True knightship oblique Geminoid working notes

[dvgrn]

Following up on the Freeze-dried slow salvos thread, here's a prototype true (2,1)c/N knightship -- just needs to be programmed a little better, you might say:

Code: Select all

x = 194, y = 185, rule = LifeHistory
2E$2E17$23.B$23.2B$23.3B$23.4B$24.4B$25.4B$26.4B$27.4B$28.4B$29.4B45.
A$30.4B44.3A$31.4B34.A11.A$19.2A3.2A6.4B17.A15.3A8.2A5.4B$18.B2AB.B2A
B6.4B14.3A18.A7.11B$19.2B2.3B3.B4.4B12.A20.2A3.B5.11B$20.3B.3B.4B3.4B
11.2A19.8B2.11B2A$12.2A5.7B.13B11.B21.19B2A$13.A5.23B9.3B19.20B$13.A.
AB.19B.8B4.6B16.20B$14.2AB.29B2.10B11.21B$16.44B3.2B2.25B$16.37B2A15B
D14B4.4B$16.37B2A15BDBD4B.6B6.4B$17.53B3D4B2.B.5B5.4B$19.53BD4B7.2A6.
B$17.59B8.A$17.2A3.25B4.13B.4B16.3A$18.A3.20B4.B4.7B.B5.3B19.A$15.3A
6.15B7.2A15.4B$15.A8.11B12.A15.2A$23.13B8.3A17.A$22.15B7.A16.3A$22.
16B23.A$22.17B$22.16B$24.13B$24.3B.2B2A5B$22.4B2.2B2A3B$22.2A3.8B$23.
A4.2B3D3B$20.3A5.3BD4B$20.A8.2B3D2B$29.7B$21.A7.6B$20.A.A6.6B$20.A.A
6.5B$18.3A.2A4.6B$17.A4.B6.6B$18.3AB2AB3.7B$20.A.2AB.8B$24.10B$24.6B
2A3B5.2A$24.6B2A2B5.A.A$24.10B5.A$23.11B2.BA.A$23.12B.B2A$22.15B$21.
16B$18.2B.16B$17.2A18B$17.2AB.17B$18.B.4B.8B2.4B$25.7B4.4B$26.6B5.4B$
28.4B6.4B$30.3BA5.4B$31.BA.A5.4B$32.A.A6.4B$33.A8.4B$34.3A6.4B$36.A7.
4B$45.B3C$46.C3B$47.C2B$48.2B4$157.A$157.3A$160.A$159.A.A$153.B5.A.AB
$153.2B5.A3B$153.3B6.4B$153.4B5.6B$154.4B4.7B$155.4B2.8B.4B.B$156.17B
.B2A$66.B90.18B2A$66.2B89.16B.2B$66.3B88.16B$66.4B87.15B$67.4B84.2AB.
12B$68.B3C82.A.AB2.11B$69.C3B81.A5.10B$70.C2B79.A.A5.2B2A6B$71.2B79.
2A5.3B2A6B$160.10B$160.8B.B2A.A$159.7B3.B2AB3A$159.6B6.B4.A$160.6B4.
2A.3A$160.5B6.A.A$159.6B6.A.A$159.6B7.A$158.7B$158.2B3D2B8.A$158.4BD
3B5.3A$158.3B3D2B4.A$159.8B3.2A$159.3B2A2B2.4B$89.B67.5B2A2B.3B$89.2B
66.13B$89.3B64.16B$89.4B62.17B$90.4B38.A23.16B$91.B3C35.3A16.A7.15B$
92.C2B11.A11.A10.A17.3A8.13B$93.CB11.3A7.3A10.2A15.A12.11B8.A$94.B14.
A5.A11.4B15.2A7.15B6.3A$108.2A4.B2A9.3B5.B.7B4.B4.20B3.A$108.9B8.4B.
13B4.25B3.2A$110.5B3.59B$109.6B2.4BD53B$109.6B2.4B3D53B$109.7B.4BDBD
15B2A37B$108.15BD15B2A37B$104.B2.20B2.2B3.44B$104.2B.17B11.10B2.29B.B
2A$104.18B16.6B4.8B.19B.BA.A$104.17B19.3B9.23B5.A$105.17B20.B11.13B.
7B5.2A$106.16B20.2A11.4B3.4B.3B.3B$107.7B3.3B.B2A19.A12.4B4.B3.3B2.2B
$108.6B7.BA.A15.3A14.4B6.B2AB.B2AB$109.4B11.A15.A17.4B6.2A3.2A$107.5B
12.2A33.4B$107.2A51.4B$108.A52.4B$105.3A54.4B$105.A57.4B$164.4B$165.
4B$166.4B$167.4B$168.3B$169.2B$170.B17$192.2E$192.2E!

It's not quite that simple, of course -- there's a little bit of switching circuitry to be added. See "Exact-Timing Loop" below. Here's a full walkthrough of how a (2,1) Geminoid knightship might work:

1 ) Start with the two halves of the Geminoid much, much farther apart.
2 ) We have a single-channel salvo of construction gliders made up of two sub-salvos.
3 ) Let's call the two sub-salvos the NW-Reflector-Constructor-building salvo and the SE-Reflector-Constructor-building salvo.
3b) Really let's call them NWRCS and SERCS for short, pronounced like "Newark's Cirques".
3c) (There were glaciers in Newark, New Jersey not long ago, so just pretend there are more mountains there.)
4 ) NWRCS always comes before SERCS, with some reasonable separation distance... maybe very short.
5 ) NWRCS and SERCS will each build a freeze-dried slow salvo off to the side of NWRC and SERC respectively.
5b) When triggered, these freeze-dried slow salvos will "relatively instantly" rebuild NWRC and SERC.

6 ) Whenever it's freshly rebuilt, SERC will include an eater on its construction lane.
6b) That takes care of not building the NWRCS recipe at SERC.
6c) We'll shoot down that NWRCS-Blocking Eater later.
7 ) The last instruction in NWRCS builds an absorbing eater on the actual NWRC.
7b) This SERCS-Blocking Eater absorbs every glider from SERCS that SERC copies to the construction arm.
7c) That takes care of not building the SERCS recipe at NWRC.

8 ) The tail end of SERCS will create a trigger glider for the SERC freeze-dried slow salvo.
8b) As it thaws, the SERCS slow salvo will shoot down and then rebuild SERC at a (2,1) offset.
8c) An early splitter in the SERC freeze-dried slow salvo will send a glider NW, chasing SERC.
8d) This NW glider will trigger the freeze-dried slow salvo built by NWRCS.
8e) That will rebuild NWRC at a (2,1) offset.
8f) It can't get rebuilt much earlier than that anyway, because SERCS is still going through SERC until about then.

9) There's still an NWRCS-Blocking Eater sitting in SERC, darn it.
9b) The NWRCS-Blocking Eater had to get shot down at just the right time...
9c) ... after NWRCS goes through SERC, but before SERCS gets there.
9d) I can't think of a really great way to to extract that eater destruct signal.
9e) The simplest mechanism might be half a dozen still lifes making an Exact-Timing Loop.
9f) Let's say it takes the NWRCs lead glider N ticks to go through NWRC and SERC and back to NWRC.
9g) Then it also has to take exactly N ticks to cycle around the Exact-Timing Loop.
9h) The one-time splitter and turners in the Exact-Timing Loop will be rebuilt along with NWRC and SERC.

10) Is there a Geminoid true (2,1) knightship design that's much simpler than this?

There! All done inside a count of ten... with a generous allowance for sub-items.

[dvgrn]

There! All done inside a count of ten... with a generous allowance for sub-items.

This is a two-reflector long-and-skinny Geminoid -- will look like a boring diagonal line, just like the linear propagator and the original Geminoid. But luckily it can at least be optimized to run well in HashLife, as long as the computer has enough memory. The loop is 0 mod 8 if the offset is (1, 2), which is the only option HashLife is really happy with. (-2,-1) would give 4 mod 8, so it's better to avoid that direction.

On the other hand, a very HashLife-happy (-3, -2) zebraship could be built with these pieces -- or an impressively slow (-1,0) orthogonal ship would work out fine, too. Really, once the compiler scripts are set up, it could be rebuilt to leap any (M,N) distance -- it's just that HashLife will crawl on some offsets and run away on others (though only if the distance between NWRC and SERC is adjusted to make a power of two).

My original intention was to write up the equivalent steps for a diamond-shaped (2,1)-offset Geminoid, but a 40sL complete programmable knightship was kind of irresistible when I started thinking about it. The programming will be pretty painful, though, because of the geometry -- you either have to build the freeze-dried slow salvo with *WSSes, or you have to use a second slow elbow to get gliders to the target. Both options are pretty expensive.

Diamond Knightship
A diamond-shaped Geminoid would need four salvos -- NRCS, ERCS, SRCS, and WRCS -- and twice as much one-time switching circuitry to unblock the four construction channels at the appropriate times. But it could use standard slow glider salvos. Each construction salvo would travel from the RC that generated it, along a full edge of the diamond, to construct the next RC's freeze-dried salvo. This is in contrast to the 180-degree RC model, where each RC constructs its own freeze-dried salvo.

In the diamond-shaped design, blocking off the construction arms is trivial again, just the last part of each sub-salvo. But unblocking needs one-time signals from somewhere, presumably traveling on a different path from the main loop. Quite possibly each salvo will generate an extra unblocking-signal glider as part of its blocking eater construction. The unblocking signal would travel just behind the salvo that generated it, to the next RC, to shoot down its blocking eater right after that salvo's last glider goes by.

There's a separate problem of when to trigger each freeze-dried salvo seed. That will need some more work. Possibilities:

1) On exactly-timed trigger glider chain travels around and around the diamond -- separate from the NRCS/ERCS/ SRCS/WRCS glider stream, but keeping up with it exactly -- and rebuilds each RC at a time when it's not in use.

2) One of the reflectors could send a retrograde glider backwards to bounce off a one-time turner, to start the reconstruction-circuit chain at an appropriate time.

3) A single glider in the loop travels far ahead of the main NRCS/ERCS/ SRCS/WRCS glider stream, hitting one-time turners left in the construction channel (in front of an eater, in three of the four cases) that trigger each freeze-dried salvo. I think this one might be the easiest. Next I'll try drawing detailed diagrams of the stages to make sure I'm not missing any annoying timing details.

The big advantage of a diamond-shaped loop is that it will run really fast in HashLife immediately -- much less time needed to fill up a big hash table, because there aren't any glider streams running in opposite directions next to each other. Having four corners also gives plenty of adjustment options for a Spartan loop that's 0 mod 8, and meets up at whatever offset might be wanted.

[chris_c]

10) Is there a Geminoid true (2,1) knightship design that's much simpler than this?

I don't know about simpler but here is an alternative at least.

Have two copies of your pattern that destroy and rebuild each other using LWSS directly from the construction elbow. The advantage is that you use direct construction (albeit with LWSS) instead of freeze-dried salvos. The disadvantage is that you will need a large gap between the NWRCS and the SERCS.

Here is a dodgy sketch:

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x = 93, y = 92, rule = LifeHistory
18.D2$18.D.D2$18.D3.D2$18.D5.D2$18.D7.D2$18.D9.D2$18.D11.D2$18.D13.D$
40.D$18.D15.D4.D.D$38.D3.D$D.D.D.D.D.D.D.D.D.D.D.D.D.D.D8.D5.D$36.D5.
D$2.D15.D16.D5.D$34.D5.D4.D$4.D13.D14.D5.D6.D$32.D5.D8.D$6.D11.D14.D
3.D10.D$34.D.D12.D$8.D9.D16.D14.D$51.D$10.D7.D33.D.D$53.2D$12.D39.3D
2$14.D$22.D$16.D4.D.D$20.D3.D$19.D5.D$18.D5.D$17.D5.D$16.D5.D$15.D5.D
$14.D5.D$15.D3.D$16.D.D$17.D37.3D$21.3D31.2D$21.2D32.D.D$21.D.D34.D$
24.D34.D$25.D34.D13.D$26.D34.D11.D.D$27.D34.D9.D3.D$28.D34.D7.D5.D$
29.D34.D5.D5.D$30.D14.D23.D5.D$46.D21.D5.D$47.D19.D5.D$48.D17.D5.D$
49.D17.D3.D$50.D17.D.D5.D$51.D17.D$52.D.D23.D$53.2D$52.3D21.D3.D2$58.
D17.D5.D$57.D.D$56.D3.D15.D7.D$55.D5.D$54.D5.D15.D9.D$53.D5.D$52.D5.D
17.D11.D$51.D5.D$50.D5.D19.D13.D$51.D3.D$52.D.D5.D3.D.D.D.D.D.D.D.D.D
.D.D.D.D.D.D$53.D$62.D13.D2$64.D11.D2$66.D9.D2$68.D7.D2$70.D5.D2$72.D
3.D2$74.D.D2$76.D!

An entire glider stream is represented by a pointed arrow. The constructors in the NE have just finished destroying and rebuilding the constructors in the SW. The recipe streams for the SW constructors are just about to enter and destory/rebuild the NE constructors.

Whether going from freeze dried salvo to LWSS construction is worth the 2x delay between the gliders streams is an open question.

EDIT: I have completely neglected to think about blocking off the NWRCS and SERCS when they are at the "wrong" end of the constructor but hopefully some kind of solution exists...

[dvgrn]

EDIT: I have completely neglected to think about blocking off the NWRCS and SERCS when they are at the "wrong" end of the constructor but hopefully some kind of solution exists...

Yeah, that's unlikely to be a problem, really. The blocking off can always be done by the tail ends of the recipes, and with a large gap between NWRCS and SERCS there's bound to be a way to extract a one-time signal from somewhere and knock out an eater at more or less the right time.

I think you could get away with slow-LWSS building at one end and direct slow-glider construction at the other:

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x = 102, y = 66, rule = LifeHistory
39.D$40.D$41.D7.D$D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D5.D.D$
41.D5.D3.D$2.D37.D5.D5.D$39.D5.D5.D$4.D33.A5.D5.D$37.A.A3.D5.D4.D$6.D
29.A3.A.D5.D6.D$35.A5.D5.D8.D$8.D25.A7.D3.D10.D$33.A9.D.D12.D$10.D21.
A11.D14.D$31.A28.D$12.D14.A2.A30.D.D$27.A.A32.2D$14.D12.2A32.3D$23.D
3.4A$16.D5.D.D$21.D3.D$20.D5.D$19.D5.D$18.D5.D$17.D5.D$16.D5.D$15.D5.
D$16.D3.D4.3D$17.D.D5.2D$18.D6.D.D$28.D$29.D34.3D$30.D33.2D$31.D32.D.
D$32.D34.D$33.D34.D$34.D34.D13.D$70.D11.D.D$71.D9.D3.D$72.D7.D5.D$73.
D5.D5.D$44.D33.D5.D$45.D31.D5.D$46.D29.D5.D$47.D27.D5.D$48.D27.D3.D$
49.D27.D.D5.D$50.D20.4A3.D$51.D.D19.2A12.D$52.2D18.A.A$51.3D17.A2.A
14.D$70.A$57.D11.A21.D$56.D.D9.A$55.D3.D7.A25.D$54.D5.D5.A$53.D5.D.A
3.A29.D$52.D5.D3.A.A$51.D5.D5.A33.D$50.D5.D5.D$49.D5.D5.D37.D$50.D3.D
5.D$51.D.D5.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D$52.D7.D$61.D$
62.D!

That's still a little bit weird and awkward... but on the other hand my original 180-degree design would have to use either *WSSes or a second slow elbow to build the freeze-dried slow salvos. And that's more like awkward squared.

Or it could be a freeze-dried *WSS salvo, of course... we have lots of horribly inefficient options!

