o62$822bo$820bobo$821b2o62$886bo$884bobo$885b2o62$950bo$948bobo$949b2o62$1014bo$1012bobo$1013b2o62$1078bo$1076bobo$1077b2o62$1142bo$1140bobo$1141b2o62$1206bo$1204bobo$1205b2o62$1270bo$1268bobo$1269b2o62$1334bo$1332bobo$1333b2o62$1398bo$1396bobo$1397b2o62$1462bo$1460bobo$1461b2o62$1526bo$1524bobo$1525b2o62$1590bo$1588bobo$1589b2o62$1654bo$1652bobo$1653b2o62$1718bo$1716bobo$1717b2o62$1782bo$1780bobo$1781b2o62$1846bo$1844bobo$1845b2o62$1910bo$1908bobo$1909b2o62$1974bo$1972bobo$1973b2o62$2038bo$2036bobo$2037b2o7$2037bo$2037bo$2036bobo2bo$2039bo$2039bo2$2037b2o$2032b2o3b2o$2033b2o$2032bo39$1987b2o97b3o$1988b2o96bo$1987bo99bo21$1968b2o$1969b2o$1968bo39$1923b2o225b3o$1924b2o224bo$1923bo227bo21$1904b2o$1905b2o$1904bo39$1859b2o353b3o$1860b2o352bo$1859bo355bo21$1840b2o$1841b2o$1840bo39$1795b2o481b3o$1796b2o480bo$1795bo483bo21$1776b2o$1777b2o$1776bo39$1731b2o609b3o$1732b2o608bo$1731bo611bo21$1712b2o$1713b2o$1712bo39$1667b2o737b3o$1668b2o736bo$1667bo739bo21$1648b2o$1649b2o$1648bo39$1603b2o865b3o$1604b2o864bo$1603bo867bo21$1584b2o$1585b2o$1584bo39$1539b2o993b3o$1540b2o992bo$1539bo995bo21$1520b2o$1521b2o$1520bo39$1475b2o1121b3o$1476b2o1120bo$1475bo1123bo21$1456b2o$1457b2o$1456bo39$1411b2o1249b3o$1412b2o1248bo$1411bo1251bo21$1392b2o$1393b2o$1392bo39$1347b2o1377b3o$1348b2o1376bo$1347bo1379bo21$1328b2o$1329b2o$1328bo39$1283b2o1505b3o$1284b2o1504bo$1283bo1507bo21$1264b2o$1265b2o$1264bo39$1219b2o1633b3o$1220b2o1632bo$1219bo1635bo21$1200b2o$1201b2o$1200bo39$1155b2o1761b3o$1156b2o1760bo$1155bo1763bo21$1136b2o$1137b2o$1136bo39$1091b2o1889b3o$1092b2o1888bo$1091bo1891bo21$1072b2o$1073b2o$1072bo39$1027b2o2017b3o$1028b2o2016bo$1027bo2019bo21$1008b2o$1009b2o$1008bo39$963b2o2145b3o$964b2o2144bo$963bo2147bo21$944b2o$945b2o$944bo39$899b2o2273b3o$900b2o2272bo$899bo2275bo21$880b2o$881b2o$880bo39$835b2o2401b3o$836b2o2400bo$835bo2403bo21$816b2o$817b2o$816bo39$771b2o2529b3o$772b2o2528bo$771bo2531bo21$752b2o$753b2o$752bo39$707b2o2657b3o$708b2o2656bo$707bo2659bo21$688b2o$689b2o$688bo39$643b2o2785b3o$644b2o2784bo$643bo2787bo21$624b2o$625b2o$624bo39$579b2o2913b3o$580b2o2912bo$579bo2915bo21$560b2o$561b2o$560bo39$515b2o3041b3o$516b2o3040bo$515bo3043bo21$496b2o$497b2o$496bo39$451b2o3169b3o$452b2o3168bo$451bo3171bo21$432b2o$433b2o$432bo39$387b2o3297b3o$388b2o3296bo$387bo3299bo21$368b2o$369b2o$368bo16$264bo$263bobo$262b2ob2o$262bo2bo$261b3o$261bobo$261b2o$247b2o12b2o$247b2o3$264bo$263bo$262b2o$262b3o3$261b3o$260bo4bo$244b2o14bo3b2o$244b2o14b4o$243b2o$244b4obo3579bo6b2o$246b2o2bo72b2o3425b3o75bobo3bo3bo$324b2o3424bo76bo3bobo3b2o$323bo3427bo76bobo2bobob2o$249bo3bo3575bo3bo2b2o$250bo2bo5b2o3572bo4bo$250bo3bo4b2o3573bo2bo10b2o$250b2ob2o3581bo11b2o$250bo2b2o$223b2o26b3o$223b2o27bo3$235bo$234bobo3619b2o$235b2o3606bo12b2o$3832b3o7bo2bo$3831bobob2o5bo3bo$3831bobob2o5bo3bo$3831bo3bo5b2o3bo4b3o$214b2o3616bobo7bo2bo4b2o2bo$212b4o27b2o3588bo15bo3b2o$211bo2b2o19bob4ob3o3603bo2b3o$211b3o3b2o16b2o4b2o3604bo2b2o$214bob2o7b2o8bo3bob2o61b2o3541bo2bo$212bo7bo4b2o9b3obo64b2o3541bo2bo11b2o$212bo8bo82bo3531b2o13bo11bobo$217b2ob3o3613b2o11bobo12bo$208bo9bobo3634b2o$209b3o8bo3626bo7b2o$209b3o4bobo3626bob2o$3844bo2b2o$3845b4o$3845b2ob2o$239b2o3606bo$238bo2bo$239b2o2$242b3o3635b2o$3880b2o15b2o$224b2o14bo3651b2o3b2o$191b2o31bobo13bo3651bo$191b2o31bo15bo3628bo22bob2o$3868bobo20b2o3bo$237b2o3616bo12b2o21bo4bo$203bo33b2o3615bobo34b2o13b2o$202bobo3649b2o38bo2bo8b2o$171b2o30b2o12bo3676bo2bo$170bo2bo42bobo3674bo2b2o$171b2o44b2o3674bobo$3864bo29bo10b3o$3863bobo38bo2b2o$3863b2o38bo5bo$208bo3694bo5bo$207bobo3693bo4bo2b3o$208b2o3694bo3bo$3903bo3bo$245b2o3656bo2b2o$178bo66b2o3649bo6bobo$177bobo3715bobo6bo$176bo2bo3714bo4bo$177b2o49b4o3662bo5bo$228bo3bo3660bo4b2o4b2o$228bo4bobo3628b2o27bobo7bo2bo$229bo4b3o3626bo2bo25bo2bo8b2o$229bo8bo20b2o3553b3o47b2o26bobo$207b2o21bobobo4bo4bo7bo7b2o3552bo46bo30b3o$206bo2bo20bo8bobo2bo7b2o5bo3555bo45bo$207b2o26b2ob2obo12bo3606bo$229b3o4b2o3bo9bob2o$210b3o30b4o4bo2bo3608b3o37bo$243bo3bo3b2ob2o3647bo$208bo37b2o3656bo$208bo32b2o2b2o3619b2o32b2o$208bo34bo3622b2o2$205b2o3680bo44b2o$205b2o3679bobo42bo2bo$194b3o3689b2o15bo2bo25b2o$139b2o3762bo3bo$138bo2bo3760bo4bo$139b2o3762bo4bo$187bo138bo3569bo6bo3bo$187bo137bobo3567bobo8b2o$187bo120b3o13bo3bo3566b2o$176bo138bo8bo3bo$175bobo134b3ob2o4b3obobo3529b2o$176b2o134b2obo5bo2bob2o3530b2o66bo$240b2o70bo8bobo3601bobo$213b2o26b2o57b2o5bo2bo11b2o3601bo2bo$146bo66b2o25bo59b2o6b3o3615b2o$145bobo$144bo2bo$145b2o$237b2o61bo3553b2o$234b2obobo60b2o3552b2o40b2o$234b2obo2bo55b2obobo3593bo2bo$217b2o15b2obob2o54b2ob3o3595b2o$175b2o40b2o16bobo58b2o3bo3591bo$174bo2bo57b2o60bo3bo3591bo$175b2o121bo2bo3591bo$234bo65bo4b2o13b2o$178b3o52b3o69b2o13b2o3573b3o$232bo3b2o10b2o$176bo56b2o13b2o3614b2o$176bo57bo33bo37b3o3554bobo32b2o$176bo56b2o3bo29bo15b2o20b2o3555b2o33b2o9bo$207b2o24b2obobo29bo3640bo$173b2o32bobo23bo2bob2o31bo9b2o3626bo54b2o$173b2o33b2o27bo2bo23b3o3bobo7b2ob3o3677bo2bo$162b3o75b2o28bobo7bo3683b2o$107b2o128bo2bo20b2o8bo$106bo2bo126bo2bo21b2o17bo2b3o3630b3o$107b2o127bo2bo2b2o36b2o9b2o$155bo81bobo42b3o6bobo3634bo$155bo82bob2o40b3o7bo3634bobo$155bo85bobo3683b2o$144bo94b2o2b3o$143bobo91b5obo2bo3643b2o$144b2o91bo3652b2o66bo$237bob2o3716bobo$181b2o63bo3710bo2bo$114bo66b2o61b2o3712b2o$113bobo165b2o$112bo2bo150bo14b2o$113b2o149bobo29b2o$265b2o29b2o3588b2o$3886b2o40b2o$278bobo3646bo2bo$185b2o92bo3648b2o$143b2o40b2o93bo3644bo$142bo2bo62b2o47b2o18bo2b4o3641bo$143b2o63b2o47bobo17bobobo3643bo$258bo19bo3bob2o$146b3o134b2o3642b3o$216b2o$144bo71b2o64bobo3611b2o$144bo91bo3658bobo32b2o$144bo91bo39b2o4b3o3610b2o33b2o9bo$175b2o59bo38bo2bo4bo3657bo$141b2o32bobo19b2o40bo11b2o23bobo3662bo54b2o$141b2o33b2o19bobo32b3o3bobo10bobo23bo3717bo2bo$130b3o65b2o38bobo11bo3743b2o$75b2o152b2o8bo$74bo2bo151b2o3717b3o$75b2o182b2o$123bo135bobo3698bo$123bo136bo3698bobo$123bo3835b2o$112bo$111bobo3808b2o$112b2o3808b2o66bo$3989bobo$149b2o77bo3760bo2bo$82bo66b2o77bo3761b2o$81bobo144bo$80bo2bo$81b2o181b2o$264b2o3652b2o$3918b2o40b2o$3959bo2bo$153b2o3805b2o$111b2o40b2o67b3o3732bo$110bo2bo62b2o3779bo$111b2o63b2o3779bo2$114b3o3842b3o$184b2o$112bo71b2o3742b2o$112bo91bo3722bobo32b2o$112bo91bo41b2o3679b2o33b2o9bo$143b2o59bo40bo2bo3724bo$109b2o32bobo19b2o40bo11b2o24bobo3725bo54b2o$109b2o33b2o19bobo32b3o3bobo10bobo24bo3780bo2bo$98b3o65b2o38bobo11bo3807b2o$197b2o8bo$197b2o59bo3721b3o$257bobo$91bo165bobo3732bo$91bo166bo3732bobo$91bo3899b2o$80bo$79bobo3872b2o$80b2o3872b2o66bo$4021bobo$117b2o77bo3824bo2bo$117b2o77bo3825b2o$196bo3$3950b2o$3950b2o40b2o$3991bo2bo$121b2o3869b2o$79b2o40b2o67b3o3796bo$78bo2bo62b2o3843bo$79b2o63b2o3843bo2$82b3o3906b3o$152b2o$80bo71b2o3806b2o$80bo91bo3786bobo32b2o$80bo91bo41b2o3743b2o33b2o9bo$111b2o59bo40bo2bo3788bo$77b2o32bobo19b2o40bo11b2o24bobo3789bo54b2o$77b2o33b2o19bobo32b3o3bobo10bobo24bo3844bo2bo$134b2o38bobo11bo3871b2o$165b2o8bo$165b2o59bo3785b3o$225bobo$225bobo3796bo$226bo3796bobo$4023b2o2$3986b2o$3986b2o66bo$4053bobo$164bo3888bo2bo$164bo3889b2o$164bo3$3982b2o$3982b2o40b2o$4023bo2bo$4024b2o$158b3o3860bo$112b2o3907bo$112b2o3907bo2$4023b3o$120b2o$120b2o3870b2o$140bo3850bobo32b2o$140bo41b2o3807b2o33b2o9bo$140bo40bo2bo3852bo$101b2o40bo11b2o24bobo3853bo54b2o$101bobo32b3o3bobo10bobo24bo3908bo2bo$102b2o38bobo11bo3935b2o$133b2o8bo$133b2o59bo3849b3o$193bobo$193bobo3860bo$194bo3860bobo$4055b2o2$4018b2o$4018b2o66bo$4085bobo$132bo3952bo2bo$132bo3953b2o$132bo3$4014b2o$4014b2o40b2o$4055bo2bo$4056b2o$126b3o3924bo$4053bo$4053bo2$4055b3o2$4024b2o$108bo3914bobo32b2o$108bo41b2o3871b2o33b2o9bo$108bo40bo2bo3916bo$111bo11b2o24bobo3917bo54b2o$104b3o3bobo10bobo24bo3972bo2bo$110bobo11bo3999b2o$101b2o8bo$101b2o59bo3913b3o$161bobo$161bobo3924bo$162bo3924bobo$4087b2o2$4050b2o$4050b2o66bo$4117bobo$4117bo2bo$4118b2o4$4046b2o$4046b2o40b2o$4087bo2bo$4088b2o$4085bo$4085bo$4085bo2$4087b3o2$4056b2o$4055bobo32b2o$4055b2o33b2o9bo$4101bo$4101bo54b2o$4155bo2bo$4156b2o2$4108b3o2$4120bo$4119bobo$4119b2o2$4082b2o$4082b2o66bo$4149bobo$4149bo2bo$4150b2o4$4078b2o$4078b2o40b2o$4119bo2bo$4120b2o$4117bo$4117bo$4117bo2$4119b3o2$4088b2o$4087bobo32b2o$4087b2o33b2o9bo$4133bo$4133bo54b2o$4187bo2bo$4188b2o2$4140b3o2$4152bo$4151bobo$4151b2o2$4114b2o$4114b2o66bo$4181bobo$4181bo2bo$4182b2o4$4110b2o$4110b2o40b2o$4151bo2bo$4152b2o$4149bo$4149bo$4149bo2$4151b3o2$4120b2o$4119bobo32b2o$4119b2o33b2o9bo$4165bo$4165bo4$4172b3o2$4184bo$4183bobo$4183b2o2$4146b2o$4146b2o!

A gap in glider stream A₀ lets gliders B, C, and E through, and if glider B is deleted beforehand, will hopefully will be done by glider A₁ (or will be done by glider A₁ for at least one of the other two timing pairs with the same set of return signals), then gliders A₀ (which can hopefully be cleanly absorbed by the ash from GPSE C's creation), C, and E will be let through. Even if this particular pair of construction signals isn't universal, or there's no way to make glider A₁ cleanly delete glider B with the relative timing that this particular circuitry uses, this is a valid proof of concept, so there's likely another 4-GPSE solution that doesn't require any logic gates besides the glider streams themselves.

Fifth edit: I tested the three timing pairs. For two of them, glider A₁ doesn't collide with any other gliders. For one of them, glider A₁ collides with the correct glider but makes a pond instead of nothing. However, this doesn't invalidate the concept; it merely means that we'll have to arrange the glider streams differently.

Sixth edit: While I initially used the longest-lasting 90° two-glider collision that produces nothing, I just realized that using a collision that produces a still life (or blinker) that is then destroyed by gliders C and E will probably make finding a universal spacing-parity combination that works and adjusting the timing much easier.

Seventh edit: One of the two-glider collisions that creates a blinker seems to work.

Code: Select all

x = 13, y = 20, rule = LifeHistory
6.A$7.A$5.3A6$7.A$6.BAB$6.BAB$5.6B$5.5B2D$5.5BD.D$5.5BDB$3A.2B3D3B$2.A2.3BD3B$.A4.BD3B$6.5B$8.2B!

I intend to post a more complete version shortly.

Eighth edit: I just realized something: Because glider A₀ is traveling northwest and glider B is traveling northeast, gliders A₀ and B must have the same height in order to collide, and because glider A₁ is traveling northwest and glider B is traveling northeast, gliders A₁ and B must have the same height in order to collide. This means that gliders A₀ and A₁ must have about the same height. This means the signal pair that I have been trying to use so far will not work, but there is an alternative where gliders A₀ and A₁ have close enough height. I didn't use it before because one of the signals also causes a glider to be sent backwards, but as long as that isn't the first signal, the glider doesn't escape (although it will still cause an inconvenience).

Here is a way where one glider on a particular lane and timing results in an glider sent back on a lane farther to the outside than the lane for the second natural gliders, and the conjugate signal/glider results in a gap in the stream of second natural gliders, which could be fed into some sort of NOT gate.

Code: Select all

x = 834, y = 788, rule = B3/S23
2o$obo$o9$19bo$17bobo$18b2o51$64b2o$64bobo$64bo62$128b2o$128bobo$128bo62$192b2o$192bobo$192bo62$256b2o$256bobo$256bo9$275bo$273bobo$274b2o51$320b2o$320bobo$320bo62$384b2o$384bobo$384bo62$448b2o$448bobo$448bo62$512b2o$512bobo$512bo62$576b2o$576bobo$576bo9$595bo$593bobo$594b2o12$683bo$683bo$683bo$684b2o$684b3o$684b2o3$694b2o2b3o$694b3o2bo$683bo13bobo$682bobo9b2ob2o$682bo2bo8b3o3$681bo2bo$681b2ob3o$683b2o2bo$684bo2bo$684bobo3$715b2o$715b2o3$704bo$703bobo$703b2o2$723b2o$723b2o3$695b2o$695b2o4$640b2o$640bobo76b3o$640bo76bo4bo7b2o$717bo12bobo$717bo4bo8bo$718bobo$709bo9bobo$708bobo7b2ob2o$708bo2bo6b2o3bo$709b2o5b3obobob2o$702b3o12bo2bobo3bo$698bo3bo15b2o3bobo$699b2obobo19bo$697bobo20bob2o$696b2o3b2o18b2o$696b2o2b4o43b2o$702b2o43b2o$704bo2$736bo$735bobo$699bo2b2o18bo12b2o30b2o$700b3o18bobo42bo2bo$701bo19b2o44b2o4$731bo$730bobo$730b2o3$761bo$760bobo$760bo2bo$761b2o5$731b2o$730bo2bo$731b2o$728bo$728bo$728bo2$730b3o3$733b2o$733b2o9bo$744bo$744bo54b2o$798bo2bo$799b2o2$751b3o2$763bo$762bobo$762b2o2$725b2o$725b2o66bo$792bobo$792bo2bo$793b2o4$721b2o$721b2o40b2o$762bo2bo$763b2o$760bo$760bo$760bo2$762b3o2$731b2o$730bobo32b2o$730b2o33b2o9bo$776bo$776bo54b2o$830bo2bo$831b2o2$783b3o2$795bo$794bobo$794b2o2$757b2o$757b2o66bo$824bobo$824bo2bo$825b2o4$753b2o$753b2o40b2o$794bo2bo$795b2o$792bo$792bo$792bo2$794b3o2$763b2o$762bobo32b2o$762b2o33b2o9bo$808bo$808bo4$815b3o2$827bo$826bobo$826b2o2$789b2o$789b2o7$785b2o$785b2o40b2o$826bo2bo$827b2o$824bo$824bo$824bo2$826b3o2$795b2o$794bobo32b2o$794b2o33b2o!

In each case, the conjugate signal sends a backwards glider, but as long as it's not used as the first signal, the backwards glider can be absorbed by debris from previous signal reflections.

Ninth edit: Yes; that aspect of the circuitry appears to work.