A diamond knightship would have the same number of RCs as the above, and would run enormously faster in HashLife. Time for some more detailed diamond diagrams, I think.

[dvgrn]

A diamond knightship would have the same number of RCs as the above, and would run enormously faster in HashLife. Time for some more detailed diamond diagrams, I think.

On a bus to Chicago yesterday, I had time to sketch out four competing designs for a diamond Geminoid spaceship that could be programmed (with some difficulty) to travel in any direction at any sufficiently slow speed (x,y)c/8n.

Thanks to a sudden burst of common sense on my part, late this afternoon, Diamond Geminoid Mark 4 looks a lot simpler than the previous three models. It might even be worth starting work on a proper blueprint for it.

The Details That I'll Be Ignoring
Really it would take two slightly different variants of the spaceship body to hit any (x,y)c/8n -- one 90-degree corner out of the four will have to change, depending on whether x+y is even or odd. A total of sixteen diamond-Geminoid models would be needed to hit any sufficiently slow (x,y)c/n.

I'm not so interested in (x,y)/(8n+1..7), just because Hashlife will be relatively unhappy simulating those speeds. For now I'll concentrate on making a true (2,1) knightship with a power-of-two period, (2,1)c/(2^k), and work on figuring out how big k has to be...!

The Main Problem
There's one big complication with a diamond Geminoid. The original Gemini and the Demonoids could re-use the exact same construction recipe at the two 180-degree corners of the recipe loop, and the linear propagator ran everything from a single construction arm at one end of the loop. By contrast, a diamond Geminoid has to run its recipe around four corners, and relative to the input glider stream, the movement is in a different direction at each corner.

So unless we build about five times as much circuitry as we need at each corner -- and that's a definite possibility, but we can call that Diamond Geminoid Mark Five and save it for later -- we'll need a totally different slow-salvo recipe to move each corner.

Two Stages of Slow Salvo
Freeze-dried slow salvos will probably be needed here, so they can do their work quickly during a short downtime period when the constructors aren't busy reflecting gliders. There are some alternatives, involving either a second slow elbow (Diamond Geminoid Mark Six) or four faraway elbows that shoot *WSSes to do the construction/destruction (Diamond Geminoid Mark Seven). But let's stick with the "simple" freeze-dried salvo idea for now:

Each constructor C builds a slow salvo c' heading toward the next constructor/reflector in the loop. Let's call the next constructor D. The c' slow salvo builds a freeze-dried salvo seed pattern, Dseed, off to one side of constructor D. While the actual c' slow salvo is building seed pattern Dseed, D is busy reflecting the recipe stream gliders that produced c'. Whenever a trigger glider hits Dseed, a slow salvo is produced that quickly shoots down most of D and rebuilds it at a (2,1)-or-whatever offset from the remaining wreckage.*

Design Considerations
On balance it seemed simpler to re-use the same reflection circuitry for all four recipes, than to set up four separate channels all exactly the same length and not conflicting with each other. That'd be a lot of extra circuitry, whereas it really doesn't take much to turn on a single-channel universal constructor (one glider to shoot down an eater) or to switch it off again (use the end of the construction recipe to build an eater that blocks the channel).

So my Mark One through Mark 3 designs consisted of a single glider loop -- travelling clockwise, let's say. Four 90-degree 90-tick recovery reflectors sit at the corners of a diamond, with an extra glider output each to make them into single-channel universal constructors.

Actually it's a glider almost-loop. The end of the loop doesn't quite hook up with the beginning -- it's offset by (2,1) for the knightship case.

The More Specific Problem
Unfortunately, if the recipe is in a single stream, each constructor has to know when to turn itself on and off, so that different corners read a different quarter of the full recipe stream.

Turning constructors off is easy: once they're turned on, they can construct whatever they're supposed to construct, and then construct an eater in the output channel. And one of the corners can be constructed in ON mode, since it will be reading the first sub-recipe of the four.

But turning the other three constructors on at the right time was a little bit painful -- it could be done, but some clever mechanism would be necessary to run around the loop separate from the recipe, and turn on each of the construction arms at a different time, just as the appropriate quarter-recipe glider stream reached that corner. And then another timed reaction would have to trigger all the freeze-dried salvos at the right time.

The easiest way might be to send retrograde gliders around the loop to some of the corners, or maybe send a *WSS straight across the middle of the diamond. Hashlife wouldn't mind the *WSS as much as the counterclockwise gliders. Still, a loop where everything moved clockwise would be better from Hashlife's point of view.

I started out thinking that the glider loop would be mostly empty, so that the first constructor could read the first quarter of the glider stream, the second constructor would read the second quarter, etc., and then there would be some "down time" while the resulting slow salvos did their work.

But...

The Sudden Attack of Common Sense
If the easy part is shutting constructors down, and the hard part is starting them up at the right time so that they read the right part of the glider stream, then why not start them all up at once? This allows a much smaller glider loop, with very little empty space in it:

rough diagram of four stages of Mark 4 Diamond Geminoid knightship

DiamondGeminoidMark4small.png (339.87 KiB) Viewed 25286 times

All four constructor corner circuits A, B, C, and D are shot down and rebuilt at the same time; they're all rebuilt with their constructor arms turned on, and each quarter-recipe glider stream a, b, c, and d includes instructions at the end to build a blocking eater on the construction channel.

The Remaining Much Smaller Problem
It's still necessary to wait for a full recipe-loop cycle before triggering the four freeze-dried slow salvos.

Here's an easy way to accomplish that:

The Stages in the Diagram

• Stage 1 shows the freeze-dried salvos in the middle of being triggered, rebuilding A, B, C, D at whatever (x,y) offset, while no recipe glider streams are running through any of the circuitry.
• Stage 2: the four quarter-recipe glider streams a, b, c, d (single red arrows) have run through their constructors A, B, C, D. This produces slow salvos a', b', c', d' (wide red arrows) running parallel and just behind their recipes.
• Stage 3: a', b', c', d' have hit a handy target near the next corner. This builds a freeze-dried salvo that sits off to the side of the corner, out of the way. All four constructors have now been programmed to shut down. At the end of construction, the starting target at each corner is rebuilt with the appropriate offset, and a single glider at each corner is launched toward the _next_ corner.
• Stage 4: The four trigger gliders hit a one-time turner -- a boat or some such -- that shunts them to the _next_ corner, where in the next Stage 1 they will trigger the freeze-dried slow salvos and move all four corners simultaneously.

I think there aren't any tricky timing problems with that. The trigger gliders ultimately derive from the ends of their respective quarter-recipes. So a gap can be left between a, b, c, and d of whatever size is needed to let the freeze-dried salvo do its reconstruction work. The trigger gliders could even be moved up to be sent a little sooner, if that was useful for the timing.

The Footnote
* Bonus points accrue whenever a block in a circuit can be moved by pulling it (2,1) with a glider, instead of destroying and rebuilding it...!

[dvgrn]

There are some alternatives, involving either a second slow elbow (Diamond Geminoid Mark Six) or four faraway elbows that shoot *WSSes to do the construction/destruction (Diamond Geminoid Mark Seven)...

I'm not sure that the Mark Seven option is going to work, because the single-channel salvos and resulting *WSSes would have to travel a fixed distance, not adjustable by moving an elbow.

For both Mark Six and Mark Seven, you'd have to leave gaps in the instruction loop that are as long as the recipes... and for Mark Seven the gaps would all have to be directly opposite their recipes. I'm not sure that's geometrically possible, unless we go back to the bad old plan of sending recipes a, b, c, d sequentially and adding a tricky extra switching system to turn on the UC in the appropriate three corners, at just the right time. Not sure that's worth it.

However, the "slow elbow" idea should work fine, at the cost of an instruction loop that might be slightly bigger than the Mark Four. It has to consist of four recipe glider streams interleaved with four stretches of empty space, each as long as the longest recipe stream. On the other hand, there are no freeze-dried salvo seeds necessary -- the recipes just have to run a "slow elbow" each, to destroy and reconstruct the associated corner. That's probably a good bit cheaper than building freeze-dried constellations.

Here's a quick sketch of the idea. Single dashed lines are the single-channel glider streams; double dashed lines are slow salvos, and double dotted lines are the "slow^2 salvos" emanating from the second elbow.

Diamond Geminoid Mark Six rough blueprint

DiamondGeminoidMarkSix_small.jpg (53.05 KiB) Viewed 24762 times

This diagram isn't quite to scale. Distances from Geminoid corners to the elbows should be only about half as long as shown here. The effect will be that the slow^2 salvos will be delayed in their arrival by 1/8 of the loop's repeat time. That way they'll arrive at the next corner and start to rebuild it, just after the last of the recipe gliders that created the slow^2 salvo pass through that corner -- and they'll finish the rebuild process just before the next recipe arrives.

...Right?

EDIT: No, not right! When all four recipe streams are in a tight loop, it would be necessary to move the recipe streams as well as the corners, all simultaneously. Offhand I don't see any way to modify the Mark Four or Mark Six designs to get around that problem.

That means I have to backtrack to Mark Two to get a diamond Geminoid design that's actually workable. Mark Two's operation is a little more complicated, but not too bad really... watch this space for a blueprint.

[dvgrn]

Offhand I don't see any way to modify the Mark Four or Mark Six designs to get around that problem.

That means I have to backtrack to Mark Two to get a diamond Geminoid design that's actually workable...

On third thought, I belive the Mark Six can be patched up, after all. The length of the paths of the slow^2 salvos is adjustable -- so it's quite possible to time each of the slow^2 salvos to arrive just after the four recipe streams go by.

That means that there will need to be a gap in the recipe loop, but it only has to be a fifth of the full loop -- i.e., the gap will be the same length as the longest recipe stream. That gives just enough time for the rebuild operation at each corner.

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x = 122, y = 132, rule = LifeHistory
87.2A$87.2A$85.D$84.D4.D$83.D6.D$82.D8.D$81.D4.D5.D$80.D6.D5.D$79.D8.
D5.D$78.D10.D5.D$77.D12.D5.D$76.D14.D5.D$75.D16.D5.D$74.D18.D5.D$73.D
20.D5.D$72.D22.D5.D$71.D24.D5.D$55.A14.D26.D5.D$54.A.A12.D28.D5.D$53.
A3.A10.D30.D5.D$49.D3.A3.A9.D32.D5.D$49.D2.A5.A7.D34.D5.D$46.D2.D2.A
5.A6.D36.D5.D$42.2A5.D2.7A5.D38.D5.D$42.2A5.D2.A5.A4.D40.D5.D$32.9D2.
D5.D2.A5.A3.D42.D5.D$36.D3.D8.D2.A5.A2.D44.D5.D$35.D4.D8.D10.D46.D5.D
$34.D5.10D9.D48.D5.D4.D$33.D5.2D17.D50.D5.D3.D$32.D5.D.D69.D5.D2.D$
31.D5.D2.D14.2A54.D5.D.D$30.D5.D3.D13.A2.A54.D5.2D$29.D5.D4.D12.A4.A
54.D5.D$28.D5.D17.A6.A54.D4.D$27.D5.D17.A8.A54.D3.D$26.D5.D17.A10.A3.
A45.9D$25.D5.D17.A12.A2.A$24.D5.D17.A14.A.A54.2A$23.D5.D17.A16.2A54.
2A$22.D5.D17.A14.5A$21.D5.D23.4C$20.D5.D26.2C61.D$19.D5.D26.C.C$18.D
5.D26.C2.C$17.D5.D26.C62.D5.D$16.D5.D26.C9.C$15.D5.D26.C$14.D5.D26.C
62.D5.D$13.D5.D26.C15.C$12.D5.D26.C$11.D5.D26.C4.3C55.D5.D$10.D5.D26.
C4.C3.C12.C$9.D5.D26.C9.C$8.D5.D26.C7.4C51.D5.D$7.D5.D26.C7.C3.C15.C
29.D$12.D26.C8.C3.C45.D$11.D26.C10.3C.C44.D2.D5.D$6.2A2.D26.C33.C26.D
$6.2A28.C26.3C32.D$35.C26.C3.C31.D5.D$8.D12.5A36.C3.C7.C11.A11.D$9.D
14.2A36.5C20.A10.D$10.D12.A.A3.4C29.C25.A9.9D$11.D10.A2.A5.2C29.C14.C
11.A$12.D8.A3.A4.C.C30.4C23.A$20.A8.C2.C58.A9.5A$3.4A12.A8.C63.A8.A4.
A$3.A3.A10.A8.C53.C11.A7.A4.A$3.A4.A8.A8.C9.C45.C11.A6.A4.A$3.A4.A7.A
8.C10.C36.C9.C11.A5.5A$3.A4.A7.A9.C9.C36.C10.C10.A5.A4.A$3.A4.A8.A9.C
8.C36.C11.C8.A6.A4.A$3.A4.A9.A9.C7.C.3C32.C10.C8.A7.A4.A$3.A3.A11.A9.
C6.2C3.C27.3C.C9.C8.A8.5A$3.4A13.A9.C5.C5.C25.C3.2C8.C8.A$21.A9.C4.C
5.C24.C5.C7.C4.A3.A6.D$6.9D7.A9.C3.2C3.C25.C5.C6.C5.A2.A8.D$14.D8.A9.
C2.C.3C27.C3.2C5.C6.A.A10.D$14.D9.A9.C34.3C.C4.C7.2A12.D$8.D5.D10.A9.
C41.C8.5A10.D$14.D21.C39.C25.D$14.D22.C37.C27.D$5.D5.D2.D23.C35.C29.D
$14.D24.C33.C31.D$14.D25.C28.C2.C33.D$2.D5.D60.C.C35.D$55.3C11.2C37.D
$43.4C7.C3.C10.4C36.D$5.D37.2C8.C56.D$43.C.C7.C57.D$43.C2.C7.C3.C7.C
45.D$2A45.C7.3C7.C47.D$2A46.C15.C49.D$49.C13.C51.D$2.9D39.C11.C53.D$
2.D3.D44.C9.C50.D$2.D4.D44.C7.C50.D5.2A$2.D5.D44.C5.C50.D6.2A$2.2D5.D
44.C3.C50.D5.D$2.D.D5.D44.C.C50.D5.D$2.D2.D5.D34.5A5.C8.A41.D5.D$2.D
3.D5.D33.2A16.A41.D5.D$2.D4.D5.D32.A.A14.A41.D5.D$8.D5.D31.A2.A12.A
41.D5.D$9.D5.D30.A3.A10.A41.D5.D$10.D5.D34.A8.A41.D5.D$11.D5.D34.A6.A
41.D5.D$12.D5.D34.A4.A41.D5.D$13.D5.D34.A2.A41.D5.D$14.D5.D34.2A41.D
5.D$15.D5.D75.D5.D$16.D5.D73.D5.D$17.D5.D71.D5.D$18.D5.D26.D9.9D24.D
5.D$19.D5.D24.D10.D31.D5.D$20.D5.D22.D4.4A3.D30.D5.D$21.D5.D20.D4.A4.
A2.D5.D23.D5.D$22.D5.D18.D4.A8.D28.D5.D$23.D5.D16.D5.A8.D27.D5.D$24.D
5.D14.D6.A8.D2.D5.D17.D5.D$25.D5.D12.D7.A8.D20.D4.D5.D$26.D5.D10.D8.A
8.D20.D3.D5.D$27.D5.D8.D10.A4.A8.D5.D8.D2.D5.D$28.D5.D6.D12.4A24.D.D
5.D$29.D5.D4.D41.2D5.D$30.D8.D30.D5.D5.D5.D$31.D6.D43.D4.D$32.D4.D44.
D3.D$36.D36.D8.9D$33.2A44.2A$33.2A44.2A!
[[ VIEWONLY THUMBNAIL THUMBSIZE 2 ZOOM 3.5 ]]

The problem from the Mark Two that comes back with this design is: how do we turn on the constructor at each corner at the appropriate time? Corner A can be constructed with the single-channel output unblocked -- it's ready to go right away, and will be turned off by the end of glider recipe "a". Corner B has to be constructed with an eater blocking the single-channel output, and that eater has to be shot down somehow _after_ the "a" gliders have all gone by... and similar eaters have to be shot down later for the C and D corners.