Code: Select all

x = 3293, y = 3300, rule = B3/S23
61bo$60bobo$60bobo$2o59bo$2o8bo$4bo4bobo11bo$4bo4bobo10bobo24bo$4bo5bo11b2o24bobo$48bo2bo$6b3o40b2o7$26bo$26bo$26bo3$67b2o$67b2o3$30b3o7$63bo$62bobo$62b2o$32b2o$32b2o8bo42b3o$b2o33bo4bobo11bo28bo3bo$obo33bo4bobo10bobo23bo2bo3b2o$2o34bo5bo11b2o23bobo$78bo2bo$38b3o38b2o$83b2o$19b2o63bo4b2o$19b2o63bo4b2o$84bo4b2o$61bo25bo$11b2o47bobo24bo$11b2o47b2o25bo$72bo$72b2o$71bobo2$99b2o$99b2o$84b2o$84b2o2$38b3o4$39bo$39bo48b2o$38bo49b2o5bo$39b2o44bo3b2o3bobo$39b2o48b2o3b2o$39bob4o19b2o15b2obo4b2o$37b2o3bo2bo18b2o8bo8bo$36bo3bobo2bo22bo4bobo10bo$35b2obobobob2o22bo4bobo4bo3b2obo$35bo2b3ob2o24bo5bo7bo4b2o$35b3o2b4o39bobo3bo20bo$70b3o11bo4bo18b2obo$85b3o20b2obo$34b2o15b2o33bo18b3o2bo$33bo2bo14b2o52bo$34b3o68bobo15b2o$106b2o15b2o$44bo52b2o$35bo7b3o49bo3bo$33b2obo9bo48bo16bo$34b2o6b5o64b3o$34b2obo3b2o51bo3bo7b2o3bo2bo$36bo3b3o55bo7b2o5b2o$39bo3bo51bo3bo13bo$39bobobo52bo13b2o$40b3o54bo2bo9b4o$98b2o11bo2bo$103b2o7bo12b5o$103b2o20bo$111bobo12b3o$110bo2bo12bobo$48bo62b2o13bo$46bobo64bo$47b2o63bo$112bo15b2o$127b3o$127bobo59$112bo$110bobo$111b2o62$176bo$174bobo$175b2o62$240bo$238bobo$239b2o62$304bo$302bobo$303b2o62$368bo$366bobo$367b2o62$432bo$430bobo$431b2o62$496bo$494bobo$495b2o62$560bo$558bobo$559b2o62$624bo$622bobo$623b2o62$688bo$686bobo$687b2o62$752bo$750bobo$751b2o62$816bo$814bobo$815b2o62$880bo$878bobo$879b2o62$944bo$942bobo$943b2o62$1008bo$1006bobo$1007b2o62$1072bo$1070bobo$1071b2o62$1136bo$1134bobo$1135b2o62$1200bo$1198bobo$1199b2o62$1264bo$1262bobo$1263b2o62$1328bo$1326bobo$1327b2o62$1392bo$1390bobo$1391b2o62$1456bo$1454bobo$1455b2o62$1520bo$1518bobo$1519b2o62$1584bo$1582bobo$1583b2o62$1648bo$1646bobo$1647b2o47$1689b2o$1689bobo$1689bo$1685b3o$1687bo$1686bo59$1753b2o$1718b2o33bobo$1718bobo32bo$1621b3o94bo$1623bo$1622bo59$1817b2o$1817bobo$1817bo$1557b3o$1559bo$1558bo59$1881b2o$1881bobo$1881bo$1493b3o$1495bo$1494bo59$1945b2o$1945bobo$1945bo$1429b3o$1431bo$1430bo59$2009b2o$2009bobo$2009bo$1365b3o$1367bo$1366bo59$2073b2o$2073bobo$2073bo$1301b3o$1303bo$1302bo59$2137b2o$2137bobo$2137bo$1237b3o$1239bo$1238bo59$2201b2o$2201bobo$2201bo$1173b3o$1175bo$1174bo59$2265b2o$2265bobo$2265bo$1109b3o$1111bo$1110bo59$2329b2o$2329bobo$2329bo$1045b3o$1047bo$1046bo59$2393b2o$2393bobo$2393bo62$2457b2o$2457bobo$2457bo62$2521b2o$2521bobo$2521bo62$2585b2o$2585bobo$2585bo62$2649b2o$2649bobo$2649bo62$2713b2o$2713bobo$2713bo62$2777b2o$2777bobo$2777bo62$2841b2o$2841bobo$2841bo62$2905b2o$2905bobo$2905bo62$2969b2o$2969bobo$2969bo62$3033b2o$3033bobo$3033bo23$3142bo$3141b3o$3140b2o2bo$3139b2o2b2o$3140b2o$3141b5o$3145b2o$3143bo2bo9bo$3144b2o9bo2b2o$3155bo4bo$3155bobob2o$3157bob2o2$3142b3o$3142bobo9b2o$3142bo11b2o$3142bo2bo$3143bobo$3144b3o$3146b2o$3140b3o4b2o$3146b2o3$3174b2o$3174b2o3$3163bo$3162bobo$3162b2o2$3182b2o$3182b2o3$3154b2o$3154b2o2$3097b2o$3097bobo$3097bo2$3189b2o$3174b3o12bobo$3174bo2b2o11bo$3174bo3b2o$3168bo6b2ob2o$3167bobo7bo3bo3bo$3167bo2bo9bobobobo$3162b3o3b2o10bobo3bo$3162bo17bo2bo2bo$3159b2o19bo4bo$3158b3o16b2o5b2o$3159b2o16b2o$3183bo$3179b4o23b2o$3181bo24b2o2$3161bo$3160bobo32bo$3159bo34bobo$3159bo2bo18bo12b2o30b2o$3158b2obo18bobo42bo2bo$3157b3o20b2o44b2o$3158b2ob2o$3158bo2b2o$3159b3o$3160bo29bo$3189bobo$3189b2o3$3220bo$3219bobo$3219bo2bo$3220b2o5$3190b2o$3189bo2bo$3190b2o$3187bo$3187bo$3187bo2$3189b3o3$3192b2o$3192b2o9bo$3203bo$3203bo54b2o$3257bo2bo$3258b2o2$3210b3o2$3222bo$3221bobo$3221b2o2$3184b2o$3184b2o66bo$3251bobo$3251bo2bo$3252b2o4$3180b2o$3180b2o40b2o$3221bo2bo$3222b2o$3219bo$3219bo$3219bo2$3221b3o2$3190b2o$3189bobo32b2o$3189b2o33b2o9bo$3235bo$3235bo54b2o$3289bo2bo$3290b2o2$3242b3o2$3254bo$3253bobo$3253b2o2$3216b2o$3216b2o66bo$3283bobo$3283bo2bo$3284b2o4$3212b2o$3212b2o40b2o$3253bo2bo$3254b2o$3251bo$3251bo$3251bo2$3253b3o2$3222b2o$3221bobo32b2o$3221b2o33b2o9bo$3267bo$3267bo4$3274b3o2$3286bo$3285bobo$3285b2o2$3248b2o$3248b2o7$3244b2o$3244b2o40b2o$3285bo2bo$3286b2o$3283bo$3283bo$3283bo2$3285b3o2$3254b2o$3253bobo32b2o$3253b2o33b2o!

I plan to add a more complete design soon.

Tenth edit: I have been intermittently pondering the possibility of a 3-GPSE solution, and I may have just conceived one: Glider stream A₀ will feed into GPSE C in addition to glider stream C₀ feeding into GPSE A. The timing will be such so that GPSE A always sends back a glider on lane A₁ when it receives a signal, and GPSE C either sends back a glider on lane C₁ or doesn't send back any signal when it releases a signal. Ordinarily, glider B will destroy gliders A₀ and C₀. However, when glider A₁ arrives, it will shift glider B's path via a logic gate, preventing it from crashing into gliders A₀ and C₀, letting them go past each other. If there is no glider C₁, then glider B will proceed to construction on its path, but if there is a glider C₁, then it will shift glider B via another logic gate, making it take a different path to construction. This seems less likely to work (because there are more things that could potentially go wrong that cannot be fixed by simply moving the collision point by a couple of full diagonals or something), and I don't want to waste time working on either solution, so I'll wait until I receive guidance from a more experienced user.

Eleventh edit: I've been doing some thinking, and I've figured out a few things. Firstly, the timing details that I was concerned about all seem to work out. Secondly, a 3-GPSE solution would best be searched for via a computer program that can likely reuse code that already exists. Thirdly, at least one or two more gliders will probably be shaved off in the future, so because the glider costs of the 3-GPSE and 4-GPSE solutions will probably be either the same or only one glider apart, we should develop both in order to give more room for future improvement. This being said, I'll resume working on the 4-GPSE solution and wait for someone to do some automated searches in order to find out which relative positions and timings of GPSEs A and C work and then which of these will let the logic gates function for some relative position and timing of GPSE B.

Twelfth edit: Here is the 4-GPSE demonstration.

Code: Select all

x = 8053, y = 8009, rule = B3/S23
112bo$111bobo$111bobo$51b2o59bo$51b2o8bo$55bo4bobo11bo$55bo4bobo10bobo24bo$55bo5bo11b2o24bobo$99bo2bo$57b3o40b2o7$77bo$77bo$77bo7$81b3o7$144bo$143bobo$143bobo$32b2o49b2o59bo$33bo49b2o8bo$33bobo16b2o33bo4bobo11bo$34b2o15bobo33bo4bobo10bobo24bo$51b2o34bo5bo11b2o24bobo$131bo2bo$89b3o40b2o2$70b2o$70b2o3$62b2o$62b2o45bo$109bo$109bo7$113b3o7$176bo$175bobo$175bobo$115b2o59bo$115b2o8bo$84b2o33bo4bobo11bo$83bobo33bo4bobo10bobo24bo$83b2o34bo5bo11b2o24bobo$163bo2bo$121b3o40b2o2$102b2o$102b2o3$94b2o$94b2o45bo$141bo$141bo4$177b2o20bo$176bo2bo18b3o$175bo4bo16bobobo$145b3o25b3obo2bo18bo$173b3ob3o22bo$173bob2ob2o15bo6bo4b2o$175b3o2b2o8bo10bo5b2o$173b4o2bo2bo6bobo4bo3bo$174bo4bo2bo6bobo5b3o$179bobo8bo$178bobo16b2o$179b2o18bo$177bobo20bo$147b2o29bo18bobo11b2o$147b2o8bo40bo11bo3b2o$116b2o33bo4bobo11bo21b2o14b5ob2o$115bobo33bo4bobo10bobo19bob2o12bob2o3b2o$115b2o34bo5bo11b2o20bobo15bob2o$189bo2b2o11bo3bob2o$153b3o33bo2bo11bo3bo3bo$190b3o12bob2ob2o$134b2o54b2o17b2o$134b2o2$176bo$126b2o47bobo$126b2o47b2o5$214b2o$214b2o10$210bo$209bobo$209b2o$179b2o$179b2o8bo$148b2o33bo4bobo11bo24bo$147bobo33bo4bobo10bobo22bobo$147b2o34bo5bo11b2o24b2o2$185b3o2$166b2o$166b2o$238b2o$208bo15b2o12b2o$158b2o47bobo14b2o$158b2o47b2o2$220b2o10b3o$220b2o9bo3bo$231bo$231b2ob2o10b2o$233bo12b2o$221b3o$221b3o$222b2o$223b4ob2o$222b5o2bo$226bo2bo5bo$224bo9b3o$222b2o9bo2b2o$233bo3bo$235bobo12b2o$226b2o20b4o$226b2o4b2ob2o$234bo13bobo4bo$250bo$248bobo$235bo11bo$235bo12bo3b2o3bo$235bo13bo$250bob2o$251b3o$252b2o8$185bo$186bo$184b3o62$249bo$250bo$248b3o62$313bo$314bo$312b3o62$377bo$378bo$376b3o62$441bo$442bo$440b3o62$505bo$506bo$504b3o62$569bo$570bo$568b3o62$633bo$634bo$632b3o62$697bo$698bo$696b3o62$761bo$762bo$760b3o62$825bo$826bo$824b3o62$889bo$890bo$888b3o62$953bo$954bo$952b3o62$1017bo$1018bo$1016b3o62$1081bo$1082bo$1080b3o62$1145bo$1146bo$1144b3o62$1209bo$1210bo$1208b3o62$1273bo$1274bo$1272b3o62$1337bo$1338bo$1336b3o62$1401bo$1402bo$1400b3o62$1465bo$1466bo$1464b3o62$1529bo$1530bo$1528b3o62$1593bo$1594bo$1592b3o62$1657bo$1658bo$1656b3o62$1721bo$1722bo$1720b3o62$1785bo$1786bo$1784b3o62$1849bo$1850bo$1848b3o62$1913bo$1914bo$1912b3o62$1977bo$1978bo$1976b3o62$2041bo$2042bo$2040b3o62$2105bo$2106bo$2104b3o62$2169bo$2170bo$2168b3o62$2233bo$2234bo$2232b3o62$2297bo$2298bo$2296b3o62$2361bo$2362bo$2360b3o62$2425bo$2426bo$2424b3o62$2489bo$2490bo$2488b3o62$2553bo$2554bo$2552b3o62$2617bo$2618bo$2616b3o62$2681bo$2682bo$2680b3o62$2745bo$2746bo$2744b3o62$2809bo$2810bo$2808b3o62$2873bo$2874bo$2872b3o62$2937bo$2938bo$2936b3o62$3001bo$3002bo$3000b3o62$3065bo$3066bo$3064b3o62$3129bo$3130bo$3128b3o62$3193bo$3194bo$3192b3o62$3257bo$3258bo$3256b3o62$3321bo$3322bo$3320b3o62$3385bo$3386bo$3384b3o62$3449bo$3450bo$3448b3o62$3513bo$3514bo$3512b3o62$3577bo$3578bo$3576b3o62$3641bo$3642bo$3640b3o42$3892bobo$3893b2o$3893bo18$3705bo$3706bo$3704b3o62$3769bo$3770bo$3768b3o62$3833bo$3834bo$3832b3o62$3897bo$3898bo$3896b3o121$3891b3o$3893bo$3892bo18$4031b3o$4031bo$3875b2o155bo$3874bobo$3876bo40$3827b3o$3829bo$3828bo18$4095b3o$4095bo$3811b2o283bo$3810bobo$3812bo40$3763b3o$3765bo$3764bo18$4159b3o$4159bo$3747b2o411bo$3746bobo$3748bo40$3699b3o$3701bo$3700bo18$4223b3o$4223bo$3683b2o539bo$3682bobo$3684bo40$3635b3o$3637bo$3636bo18$4287b3o$4287bo$3619b2o667bo$3618bobo$3620bo40$3571b3o$3573bo$3572bo18$4351b3o$4351bo$3555b2o795bo$3554bobo$3556bo40$3507b3o$3509bo$3508bo18$4415b3o$4415bo$3491b2o923bo$3490bobo$3492bo40$3443b3o$3445bo$3444bo18$4479b3o$4479bo$3427b2o1051bo$3426bobo$3428bo40$3379b3o$3381bo$3380bo18$4543b3o$4543bo$3363b2o1179bo$3362bobo$3364bo40$3315b3o$3317bo$3316bo18$4607b3o$4607bo$3299b2o1307bo$3298bobo$3300bo40$3251b3o$3253bo$3252bo18$4671b3o$4671bo$3235b2o1435bo$3234bobo$3236bo40$3187b3o$3189bo$3188bo18$4735b3o$4735bo$3171b2o1563bo$3170bobo$3172bo40$3123b3o$3125bo$3124bo18$4799b3o$4799bo$3107b2o1691bo$3106bobo$3108bo40$3059b3o$3061bo$3060bo18$4863b3o$4863bo$3043b2o1819bo$3042bobo$3044bo40$2995b3o$2997bo$2996bo18$4927b3o$4927bo$2979b2o1947bo$2978bobo$2980bo40$2931b3o$2933bo$2932bo18$4991b3o$4991bo$2915b2o2075bo$2914bobo$2916bo40$2867b3o$2869bo$2868bo18$5055b3o$5055bo$2851b2o2203bo$2850bobo$2852bo40$2803b3o$2805bo$2804bo18$5119b3o$5119bo$2787b2o2331bo$2786bobo$2788bo40$2739b3o$2741bo$2740bo18$5183b3o$5183bo$2723b2o2459bo$2722bobo$2724bo40$2675b3o$2677bo$2676bo18$5247b3o$5247bo$2659b2o2587bo$2658bobo$2660bo40$2611b3o$2613bo$2612bo18$5311b3o$5311bo$2595b2o2715bo$2594bobo$2596bo40$2547b3o$2549bo$2548bo18$5375b3o$5375bo$2531b2o2843bo$2530bobo$2532bo40$2483b3o$2485bo$2484bo18$5439b3o$5439bo$2467b2o2971bo$2466bobo$2468bo40$2419b3o$2421bo$2420bo18$5503b3o$5503bo$2403b2o3099bo$2402bobo$2404bo40$2355b3o$2357bo$2356bo18$5567b3o$5567bo$2339b2o3227bo$2338bobo$2340bo40$2291b3o$2293bo$2292bo18$5631b3o$5631bo$2275b2o3355bo$2274bobo$2276bo40$2227b3o$2229bo$2228bo18$5695b3o$5695bo$2211b2o3483bo$2210bobo$2212bo40$2163b3o$2165bo$2164bo18$5759b3o$5759bo$2147b2o3611bo$2146bobo$2148bo40$2099b3o$2101bo$2100bo18$5823b3o$5823bo$2083b2o3739bo$2082bobo$2084bo40$2035b3o$2037bo$2036bo18$5887b3o$5887bo$2019b2o3867bo$2018bobo$2020bo40$1971b3o$1973bo$1972bo18$5951b3o$5951bo$1955b2o3995bo$1954bobo$1956bo40$1907b3o$1909bo$1908bo18$6015b3o$6015bo$1891b2o4123bo$1890bobo$1892bo40$1843b3o$1845bo$1844bo18$6079b3o$6079bo$1827b2o4251bo$1826bobo$1828bo40$1779b3o$1781bo$1780bo18$6143b3o$6143bo$1763b2o4379bo$1762bobo$1764bo40$1715b3o$1717bo$1716bo18$6207b3o$6207bo$1699b2o4507bo$1698bobo$1700bo40$1651b3o$1653bo$1652bo18$6271b3o$6271bo$1635b2o4635bo$1634bobo$1636bo40$1587b3o$1589bo$1588bo18$6335b3o$6335bo$1571b2o4763bo$1570bobo$1572bo40$1523b3o$1525bo$1524bo18$6399b3o$6399bo$1507b2o4891bo$1506bobo$1508bo40$1459b3o$1461bo$1460bo18$6463b3o$6463bo$1443b2o5019bo$1442bobo$1444bo40$1395b3o$1397bo$1396bo18$6527b3o$6527bo$1379b2o5147bo$1378bobo$1380bo40$1331b3o$1333bo$1332bo18$6591b3o$6591bo$1315b2o5275bo$1314bobo$1316bo40$1267b3o$1269bo$1268bo18$6655b3o$6655bo$1251b2o5403bo$1250bobo$1252bo40$1203b3o$1205bo$1204bo18$6719b3o$6719bo$1187b2o5531bo$1186bobo$1188bo40$1139b3o$1141bo$1140bo18$6783b3o$6783bo$1123b2o5659bo$1122bobo$1124bo40$1075b3o$1077bo$1076bo18$6847b3o$6847bo$1059b2o5787bo$1058bobo$1060bo40$1011b3o$1013bo$1012bo18$6911b3o$6911bo$995b2o5915bo$994bobo$996bo40$947b3o$949bo$948bo18$6975b3o$6975bo$931b2o6043bo$930bobo$932bo40$883b3o$885bo$884bo18$7039b3o$7039bo$867b2o6171bo$866bobo$868bo40$819b3o$821bo$820bo18$7103b3o$7103bo$803b2o6299bo$802bobo$804bo40$755b3o$757bo$756bo18$7167b3o$7167bo$739b2o6427bo$738bobo$740bo40$691b3o$693bo$692bo18$7231b3o$7231bo$675b2o6555bo$674bobo$676bo40$627b3o$629bo$628bo18$7295b3o$7295bo$611b2o6683bo$610bobo$612bo40$563b3o$565bo$564bo18$7359b3o$7359bo$547b2o6811bo$546bobo$548bo40$499b3o$501bo$500bo18$7423b3o$7423bo$483b2o6939bo$482bobo$484bo40$435b3o$437bo$436bo18$7487b3o$7487bo$419b2o7067bo$418bobo$420bo40$371b3o$373bo$372bo18$7551b3o$7551bo$355b2o7195bo$354bobo$356bo40$307b3o$309bo$308bo18$7615b3o$7615bo$291b2o7323bo$290bobo$292bo31$166bo$166b2o$165b2obo$164b2o2bo$163b3ob4o$162b2o2bobo2bo$162b3obobobo$162bob3ob2o$161bobo2b4o$162bo3bo76b3o$162bo3bo78bo$149b2o12bo2bo77bo$149b2o4$164b2o3$141b2o$141b2o$159b2o$158bo2bo$148bo8b2o2bo4b3o$147b2o9b2o2bo$146bo2bo9b4o$146bobo$147b2o2$156bo7522b3o$134b2o18b2o7523bo$133bobo19bo2bo2b2o64b2o7451bo$134bo20bo2bo2b2o63bobo$142b2o10bo73bo$142b2o8b4o$152bobo2bo$151b2o4b2o$146b2o5bo$146b2o5$117b2o$100b3o14b2o$101bo$99bob2obo$99b2o3b2o23bo$104b3o21bobo$102b2o2bo22b2o12bo$91b2o9bo2b2o35bobo$91b2o9bobo38b2o$105bobo$105bobo$105bo$134bo$133bobo$89b3o15bo26b2o$87b2o3bo$87b2o4bo4bo$87b2o4bo3b3o$89b5o2bo$97b2o3$102b2o$101b2obobo$93bo9bo2bo$93b2o8bob2o26b2o$94bo9b2o26bo2bo$105bo27b2o$137bo$137bo$137bo41b3o$181bo$133b3o44bo$93bobo$93bo$88b2o3b3o35b2o$87bo2bo6b2o32b2o$88bobo6b2o$65b2o21b2obo6bo12bo$64bo2bo20bob3o17bobo$65b2o21b2o3bo17b2o$90b4o$91b3o2$102bo$101bobo$102b2o2$139b2o$72bo66b2o$71bobo7669b3o$70bo2bo7669bo$71b2o90b2o7579bo$162bobo$164bo2$143b2o$101b2o40b2o$100bo2bo$101b2o$105bo$105bo$105bo126bo$231bobo$101b3o125b2o2bo$214bo14b7o$133b2o79bo14bo3bo2bo$99b2o32bobo78bo11b7o2b3o$89bo9b2o33b2o85bo8bo2b3o$89bo131bo8b2ob2o$33b2o54bo136bo2bob3o$32bo2bo169b2o5b2o13b2ob3o$33b2o170b2o5bob2o13bo$212bo3bo$80b3o129b2o2bo$201bo3b2o6b3o$70bo130b2o11bo$69bobo136bo$70b2o131bob3o$202b3o2bo$107b2o91bo2bo$40bo66b2o92b3o$39bobo159bo$38bo2bo183b2o$39b2o171bo12b2o$210b2ob2o$199b2o9bo2bo$199b2o10b2o$111b2o$69b2o40b2o24b2o47b2o$68bo2bo65b2o47bobo14b2o$69b2o116bo15b2o12b2o$73bo143b2o$73bo71b2o$73bo71b2o2$69b3o92b3o2$101b2o23b2o34bo5bo11b2o24b2o$67b2o32bobo22bobo33bo4bobo10bobo22bobo$57bo9b2o33b2o23b2o33bo4bobo11bo24bo$57bo100b2o8bo$b2o54bo100b2o$o2bo184b2o$b2o185bobo$189bo7696bo$48b3o7834b2o$7884bob2o$38bo7845bo2b2o$37bobo7842b4ob3o$38b2o7841bo2bobo2b2o$7882bobobob3o$75b2o7806b2ob3obo$8bo66b2o7806b4o2bobo$7bobo7797b3o76bo3bo$6bo2bo183b2o7612bo78bo3bo$7b2o184b2o7613bo77bo2bo12b2o$7902b2o3$79b2o$37b2o40b2o24b2o47b2o7731b2o$36bo2bo65b2o47bobo$37b2o116bo$41bo7868b2o$41bo71b2o7795b2o$41bo71b2o65bo3b2o7706b2o$169b3o15b3o7701bo2bo$37b3o92b3o32b3o13b3obob2o7693b3o4bo2b2o8bo$168bo2bo14bo2b3o7698bo2b2o9b2o$69b2o23b2o34bo5bo11b2o19b2obo15bo7701b4o9bo2bo$35b2o32bobo22bobo33bo4bobo10bobo20b2o13b3o2bobo7710bobo$25bo9b2o33b2o23b2o33bo4bobo11bo21bo19b3o7710b2o$25bo100b2o8bo53bo2bo$25bo100b2o49bo12b2o7704bo$156b3o16bob2o7718b2o18b2o$157b2o16bobo7712b2o2bo2bo19bobo$176bo7713b2o2bo2bo20bo$16b3o140bobo7736bo10b2o$159bo8b2o7727b4o8b2o$6bo145b3o4b3o7b2o5b3o7716bo2bobo$5bobo144b2obo20bo2bo6b2o7706b2o4b2o$6b2o144b2ob2o19bo3bo5b2o7711bo5b2o$153bobob2o17bo3bo7724b2o$43b2o79b3o27bobo2bo16bo3bo$43b2o109b4obo17b3o$158bo18b3o2$7934b2o$7934b2o14b3o$7951bo$120bo7827bob2obo$47b2o71bo7802bo23b2o3b2o$5b2o40b2o24b2o45bo7801bobo21b3o$4bo2bo65b2o7834bo12b2o22bo2b2o$5b2o7901bobo35b2o2bo9b2o$9bo7898b2o38bobo9b2o$9bo71b2o7862bobo$9bo71b2o7862bobo$7947bo$5b3o92b3o40b2o7773bo$142bo2bo7771bobo$37b2o23b2o34bo5bo11b2o24bobo7772b2o26bo15b3o$3b2o32bobo22bobo33bo4bobo10bobo24bo7816bo3b2o$3b2o33b2o23b2o33bo4bobo11bo7836bo4bo4b2o$94b2o8bo7848b3o3bo4b2o$94b2o59bo7800bo2b5o$154bobo7797b2o$154bobo$155bo$7949b2o$7946bobob2o$7946bo2bo9bo$7918b2o26b2obo8b2o$7917bo2bo26b2o9bo$7918b2o27bo$92b3o7820bo$7915bo$7871b3o41bo$7871bo$7872bo44b3o$7957bobo$7959bo$88bo7831b2o35b3o3b2o$88bo7831b2o32b2o6bo2bo$41b2o45bo7865b2o6bobo$41b2o7898bo12bo6bob2o21b2o$7940bobo17b3obo20bo2bo$7940b2o17bo3b2o21b2o$49b2o7908b4o$49b2o7908b3o2$68b3o40b2o7837bo$110bo2bo7835bobo$30b2o34bo5bo11b2o24bobo7836b2o$30bobo33bo4bobo10bobo24bo$31b2o33bo4bobo11bo7826b2o$62b2o8bo7839b2o66bo$62b2o59bo7855bobo$122bobo7854bo2bo$122bobo7855b2o$123bo3$7908b2o$7908b2o40b2o$7949bo2bo$7950b2o$60b3o7884bo$7947bo$7947bo2$7949b3o2$7918b2o$56bo7860bobo32b2o$56bo7860b2o33b2o9bo$56bo7906bo$7963bo54b2o$8017bo2bo$8018b2o2$7970b3o2$36b3o40b2o7901bo$78bo2bo7899bobo$34bo5bo11b2o24bobo7900b2o$34bo4bobo10bobo24bo$34bo4bobo11bo7890b2o$30b2o8bo7903b2o66bo$30b2o59bo7919bobo$90bobo7918bo2bo$90bobo7919b2o$91bo3$7940b2o$7940b2o40b2o$7981bo2bo$7982b2o$7979bo$7979bo$7979bo2$7981b3o2$7950b2o$7949bobo32b2o$7949b2o33b2o9bo$7995bo$7995bo54b2o$8049bo2bo$8050b2o2$8002b3o2$8014bo$8013bobo$8013b2o2$7976b2o$7976b2o66bo$8043bobo$8043bo2bo$8044b2o4$7972b2o$7972b2o40b2o$8013bo2bo$8014b2o$8011bo$8011bo$8011bo2$8013b3o2$7982b2o$7981bobo32b2o$7981b2o33b2o9bo$8027bo$8027bo4$8034b3o2$8046bo$8045bobo$8045b2o2$8008b2o$8008b2o7$8004b2o$8004b2o40b2o$8045bo2bo$8046b2o$8043bo$8043bo$8043bo2$8045b3o2$8014b2o$8013bobo32b2o$8013b2o33b2o!