I can see two reasonable ways to produce the signals that shoot down those eaters. One is to maintain a ring of one-time turners some distance out from the corners, but not as far away as the first and second elbows. These one-time turners have to be "some distance out" because they'll have to travel significantly slower than the recipe loop: the TURN_ON_CONSTRUCTOR signal has to fall behind by 1/5 of the loop length at each corner.

That's doable, but it's a bit tricky, and the easiest way to do it (that I can think of) would have to be custom-designed for each possible speed of the diamond Geminoid.

However, there's another option, which I'll explain in the next post -- a way to have a TURN_ON_CONSTRUCTOR_A signal encoded in the beginning of the "a" glider stream, and a TURN_ON_CONSTRUCTOR_B signal encoded in the beginning of the "b" glider stream, and so on.

Anyone care to speculate on the mechanism, and how many extra still lifes it will take per corner to implement it?

[dvgrn]

Anyone care to speculate on the mechanism, and how many extra still lifes it will take per corner to implement it?

No? Well, okay, I guess I can keep talking to myself for a while --

Not the only possibility, but here’s one idea. Building 21 extra still lifes can allow a one-time signal to be extracted from a single-channel glider stream, to run circuit-switching operations. The marker for the signal is two gliders on the tape, exactly K ticks apart, where K is some specific integer, 277+8N.

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x = 391, y = 378, rule = LifeHistory
22.A$22.3A$25.A$24.2A6.A$24.4B3.A.A$26.5B.A$25.7B$20.B.10B$19.2AB.9B$
19.2A6B2A3B$20.2B.4B2A3B$23.10B2.2B$23.13B2A$23.13B2A$23.11B.2B$21.2A
B.9B$20.A.AB.4B$20.A5.3B$19.2A5.3B$25.4B$24.4B24.2A$23.4B25.A$12.2A8.
4B24.A.A$11.B2AB6.4B25.2A$11.4B5.4B$12.2B5.4B$4.A7.4B2.4B10.E$3.A.A5.
5B4.B10.E.E$4.A.10B16.2E$5.11B$5.11B$5.4B2A5B$4.5B2A10B11.2E$4.18B10.
E.E$2.2AB.11B2.4B10.E3.B$.A.AB2.8B5.4B12.4B$.A5.10B4.4B10.4B10.3C$2A
5.B.B5.2A5.4B8.4B11.C.B$8.3B4.A7.4B6.4B12.BC$7.B2AB5.3A5.4B4.4B$8.2A
8.A6.B5.4B$31.3B5.2A$31.3B5.A$31.4B.BA.A$26.9B.B2A$23.2B.11B$22.2A13B
$22.2A13B$23.2B2.10B$28.3B2A4B.2B$28.3B2A6B2A$28.9B.B2A$28.10B.B$28.
7B$27.A.5B$26.A.A3.4B$27.A6.2A$34.A$35.3A$37.A36$109.2C$108.2C$110.C
79$189.3C$189.C$190.C18$209.3C$209.C$210.C18$229.3C$229.C$230.C18$
249.3C$249.C$250.C18$269.3C$269.C$270.C18$289.3C$289.C$290.C28$319.3C
$319.C$320.C67$389.2C$388.2C$390.C!

In the single-channel recipes, other gliders with the same mod-8 index numbers (8i and 8i+1, let’s say) can’t be separated by K-1..K+36 ticks -- that would cause an explosion in the circuit. But K is adjustable. So we can adjust the semi-Snark loop to trigger on a range that’s not used anywhere in the recipes.

Or we can set up the compiler to change spacing between glider pairs to avoid the forbidden range. If we’re using single-channel recipes made up of glider pairs, and the (8i) glider belongs to one pair and the (8i+1) glider belongs to the next pair, then it’s trivial to adjust the interpair spacing so as to avoid that range.

We’d actually only have to worry for one out of every four pairs. For gliders with numbers besides (8i, 8i+1), the key offset K would be ignored anyway. It wouldn’t trigger a signal or cause an explosion, it would just be absorbed in getting the semi-Snarks back to the critical state for the next test.

Three of these mechanisms, adjusted to have non-overlapping ranges, could provide the CONSTRUCTOR_ON signals for the three corners that need such a signal.

[dvgrn]

Here’s an alternate idea: we can get away without extracting a CONSTRUCTOR_ON switching signal from the glider stream, if we use the constructor at each corner to build the switch signal.

It’s worth doing a quick blueprint for this idea. Let’s try a diagram with an old-fashioned straight-line Geminoid recipe loop, with only two 180-degree reflectors instead of the four in the diamond Geminoids. Straight-line Geminoids are definitely simpler, they just don’t run nearly as well in Golly. But we might be able to get around that if we make the period a pure power of two, as described in the first post in this thread.

Here’s a trial straight-line Geminoid knightship blueprint, with slow^2 construction arms instead of freeze-dried slow salvos. I'm hoping it might end up looking like it’s worth building, just for practice if nothing else, on the way to a diamond Geminoid or a quadratic replicator…!

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x = 339, y = 332, rule = LifeHistory
13.198B$4.2B7.198B$2E2.3B5.199B6.2E$2E2.4B6.197B6.2E$5.4B5.197B$6.4B$
7.4B$8.4B21.C$9.4B21.C176.4B$10.4B18.3C175.4B$11.4B194.4B$12.4B192.4B
$13.4B190.4B$14.4B188.4B$15.4B186.4B$16.4B184.4B$17.4B182.4B$18.4B
180.4B$19.4B178.4B$20.4B176.4B$21.4B174.4B$22.4B172.4B$23.4B170.4B$
24.4B168.4B$25.4B166.4B$26.4B164.4B$27.4B162.4B$28.4B160.4B$29.4B158.
4B$30.4B156.4B$31.4B154.4B$32.4B152.4B$33.4B150.4B$34.4B148.4B$35.4B
146.4B$36.4B144.4B$37.4B142.4B$38.4B140.4B$39.4B138.4B$40.4B136.4B$
41.4B134.4B$42.4B132.4B$43.4B130.4B$44.4B128.4B$45.4B126.4B$46.4B124.
4B$47.4B122.4B$48.4B120.4B$49.4B118.4B$50.4B116.4B$51.4B114.4B$52.4B
112.4B$53.4B110.4B$54.4B108.4B$55.4B106.4B$56.4B104.4B$57.4B102.4B$
58.4B100.4B$59.4B98.4B$60.4B96.4B$61.4B94.4B$62.4B92.4B$63.4B90.4B$
64.4B88.4B$65.4B86.4B$66.4B84.4B$67.4B82.4B$68.4B80.4B$69.4B78.4B$70.
4B76.4B$71.4B74.4B$72.4B72.4B$73.4B70.4B$74.4B68.4B$75.4B66.4B$76.4B
64.4B$77.4B62.4B$78.4B60.4B$79.4B58.4B$80.4B56.4B$81.4B54.4B$82.4B52.
4B$83.4B50.4B$84.4B48.4B$85.4B46.4B$86.4B36.2B6.4B$87.4B35.2B5.4B$88.
4B34.2B4.4B$89.4B33.2B3.4B$90.4B32.2B2.4B$91.4B31.2B.4B$92.4B30.6B$
93.4B29.5B$94.4B28.4B$95.4B28.9B$96.4B27.9B$97.4B$98.4B$99.4B$100.4B$
101.4B45.A$102.4B44.3A$103.4B34.A11.A$91.2A3.2A6.4B12.2A19.3A8.2A5.4B
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92.3B.3B.4B3.4B11.2A19.8B2.11B2A$84.2A5.7B.13B11.B21.19B2A$85.A5.23B
9.3B19.20B$85.A.AB.19B.8B4.6B16.20B$86.2AB.29B2.10B11.21B$88.44B3.2B
2.25B$88.37B2A15BD14B4.4B$88.37B2A15BDBD4B.6B6.4B$89.53B3D4B2.B.5B5.
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32.4B$73.2D20.13B8.3A17.A33.4B$73.2D19.15B7.A16.3A35.4B$72.4D18.16B
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3.8B71.4B$69.2D6.2D16.A4.2B3D3B71.4B$68.12D12.3A5.3BD4B72.4B$68.12D
12.A8.2B3D2B73.4B$68.2D8.2D21.7B74.4B$68.2D8.2D13.A7.6B76.4B$68.2D8.
2D12.A.A6.6B77.4B$68.2D8.2D12.A.A6.5B$68.2D8.2D10.3A.2A4.6B$68.2D8.2D
9.A4.B6.6B$90.3AB2AB3.7B$92.A.2AB.8B$96.10B$96.6B2A3B$96.6B2A2B5.2A$
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5.4B$103.BA.A5.4B$104.A.A6.4B$105.A8.4B$106.3A6.4B$108.A7.4B$117.4B$
118.4B$119.4B$120.4B$121.4B$122.4B$123.4B$124.4B$125.4B$126.4B$127.4B
$128.4B$129.4B$130.4B$131.4B$132.4B$133.4B$134.4B$135.4B$136.4B$137.
4B$138.4B$134.D4.4B$134.D5.4B$134.D6.4B90.4B$134.D7.4B90.4B$134.D8.4B
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12.D$134.D5.D100.4B8.4D$134.D5.D101.4B6.D3.D$134.2D3.D103.4B5.D3.D$
134.D.3D105.4B5.3D.D$150.D94.3BC$246.3BC$152.D94.3CB$248.4B7.A$154.D
94.4B6.3A$250.4B8.A$156.D94.4B6.A.A$252.4B5.A.AB$158.D94.4B5.A3B$254.
4B6.4B$160.D94.4B5.6B$256.4B4.7B$162.D94.4B2.8B.4B.B$258.17B.B2A$164.
D94.18B2A$259.16B.2B2D$166.D92.16B3.2D$259.15B$168.D71.B16.2AB.12B$
240.2B14.A.AB2.11B$170.D69.3B3.4B6.A5.10B$240.4B.6B4.2A5.2B2A6B$172.D
68.10B10.3B2A6B$242.9B11.10B$174.D67.9B11.8B.B2A.A$241.10B10.7B3.B2AB
3A$176.D63.4B.4BC2B9.6B6.B4.A$240.3B3.2BCBCB10.6B4.2A.3A$178.F.2B58.
2B5.B2C2B10.5B6.A.A$180.3B57.B6.4B10.6B6.A.A$180.4B52.B11.3B10.6B7.A$
181.4B50.2B23.7B$182.4B41.4B3.3B23.2B3D2B8.A$183.4B39.6B.4B5.A17.4BD
3B5.3A$184.4B38.10B4.3A17.3B3D2B4.A19.9D$185.4B37.9B4.A21.8B3.2A18.
10D$186.4B36.9B4.2A20.3B2A2B2.4B18.2D6.3D$187.4B35.10B23.5B2A2B.3B20.
2D7.3D$188.4B33.2BC4B.4B22.13B20.2D8.2D$189.4B32.BCBC2B3.3B21.16B18.
2D8.2D$190.4B31.2B2CB5.2B20.17B18.2D7.3D$191.4B31.4B6.B21.16B18.2D6.
3D$192.4B30.3B22.A7.15B18.10D$193.4B11.A11.A28.3A8.13B19.10D$194.4B
10.3A7.3A27.A12.11B8.A11.2D6.3D$195.4B12.A5.A30.2A7.15B6.3A11.2D7.3D$
196.4B10.2A4.B2A9.3B5.B.7B4.B4.20B3.A14.2D8.2D$197.4B9.9B8.4B.13B4.
25B3.2A13.2D8.2D$198.4B10.5B3.59B13.2D8.2D$199.4B8.6B2.4BD53B15.2D7.
3D$200.4B7.6B2.4B3D53B13.2D6.3D$201.4B6.7B.4BDBD15B2A37B12.10D$202.4B
4.15BD15B2A37B12.9D$203.4B2.20B2.2B3.44B$204.4B.17B11.10B2.29B.B2A$
205.19B16.6B4.8B.19B.BA.A$206.17B19.3B9.23B5.A$207.17B20.B11.13B.7B5.
2A$208.16B20.2A11.4B3.4B.3B.3B$209.7B3.3B.B2A19.A12.4B4.B3.3B2.2B$
210.6B7.BA.A15.3A14.B2AB6.B2AB.B2AB$211.4B11.A15.A17.A3B6.2A3.2A$209.
5B12.2A33.3AB$209.2A42.2A7.BA2B$210.A42.2A8.4B$207.3A17.9B28.4B$207.A
19.9B29.4B$232.4B30.B$231.5B$230.6B$229.4B.2B$228.4B2.2B$227.4B3.2B
38.B$226.4B4.2B38.2B$225.4B5.2B37.4B$224.4B46.4B$223.4B48.4B$222.4B
50.4B$221.4B52.4B$220.4B54.4B$219.4B56.4B$218.4B58.4B$217.4B60.4B$
216.4B62.4B$215.4B64.4B$214.4B66.4B$213.4B68.4B$212.4B70.4B$211.4B72.
4B$210.4B74.4B$209.4B76.4B$208.4B78.4B$207.4B80.4B$206.4B82.4B$205.4B
84.4B$204.4B86.4B$203.4B88.4B$202.4B90.4B$201.4B92.4B$200.4B94.4B$
199.4B96.4B$198.4B98.4B$197.4B100.4B$196.4B102.4B$195.4B104.4B$194.4B
106.4B$193.4B108.4B$192.4B110.4B$191.4B112.4B$190.4B114.4B$189.4B116.
4B$188.4B118.4B$187.4B120.4B$186.4B122.4B$185.4B124.4B$184.4B126.4B$
183.4B128.4B$182.4B130.4B$181.4B132.4B$180.4B134.4B$179.4B136.4B$178.
4B138.4B$177.4B140.4B$176.4B142.4B$175.4B144.4B$174.4B146.4B$173.4B
148.4B$172.4B150.4B$327.4B$328.4B$329.4B$176.149B5.4B$168.2E6.149B6.
4B2.2E$168.2E6.151B5.3B2.2E$176.150B7.2B$176.150B!
#C [[ THUMBNAIL THUMBSIZE 2 ZOOM 1.5 HEIGHT 600 STEP 16 ]]

I've given up on the NWRCS and SERCS labels -- let's just call the two constructors A and B, and the two sequential glider streams are "a" and "b". In this design, Constructor A reads "a", which rebuilds A. Constructor B reads "b", which rebuilds B.

Both construction arms have slow^2 elbows with a *WSS stage (new feature!). Those triangles at the top and bottom can be as large as they need to be, to allow the two recipe streams (a, b) to pass by before the rebuilding starts. In this case we'll need the recipe loop to be divided roughly into three equal-length parts (a, b, e), where 'e' is empty.

The upper triangle is larger, because it has to build in a long enough delay to allow both 'a' and 'b' recipes to pass, where the lower triangle only has to wait long enough for the 'b' recipe to go by. The elbows will both have to be left in the same position that they started, but offset by (1, 2) -- that shouldn't be difficult.

The only other problem is how to generate the CONSTRUCTOR_B_ON signal shown above (the white glider at top left). I'm thinking maybe it can be done by bouncing a signal back from the first A elbow, right at the appropriate time (which I think is two thirds of the way through the 'a' recipe, so that it gets back to the A constructor just as the last 'a' recipe glider is being processed). EDIT: moved the bounced-back glider to the correct place on the NW side of the top triangle.

No self-destruct circuitry is needed at all, we'd just have to add to the beginning of each salvo some extra gliders to shoot down most of an identical arrangement at a (-1,-2) offset.