When an A₁ glider comes, it allows an A₀ glider to escape to the northwest; however, there's probably a four-glider synthesis of GPSE C so that the ash of the synthesis can absorb the A₀ gliders without emitting any gliders. I've represented this with a fishhook, but other methods are more likely. If we use a fishhook and synthesize GPSEs B and E (the latter of which shall now be renamed to GPSE D for all future posts) with eight gliders instead of finding a way to synthesize them with only seven, this leads to universal construction with only nineteen gliders.

Thirteenth edit: It turns out that we can't use the crystal reaction because it's close enough to the Herschel ash to interact with it and sometimes form escaping gliders. Here's a demonstration:

Code: Select all

x = 1992, y = 2021, rule = B3/S23
86bo$85bobo$85bobo$25b2o59bo$25b2o8bo$29bo4bobo11bo$29bo4bobo10bobo24bo$29bo5bo11b2o24bobo$73bo2bo$31b3o40b2o7$51bo$51bo$51bo5$2o$2o$55b3o7$118bo$117bobo$5b3o109bobo$5bo51b2o59bo$6bo50b2o8bo$26b2o33bo4bobo11bo$25bobo33bo4bobo10bobo24bo$25b2o34bo5bo11b2o24bobo$105bo2bo$63b3o40b2o2$44b2o$44b2o3$36b2o$36b2o45bo$83bo$83bo7$87b3o10$89b2o$89b2o8bo$58b2o33bo4bobo11bo$57bobo33bo4bobo10bobo$57b2o34bo5bo11b2o2$95b3o2$76b2o$76b2o3$68b2o$68b2o45bo$115bo$115bo7$119b3o9$69b3o$69bo51b2o$70bo50b2o8bo$90b2o33bo4bobo$89bobo33bo4bobo$89b2o34bo5bo2$127b3o2$108b2o$108b2o3$100b2o$100b2o21$122b2o$121bobo$121b2o8$132b2o$132b2o18$133b3o$133bo$134bo62$197b3o$197bo$198bo62$261b3o$261bo$262bo62$325b3o$325bo$326bo62$389b3o$389bo$390bo62$453b3o$453bo$454bo62$517b3o$517bo$518bo62$581b3o$581bo$582bo62$645b3o$645bo$646bo62$709b3o$709bo$710bo62$773b3o$773bo$774bo62$837b3o$837bo$838bo62$901b3o$901bo$902bo62$965b3o$965bo$966bo62$1029b3o$1029bo$1030bo62$1093b3o$1093bo$1094bo62$1157b3o$1157bo$1158bo62$1221b3o$1221bo$1222bo62$1285b3o$1285bo$1286bo62$1349b3o$1349bo$1350bo62$1413b3o$1413bo$1414bo62$1477b3o$1477bo$1478bo62$1541b3o$1541bo$1542bo62$1605b3o$1605bo$1606bo62$1669b3o$1669bo$1670bo62$1733b3o$1733bo$1734bo62$1797b3o$1797bo$1798bo62$1861b3o$1861bo$1862bo62$1925b3o$1925bo$1926bo62$1989b3o$1989bo$1990bo!

The crystal reaction repeats every nineteen full diagonals, and the GPSE's ash repeats every thirty-two full diagonals. These numbers are relatively prime, so there's no way to simply realign the reactions in order to avoid this. However, not all of the interactions between the crystal reaction result in escaping gliders, so there might be a reaction that rephases the crystal reaction in a way so that before it produces escaping gliders, it's rephased in the same way again.

Fourteenth edit: None of the initial spacings of crystal seem to work. Hopefully there's something else that does. (The formation of a crystal might be okay if there's something behind the crystal that can cleanly absorb the gliders because some interactions of the crystal with the Herschel ash cause the crystal to be cleaned destroyed (Each successive glider alternately turns half of a honey farm into a blinker or deletes the blinker.) without releasing any gliders. It's probably better to simply test the possibilities out on each four-glider synthesis of a GPSE instead of looking for a reaction that works then hoping that there's some way to activate it. If nothing better works, then if the gliders burn through GPSE's ash of synthesis (and they probably will for at least one synthesis), then we can use one extra glider to make a honey farm and start a crystal reaction sufficiently far back from the GPSE's ash of formation.

Fifteenth edit: Mark Niemiec's database (which I'd like to thank dvgrn for informing me of) doesn't have any four-glider syntheses of the GPSE. Is there an updated site that has every minimal-cost glider synthesis for various patterns?

Sixteenth edit: I just thought of a potential solution to the problem of preventing A₀ gliders from escaping. I remember when I was playing around with GPSEs earlier that the timing separation between a GPSE's gliders allows a kickback reaction with one glider to send a glider back towards the GPSE and trigger a 180° kickback reaction sending a glider away from the GPSE. I think that the original kickback reaction was 90°, but I can't remember for sure. I'll check, and if the original kickback reaction is indeed 90°, I'll attempt to make a functional 4-GPSE universal constructor utilizing a pair of kickback reactions between two B gliders and one A₁ glider.

Seventeenth edit: I apparently misremembered. The 90° kickback reaction results in a block, and the 180* reaction results in a banana spark. Does anyone else have any ideas for how to prevent escaping gliders?

Eighteenth edit: I just had another idea for a 3-GPSE universal constructor. Under normal circumstances, gliders A₀ and B collide and, with the help of a logic gate, make another glider (which shall be called glider B′) that then collides with and annihilates glider C. If there is a gap in glider stream A₀, then glider B is let through as a construction glider, and glider C is let through in order to send another signal to GPSE A. If a glider comes on lane A₁, then it will annihilate glider B, letting glider C be sent to GPSE A and letting glider A₀ be sent to GPSE C. The signal to GPSE C will return first as a gap in glider stream C that will let glider B′ through as a construction glider. Then the signal sent to GPSE A will return either as a gap in glider stream A₀ or as a glider on line A₁, and the cycle will proceed again.

Nineteenth edit: I just remembered that when I was manually searching for ways of shooting a glider at a GPSE to get two different return signals, some of the timings results in no return signals or escaping spaceships, i.e. GPSE C can probably serve as a glider eater for our purposes. I'll test whether or not there's a way to make this happen.

Twentieth edit: Here's one possible method. It creates a backwards glider, but this can be absorbed by ash from the previous reaction, so the ash of synthesis only needs to absorb one glider.

Code: Select all

x = 795, y = 736, rule = B3/S23
43b2o$43b2o2$6b2o$5bobo$6bo$17bo$17bo$17bo4$24b3o$35b2o33b2o$35b2o32bobo$69b2o$38bo$38bo$38bo2$40b3o2$37b2o$36bo2bo$37b2o40b2o$79b2o4$7b2o$6bo2bo$7bobo$8bo66b2o$75b2o2$38b2o$37bobo$38bo4$b2o$o2bo45b2o$b2o42b2o2bobo$46b4ob2o$47b5o15b2o$48b3o16b2o2$70bo$70bo$70bo2$72b3o2$69b2o$68bo2bo$69b2o5$39b2o$38bo2bo$39bobo$40bo3$70b2o$69bobo$70bo4$33b2o44b2o$32bo2bo42bobo$33b2o30b2o12bo$64bobo$65bo3$53b2o$53b2o3$149bobo$150b2o$150bo$89b2o$96b2o$85bo5b2o2bo3b2o$78b2o4bo6b2o7b2o$78b2o4bo4bob2o5b2o2bo$70bo13b2o4bo4b2o4b3o$69bobo15b3o11b2o$70b2o26b4o$98b3o$99bo4$105b2o$105b2o3$77b2o$77b2o2$105bob2o$104b2o3b2o$104bo3b3o$104bo2bo2bo$105bobo3b3o$85b2o7b3o14b3o$85b2o$92bo5bo$92bo5bo$92bo5bo2$94b3o2$101b3o$100bo2bo11b2o$105bo8bobo$105b2obo5bo2bob2o$105b3ob2o4b3obobo$108bo8bo3bo$101b3o13bo3bo$118bobo$119bo20$213bobo$214b2o$214bo62$277bobo$278b2o$278bo7$281bo$280b2o$280bobo510$793bo$792b2o$792bobo!

I will keep looking for examples in case there is a way that does not result in any backward gliders.

Twenty-first edit: I found a method that results in a minimal change in ash and no backward gliders.

Code: Select all

x = 285, y = 226, rule = B3/S23
43b2o$43b2o2$6b2o$5bobo$6bo$17bo$17bo$17bo4$24b3o$35b2o33b2o$35b2o32bobo$69b2o$38bo$38bo$38bo2$40b3o2$37b2o$36bo2bo$37b2o40b2o$79b2o4$7b2o$6bo2bo$7bobo$8bo66b2o$75b2o2$38b2o$37bobo$38bo4$b2o47b3o$o2bo48b3o$b2o42b2o2b2o4bo$45b2o2bo2bo3bo$50bo4bo11b2o$53bo13b2o$51bobo$52bo17bo$70bo$70bo2$72b3o2$69b2o$68bo2bo$69b2o5$39b2o$38bo2bo$39bobo$40bo3$70b2o$69bobo$70bo4$33b2o44b2o$32bo2bo42bobo$33b2o30b2o12bo$64bobo$65bo3$53b2o$53b2o5$100b2o49bobo$91b2o7b2o50b2o$90bo2bo5bo2bo49bo$79b6o6bobo5bo2bo$78bo5bo7bo5bo2bo$78bo20bo2bo$70bo8bo4bo14b4o$69bobo10b3o15bo$70b2o31bo$101bo$101b2o4$105b2o$105b2o3$77b2o$77b2o3$107bo$107b2o$109bo2$85b2o7b3o$85b2o$92bo5bo12bo$92bo5bo$92bo5bo2b3o$100bo2bo$94b3o3bo3bo$99b2obobo$99b2ob2o12b4o$100b3o12b2o4bo$115b3o4bo$117bo5bo$115b2o$115b2o2b2o4bo$101b3o11bo9bo$116bo2bo3bo$117bo$118b2obo$120bo20$215bobo$216b2o$216bo62$279bobo$280b2o$280bo7$283bo$282b2o$282bobo!

I plan to use this for a universal constructor that can be synthesized with seventeen gliders soon.

Twenty-second edit: Here is the seventeen-glider version. I haven't included the syntheses here, but each component has a known maximum glider cost. I typed maximum because there is a chance that GPSEs B and D could be constructed with a total of less than eight gliders, but they will definitely not cost more than eight gliders.

Code: Select all

x = 8114, y = 8028, rule = B3/S23
3b2o33b2o$3b2o32bobo$37b2o$6bo$6bo$6bo2$8b3o2$5b2o$4bo2bo$5b2o40b2o$47b2o7$43b2o$43b2o2$6b2o$5bobo$6bo4$18b3o$20b3o$13b2o2b2o4bo$13b2o2bo2bo3bo$18bo4bo11b2o$21bo13b2o$19bobo$20bo17bo$38bo$38bo2$40b3o2$37b2o$36bo2bo$37b2o5$7b2o$6bo2bo$7bobo$8bo3$38b2o$37bobo$38bo4$b2o44b2o$o2bo42bobo$b2o30b2o12bo$32bobo$33bo3$21b2o$21b2o5$68b2o49bobo$59b2o7b2o50b2o$58bo2bo5bo2bo49bo$47b6o6bobo5bo2bo$46bo5bo7bo5bo2bo$46bo20bo2bo$38bo8bo4bo14b4o$37bobo10b3o15bo$38b2o31bo$69bo$69b2o4$73b2o$73b2o3$45b2o$45b2o3$75bo$75b2o$77bo2$53b2o7b3o$53b2o$60bo5bo12bo$60bo5bo$60bo5bo2b3o$68bo2bo$62b3o3bo3bo$67b2obobo$67b2ob2o12b4o$68b3o12b2o4bo$83b3o4bo$85bo5bo$83b2o$83b2o2b2o4bo$69b3o11bo9bo$84bo2bo3bo$85bo$86b2obo$88bo20$183bobo$184b2o$184bo62$247bobo$248b2o$248bo62$311bobo$312b2o$312bo62$375bobo$376b2o$376bo62$439bobo$440b2o$440bo62$503bobo$504b2o$504bo62$567bobo$568b2o$568bo62$631bobo$632b2o$632bo62$695bobo$696b2o$696bo62$759bobo$760b2o$760bo62$823bobo$824b2o$824bo62$887bobo$888b2o$888bo62$951bobo$952b2o$952bo62$1015bobo$1016b2o$1016bo62$1079bobo$1080b2o$1080bo62$1143bobo$1144b2o$1144bo62$1207bobo$1208b2o$1208bo62$1271bobo$1272b2o$1272bo62$1335bobo$1336b2o$1336bo62$1399bobo$1400b2o$1400bo62$1463bobo$1464b2o$1464bo62$1527bobo$1528b2o$1528bo62$1591bobo$1592b2o$1592bo62$1655bobo$1656b2o$1656bo62$1719bobo$1720b2o$1720bo62$1783bobo$1784b2o$1784bo62$1847bobo$1848b2o$1848bo62$1911bobo$1912b2o$1912bo62$1975bobo$1976b2o$1976bo62$2039bobo$2040b2o$2040bo62$2103bobo$2104b2o$2104bo62$2167bobo$2168b2o$2168bo62$2231bobo$2232b2o$2232bo62$2295bobo$2296b2o$2296bo62$2359bobo$2360b2o$2360bo62$2423bobo$2424b2o$2424bo62$2487bobo$2488b2o$2488bo62$2551bobo$2552b2o$2552bo62$2615bobo$2616b2o$2616bo62$2679bobo$2680b2o$2680bo62$2743bobo$2744b2o$2744bo62$2807bobo$2808b2o$2808bo62$2871bobo$2872b2o$2872bo62$2935bobo$2936b2o$2936bo62$2999bobo$3000b2o$3000bo62$3063bobo$3064b2o$3064bo62$3127bobo$3128b2o$3128bo62$3191bobo$3192b2o$3192bo62$3255bobo$3256b2o$3256bo62$3319bobo$3320b2o$3320bo62$3383bobo$3384b2o$3384bo62$3447bobo$3448b2o$3448bo62$3511bobo$3512b2o$3512bo62$3575bobo$3576b2o$3576bo62$3639bobo$3640b2o$3640bo62$3703bobo$3704b2o$3704bo41$3957bo$3955bobo$3956b2o19$3767bobo$3768b2o$3768bo62$3831bobo$3832b2o$3832bo62$3895bobo$3896b2o$3896bo62$3959bobo$3960b2o$3960bo115$3955bo$3955b2o$3954bobo18$4091bo$4090b2o$4090bobo$3938b2o$3939b2o$3938bo39$3891bo$3891b2o$3890bobo18$4155bo$4154b2o$4154bobo$3874b2o$3875b2o$3874bo39$3827bo$3827b2o$3826bobo18$4219bo$4218b2o$4218bobo$3810b2o$3811b2o$3810bo39$3763bo$3763b2o$3762bobo18$4283bo$4282b2o$4282bobo$3746b2o$3747b2o$3746bo39$3699bo$3699b2o$3698bobo18$4347bo$4346b2o$4346bobo$3682b2o$3683b2o$3682bo39$3635bo$3635b2o$3634bobo18$4411bo$4410b2o$4410bobo$3618b2o$3619b2o$3618bo39$3571bo$3571b2o$3570bobo18$4475bo$4474b2o$4474bobo$3554b2o$3555b2o$3554bo39$3507bo$3507b2o$3506bobo18$4539bo$4538b2o$4538bobo$3490b2o$3491b2o$3490bo39$3443bo$3443b2o$3442bobo18$4603bo$4602b2o$4602bobo$3426b2o$3427b2o$3426bo39$3379bo$3379b2o$3378bobo18$4667bo$4666b2o$4666bobo$3362b2o$3363b2o$3362bo39$3315bo$3315b2o$3314bobo18$4731bo$4730b2o$4730bobo$3298b2o$3299b2o$3298bo39$3251bo$3251b2o$3250bobo18$4795bo$4794b2o$4794bobo$3234b2o$3235b2o$3234bo39$3187bo$3187b2o$3186bobo18$4859bo$4858b2o$4858bobo$3170b2o$3171b2o$3170bo39$3123bo$3123b2o$3122bobo18$4923bo$4922b2o$4922bobo$3106b2o$3107b2o$3106bo39$3059bo$3059b2o$3058bobo18$4987bo$4986b2o$4986bobo$3042b2o$3043b2o$3042bo39$2995bo$2995b2o$2994bobo18$5051bo$5050b2o$5050bobo$2978b2o$2979b2o$2978bo39$2931bo$2931b2o$2930bobo18$5115bo$5114b2o$5114bobo$2914b2o$2915b2o$2914bo39$2867bo$2867b2o$2866bobo18$5179bo$5178b2o$5178bobo$2850b2o$2851b2o$2850bo39$2803bo$2803b2o$2802bobo18$5243bo$5242b2o$5242bobo$2786b2o$2787b2o$2786bo39$2739bo$2739b2o$2738bobo18$5307bo$5306b2o$5306bobo$2722b2o$2723b2o$2722bo39$2675bo$2675b2o$2674bobo18$5371bo$5370b2o$5370bobo$2658b2o$2659b2o$2658bo39$2611bo$2611b2o$2610bobo18$5435bo$5434b2o$5434bobo$2594b2o$2595b2o$2594bo39$2547bo$2547b2o$2546bobo18$5499bo$5498b2o$5498bobo$2530b2o$2531b2o$2530bo39$2483bo$2483b2o$2482bobo18$5563bo$5562b2o$5562bobo$2466b2o$2467b2o$2466bo39$2419bo$2419b2o$2418bobo18$5627bo$5626b2o$5626bobo$2402b2o$2403b2o$2402bo39$2355bo$2355b2o$2354bobo18$5691bo$5690b2o$5690bobo$2338b2o$2339b2o$2338bo39$2291bo$2291b2o$2290bobo18$5755bo$5754b2o$5754bobo$2274b2o$2275b2o$2274bo39$2227bo$2227b2o$2226bobo18$5819bo$5818b2o$5818bobo$2210b2o$2211b2o$2210bo39$2163bo$2163b2o$2162bobo18$5883bo$5882b2o$5882bobo$2146b2o$2147b2o$2146bo39$2099bo$2099b2o$2098bobo18$5947bo$5946b2o$5946bobo$2082b2o$2083b2o$2082bo39$2035bo$2035b2o$2034bobo18$6011bo$6010b2o$6010bobo$2018b2o$2019b2o$2018bo39$1971bo$1971b2o$1970bobo18$6075bo$6074b2o$6074bobo$1954b2o$1955b2o$1954bo39$1907bo$1907b2o$1906bobo18$6139bo$6138b2o$6138bobo$1890b2o$1891b2o$1890bo39$1843bo$1843b2o$1842bobo18$6203bo$6202b2o$6202bobo$1826b2o$1827b2o$1826bo39$1779bo$1779b2o$1778bobo18$6267bo$6266b2o$6266bobo$1762b2o$1763b2o$1762bo39$1715bo$1715b2o$1714bobo18$6331bo$6330b2o$6330bobo$1698b2o$1699b2o$1698bo39$1651bo$1651b2o$1650bobo18$6395bo$6394b2o$6394bobo$1634b2o$1635b2o$1634bo39$1587bo$1587b2o$1586bobo18$6459bo$6458b2o$6458bobo$1570b2o$1571b2o$1570bo39$1523bo$1523b2o$1522bobo18$6523bo$6522b2o$6522bobo$1506b2o$1507b2o$1506bo39$1459bo$1459b2o$1458bobo18$6587bo$6586b2o$6586bobo$1442b2o$1443b2o$1442bo39$1395bo$1395b2o$1394bobo18$6651bo$6650b2o$6650bobo$1378b2o$1379b2o$1378bo39$1331bo$1331b2o$1330bobo18$6715bo$6714b2o$6714bobo$1314b2o$1315b2o$1314bo39$1267bo$1267b2o$1266bobo18$6779bo$6778b2o$6778bobo$1250b2o$1251b2o$1250bo39$1203bo$1203b2o$1202bobo18$6843bo$6842b2o$6842bobo$1186b2o$1187b2o$1186bo39$1139bo$1139b2o$1138bobo18$6907bo$6906b2o$6906bobo$1122b2o$1123b2o$1122bo39$1075bo$1075b2o$1074bobo18$6971bo$6970b2o$6970bobo$1058b2o$1059b2o$1058bo39$1011bo$1011b2o$1010bobo18$7035bo$7034b2o$7034bobo$994b2o$995b2o$994bo39$947bo$947b2o$946bobo18$7099bo$7098b2o$7098bobo$930b2o$931b2o$930bo39$883bo$883b2o$882bobo18$7163bo$7162b2o$7162bobo$866b2o$867b2o$866bo39$819bo$819b2o$818bobo18$7227bo$7226b2o$7226bobo$802b2o$803b2o$802bo39$755bo$755b2o$754bobo18$7291bo$7290b2o$7290bobo$738b2o$739b2o$738bo39$691bo$691b2o$690bobo18$7355bo$7354b2o$7354bobo$674b2o$675b2o$674bo39$627bo$627b2o$626bobo18$7419bo$7418b2o$7418bobo$610b2o$611b2o$610bo39$563bo$563b2o$562bobo18$7483bo$7482b2o$7482bobo$546b2o$547b2o$546bo39$499bo$499b2o$498bobo18$7547bo$7546b2o$7546bobo$482b2o$483b2o$482bo39$435bo$435b2o$434bobo18$7611bo$7610b2o$7610bobo$418b2o$419b2o$418bo39$371bo$371b2o$370bobo18$7675bo$7674b2o$7674bobo$354b2o$355b2o$354bo38$230bo$223bo5bobo75bo$221b2ob2o81b2o$221b2o3bo2b3o74bobo$221b2ob2o$222b4o$210b2o$210b2o7$202b2o$202b2o$216b3o$214b2ob4o4b4o$214bo2b2o4b2obobo$206b2o6b3o9b2o$205bo2bo10bobo3bo$205bo2bo7530bo$206bobo7529b2o$208b4o7526bobo$207b2o2bo78b2o$195b2o11b3o80b2o$194bobo12bo12b2o66bo$195bo26b2o$203b2o5bobo$203b2o5bo$213bo$208bo4b2o$207bo6bo$207bo2b4o5$178b2o$161b2o3bo11b2o$162bo4bo$166bo$163bobo24bo$164bo24bobo$168bo21b2o12bo$152b2o11b3obo33bobo$152b2o10b3o2bo34b2o$163b2o2bo$164b2o$165bo$195bo$152b3o39bobo$151b2ob3o38b2o$147bo$147bo3bo$147bo7b2o$152b2obo$154b2o$155bo6b2o$162b2o$159b2ob2o$160b2o$154b2o9bo$153bo2bo7b3o27b2o$154b2o8b2obo25bo2bo$166b2o26b2o47bo$243b2o$197b3o42bobo2$153b2o40bo$155bo39bo$150bo4b2o38bo$149bo3bo5bo$150b2o7b2o31b2o$159b2o31b2o2$126b2o44bo$125bo2bo42bobo$126b2o44b2o$154b3o$152b2ob2o$152b2ob2o$152b2o9bo$162bobo$163b2o$7803bo$200b2o7600b2o$133bo66b2o7600bobo$132bobo91b2o$131bo2bo92b2o$132b2o92bo4$204b2o$162b2o40b2o$161bo2bo$162b2o2$165b3o2$163bo126bobo$163bo126bo2bo$163bo126bobo$194b2o79b2o$160b2o32bobo77bobo$160b2o33b2o77b3o13bo$149b3o121bo2bo11b2obo$94b2o179bo12b2obo$93bo2bo169b2o7bo12bo3bo$94b2o170b2o20b4o$142bo130bo15b3o$142bo133bo$142bo130bo2bo$131bo143b3o$130bobo142b3o$131b2o141bo2bo$274bobo$168b2o91b2o11b3o$101bo66b2o90bob2o$100bobo157bo4bo$99bo2bo157bo8b2o15b2o$100b2o158bo3b2o2bobo15b2o$267b2obo$262bo5b6o$260b2o7bo4bo$172b2o97bo2bo$130b2o40b2o24b2o47b2o23b2o$129bo2bo65b2o47bobo14b2o$130b2o116bo15b2o12b2o$278b2o$133b3o70b2o$206b2o$131bo94bo$131bo94bo$131bo94bo$162b2o23b2o40bo11b2o24b2o$128b2o32bobo22bobo32b3o3bobo10bobo22bobo$128b2o33b2o23b2o38bobo11bo24bo$117b3o99b2o8bo$62b2o155b2o$61bo2bo184b2o$62b2o185bobo$110bo139bo$110bo$110bo$99bo$98bobo$99b2o7843bo$7867bo75bobo5bo$136b2o7728b2o81b2ob2o$69bo66b2o7728bobo74b3o2bo3b2o$68bobo7878b2ob2o$67bo2bo183b2o7693b4o$68b2o184b2o7707b2o$7963b2o3$140b2o$98b2o40b2o24b2o47b2o$97bo2bo65b2o47bobo$98b2o116bo$7971b2o$101b3o70b2o71b2o7722b2o$174b2o73bo7706b3o$99bo94bo33b2o16bobo4bo7692b4o4b4ob2o$99bo94bo33bobo16b2o3bobo7691bobob2o4b2o2bo$99bo94bo34b3o12b2ob2o2bo7695b2o9b3o6b2o$130b2o23b2o40bo11b2o18b2o14b3o2bo7698bo3bobo10bo2bo$96b2o32bobo22bobo32b3o3bobo10bobo21b3o10bo4bo7714bo2bo$96b2o33b2o23b2o38bobo11bo22b3o17b2o7711bobo$85b3o99b2o8bo34bo21bo7708b4o$187b2o30b2o11b2o7729bo2b2o$219b3o11bo7730b3o11b2o$7951b2o12bo12bobo$78bo7872b2o26bo$78bo133b3o7bo7bo7bo2bo7720bobo5b2o$78bo133b3o7b2o5bobo3b4o2bo7722bo5b2o$67bo146bo9bo4bobo4bo4b2o7718bo$66bobo142b3o7bo2bo5bo6bo4bo4b2o7711b2o4bo$67b2o142b3o23bo3b2o4b2o7711bo6bo$186bo33bo18bobo7719b4o2bo$104b2o80bo33bobo$104b2o80bo34bo2$238b3o$7995b2o$7995b2o11bo3b2o$8007bo4bo$8008bo$108b2o70b3o7801bo24bobo$66b2o40b2o24b2o7847bobo24bo$65bo2bo65b2o7834bo12b2o21bo$66b2o7901bobo33bob3o11b2o$7969b2o34bo2b3o10b2o$69b3o70b2o7863bo2b2o$142b2o7865b2o$67bo94bo7846bo$67bo94bo41b2o7773bo$67bo94bo40bo2bo7771bobo39b3o$98b2o23b2o40bo11b2o24bobo7772b2o38b3ob2o$64b2o32bobo22bobo32b3o3bobo10bobo24bo7822bo$64b2o33b2o23b2o38bobo11bo7844bo3bo$155b2o8bo7852b2o7bo$155b2o59bo7802bob2o$215bobo7801b2o$215bobo7793b2o6bo$216bo7794b2o$8011b2ob2o$8013b2o$8009bo9b2o$7979b2o27b3o7bo2bo$7978bo2bo25bob2o8b2o$154bo7776bo47b2o26b2o$154bo7775b2o$154bo7775bobo42b3o2$7979bo40b2o$7979bo39bo$7979bo38b2o4bo$8015bo5bo3bo$7981b2o31b2o7b2o$148b3o7830b2o31b2o$102b2o$102b2o7898bo44b2o$8001bobo42bo2bo$8001b2o44b2o$110b2o7906b3o$110b2o7906b2ob2o$130bo7887b2ob2o$130bo41b2o7837bo9b2o$130bo40bo2bo7835bobo$91b2o40bo11b2o24bobo7836b2o$91bobo32b3o3bobo10bobo24bo$92b2o38bobo11bo7826b2o$123b2o8bo7839b2o66bo$123b2o59bo7855bobo$183bobo7854bo2bo$183bobo7855b2o$184bo3$7969b2o$7969b2o40b2o$8010bo2bo$122bo7888b2o$122bo$122bo7884b3o2$8011bo$8011bo$8011bo$7979b2o$7978bobo32b2o$116b3o7859b2o33b2o$8023b3o$8079b2o$8078bo2bo$8079b2o$8032bo$8032bo$98bo7933bo$98bo41b2o7901bo$98bo40bo2bo7899bobo$101bo11b2o24bobo7900b2o$94b3o3bobo10bobo24bo$100bobo11bo7890b2o$91b2o8bo7903b2o66bo$91b2o59bo7919bobo$151bobo7918bo2bo$151bobo7919b2o$152bo3$8001b2o$8001b2o40b2o$8042bo2bo$8043b2o2$8039b3o2$8043bo$8043bo$8043bo$8011b2o$8010bobo32b2o$8010b2o33b2o$8055b3o$8111b2o$8110bo2bo$8111b2o$8064bo$8064bo$8064bo$8075bo$8074bobo$8074b2o2$8037b2o$8037b2o66bo$8104bobo$8104bo2bo$8105b2o4$8033b2o$8033b2o40b2o$8074bo2bo$8075b2o2$8071b3o2$8075bo$8075bo$8075bo$8043b2o$8042bobo32b2o$8042b2o33b2o$8087b3o4$8096bo$8096bo$8096bo$8107bo$8106bobo$8106b2o2$8069b2o$8069b2o7$8065b2o$8065b2o40b2o$8106bo2bo$8107b2o2$8103b3o2$8107bo$8107bo$8107bo$8075b2o$8074bobo32b2o$8074b2o33b2o!