Then we'll have to come up with an appropriate single-channel -> *WSS -> slow^2 elbow operation toolkit... but that seems like it should be relatively straightforward.

Other than that, I think this design is ready to program. It seems a good bit simpler than the original version, because no separate exact-timing loops are needed -- just slow^2 salvos (which are probably more efficient than freeze-dried slow salvos anyway) and some empty space in the recipe loop to leave room for the two reconstruction salvos to do their work.

But I've been making some serious design errors recently. What am I missing this time? And is there any way to cut the circuitry down to less than these 45 still lifes?

[dvgrn]

A few minutes of experimenting seems to indicate that it will be possible to do a little better than one glider per still life for the destruction stage of the A and B constructor circuitry, but not by much:

Code: Select all

#C Seeds of Destruction
x = 302, y = 279, rule = LifeHistory
277.A$277.3A$280.A$279.A.A$279.A.A$280.A5$295.2A$295.2A4$
275.2A$274.A.A$274.A$273.2A7.2A$282.2A2$290.2A.A$290.2A.3A$
296.A$290.2A.3A$291.A.A$291.A.A$292.A2$293.A$291.3A$290.A$
290.2A$282.2A$282.2A4$252.A$250.3A16.A$226.A11.A10.A17.3A$
226.3A7.3A10.2A15.A31.A$229.A5.A30.2A28.3A$228.2A5.2A58.A$
295.2A4$223.2A34.2A$222.A.A34.2A$224.A$298.2A$298.A.A$300.A$
300.2A$262.2A$242.2A19.A$242.A.A15.3A25.2A3.2A$244.A15.A27.
2A3.2A$244.2A$227.2A$228.A$209.2A14.3A$208.A.A14.A$210.A12$
205.2A$204.A.A$206.A20$198.2A$197.A.A$199.A6$188.2A$187.A.A$
189.A18$185.2A$184.A.A$186.A5$173.2A$172.A.A$174.A6$165.2A$
164.A.A$166.A19$152.2A$151.A.A$153.A31$148.2A$147.A.A$149.A
11$141.2A$140.A.A$142.A14$123.2A$122.A.A$124.A12$101.2A$100.
A.A$102.A20$78.2A$77.A.A$79.A4$20.2A$19.A.A$21.A8$.2A$A.A$2.
A!
#C [[ STEP 16 ]]

Now, we have simeks' tool to add self-destruct circuitry to knock out the whole circuit with one glider. But in this case, each new still life that we add will cost several slow^2 gliders to rebuild, and we'll save no more than 15 gliders (in the above example). So probably unless there's a clean self-destruct with just two or three additional still lifes, it won't be worth worrying about.

Come to think of it, there's no point in cleaning up to the point where there's only one target object left. All we need to do is get the old objects out of the way, and provide a variety of targets toward the back for starting the new construction:

Code: Select all

x = 179, y = 211, rule = LifeHistory
153.A$153.3A$154.D.A$154.DCDA$155.A.C$156.C.D$156.D.D$157.D3$171.2A$
171.2A$172.2D$172.2D2$151.2A$150.A.A$150.A.2D$149.2AD.D4.2A$151.D6.2A
$150.2D7.2D$159.2D5.2A.A$166.2A.3A$167.2D.D.A$166.ACDA2CD$144.D22.A.A
3.D$143.D.D21.CDA3D$143.2D23.C.D$168.D.D$169.A$136.A30.3A$134.3A29.A
3.D$133.A3.D28.2A3D$133.2A3D20.2A7.D$134.D23.2A7.2D$134.2D23.2D$159.
2D$122.D$121.D.D$122.2D21.A$102.A11.A28.3A$102.3A7.3A27.A3.D27.A$103.
D.A5.A3.D26.2A3D25.3A$103.D2C5.2A3D27.D27.A3.D$106.D5.D30.2D26.2A3D$
105.2D5.2D58.D$172.2D2$135.2A$135.2A$136.2D$98.2A36.2D36.2A$97.A.A74.
A.A$99.A75.DC$175.DAC$138.2A37.D$118.2A19.A37.2D$118.A.A15.3A2D23.2A
3.2A$119.DC15.A3.D23.2A3.2A$82.A36.DAC15.3D15.2D8.2D3.2D$82.2A19.2A
16.D15.D17.D9.2D3.2D$81.A.A20.A16.2D33.3D$101.3A2D42.2D8.D$101.A3.D
42.2D$102.3D$102.D20$87.A$87.2A$86.A.A7$70.A$70.2A$69.A.A25$75.A$75.
2A$74.A.A16$43.A$43.2A$42.A.A11$20.A$20.2A$19.A.A24$51.A$51.2A$50.A.A
28$.A$.2A$A.A!
[[ STEP 16 ]]

The junk will still have to be pruned down and pushed back a bit farther, but something like this gives more possible targets to choose from, when the new construction is getting started.

EDIT: The blueprint in the previous post has been patched now to keep the CONSTRUCTOR_B_ON one-time turners near the B circuitry. I've fixed the above pattern to match the new boat and block and eater locations. The boats could trivially be moved to the side a little more; that might come in handy, because then the destruction and construction recipes for Constructors A and B could be substantially identical -- just a few gliders different at the beginning, and a few dozen gliders different at the end.

[dvgrn]

The blueprint in the previous post has been patched now to keep the CONSTRUCTOR_B_ON one-time turners near the B circuitry...

Another possible geometry: the Geminoid knightship could perfectly well have only one constructor arm, similar to the design of the linear propagator. So Constructor A would be a real constructor, but B would just be a reflector -- all the reconstruction salvos would come from A. The new blueprint would look something like this:

Code: Select all

#C Option 1 for single-arm true-knightship geometry
x = 373, y = 252, rule = LifeHistory
81.D$75.3D3.D$74.D3.D$78.D$75.4D$74.D3.D$74.D3.D$75.3D.D3$65.5D$66.D
3.D$67.D3.D$68.D3.D$69.D3.D$70.D3.D$13.56B2.D3.D2.79B$4.2B7.57B2.D3.D
2.78B$2E2.3B5.59B2.D3.D2.77B6.2E$2E2.4B6.56B2.D3.D2.78B6.2E$5.4B5.55B
2.D3.D2.79B$6.4B60.D3.D$7.4B58.D3.D$8.4B56.D3.D$9.4B54.D3.D85.4B$10.
4B52.D3.D85.4B$11.4B50.5D85.4B$12.4B138.4B$13.4B136.4B$14.4B134.4B$
15.4B132.4B$16.4B130.4B$17.4B128.4B$18.4B126.4B$19.4B124.4B$20.4B122.
4B$21.4B120.4B$22.4B118.4B$23.4B116.4B$24.4B114.4B$25.4B112.4B$26.4B
110.4B$27.4B108.4B$28.4B106.4B$29.4B104.4B$30.4B102.4B$31.4B100.4B$
32.4B98.4B$33.4B96.4B$34.4B94.4B$35.4B92.4B102.D$36.4B90.4B96.D6.D$
37.4B88.4B97.D6.D$38.4B86.4B98.D6.D$39.4B84.4B99.D$40.4B82.4B100.D$
41.4B80.4B101.D$42.4B70.2B6.4B102.D.3D$43.4B69.2B5.4B103.2D3.D$44.4B
68.2B4.4B104.D5.D$45.4B67.2B3.4B105.D5.D$46.4B66.2B2.4B106.2D3.D$47.
4B65.2B.4B107.D.3D$48.4B64.6B$49.4B63.5B$50.4B62.4B$51.4B61.10B$52.4B
60.10B$53.4B$54.4B$55.4B$56.4B$57.4B168.5D$58.4B168.D3.D$59.4B168.D3.
D$60.4B168.D3.D$61.4B168.D3.D$62.4B168.D3.D$63.4B8.158B2.D3.D2.123B$
64.4B7.159B2.D3.D2.122B$62.2E.4B5.161B2.D3.D2.121B6.2E$62.2E2.4B6.
158B2.D3.D2.122B6.2E$67.4B5.157B2.D3.D2.123B$68.4B162.D3.D$69.4B160.D
3.D$70.4B158.D3.D$71.4B156.D3.D129.4B$72.4B154.D3.D129.4B$73.4B152.5D
129.4B$74.4B45.A238.4B$75.4B44.3A235.4B$76.4B34.A11.A233.4B$64.2A3.2A
6.4B12.2A19.3A8.2A5.4B223.4B$63.B2AB.B2AB6.4B11.A.A21.A7.11B222.4B$
64.2B2.3B3.B4.4B12.A20.2A3.B5.11B219.4B$65.3B.3B.4B3.4B11.2A19.8B2.
11B2A217.4B$57.2A5.7B.13B11.B21.19B2A216.4B$58.A5.23B9.3B19.20B216.4B
$58.A.AB.19B.8B4.6B16.20B216.4B$59.2AB.29B2.10B11.21B216.4B$61.44B3.
2B2.25B214.4B$61.37B2A15BD14B4.4B212.4B$61.37B2A15BDBD4B.6B6.4B210.4B
$62.53B3D4B2.B.5B5.4B208.4B$64.53BD4B7.2A6.4B206.4B$62.59B8.A8.4B204.
4B$62.2A3.25B4.13B.4B16.3A6.4B202.4B$63.A3.20B4.B4.7B.B5.3B19.A7.4B
200.4B$60.3A6.15B7.2A15.4B29.4B198.4B$60.A8.11B12.A15.2A32.4B196.4B$
68.13B8.3A17.A33.4B194.4B$67.15B7.A16.3A35.4B192.4B$67.16B23.A38.4B
190.4B$67.17B62.4B188.4B$67.16B14.2D48.4B186.4B$69.13B15.2D49.4B184.
4B$69.3B.2B2A5B14.4D49.4B182.4B$67.4B2.2B2A3B16.4D50.4B180.4B$67.2A3.
8B15.2D2.2D50.4B178.4B$68.A4.2B3D3B14.2D2.2D51.4B176.4B$65.3A5.3BD4B
13.2D4.2D51.3B175.4B$65.A8.2B3D2B13.2D4.2D52.2B174.4B$74.7B12.2D6.2D
52.B173.4B$66.A7.6B13.2D6.2D225.4B$65.A.A6.6B12.12D223.4B$65.A.A6.5B
13.12D222.4B$63.3A.2A4.6B13.2D8.2D221.4B$62.A4.B6.6B12.2D8.2D220.4B$
63.3AB2AB3.7B12.2D8.2D219.4B$65.A.2AB.8B13.2D8.2D218.4B$69.10B13.2D8.
2D217.4B$69.6B2A3B12.2D8.2D216.4B$69.6B2A2B5.2A233.4B$69.10B5.A233.4B
$68.11B2.BA.A232.4B$68.12B.B2A232.4B$67.15B233.4B$66.16B232.4B$63.2B.
16B231.4B$62.2A18B230.4B$62.2AB.17B228.4B$63.2D4B.8B2.4B226.4B$63.2D
5.7B4.4B224.4B$71.6B5.4B222.4B$73.4B6.4B221.3B$75.3BA5.4B218.4B$76.BA
.A5.2B218.4B$77.A.A6.B217.4B$78.A224.4B$79.3A220.4B$81.A9.D.D.D.D.D
11.D189.4B$111.D188.4B$91.D.D17.D187.4B$111.D186.4B$91.D3.D15.D185.4B
$111.D184.4B$91.D5.D13.D.3D179.4B$111.2D3.D177.4B$91.D7.D11.D5.D175.
4B$111.D5.D174.4B$101.D9.2D3.D174.4B$111.D.3D174.4B$103.D185.4B$288.
4B$105.D181.4B$286.4B$107.D177.4B$284.4B$109.D173.4B$282.4B$111.D169.
4B$280.4B$113.D165.4B$278.4B$115.D161.4B$276.4B$117.D157.4B$274.4B$
119.D153.4B$272.4B$121.D149.4B$270.4B$123.D145.4B$268.4B$125.D141.4B$
266.4B$127.D137.4B$223.B33.2B5.4B$223.2B7.A24.2B4.4B$222.4B6.3A22.2B
3.4B$223.4B8.A21.2B2.4B$224.4B6.A.A20.2B.4B$133.D.D.D.D.D83.4B5.A.AB
19.6B$226.4B5.A3B18.5B$133.D.D91.4B6.4B16.4B$228.4B5.6B14.9B$133.D3.D
91.4B4.7B13.9B$153.3D74.4B2.8B.4B.B$133.D5.D12.D3.D74.17B.B2A$156.D
75.18B2A$133.D7.D11.4D75.16B.2B2D$152.D3.D75.16B3.2D$143.D8.D3.D75.
15B$153.3D.D72.2AB.12B$145.D83.A.AB2.11B$212.9D8.A5.10B$147.D64.10D6.
2A5.2B2A6B$212.2D6.3D11.3B2A6B$149.D62.2D7.3D11.10B$212.2D8.2D11.8B.B
2A.A$151.D60.2D8.2D10.7B3.B2AB3A$212.2D7.3D10.6B6.B4.A$153.D58.2D6.3D
12.6B4.2A.3A$212.10D13.5B6.A.A$155.D56.10D12.6B6.A.A$212.2D6.3D11.6B
7.A$157.D54.2D7.3D9.7B$212.2D8.2D9.2B3D2B8.A$159.D52.2D8.2D9.4BD3B5.
3A$212.2D8.2D9.3B3D2B4.A$161.D50.2D7.3D10.8B3.2A$212.2D6.3D11.3B2A2B
2.4B$163.D48.10D10.5B2A2B.3B$212.9D11.13B$165.D65.16B$230.17B$167.D
39.A23.16B$205.3A16.A7.15B$169.D11.A11.A10.A17.3A8.13B$181.3A7.3A10.
2A15.A12.11B8.A$184.A5.A11.4B15.2A7.15B6.3A$183.2A4.B2A9.3B5.B.7B4.B
4.20B3.A$183.9B8.4B.13B4.25B3.2A$185.5B3.59B$184.6B2.4BD53B$184.6B2.
4B3D53B$177.B6.7B.4BDBD15B2A37B$177.2B4.15BD15B2A37B$177.3B2.20B2.2B
3.44B$177.4B.17B11.10B2.29B.B2A$178.19B16.6B4.8B.19B.BA.A$179.17B19.
3B9.23B5.A$180.17B20.B11.13B.7B5.2A$181.16B20.2A11.3B4.4B.3B.3B$182.
7B3.3B.B2A19.A12.4B4.B3.3B2.2B$183.6B7.BA.A15.3A15.2A7.B2AB.B2AB$184.
4B11.A15.A17.A9.2A3.2A$182.5B12.2A33.3A$182.2A52.A$183.A$180.3A$180.A!
#C [[ THUMBNAIL THUMBSIZE 2 ZOOM 1.5 ]]

That would mean that no signal-bouncing trickery is needed at A, and no one-time turners are needed at B. The only new thing is that the order of the a and b glider streams are reversed, and an extra block will get dropped on the construction lane right next to A, during A's reconstruction.

That block is used as an elbow to send the b' *WSS salvo. Then it can get shot down by the very end of the b stream, and the "a" stream will use the permanent elbows to the north, to bounce around a much smaller triangle and reconstruct A. Thanks to the size of the second triangle, the b' salvo won't get around the second slow^2 elbow to its destination until after the "a" stream has gone by. The only requirement is that the recipe loop will have to be half-empty instead of just one-third empty (I think).