Unless someone else responds soon, I will probably work on the 3-GPSE solution mentioned in edit #18 next.

Twenty-third edit: Actually, there's a problem: An A₀ glider sent at GPSE C 128 ticks off from when it is in the example causes the formation of a C₁ glider. However, this can be solved by constructing a fishhook in the appropriate place before any C₁ gliders arrive. Will placing GPSE C about 770 times as far from the interaction point as GPSE A be sufficient?

Twenty-fourth edit: Unfortunately, the 3-GPSE idea that I mentioned in edit #18 does not seem to work, at least not how I originally planned it, because a two-glider collision that needs to result in nothing in order for the mechanism to work creates a bi-block instead.

Code: Select all

x = 82, y = 26, rule = DoubleB3S23
43.2C$43.2C21$80.2C$2C43.2A32.2C$.2C41.2A35.C$C45.A!

However, there might be a way to make it work by inputting gliders B and C into the logic gate instead of gliders B and A₀ and then have glider A₀ annihilate glider B′. I'll try that soon.

Twenty-fifth edit: That does not work either because setting the heights close enough makes glider A₀ interfere with the logic gate.

[calcyman]

Very impressive work!

Your two construction lanes are the same phase and 6hd apart. Is it possible to make them 3hd apart instead? I don't think we have a universal 6hd same-phase set of Fibonacci slow salvos.

EDIT: it looks as though they can be made 9hd apart, which might be sufficient (Chris mentioned that (9, 0) looked promising):

Code: Select all

x = 625, y = 613, rule = B3/S23
23bo$21bobo$22b2o62$87bo$85bobo$86b2o62$151bo$149bobo$150b2o62$215bo$
213bobo$214b2o62$279bo$277bobo$278b2o36$310bo$310bo$310bo19$286b2o$
285bobo$287bo34$366b2o$366bobo$366bo$256b3o$258bo$257bo23$222b2o$221bo
bo$223bo34$430b2o$430bobo$430bo$192b3o$194bo$193bo23$158b2o$157bobo$
159bo34$494b2o$494bobo$494bo$128b3o$130bo$129bo23$94b2o$93bobo$95bo34$
558b2o$558bobo$558bo$64b3o$66bo$65bo23$30b2o$29bobo$31bo34$622b2o$622b
obo$622bo$3o$2bo$bo!