The following geometry would work equally well, I believe:

Code: Select all

#C Option 2 for single-arm true-knightship geometry
x = 257, y = 400, rule = LifeHistory
81.D$75.3D3.D$74.D3.D$78.D$75.4D$74.D3.D$74.D3.D$75.3D.D3$65.5D$66.D
3.D$67.D3.D$68.D3.D$69.D3.D$70.D3.D$13.56B2.D3.D2.79B$4.2B7.57B2.D3.D
2.78B$2E2.3B5.59B2.D3.D2.77B6.2E$2E2.4B6.56B2.D3.D2.78B6.2E$5.4B5.55B
2.D3.D2.79B$6.4B60.D3.D$7.4B58.D3.D$8.4B56.D3.D$9.4B54.D3.D85.4B$10.
4B52.D3.D85.4B$11.4B50.5D85.4B$12.4B138.4B$13.4B136.4B$14.4B134.4B$
15.4B132.4B$16.4B130.4B$17.4B128.4B$18.4B126.4B$19.4B124.4B$20.4B122.
4B$21.4B120.4B$22.4B118.4B$23.4B116.4B$24.4B114.4B$25.4B112.4B$26.4B
110.4B$27.4B108.4B$28.4B106.4B$29.4B104.4B$30.4B102.4B$31.4B100.4B$
32.4B98.4B$33.4B96.4B$34.4B94.4B$35.4B92.4B$36.4B90.4B$37.4B88.4B$38.
4B86.4B$39.4B84.4B$40.4B82.4B$41.4B80.4B$42.4B78.4B$43.4B76.4B$44.4B
74.4B$45.4B2.2E68.4B$46.4B.2E67.4B$47.4B68.4B$48.4B66.4B$49.4B64.4B$
50.4B62.4B$51.4B60.4B$52.4B58.4B$53.4B56.4B$54.4B54.4B$55.4B52.4B$56.
4B50.4B$51.B5.4B48.4B$49.3B6.4B46.4B$49.5B5.4B36.2B6.4B$49.5B6.4B35.
2B5.4B$49.5B7.4B34.2B4.4B$49.5B8.4B33.2B3.4B$49.5B9.4B32.2B2.4B$49.5B
10.4B31.2B.4B$49.5B11.4B30.6B$49.5B12.4B29.5B$49.5B13.4B28.4B$49.5B
14.4B28.9B$49.5B15.4B27.9B$49.5B16.4B$49.5B17.4B$49.5B18.4B$49.5B19.
4B$49.5B20.4B45.A$49.5B21.4B44.3A$49.5B22.4B34.A11.A$49.5B10.2A3.2A6.
4B12.2A19.3A8.2A5.4B$49.5B9.B2AB.B2AB6.4B11.A.A21.A7.11B$49.5B10.2B2.
3B3.B4.4B12.A20.2A3.B5.11B$49.5B11.3B.3B.4B3.4B11.2A19.8B2.11B2A$49.
5B3.2A5.7B.13B11.B21.19B2A$49.5B4.A5.23B9.3B19.20B$49.5B4.A.AB.19B.8B
4.6B16.20B$49.5B5.2AB.29B2.10B11.21B$49.5B7.44B3.2B2.25B$49.5B7.37B2A
15BD14B4.4B$49.5B7.37B2A15BDBD4B.6B6.4B$49.5B8.53B3D4B2.B.5B5.4B$49.
5B10.53BD4B7.2A6.4B$49.5B8.59B8.A8.4B$49.5B8.2A3.25B4.13B.4B16.3A6.4B
$49.5B9.A3.20B4.B4.7B.B5.3B19.A7.4B$49.5B6.3A6.15B7.2A15.4B29.4B$49.
5B6.A8.11B12.A15.2A32.4B$49.5B14.13B8.3A17.A33.4B$49.5B13.15B7.A16.3A
35.4B$49.5B13.16B23.A38.4B$49.5B13.17B62.4B$49.5B13.16B14.2D48.4B$49.
5B15.13B15.2D49.4B$49.5B15.3B.2B2A5B14.4D49.4B$49.5B13.4B2.2B2A3B16.
4D50.4B$49.5B13.2A3.8B15.2D2.2D50.4B$49.5B14.A4.2B3D3B14.2D2.2D51.4B$
49.5B11.3A5.3BD4B13.2D4.2D51.3B$49.5B11.A8.2B3D2B13.2D4.2D52.2B$49.5B
20.7B12.2D6.2D52.B$49.5B12.A7.6B13.2D6.2D$49.5B11.A.A6.6B12.12D$49.5B
11.A.A6.5B13.12D$49.5B9.3A.2A4.6B13.2D8.2D$49.5B8.A4.B6.6B12.2D8.2D$
49.5B9.3AB2AB3.7B12.2D8.2D$49.5B11.A.2AB.8B13.2D8.2D$49.5B15.10B13.2D
8.2D$49.5B15.6B2A3B12.2D8.2D$49.5B15.6B2A2B5.2A$49.5B15.10B5.A$49.5B
14.11B2.BA.A$49.5B14.12B.B2A$49.5B13.15B$49.5B12.16B$49.5B9.2B.16B$
49.5B8.2A18B$49.5B8.2AB.17B$49.5B9.2D4B.8B2.4B$49.5B9.2D5.7B4.4B$49.
5B17.6B5.4B$49.5B19.4B6.4B$49.5B21.3BA5.4B$49.5B22.BA.A5.2B$49.5B23.A
.A6.B$49.5B24.A$49.5B25.3A$49.5B27.A9.D.D.D.D.D11.D$49.5B57.D$49.5B
37.D.D17.D$49.5B57.D$49.5B37.D3.D15.D$49.5B57.D$49.5B37.D5.D13.D.3D$
49.5B57.2D3.D$49.5B37.D7.D11.D5.D$49.5B57.D5.D$49.5B47.D9.2D3.D$49.5B
57.D.3D$49.5B49.D$49.5B$49.5B51.D$49.5B$49.5B53.D$49.5B$49.5B55.D$49.
5B$49.5B57.D$49.5B$49.5B59.D$49.5B$49.5B61.D$49.5B$49.5B63.D$49.5B$
49.5B65.D$49.5B$49.5B67.D$49.5B$49.5B69.D$49.5B$49.5B71.D$49.5B$49.5B
73.D$49.5B169.B$49.5B169.2B7.A$49.5B168.4B6.3A$49.5B169.4B8.A$49.5B
170.4B6.A.A$49.5B79.D.D.D.D.D83.4B5.A.AB$49.5B172.4B5.A3B$49.5B79.D.D
91.4B6.4B$49.5B174.4B5.6B$49.5B79.D3.D91.4B4.7B$49.5B99.3D74.4B2.8B.
4B.B$49.5B79.D5.D12.D3.D74.17B.B2A$49.5B102.D75.18B2A$49.5B79.D7.D11.
4D75.16B.2B2D$49.5B98.D3.D75.16B3.2D$49.5B89.D8.D3.D75.15B$49.5B99.3D
.D72.2AB.12B$49.5B91.D83.A.AB2.11B$49.5B158.9D8.A5.10B$49.5B93.D64.
10D6.2A5.2B2A6B$49.5B158.2D6.3D11.3B2A6B$49.5B95.D62.2D7.3D11.10B$49.
5B158.2D8.2D11.8B.B2A.A$49.5B97.D60.2D8.2D10.7B3.B2AB3A$49.5B158.2D7.
3D10.6B6.B4.A$49.5B99.D58.2D6.3D12.6B4.2A.3A$49.5B158.10D13.5B6.A.A$
49.5B101.D56.10D12.6B6.A.A$49.5B158.2D6.3D11.6B7.A$49.5B103.D54.2D7.
3D9.7B$49.5B158.2D8.2D9.2B3D2B8.A$49.5B105.D52.2D8.2D9.4BD3B5.3A$49.
5B158.2D8.2D9.3B3D2B4.A$49.5B107.D50.2D7.3D10.8B3.2A$49.5B158.2D6.3D
11.3B2A2B2.4B$49.5B109.D48.10D10.5B2A2B.3B$49.5B158.9D11.13B$49.5B
111.D65.16B$49.5B176.17B$49.5B113.D39.A23.16B$36.D6.D5.5B5.D145.3A16.
A7.15B$29.D6.D6.2D4.5B4.2D109.D11.A11.A10.A17.3A8.13B$29.D6.D6.D.D3.
5B3.D.D121.3A7.3A10.2A15.A12.11B8.A$29.D6.D6.D2.D2.5B2.D2.D124.A5.A
11.4B15.2A7.15B6.3A$29.D13.D3.D2.3B2.D3.D123.2A4.B2A9.3B5.B.7B4.B4.
20B3.A$29.D14.D3.D2.B2.D3.D124.9B8.4B.13B4.25B3.2A$29.D15.D3.D3.D3.D
127.5B3.59B$29.D.3D12.D3.D.D3.D127.6B2.4BD53B$29.2D3.D12.D3.D3.D128.
6B2.4B3D53B$29.D5.D12.D5.D122.B6.7B.4BDBD15B2A37B$29.D5.D13.D3.D123.
2B4.15BD15B2A37B$29.2D3.D15.D.D124.3B2.20B2.2B3.44B$29.D.3D17.D125.4B
.17B11.10B2.29B.B2A$49.B3.B124.19B16.6B4.8B.19B.BA.A$49.2B.2B125.17B
19.3B9.23B5.A$49.5B126.17B20.B11.13B.7B5.2A$49.5B127.16B20.2A11.3B4.
4B.3B.3B$49.5B128.7B3.3B.B2A19.A12.4B4.B3.3B2.2B$49.5B129.6B7.BA.A15.
3A15.2A7.B2AB.B2AB$49.5B130.4B11.A15.A17.A9.2A3.2A$49.5B128.5B12.2A
33.3A$49.5B128.2A52.A$49.5B129.A$49.5B126.3A$49.5B126.A$49.5B$49.5B$
49.5B134.10B$49.5B134.10B$49.5B139.5B$49.5B138.6B$49.5B137.4B.2B$49.
5B136.4B2.2B$49.5B135.4B3.2B$49.5B134.4B4.2B$49.5B133.4B5.2B$49.5B
132.4B$49.5B131.4B$49.5B130.4B$49.5B129.4B$49.5B128.4B$49.5B127.4B$
49.5B126.4B$49.5B125.4B$49.5B124.4B$49.5B123.4B$49.5B122.4B$49.5B121.
4B$49.5B120.4B$49.5B119.4B$49.5B118.4B$49.5B117.4B$49.5B116.4B$49.5B
115.4B$49.5B114.4B$49.5B113.4B$49.5B112.4B$49.5B111.4B$49.5B110.4B$
49.5B109.4B$49.5B108.4B$49.5B107.4B$49.5B106.4B$49.5B105.4B$49.5B104.
4B$49.5B103.4B$49.5B102.4B$49.5B101.4B$49.5B100.4B$49.5B99.4B$49.5B
98.4B$49.5B97.4B$49.5B96.4B$49.5B95.4B$49.5B94.4B$49.5B93.4B$49.5B92.
4B$49.5B91.4B$49.5B90.4B$49.5B89.4B$49.5B88.4B$49.5B87.4B$49.5B86.4B$
49.5B85.4B$49.5B84.4B$49.5B83.4B$49.5B82.4B$49.5B81.4B$49.5B80.4B$49.
5B79.4B$49.5B78.4B$49.5B77.4B$49.5B76.4B$49.5B75.4B$49.5B74.4B$49.5B
73.4B$49.5B72.4B$49.5B71.4B$49.5B70.4B$49.5B69.4B$49.5B68.4B$49.5B67.
4B$49.5B66.4B$49.5B65.4B$49.5B64.4B$49.5B63.4B$49.5B62.4B$49.5B62.3B$
49.5B60.4B$49.5B59.4B$49.5B58.4B$49.5B57.4B$49.5B56.4B$49.5B55.4B$49.
5B54.4B$49.5B53.4B$49.5B52.4B$49.5B51.4B$49.5B50.4B$49.5B49.4B$49.5B
48.4B$49.5B47.4B$49.5B46.4B$49.5B45.4B$49.5B44.4B$49.5B43.4B$49.5B42.
4B$49.5B41.4B$49.5B40.4B$49.5B39.4B$49.5B38.4B$49.5B37.4B$49.5B36.4B$
49.5B35.4B$49.5B34.4B$49.5B33.4B$49.5B32.4B$49.5B31.4B$49.5B30.4B$49.
5B29.4B$49.5B28.4B$49.5B27.4B$49.5B26.4B$49.5B25.4B$49.5B24.4B$49.5B
23.4B$49.5B22.4B$49.5B21.4B$49.5B20.4B$49.5B19.4B$49.5B18.4B$49.5B17.
4B$49.5B16.4B$49.5B15.4B$49.5B14.4B$49.5B13.4B$49.5B12.4B$49.5B11.4B$
49.5B10.4B$49.5B9.4B$49.5B8.4B$49.5B7.4B$49.5B6.4B$49.5B5.4B$49.5B4.
4B$57.4B$57.3B$57.2B$57.B3$51.2E$51.2E!
#C [[ HEIGHT 600 THUMBNAIL THUMBSIZE 2 ZOOM 1.3 ]]

but for no particularly good reason I think I like having all signals traveling clockwise. Not sure how Hashlife will handle this mix of *WSS and glider signals, but I suspect that either of these new triangle setups will be fine. The problem will be the original streams of glider recipes, when they're folded over 180 degrees, and there's no way to fix that without moving back to a diamond-shaped design.

Anyway, that should cut the number of still lifes that need constructing in each cycle, down to 42 -- a most auspicious number. Or can anyone see any showstopping problems that I've missed?

EDIT: Oops, no, it's 43 -- not quite so auspicious. And two of them are eater2s, of course. With my preferred geometry, it wouldn't be possible to re-use the construction recipe, because the reconstruction salvo for B would come from the opposite direction. With the second option, re-use would still be possible... hmm.

[dvgrn]

The oblique Geminoid blueprint just got a lot smaller for the same reason...

EDIT: Thinking about this again -- it's not quite as easy as I was thinking, because the loops are so big -- it would take a return glider quite a while to get back from the final elbow to hit the Snark and turn it into a new hand target... which would then have to be manipulated to produce an appropriate (2,1) offset block for that corner, plus a return glider. Then there's another long wait to destroy the previous Snark and turn it into a different (2,1) offset block... it's not clear that there's enough space in the main loop to hold all those long wait times.

One more round of thinking: it may be that all we need to do is consider each Snark to be a starting point for a single-channel search tree, with the lane offset by one lane, or three lanes:

Code: Select all

x = 400, y = 492, rule = LifeHistory
224.2D$224.D.D$225.2A4.2D$222.3DA.AD2.D2.D$222.D2.D.A.D.D2AD$223.4AD
2A.DA2.A$223.A2.ADADADA.2A$225.BABABA.A$226.B2ABA.A$216.2D9.2B.BA$
217.D7.D3B$217.2AD5.4B$218.AD5.B2A3B$218.A.AB3.B2A3B$219.2AB.10B$221.
13B$221.14B$221.15B$223.8B2.4B$223.6BD4.4B$222.9B4.4B$221.4B4.2AD4.4B
$220.4B5.A.D5.4B$212.11B7.3A5.4B$212.10B10.A6.4B$217.4B19.4B$216.5B
20.4B$215.6B21.4B$214.4B.2B22.4B$213.4B2.2B23.4B$212.4B3.2B24.4B$211.
4B4.2B25.4B$210.4B5.2B26.4B$209.4B35.4B$208.4B37.4B$207.4B39.4B$206.
4B41.4B$205.4B43.4B$204.4B45.4B$203.4B47.4B$202.4B49.4B$201.4B51.4B$
200.4B53.4B$199.4B55.4B$198.4B57.4B$197.4B59.4B$196.4B61.4B$195.4B63.
4B$194.4B65.4B$193.4B67.4B$192.4B69.4B$191.4B71.4B$190.4B73.4B$189.4B
75.4B$188.4B77.4B$187.4B79.4B$186.4B81.4B$185.4B83.4B$184.4B85.4B$
183.4B87.4B$182.4B89.4B$181.4B91.4B$180.4B93.4B$179.4B95.4B$178.4B97.
4B$177.4B99.4B$176.4B101.4B$175.4B103.4B$174.4B105.4B$173.4B107.4B$
172.4B109.4B$171.4B111.4B$170.4B113.4B$169.4B115.4B$168.4B117.4B$167.
4B119.4B$166.4B121.4B$165.4B123.4B$164.4B125.4B$163.4B127.4B$162.4B
129.4B$161.4B131.4B$160.4B133.4B5.2B$159.4B135.4B4.2B$158.4B137.4B3.
2B$146.D10.4B139.4B2.2B$140.3D3.D9.4B141.4B.2B$139.D3.D11.4B143.6B$
143.D10.4B145.5B$140.4D9.4B141.10B$139.D3.D8.4B142.10B$139.D3.D7.4B$
140.3D.D5.4B$149.4B$148.4B$132.2D13.4B$133.D12.4B167.2D$131.D.2A10.4B
168.2D$131.3DAD8.4B2.2D166.2A$132.A3.D6.4B3.D167.2A$132.5A5.4B2.D.D2A
$132.D4.A4.4B2.2D.A$132.2D3AB2.7B.BA.A$130.2D.A.2B2.D7B.B2A$129.D2.D
4A12B$129.2D2A2.BA3B2A7B$130.A.D3AB.2B2A7B$130.2ADA.B3.10B$133.A8.8B
157.B$133.2A7.9B155.2B$140.2D.3B2.4B153.3B$141.5B3.4B151.4B$138.3D2A
7.11B142.4B$138.D3.A8.10B141.4B$139.3A9.5B145.4B$139.A11.6B143.4B$
151.2B.4B141.4B$151.2B2.4B139.4B$151.2B3.4B137.4B$151.2B4.4B135.4B$
151.2B5.4B133.4B$159.4B131.4B$160.4B129.4B$161.4B127.4B$162.4B125.4B$
163.4B123.4B$164.4B121.4B$165.4B119.4B$166.4B117.4B$167.4B115.4B$168.
4B113.4B$169.4B111.4B$170.4B109.4B$171.4B107.4B$172.4B105.4B$173.4B
103.4B$174.4B101.4B$175.4B99.4B$176.4B97.4B$177.4B95.4B$178.4B93.4B$
179.4B91.4B$177.2D.4B89.4B$177.2D2.4B87.4B$178.2A2.4B85.4B$172.2B4.2A
3.4B83.4B$171.4B9.4B81.4B$170.4B11.4B79.4B$169.4B13.4B77.4B$168.4B15.
4B75.4B$167.4B17.4B73.4B$166.4B19.4B71.4B$165.4B21.4B69.4B$164.4B23.
4B67.4B$163.4B25.4B65.4B$162.4B27.4B63.4B$161.4B29.4B61.4B$160.4B31.
4B59.4B$159.4B33.4B57.4B$158.4B35.11B48.4B$157.4B37.10B47.4B$156.4B
39.4B51.4B$155.4B40.5B49.4B$154.4B41.6B47.4B$153.4B42.2B.4B45.4B$152.
4B43.2B2.4B35.2B6.4B$151.4B44.2B3.4B34.2B5.4B$150.4B45.2B4.4B33.2B4.
4B$149.4B46.2B5.4B32.2B3.4B$148.4B55.4B31.2B2.4B$132.D14.4B57.4B30.2B
.4B$125.D6.D13.4B59.4B29.6B$125.D6.D12.4B61.4B28.5B$125.D6.D11.4B63.
4B27.4B$125.D17.4B65.4B27.9B$125.D16.4B67.4B26.9B$125.D15.4B69.4B$
125.D.3D10.4B71.4B46.D$125.2D3.D8.4B73.4B45.3D$125.D5.D6.4B75.4B35.D
9.A.D$125.D5.D5.4B65.2D3.2D5.4B13.2D19.3D7.3A$125.2D3.D5.4B66.2D3.2D
6.4B12.D.D19.A.D9.A$125.D.3D5.4B68.2A3.2A6.4B12.2A19.3A8.2A5.4B$134.
4B68.B2AB.B2AB6.4B11.ADA21.A7.11B2D$133.4B62.2D6.2B2.3B3.B4.4B12.A20.
2A3.B5.11B$132.4B64.D7.3B.3B.4B3.4B11.2A19.8B2.11B2A$131.4B65.2AD4.7B
.13B11.B21.19B2A$130.4B67.AD4.23B9.3B19.20B$129.4B68.A.AB.19B.8B4.6B
16.20B$128.4B70.2AB.29B2.10B11.21B$127.4B73.44B3.2B2.25B$126.4B74.37B
2A15BD14B4.4B$125.4B75.37B2A15BDBD4B.6BD5.4B$124.4B77.53B3D4B2.B.5B5.
4B$123.4B77.2D.53BD4B7.2AD5.4B$122.4B79.59B8.A.D6.4B$121.4B77.3D2A3.
25B4.13B.4B16.3A6.4B$120.4B78.D3.A3.20B4.B4.7B.B2.2D.3B19.A7.4B$119.
4B80.3A6.15B4.3D2A15.4B29.4B$118.4B81.A8.11B8.D3.A12.3D2A32.4B$117.4B
90.13B8.3A13.D3.A33.4B$116.4B90.15B7.A16.3A35.4B$115.4B91.16B23.A38.
4B$114.4B92.17B62.4B$113.4B93.16B14.2D48.4B$112.4B96.13B15.2D49.4B$
111.4B94.2D.3B.2B2A5B14.4D49.4B$110.4B96.4B2.2B2A3B16.4D50.4B$109.4B
94.3D2A3.8B15.2D2.2D50.4B$108.4B95.D3.A4.2B3D3B14.2D2.2D51.4B$107.4B
97.3A5.3BD4B13.2D4.2D51.4B$106.4B98.A8.2B3D2B13.2D4.2D52.4B$105.4B98.
D.D7.7B12.2D6.2D52.4B$104.4B99.D.A7.6B13.2D6.2D53.4B$103.4B98.3DADA6.
6B12.12D53.4B$102.4B98.D3.A.A6.5B13.12D54.4B$101.4B100.D3AD2A4.6B13.
2D8.2D55.4B$100.4B101.A.D.DB6.6B12.2D8.2D56.4B$99.4B103.3AB2AB3.7B12.
2D8.2D57.4B$98.4B106.A.2AB.8B13.2D8.2D58.4B$97.4B111.10B4.2D7.2D8.2D
59.4B$96.4B112.6B2A3B3.D8.2D8.2D60.4B$95.4B113.6B2A2B2.D.D2A79.4B$94.
4B114.10B2.2D.A81.4B$93.4B114.11B2.BA.A82.4B$92.4B115.12B.B2A84.4B$
91.4B115.15B87.4B$90.4B110.2D3.16B88.4B$89.4B111.2D2B.16B89.4B$88.4B
113.2A18B90.4B$87.4B114.2AB.17B90.4B$86.4B116.2D4B.8B2.4B90.4B$85.4B
117.2D5.7B4.4B90.4B$84.4B119.2D5.6BD4.4B90.4B$83.4B120.2D7.4B.D4.4B
90.4B$82.4B122.2D8.3BA5.4B90.4B$81.4B123.2D9.BA.A5.3B91.4B$80.4B125.
2D9.ADAD5.B93.4B$79.4B126.2D10.A.D100.4B$78.4B128.2D10.3A100.4B$77.4B
129.2D12.A9.D.D.D.D.D11.D71.4B$76.4B131.2D41.D72.4B$75.4B132.2D21.D.D
17.D73.4B$74.4B176.D74.4B$73.4B136.D20.D3.D15.D75.4B$72.4B178.D76.4B$
71.4B139.D19.D5.D13.D.3D73.4B$70.4B180.2D3.D73.4B$69.4B142.D18.D7.D
11.D5.D73.4B$68.4B182.D5.D74.4B$67.4B145.D5.D21.D9.2D3.D76.4B$66.4B
184.D.3D78.4B$65.4B148.D3.D24.D91.4B$64.4B143.D127.4B$63.4B146.D4.D.D
27.D91.4B$62.4B149.D125.4B$61.4B152.D.D30.D91.4B$60.4B279.4B$59.4B
189.D91.4B$58.4B283.4B$57.4B193.D91.4B$56.4B287.4B$55.4B197.D91.4B$
54.4B291.4B$53.4B201.D91.4B$52.4B295.4B$51.4B205.D91.4B$50.4B299.4B$
49.4B209.D91.4B$48.4B303.4B$47.4B213.D91.4B$46.4B307.4B$45.4B217.D91.
4B$44.4B311.4B$43.4B221.D91.4B$42.4B315.4B$41.4B225.D91.4B8.D$40.4B
319.4B7.3D$39.4B321.4B7.A.D$38.4B323.4B6.3AD$37.4B325.4B6.D.A$36.4B
327.4B6.A.A$35.4B237.D.D.D.D.D83.4B5.A.AB$34.4B331.4B5.A3B$33.4B239.D
.D91.4B6.4B$32.4B335.4B5.6B$31.4B241.D3.D91.4B4.7B5.2D$30.4B262.3D74.
4B2.8B.4BDB$22.2B5.4B243.D5.D12.D3.D74.17B.B2A$22.2B4.4B267.D75.18B2A
$22.2B3.4B245.D6.3D10.4D75.16B.2B2D$9.D12.2B2.4B253.D11.D3.D72.2D.16B
3.2D$9.3D10.2B.4B255.2AC8.D3.D71.D.D.15B$10.A.D9.6B256.A3B8.3D.D70.D.
2AB.12B$10.3A9.5B258.A2BD81.2DA.AB2.11B$13.A8.10B254.4B65.9D8.A5.10B$
12.2A7.11B255.3BD64.10D6.2A5.2B2A6B$3.2D7.5B3.4B264.4B63.2D6.3D11.3B
2A6BD.D$3.D10.3B2.4B266.3BD62.2D7.3D11.10BD.3D$2D.D2A7.9B268.4B61.2D
8.2D11.8B.B2A.A.D$D2.DAD4.2D.8B270.3BD60.2D8.2D10.7B3.B2AB3A$.2A.A.B
3.10B272.4B59.2D7.3D10.6B5.DBD3.A$.A.D3AB.2B2A7B273.3BD58.2D6.3D12.6B
4.2AD3A$2.2A2.BA3B2A7BD273.4B57.10D13.5B6.A.A$4.4A12B.D273.3BD56.10D
12.6B6.A.A$4.A.2B3.7B.B2A274.4B55.2D6.3D11.6B7.A$2.3D3AB2.7B.BADA274.
3BD54.2D7.3D9.7B5.3D$2.D5.A4.4B5.A275.4B53.2D8.2D9.2B3D2B4.D3.A$3.5A
5.4B5.2A275.3BD52.2D8.2D9.4BD3B3.2D3A$3.AD9.4B282.4B51.2D8.2D9.3B3D2B
4.A$5.A9.4B282.3BD50.2D7.3D10.8B3.2A$4.2A10.4B282.4B49.2D6.3D11.3B2A
2B2.4B$17.4B282.3BD48.10D10.5B2A2B.3B$18.4B282.4B47.9D11.13B$19.4B
282.3BD40.D24.16B$20.4B282.4B37.3D16.D6.17B$21.4B282.3BD12.D11.D10.D
3.A13.3D7.16B$22.4B282.4B11.3D7.3D10.2D3A12.D3.A7.15B5.D$23.4B282.3BD
11.A.D5.D3.A10.A15.2D3A8.13B4.3D$24.4B282.4B10.3A5.2D3A10.2A15.A12.
11B4.D3.A$25.4B282.4B12.A5.A11.4B15.2A7.15B4.2D3A$26.4B282.4B10.2A4.B
2A9.3B5.B.7B4.B4.20B3.A$27.4B282.4B9.9B8.4B.13B4.25B3.2A$28.4B282.4B
10.5B3.59B$29.4B282.4B8.6B2.4BD53B$30.4B282.4B7.6B2.4B3D53B$31.4B282.
4B6.7B.4BDBD15B2A37B$32.4B282.4B4.15BD15B2A37BD$33.4B282.4B2.20B2.2B
3.44B.D$34.4B282.4B.17B11.10B2.29B.B2A$35.4B282.19B16.6B4.8B.19B.BADA
$36.4B282.17B19.3B9.23B5.A$37.4B282.17BD19.B11.13B.7B5.2A$38.4B282.
16B.D15.3D2A11.3BD3.4B.3B.3B$39.4B282.7B3.3B.B2A15.D3.A12.4B4.B2.D3B.
D2B$40.4B282.6B7.BADA15.3A15.2AD6.B2AB.B2AB$41.4B279.2D.4B11.A15.A17.
A.D7.2A3.2A$42.4B279.5B12.2A33.3A$43.4B275.3D2A52.A$44.4B274.D3.A$45.
4B274.3A$46.4B273.A$47.4B$48.4B$49.4B278.10B$50.4B277.10B$51.4B281.5B
$52.4B279.6B$53.4B277.4B.2B$54.4B275.4B2.2B$55.4B273.4B3.2B$56.4B271.
4B4.2B$57.4B269.4B5.2B$58.4B267.4B$59.4B265.4B$60.4B263.4B$61.4B261.
4B$62.4B259.4B$63.4B257.4B$64.4B255.4B$65.4B253.4B$66.4B251.4B$67.4B
249.4B$68.4B247.4B$69.4B245.4B$70.4B243.4B$71.4B241.4B$72.4B239.4B$
73.4B237.4B$74.4B235.4B$75.4B233.4B$76.4B231.4B$77.4B229.4B$78.4B227.
4B$79.4B225.4B$80.4B223.4B$81.4B221.4B$82.4B219.4B$83.4B217.4B$84.4B
215.4B$85.4B213.4B$86.4B211.4B$87.4B209.4B$88.4B207.4B$89.4B205.4B$
90.4B203.4B$91.4B201.4B$92.4B199.4B$93.4B197.4B$94.4B195.4B$95.4B193.
4B$96.4B191.4B$97.4B189.4B$98.4B187.4B$99.4B185.4B$100.4B183.4B$101.
4B181.4B$102.3B180.4B$103.4B177.4B$104.4B175.4B$105.4B173.4B$106.4B
171.4B$107.4B169.4B$108.4B167.4B$109.4B165.4B$110.4B163.4B$111.4B161.
4B$112.4B159.4B$113.4B157.4B$114.4B155.4B$115.4B153.4B$116.4B151.4B$
117.4B149.4B$118.4B147.4B$119.4B145.4B$120.4B143.4B$121.4B141.4B$122.
4B139.4B$123.4B137.4B$124.4B135.4B$125.4B133.4B$126.4B131.4B$127.4B
129.4B$128.4B127.4B$129.4B126.3B$130.4B123.4B$131.4B121.4B$132.4B119.
4B$133.4B117.4B$134.4B115.4B$135.4B113.4B$136.4B111.4B$137.4B109.4B$
138.4B107.4B$139.4B105.4B$140.4B103.4B$141.4B101.4B$142.4B99.4B$143.
4B97.4B$144.4B95.4B$145.4B93.4B$146.4B91.4B$147.4B89.4B$148.4B87.4B$
149.4B85.4B$150.4B83.4B$151.4B81.4B$152.4B79.4B$153.4B77.4B$154.4B75.
4B$155.4B73.4B$156.4B71.4B$157.4B69.4B$158.4B67.4B$159.4B65.4B$160.4B
63.4B$161.4B61.4B$162.4B59.4B$163.4B57.4B$164.4B55.4B$165.4B53.4B$
166.4B51.4B$167.4B49.4B$168.4B47.4B$169.4B45.4B$170.4B43.4B$171.4B41.
4B$172.4B39.4B$173.4B37.4B$174.4B35.4B$175.4B5.2B26.4B$176.4B4.2B25.
4B$177.4B3.2B24.4B$178.4B2.2B23.4B$179.4B.2B22.4B$180.6B21.4B$181.5B
20.4B$182.4B19.4B$177.9B18.4B$177.9B17.4B9$192.2D$192.2D$193.2A$193.
2A!