[calcyman]

Actually, it looks very probable that MathAndCode's existing 17-glider solution is universal.

Here's a clean perpendicular glider production recipe (found by automated search) which is very suggestive of universality:

Code: Select all

#C successfully constructed glider332877006328342046399932478274137283588089
#C recipe = 2928017112618217732483941439069491518720250378912248812
#CLL state-numbering golly
x = 46356, y = 46356, rule = B3/S23
46349bo$46348bobo$46348bobo$46349bo2$46344b2o7b2o$46343bo2bo5bo2bo
$46344b2o7b2o2$46349bo$46348bobo$46348bobo$46349bo389$45952b2o$
45953b2o$45952bo254$45696b2o$45697b2o$45696bo254$45440b2o$45441b2o
$45440bo340$45104bo$45104b2o$45103bobo40$45056b2o$45057b2o$45056bo
126$44928b2o$44929b2o$44928bo340$44592bo$44592b2o$44591bobo40$
44544b2o$44545b2o$44544bo212$44336bo$44336b2o$44335bobo40$44288b2o
$44289b2o$44288bo126$44160b2o$44161b2o$44160bo340$43824bo$43824b2o
$43823bobo40$43776b2o$43777b2o$43776bo212$43568bo$43568b2o$43567bo
bo40$43520b2o$43521b2o$43520bo212$43312bo$43312b2o$43311bobo40$
43264b2o$43265b2o$43264bo126$43136b2o$43137b2o$43136bo254$42880b2o
$42881b2o$42880bo254$42624b2o$42625b2o$42624bo254$42368b2o$42369b
2o$42368bo340$42032bo$42032b2o$42031bobo40$41984b2o$41985b2o$
41984bo212$41776bo$41776b2o$41775bobo40$41728b2o$41729b2o$41728bo
126$41600b2o$41601b2o$41600bo254$41344b2o$41345b2o$41344bo340$
41008bo$41008b2o$41007bobo40$40960b2o$40961b2o$40960bo126$40832b2o
$40833b2o$40832bo340$40496bo$40496b2o$40495bobo40$40448b2o$40449b
2o$40448bo212$40240bo$40240b2o$40239bobo40$40192b2o$40193b2o$
40192bo126$40064b2o$40065b2o$40064bo254$39808b2o$39809b2o$39808bo
340$39472bo$39472b2o$39471bobo40$39424b2o$39425b2o$39424bo126$
39296b2o$39297b2o$39296bo254$39040b2o$39041b2o$39040bo340$38704bo$
38704b2o$38703bobo40$38656b2o$38657b2o$38656bo126$38528b2o$38529b
2o$38528bo254$38272b2o$38273b2o$38272bo340$37936bo$37936b2o$37935b
obo40$37888b2o$37889b2o$37888bo126$37760b2o$37761b2o$37760bo254$
37504b2o$37505b2o$37504bo340$37168bo$37168b2o$37167bobo40$37120b2o
$37121b2o$37120bo126$36992b2o$36993b2o$36992bo254$36736b2o$36737b
2o$36736bo340$36400bo$36400b2o$36399bobo40$36352b2o$36353b2o$
36352bo126$36224b2o$36225b2o$36224bo254$35968b2o$35969b2o$35968bo
340$35632bo$35632b2o$35631bobo40$35584b2o$35585b2o$35584bo126$
35456b2o$35457b2o$35456bo254$35200b2o$35201b2o$35200bo254$34944b2o
$34945b2o$34944bo254$34688b2o$34689b2o$34688bo254$34432b2o$34433b
2o$34432bo340$34096bo$34096b2o$34095bobo40$34048b2o$34049b2o$
34048bo126$33920b2o$33921b2o$33920bo254$33664b2o$33665b2o$33664bo
340$33328bo$33328b2o$33327bobo40$33280b2o$33281b2o$33280bo126$
33152b2o$33153b2o$33152bo254$32896b2o$32897b2o$32896bo340$32560bo$
32560b2o$32559bobo40$32512b2o$32513b2o$32512bo126$32384b2o$32385b
2o$32384bo340$32048bo$32048b2o$32047bobo40$32000b2o$32001b2o$
32000bo126$31872b2o$31873b2o$31872bo254$31616b2o$31617b2o$31616bo
254$31360b2o$31361b2o$31360bo340$31024bo$31024b2o$31023bobo40$
30976b2o$30977b2o$30976bo126$30848b2o$30849b2o$30848bo254$30592b2o
$30593b2o$30592bo340$30256bo$30256b2o$30255bobo40$30208b2o$30209b
2o$30208bo126$30080b2o$30081b2o$30080bo254$29824b2o$29825b2o$
29824bo340$29488bo$29488b2o$29487bobo40$29440b2o$29441b2o$29440bo
126$29312b2o$29313b2o$29312bo254$29056b2o$29057b2o$29056bo340$
28720bo$28720b2o$28719bobo40$28672b2o$28673b2o$28672bo126$28544b2o
$28545b2o$28544bo254$28288b2o$28289b2o$28288bo254$28032b2o$28033b
2o$28032bo254$27776b2o$27777b2o$27776bo254$27520b2o$27521b2o$
27520bo340$27184bo$27184b2o$27183bobo40$27136b2o$27137b2o$27136bo
126$27008b2o$27009b2o$27008bo254$26752b2o$26753b2o$26752bo340$
26416bo$26416b2o$26415bobo40$26368b2o$26369b2o$26368bo126$26240b2o
$26241b2o$26240bo254$25984b2o$25985b2o$25984bo340$25648bo$25648b2o
$25647bobo40$25600b2o$25601b2o$25600bo126$25472b2o$25473b2o$25472b
o254$25216b2o$25217b2o$25216bo340$24880bo$24880b2o$24879bobo40$
24832b2o$24833b2o$24832bo212$24624bo$24624b2o$24623bobo40$24576b2o
$24577b2o$24576bo126$24448b2o$24449b2o$24448bo254$24192b2o$24193b
2o$24192bo340$23856bo$23856b2o$23855bobo40$23808b2o$23809b2o$
23808bo126$23680b2o$23681b2o$23680bo254$23424b2o$23425b2o$23424bo
340$23088bo$23088b2o$23087bobo40$23040b2o$23041b2o$23040bo126$
22912b2o$22913b2o$22912bo340$22576bo$22576b2o$22575bobo40$22528b2o
$22529b2o$22528bo126$22400b2o$22401b2o$22400bo254$22144b2o$22145b
2o$22144bo340$21808bo$21808b2o$21807bobo40$21760b2o$21761b2o$
21760bo126$21632b2o$21633b2o$21632bo254$21376b2o$21377b2o$21376bo
340$21040bo$21040b2o$21039bobo40$20992b2o$20993b2o$20992bo126$
20864b2o$20865b2o$20864bo254$20608b2o$20609b2o$20608bo254$20352b2o
$20353b2o$20352bo254$20096b2o$20097b2o$20096bo254$19840b2o$19841b
2o$19840bo340$19504bo$19504b2o$19503bobo40$19456b2o$19457b2o$
19456bo126$19328b2o$19329b2o$19328bo340$18992bo$18992b2o$18991bobo
40$18944b2o$18945b2o$18944bo126$18816b2o$18817b2o$18816bo254$
18560b2o$18561b2o$18560bo254$18304b2o$18305b2o$18304bo254$18048b2o
$18049b2o$18048bo340$17712bo$17712b2o$17711bobo40$17664b2o$17665b
2o$17664bo126$17536b2o$17537b2o$17536bo254$17280b2o$17281b2o$
17280bo340$16944bo$16944b2o$16943bobo40$16896b2o$16897b2o$16896bo
126$16768b2o$16769b2o$16768bo254$16512b2o$16513b2o$16512bo254$
16256b2o$16257b2o$16256bo254$16000b2o$16001b2o$16000bo340$15664bo$
15664b2o$15663bobo40$15616b2o$15617b2o$15616bo126$15488b2o$15489b
2o$15488bo254$15232b2o$15233b2o$15232bo340$14896bo$14896b2o$14895b
obo40$14848b2o$14849b2o$14848bo126$14720b2o$14721b2o$14720bo254$
14464b2o$14465b2o$14464bo340$14128bo$14128b2o$14127bobo40$14080b2o
$14081b2o$14080bo126$13952b2o$13953b2o$13952bo254$13696b2o$13697b
2o$13696bo254$13440b2o$13441b2o$13440bo254$13184b2o$13185b2o$
13184bo254$12928b2o$12929b2o$12928bo254$12672b2o$12673b2o$12672bo
254$12416b2o$12417b2o$12416bo254$12160b2o$12161b2o$12160bo254$
11904b2o$11905b2o$11904bo340$11568bo$11568b2o$11567bobo40$11520b2o
$11521b2o$11520bo212$11312bo$11312b2o$11311bobo40$11264b2o$11265b
2o$11264bo126$11136b2o$11137b2o$11136bo254$10880b2o$10881b2o$
10880bo340$10544bo$10544b2o$10543bobo40$10496b2o$10497b2o$10496bo
212$10288bo$10288b2o$10287bobo40$10240b2o$10241b2o$10240bo126$
10112b2o$10113b2o$10112bo340$9776bo$9776b2o$9775bobo40$9728b2o$
9729b2o$9728bo212$9520bo$9520b2o$9519bobo40$9472b2o$9473b2o$9472bo
126$9344b2o$9345b2o$9344bo340$9008bo$9008b2o$9007bobo40$8960b2o$
8961b2o$8960bo126$8832b2o$8833b2o$8832bo254$8576b2o$8577b2o$8576bo
254$8320b2o$8321b2o$8320bo340$7984bo$7984b2o$7983bobo40$7936b2o$
7937b2o$7936bo126$7808b2o$7809b2o$7808bo254$7552b2o$7553b2o$7552bo
254$7296b2o$7297b2o$7296bo254$7040b2o$7041b2o$7040bo254$6784b2o$
6785b2o$6784bo254$6528b2o$6529b2o$6528bo340$6192bo$6192b2o$6191bob
o40$6144b2o$6145b2o$6144bo126$6016b2o$6017b2o$6016bo340$5680bo$
5680b2o$5679bobo40$5632b2o$5633b2o$5632bo212$5424bo$5424b2o$5423bo
bo40$5376b2o$5377b2o$5376bo126$5248b2o$5249b2o$5248bo254$4992b2o$
4993b2o$4992bo254$4736b2o$4737b2o$4736bo254$4480b2o$4481b2o$4480bo
254$4224b2o$4225b2o$4224bo254$3968b2o$3969b2o$3968bo340$3632bo$
3632b2o$3631bobo40$3584b2o$3585b2o$3584bo126$3456b2o$3457b2o$3456b
o254$3200b2o$3201b2o$3200bo340$2864bo$2864b2o$2863bobo40$2816b2o$
2817b2o$2816bo212$2608bo$2608b2o$2607bobo40$2560b2o$2561b2o$2560bo
126$2432b2o$2433b2o$2432bo254$2176b2o$2177b2o$2176bo254$1920b2o$
1921b2o$1920bo254$1664b2o$1665b2o$1664bo254$1408b2o$1409b2o$1408bo
340$1072bo$1072b2o$1071bobo40$1024b2o$1025b2o$1024bo126$896b2o$
897b2o$896bo254$640b2o$641b2o$640bo340$304bo$304b2o$303bobo40$256b
2o$257b2o$256bo212$48bo$48b2o$47bobo40$2o$b2o$o!