When each cycle starts, the Snarks will all be in the wrong place. So the question is just whether there's a single-channel recipe that can treat each offset Snark as a random-debris target, and convert it into a workable elbow block:

[corrected pattern after 6/18/2017 -- see below]

Code: Select all

x = 311, y = 114, rule = LifeHistory
128.4B$33.B93.4B$32.4B75.2D13.4B82.4B$19.2A10.4B77.D12.4B70.2A10.4B$
8D9.2D.A9.4B62.8D6.D.2A10.4B72.A9.4B$D17.A10.4B63.D13.3DAD8.4B2.2D67.
AD9.4B$D15.D.5A5.4B5.2A57.D14.A3.D6.4B3.D54.5D9.5A5.4B5.2A$D15.5D2.A
4.4B3.2DA58.D14.5A5.4B2.D.D2A51.D5.D7.D5.A4.4B5.A$D19.3AB2.7B.BA.A58.
D14.D4.A3.5B2.2D.A51.D14.3D3AB2.7B.BADA$4D14.DAD2B3.7BDB2A59.4D11.2D
3AB2.7B.BA.A2B49.D16.A.2B3.7B.B2A$D16.D.4A10B2D61.D12.2D.A.2B2.2D6B.B
2A.B50.D16.4A11BD.D$D16.2A2DBA3B2A7B61.D11.D2.D4A2B2D8B.B.B50.D14.2A
2.BA3B2A6B2D$D14.DA2.3AB.2D2A7B61.D11.2D2A2.BA3B2A7B.2B51.D13.A.D3AB.
2B2A7B$D13.D.2ADA.B2.2D9B61.D12.A.D3AB.2B2A7B54.D13.2A.A.B3.2D8B$D13.
2D.D.A8.8B60.8D5.2ADA.B3.10B54.D12.D2.DAD4.2D.8B$17.D.2A7.9B75.A8.8B
54.D5.D5.2D.D2A7.9B$17.2D10.3B2.4B74.2A7.9B54.5D9.D10.3B2.4B3C$27.5B
7.3C77.2D.3B2.4B67.2D7.5B3.3BC$27.2A10.C80.D4B3.4B75.2A7.3BC$25.2D.A
11.C76.3D2A7.4B75.A$25.3A89.D3.A8.4B71.3A$23.2DA92.3A2B6.2B3C71.A.D$
23.D94.A3.B7.BC72.3D$119.3B10.C71.D$119.B14$241.2C$62.2C177.C.C$62.C.
C176.C$62.C2$154.2C$154.C.C$154.C16$263.3C$84.3C176.C$84.C179.C$85.C
2$176.3C$176.C$177.C15$286.2C$107.2C177.C.C$107.C.C176.C$107.C2$199.
2C$199.C.C$199.C16$308.3C$129.3C176.C$129.C179.C$130.C2$221.3C$221.C$
222.C!

The Snark on the far right seems to be a case where the single-channel gliders will inevitably just knock a hole through the Snark, with no way to start a search tree before gliders start escaping. So an extra block will have to be left behind that Snark to solve that problem. That doesn't seem too terrible. Am I missing any other problems here?

EDIT: Oops, no, it's the Snark in the middle -- the one near the a' label. I had the following gliders lined up incorrectly. Hopefully it's fixed now.

EDIT2 6/18/2017: Nope, I still had the shift exactly backwards in all cases. Have now fixed this, and added labels to match the C, E, and F labels in the blueprint a few posts down. All Snarks have been adjusted to a standard 90-degree counterclockwise turn -- yes, this is confusing, but maybe less confusing than leaving them all pointing in different directions. Hopefully it's all fixed now.

[chris_c]

One more round of thinking: it may be that all we need to do is consider each Snark to be a starting point for a single-channel search tree, with the lane offset by one lane, or three lanes

The design seems good. I added a couple of labels C, D and S and a one-time-turner to your pattern. Let me give some thoughts to double check:

Code: Select all

x = 419, y = 492, rule = LifeHistory
243.2D$243.D.D$244.2A4.2D$241.3DA.AD2.D2.D$241.D2.D.A.D.D2AD$242.4AD
2A.DA2.A$242.A2.ADADADA.2A$244.BABABA.A$245.B2ABA.A$235.2D9.2B.BA$
236.D7.D3B$236.2AD5.4B$237.AD5.B2A3B$237.A.AB3.B2A3B$238.2AB.10B$240.
13B$240.14B$240.15B$242.8B2.4B$242.6BD4.4B$241.9B4.4B$240.4B4.2AD4.4B
$239.4B5.A.D5.4B$231.11B7.3A5.4B$231.10B10.A6.4B$236.4B19.4B$235.5B
20.4B$234.6B21.4B$233.4B.2B22.4B$232.4B2.2B23.4B$231.4B3.2B24.4B$230.
4B4.2B25.4B$229.4B5.2B26.4B$228.4B35.4B$227.4B37.4B$226.4B39.4B$225.
4B41.4B$224.4B43.4B$223.4B45.4B$222.4B47.4B$221.4B49.4B$220.4B51.4B$
219.4B53.4B$218.4B55.4B$217.4B57.4B$216.4B59.4B$215.4B61.4B$214.4B63.
4B$213.4B65.4B$212.4B67.4B$211.4B69.4B$210.4B71.4B$209.4B73.4B$208.4B
75.4B$207.4B77.4B$206.4B79.4B$205.4B81.4B$204.4B83.4B$203.4B85.4B$
202.4B87.4B$201.4B89.4B$200.4B91.4B$199.4B93.4B$198.4B95.4B$197.4B97.
4B$196.4B99.4B$195.4B101.4B$194.4B103.4B$193.4B105.4B8.C$192.4B107.4B
6.C.C$191.4B109.4B5.2C$190.4B111.4B$189.4B113.4B$188.4B115.4B$187.4B
117.4B$186.4B119.4B$185.4B121.4B$184.4B123.4B$183.4B125.4B$182.4B127.
4B$181.4B129.4B$180.4B131.4B$179.4B133.4B5.2B$178.4B135.4B4.2B$177.4B
137.4B3.2B$165.D10.4B68.8D63.4B2.2B$159.3D3.D9.4B69.D7.5D59.4B.2B$
158.D3.D11.4B69.D13.3D57.6B$162.D10.4B69.D75.5B$159.4D9.4B70.D70.10B$
158.D3.D8.4B70.D71.10B$158.D3.D7.4B71.D$159.3D.D5.4B72.D$168.4B73.D$
167.4B74.D$151.2D13.4B75.D$152.D12.4B77.D89.2D$150.D.2A10.4B79.2D87.
2D$150.3DAD8.4B2.2D78.D87.2A$151.A3.D6.4B3.D80.4D83.2A$151.5A5.4B2.D.
D2A82.2D$151.D4.A4.4B2.2D.A85.2D$151.2D3AB2.7B.BA.A87.2D$149.2D.A.2B
2.D7B.B2A90.2D$148.D2.D4A12B94.D$148.2D2A2.BA3B2A7B95.D$149.A.D3AB.2B
2A7B96.D$149.2ADA.B3.10B96.D$152.A8.8B95.D61.B$152.2A7.9B94.D60.2B$
159.2D.3B2.4B69.D23.D59.3B$160.5B3.4B68.2D21.2D58.4B$157.3D2A7.11B61.
3D15.4D59.4B$157.D3.A8.10B64.4D6.5D62.4B$158.3A9.5B73.6D66.4B$158.A
11.6B143.4B$170.2B.4B141.4B$170.2B2.4B139.4B$170.2B3.4B137.4B$170.2B
4.4B135.4B$170.2B5.4B133.4B$178.4B131.4B$179.4B129.4B$180.4B127.4B$
181.4B125.4B$182.4B123.4B$183.4B121.4B$184.4B119.4B$185.4B117.4B$186.
4B115.4B$187.4B113.4B$188.4B15.6D90.4B$189.4B14.D5.D88.4B$190.4B13.D
6.D86.4B$191.4B12.D6.D85.4B$192.4B11.D6.D84.4B$193.4B10.D6.D83.4B$
194.4B9.D6.D82.4B$195.4B8.D6.D81.4B$196.4B7.D5.D81.4B$197.4B6.6D81.4B
$198.4B91.4B$196.2D.4B89.4B$196.2D2.4B87.4B$197.2A2.4B85.4B$191.2B4.
2A3.4B83.4B$190.4B9.4B81.4B$189.4B11.4B79.4B$188.4B13.4B77.4B$187.4B
15.4B75.4B$186.4B17.4B73.4B$185.4B19.4B71.4B$184.4B21.4B69.4B$183.4B
23.4B67.4B$182.4B25.4B65.4B$181.4B27.4B63.4B$180.4B29.4B61.4B$179.4B
31.4B59.4B$178.4B33.4B57.4B$177.4B35.11B48.4B$176.4B37.10B47.4B$175.
4B39.4B51.4B$174.4B40.5B49.4B$173.4B41.6B47.4B$172.4B42.2B.4B45.4B$
171.4B43.2B2.4B35.2B6.4B$170.4B44.2B3.4B34.2B5.4B$169.4B45.2B4.4B33.
2B4.4B$168.4B46.2B5.4B32.2B3.4B$167.4B55.4B31.2B2.4B$151.D14.4B57.4B
30.2B.4B$144.D6.D13.4B59.4B29.6B$144.D6.D12.4B61.4B28.5B$144.D6.D11.
4B63.4B27.4B$144.D17.4B65.4B27.9B$144.D16.4B67.4B26.9B$144.D15.4B69.
4B$144.D.3D10.4B71.4B46.D$144.2D3.D8.4B73.4B45.3D$144.D5.D6.4B75.4B
35.D9.A.D$144.D5.D5.4B65.2D3.2D5.4B13.2D19.3D7.3A$144.2D3.D5.4B66.2D
3.2D6.4B12.D.D19.A.D9.A$144.D.3D5.4B68.2A3.2A6.4B12.2A19.3A8.2A5.4B$
153.4B68.B2AB.B2AB6.4B11.ADA21.A7.11B2D$152.4B62.2D6.2B2.3B3.B4.4B12.
A20.2A3.B5.11B$151.4B64.D7.3B.3B.4B3.4B11.2A19.8B2.11B2A$150.4B65.2AD
4.7B.13B11.B21.19B2A$149.4B67.AD4.23B9.3B19.20B$148.4B68.A.AB.19B.8B
4.6B16.20B$147.4B70.2AB.29B2.10B11.21B$146.4B73.44B3.2B2.25B$145.4B
74.37B2A15BD14B4.4B$144.4B75.37B2A15BDBD4B.6BD5.4B$143.4B77.53B3D4B2.
B.5B5.4B$142.4B77.2D.53BD4B7.2AD5.4B$141.4B79.59B8.A.D6.4B$140.4B77.
3D2A3.25B4.13B.4B16.3A6.4B$139.4B78.D3.A3.20B4.B4.7B.B2.2D.3B19.A7.4B
$138.4B80.3A6.15B4.3D2A15.4B29.4B$137.4B81.A8.11B8.D3.A12.3D2A32.4B$
136.4B90.13B8.3A13.D3.A33.4B$135.4B90.15B7.A16.3A35.4B$134.4B91.16B
23.A38.4B$133.4B92.17B62.4B$132.4B93.16B14.2D48.4B$131.4B96.13B15.2D
49.4B$130.4B94.2D.3B.2B2A5B14.4D49.4B$129.4B96.4B2.2B2A3B16.4D50.4B$
128.4B94.3D2A3.8B15.2D2.2D50.4B$127.4B95.D3.A4.2B3D3B14.2D2.2D51.4B$
126.4B97.3A5.3BD4B13.2D4.2D51.4B$125.4B98.A8.2B3D2B13.2D4.2D52.4B$
124.4B98.D.D7.7B12.2D6.2D52.4B$123.4B99.D.A7.6B13.2D6.2D53.4B$122.4B
98.3DADA6.6B12.12D53.4B$121.4B98.D3.A.A6.5B13.12D54.4B$120.4B100.D3AD
2A4.6B13.2D8.2D55.4B$119.4B101.A.D.DB6.6B12.2D8.2D56.4B$118.4B103.3AB
2AB3.7B12.2D8.2D57.4B$117.4B106.A.2AB.8B13.2D8.2D58.4B$116.4B111.10B
4.2D7.2D8.2D59.4B$115.4B112.6B2A3B3.D8.2D8.2D60.4B$114.4B113.6B2A2B2.
D.D2A79.4B$113.4B114.10B2.2D.A81.4B$112.4B114.11B2.BA.A82.4B$111.4B
115.12B.B2A84.4B$110.4B115.15B87.4B$109.4B110.2D3.16B88.4B$108.4B111.
2D2B.16B89.4B$107.4B113.2A18B90.4B$106.4B114.2AB.17B90.4B$105.4B116.
2D4B.8B2.4B90.4B$104.4B117.2D5.7B4.4B90.4B$103.4B119.2D5.6BD4.4B90.4B
$102.4B120.2D7.4B.D4.4B90.4B$101.4B122.2D8.3BA5.4B90.4B$100.4B123.2D
9.BA.A5.3B91.4B$99.4B125.2D9.ADAD5.B93.4B$98.4B126.2D10.A.D100.4B$97.
4B128.2D10.3A100.4B$96.4B129.2D12.A9.D.D.D.D.D11.D71.4B$95.4B131.2D
41.D72.4B$94.4B132.2D21.D.D17.D73.4B$93.4B176.D74.4B$92.4B136.D20.D3.
D15.D75.4B$91.4B178.D76.4B$90.4B139.D19.D5.D13.D.3D73.4B$89.4B180.2D
3.D73.4B$88.4B142.D18.D7.D11.D5.D73.4B$87.4B182.D5.D74.4B$86.4B145.D
5.D21.D9.2D3.D76.4B$85.4B184.D.3D78.4B$84.4B148.D3.D24.D91.4B$83.4B
143.D127.4B$82.4B146.D4.D.D27.D91.4B$81.4B149.D125.4B$80.4B152.D.D30.
D91.4B$79.4B279.4B$78.4B189.D91.4B$77.4B283.4B$76.4B193.D91.4B$75.4B
287.4B$74.4B197.D91.4B$73.4B291.4B$72.4B201.D91.4B$71.4B295.4B$70.4B
205.D91.4B$69.4B299.4B$68.4B209.D91.4B$67.4B303.4B$66.4B213.D91.4B$
65.4B307.4B$64.4B217.D91.4B$63.4B311.4B$62.4B221.D91.4B$61.4B315.4B$
60.4B225.D91.4B8.D$59.4B319.4B7.3D$58.4B321.4B7.A.D$57.4B323.4B6.3AD$
56.4B325.4B6.D.A$55.4B327.4B6.A.A$54.4B237.D.D.D.D.D83.4B5.A.AB$53.4B
331.4B5.A3B$52.4B239.D.D91.4B6.4B$51.4B335.4B5.6B$50.4B241.D3.D91.4B
4.7B5.2D$49.4B262.3D74.4B2.8B.4BDB$41.2B5.4B243.D5.D12.D3.D74.17B.B2A
$41.2B4.4B267.D75.18B2A$41.2B3.4B245.D6.3D10.4D75.16B.2B2D$28.D12.2B
2.4B253.D11.D3.D72.2D.16B3.2D$28.3D10.2B.4B255.2AC8.D3.D71.D.D.15B$
29.A.D9.6B256.A3B8.3D.D70.D.2AB.12B$29.3A9.5B258.A2BD81.2DA.AB2.11B$
32.A8.10B254.4B65.9D8.A5.10B$31.2A7.11B255.3BD64.10D6.2A5.2B2A6B$3.7D
12.2D7.5B3.4B264.4B63.2D6.3D11.3B2A6BD.D$2.D19.D10.3B2.4B266.3BD62.2D
7.3D11.10BD.3D$.D17.2D.D2A7.9B268.4B61.2D8.2D11.8B.B2A.A.D$D18.D2.DAD
4.2D.8B270.3BD60.2D8.2D10.7B3.B2AB3A$D19.2A.A.B3.10B272.4B59.2D7.3D
10.6B5.DBD3.A$D19.A.D3AB.2B2A7B273.3BD58.2D6.3D12.6B4.2AD3A$D20.2A2.B
A3B2A7BD273.4B57.10D13.5B6.A.A$D22.4A12B.D273.3BD56.10D12.6B6.A.A$D
22.A.2B3.7B.B2A274.4B55.2D6.3D11.6B7.A$D20.3D3AB2.7B.BADA274.3BD54.2D
7.3D9.7B5.3D$D20.D5.A4.4B5.A275.4B53.2D8.2D9.2B3D2B4.D3.A$.D20.5A5.4B
5.2A275.3BD52.2D8.2D9.4BD3B3.2D3A$2.D19.AD9.4B282.4B51.2D8.2D9.3B3D2B
4.A$3.7D14.A9.4B282.3BD50.2D7.3D10.8B3.2A$23.2A10.4B282.4B49.2D6.3D
11.3B2A2B2.4B$36.4B282.3BD48.10D10.5B2A2B.3B$37.4B282.4B47.9D11.13B$
38.4B282.3BD40.D24.16B$39.4B282.4B37.3D16.D6.17B$40.4B282.3BD12.D11.D
10.D3.A13.3D7.16B$41.4B282.4B11.3D7.3D10.2D3A12.D3.A7.15B5.D$42.4B
282.3BD11.A.D5.D3.A10.A15.2D3A8.13B4.3D$43.4B282.4B10.3A5.2D3A10.2A
15.A12.11B4.D3.A$44.4B282.4B12.A5.A11.4B15.2A7.15B4.2D3A$45.4B282.4B
10.2A4.B2A9.3B5.B.7B4.B4.20B3.A$46.4B282.4B9.9B8.4B.13B4.25B3.2A$47.
4B282.4B10.5B3.59B$48.4B282.4B8.6B2.4BD53B$49.4B282.4B7.6B2.4B3D53B$
50.4B282.4B6.7B.4BDBD15B2A37B$51.4B282.4B4.15BD15B2A37BD$52.4B282.4B
2.20B2.2B3.44B.D$53.4B282.4B.17B11.10B2.29B.B2A$54.4B282.19B16.6B4.8B
.19B.BADA$55.4B282.17B19.3B9.23B5.A$56.4B282.17BD19.B11.13B.7B5.2A$
57.4B282.16B.D15.3D2A11.3BD3.4B.3B.3B$58.4B282.7B3.3B.B2A15.D3.A12.4B
4.B2.D3B.D2B$59.4B282.6B7.BADA15.3A15.2AD6.B2AB.B2AB$60.4B279.2D.4B
11.A15.A17.A.D7.2A3.2A$61.4B279.5B12.2A33.3A$62.4B275.3D2A52.A$63.4B
274.D3.A$64.4B274.3A$65.4B273.A$66.4B$67.4B$68.4B278.10B$69.4B277.10B
$70.4B281.5B$71.4B279.6B$72.4B277.4B.2B$73.4B275.4B2.2B$74.4B273.4B3.
2B$75.4B271.4B4.2B$76.4B269.4B5.2B$77.4B267.4B$78.4B265.4B$79.4B263.
4B$80.4B261.4B$81.4B259.4B$82.4B257.4B$83.4B255.4B$84.4B253.4B$85.4B
251.4B$86.4B249.4B$87.4B247.4B$88.4B245.4B$89.4B243.4B$90.4B241.4B$
91.4B239.4B$92.4B237.4B$93.4B235.4B$94.4B233.4B$95.4B231.4B$96.4B229.
4B$97.4B227.4B$98.4B225.4B$99.4B223.4B$100.4B221.4B$101.4B219.4B$102.
4B217.4B$103.4B215.4B$104.4B213.4B$105.4B211.4B$106.4B209.4B$107.4B
207.4B$108.4B205.4B$109.4B203.4B$110.4B201.4B$111.4B199.4B$112.4B197.
4B$113.4B195.4B$114.4B193.4B$115.4B191.4B$116.4B189.4B$117.4B187.4B$
118.4B185.4B$119.4B183.4B$120.4B181.4B$121.3B180.4B$122.4B177.4B$123.
4B175.4B$124.4B173.4B$125.4B171.4B$126.4B169.4B$127.4B167.4B$128.4B
165.4B$129.4B163.4B$130.4B161.4B$131.4B159.4B$132.4B157.4B$133.4B155.
4B$134.4B153.4B$135.4B151.4B$136.4B149.4B$137.4B147.4B$138.4B145.4B$
139.4B143.4B$140.4B141.4B$141.4B139.4B$142.4B137.4B$143.4B135.4B$144.
4B133.4B$145.4B131.4B$146.4B129.4B$147.4B127.4B$148.4B126.3B$149.4B
123.4B$150.4B121.4B$151.4B119.4B$152.4B117.4B$153.4B115.4B$154.4B113.
4B$155.4B111.4B$156.4B109.4B$157.4B107.4B$158.4B105.4B$159.4B103.4B$
160.4B101.4B$161.4B99.4B$162.4B97.4B$163.4B95.4B$164.4B93.4B$165.4B
91.4B$166.4B89.4B$167.4B87.4B$168.4B85.4B$169.4B83.4B$170.4B81.4B$
171.4B79.4B$172.4B77.4B$173.4B75.4B$174.4B73.4B$175.4B71.4B$176.4B69.
4B$177.4B67.4B$178.4B65.4B$179.4B63.4B$180.4B61.4B$181.4B59.4B$182.4B
57.4B$183.4B55.4B$184.4B53.4B$185.4B51.4B$186.4B49.4B$187.4B47.4B$
188.4B45.4B$189.4B43.4B$190.4B41.4B$191.4B39.4B$192.4B37.4B$193.4B35.
4B$194.4B5.2B26.4B$195.4B4.2B25.4B$196.4B3.2B24.4B$197.4B2.2B23.4B$
198.4B.2B22.4B$199.6B21.4B$200.5B20.4B$201.4B19.4B$196.9B18.4B$196.9B
17.4B9$211.2D$211.2D$212.2A$212.2A!

Recipes a and b are going to have roughly the same length. Call the length d. The square S should have perimeter d so that information from the start of both recipes travels around the loop by the time the recipe gets to the end.

Recipe b starts by sending a 0-degree glider from D around the loop S and hitting the boat. It then builds a Snark at D, reconstructs the Snark at C and reconstructs the constellation at B. By the time recipe has finished the original 0-degree glider is returning and destroys the Snark at D, letting recipe a do it's work.

Recipe a reconstructs the Snarks around S and reconstructs the constellation at A. The perimeter of S is roughly d so that recipe a has already gone past before any reconstruction gliders arrive.

Final thought: I think that the length AB should be roughly 1.5d and the length CD should be roughly d. That way the front of recipe b travels d + 1.5d + d = 3.5d to get to B and the back of recipe a travels d + d + 1.5d = 3.5d to get to B. No conflicts should occur and construction/destruction should be taking place 2/3 of the time.

EDIT: It looks like I am assuming the existence of a pair of working Snarks at the beginning of recipe b, therefore recipe a should use these working snarks and reconstruct them in the new positions at the end of it's recipe.

EDIT2: Now I'm not sure that this all works as claimed because reconstructing the Snarks at the end of recipe a will involve quite a lot of wasted time waiting for return gliders to arrive.

EDIT3: Ah, I think it's ok. The Snarks used at the start of recipe b do not need to be aligned on the "natural" channel: there is no problem sending a 0-degree glider on a non-zero lane. So recipe a can go back to reconstruction of the snarks at the start of the recipe.

[dvgrn]

EDIT3: Ah, I think it's ok. The Snarks used at the start of recipe b do not need to be aligned on the "natural" channel: there is no problem sending a 0-degree glider on a non-zero lane. So recipe a can go back to reconstruction of the snarks at the start of the recipe.

Whew, you're right. Luckily I didn't see your earlier edits or I would have worried for a while too -- wasn't sure exactly how the switch from Snark to elbow at D was going to be triggered, but I had figured out that the Snarks couldn't be moved efficiently at the end of the recipe, only at the beginning.

So the only little problem that I see is that the Snark construction recipe at C -- EDIT: sorry, at a' -- will have to be modified, to add a piece of junk somewhere out of the way of the construction, such that a single-channel destruction recipe can be found that produces a working elbow.

Even if no clean destruction recipe can be found for some of these Snark offsets, it's okay, as long as a workable elbow shows up in front of the mess and no gliders are released. The rest of the cleanup could always be done with 0-degree gliders.

-- Or I guess it would be okay in some cases to let the single-channel stream bore a hole in the Snark and get to an elbow beyond, and then use 180-degree gliders and/or elbow-move sparks to do the cleanup. Lots of options. Obviously two blocks is enough -- an elbow block some distance behind the a' Snark, plus another block to stop the 180-degree return glider that seems to be inevitable. But no doubt it can be done with just one additional still life.

[simeks]

So the only little problem that I see is that the Snark construction recipe at C -- EDIT: sorry, at a' -- will have to be modified, to add a piece of junk somewhere out of the way of the construction, such that a single-channel destruction recipe can be found that produces a working elbow.

An example solution of this, with the extra block out of reach of the Snark slow-salvo recipe.
I used the first intermediate result of my self-destruct search program to find a suitable extra still life.

Code: Select all

#C /* E41->E00, +28 */  {  0,   0,   1, 122,   0,   1, 164,   1,   1,  92,   0, 151,   1,  -1}
x = 808, y = 786, rule = LifeHistory
789.2A$789.A$791.A$771.2A14.5A$772.A13.A$772.A.A12.3A$773.2A15.A15.2C
$787.4A15.2C$782.2A3.A3.2A$782.2A4.3A2.A$790.A.2A$773.2A15.A$772.A.A
14.2A$774.A2$781.2A$781.A$782.3A$784.A73$693.2A$692.A.A$694.A78$613.A
$613.2A$612.A.A29$582.3A$584.A$583.A78$502.3A$504.A$503.A78$422.2A$
423.2A$422.A39$381.3A$383.A$382.A78$301.2A$302.2A$301.A78$221.2A$222.
2A$221.A21$198.3A$200.A$199.A78$118.3A$120.A$119.A35$81.A$81.2A$80.A.
A78$.A$.2A$A.A!

[dvgrn]

So the only little problem that I see is that the Snark construction recipe at C -- EDIT: sorry, at a' -- will have to be modified, to add a piece of junk somewhere out of the way of the construction, such that a single-channel destruction recipe can be found that produces a working elbow.

An example solution of this, with the extra block out of reach of the Snark slow-salvo recipe.

Thanks! I'll recompile the 0-degree Snark recipe with that additional block.

For the other two Snarks I guess just Snark-to-elbow recipes are needed, unless some similar problem turns up where the search tree runs out before a cleanup is found.

[chris_c]

It seems that dvgrn and I disagree on the relative positions of these Snarks that need to be cleaned up. Also I have an idea that instead of adding extra still lifes around the Snarks they can be damaged by cheap orthogonal gliders until they end up being lumps of junk that behave themselves better.

I am just going to post the pattern I have been working on with explanation afterwards:

Code: Select all

x = 5592, y = 3354, rule = LifeHistory
3334.2A$3334.A.A$3336.A4.2A$3332.4A.2A2.A2.A$3332.A2.A.A.A.A.2A$3335.
A.A.A.A$3336.2A.A.A$3340.A2$3326.2A$3327.A7.2A$3327.A.A5.2A$3328.2A7$
3338.2A$3338.A$3339.3A$3341.A5$3354.A.A$3355.2A$3355.A22$3380.A$3381.
A$3379.3A16$3268.2A$3269.A$3267.A$3267.5A14.2A$3272.A13.A$3269.3A12.A
.A$3268.A15.2A$3268.4A$3266.2A3.A3.2A129.A$3265.A2.3A4.2A127.A.A$
3265.2A.A136.2A$3268.A$3268.2A3$3276.2A$3277.A$3274.3A$3274.A15$3429.
A.A$3430.2A$3430.A2$3309.2A$3308.2A$3310.A26$3462.A$3463.2A$3462.2A
25$3490.A$3491.A$3489.3A26$3513.2A$3513.2A42$3449.2A$3448.A.A$3442.2A
4.A$3440.A2.A2.2A.4A$3440.2A.A.A.A.A2.A$3443.A.A.A.A$3443.A.A.2A$
3444.A2$3457.2A$3448.2A7.A$3448.2A5.A.A$3455.2A7$3445.2A$3446.A$3443.
3A$3443.A332$3789.A$3788.2A$3788.A.A64$3854.2A$3853.2A$3855.A62$3918.
2A$3918.A.A$3918.A21$3940.3A$3940.A$3941.A62$4005.2A$4004.2A$4006.A
20$4028.A$4027.2A$4027.A.A63$4091.3A$4091.A$4092.A20$4114.2A$4114.A.A
$4114.A63$4178.3A$4178.A$4179.A39$4221.A$4220.2A$4220.A.A331$4553.2A$
4553.A.A$4553.A62$4617.2A$4617.A.A$4617.A27$4647.A$4646.2A$4646.A.A
63$4710.3A$4710.A$4711.A20$4733.2A$4733.A.A$4733.A62$4797.2A$4797.A.A
$4797.A21$4820.2A$4819.2A$4821.A62$4885.A$4884.2A$4884.A.A24$4909.3A$
4909.A$4910.A62$4973.3A$4973.A$4974.A38$5013.3A$5013.A$5014.A62$5078.
2A$5077.2A$5079.A25$5105.2A$5104.2A$5106.A62$5169.2A$5169.A.A$5169.A
62$5234.A$5233.2A$5233.A.A22$5256.3A$5256.A$5257.A62$5320.3A$5320.A$
5321.A62$5384.3A$5384.A$5385.A20$5408.A$5407.2A$5407.A.A63$5471.3A$
5471.A$5472.A24$5499.A$5498.2A$5498.A.A63$5562.3A$5562.A$5563.A24$
5589.2A$5589.A.A$5589.A199$745.2A$744.A.A$746.A7$752.2A$751.A.A$753.A
49$704.2A$703.A.A$705.A25$677.2A$678.2A$677.A62$613.2A$612.A.A$614.A
62$549.2A$548.A.A$550.A24$523.2A$524.2A$523.A62$459.2A$458.A.A$460.A
21$436.2A$437.2A$436.A62$372.2A$371.A.A$373.A35$335.2A$336.2A$335.A
62$271.2A$270.A.A$272.A21$248.3A$250.A$249.A62$184.3A$186.A$185.A25$
157.2A$156.A.A$158.A62$93.2A$92.A.A$94.A62$29.2A$28.A.A$30.A26$.2A$A.
A$2.A!

The Snarks in the NW are from the previous iteration.

The gliders heading SE are from the very end of the previous recipe a.

The lone glider heading NW is a 0-degree glider on lane 1 fired at the
start of recipe b.

The other Snark has been constructed by recipe b in the current iteration.

Eventually the lone glider makes it around to the junk and turns into a
glider heading SW and a pair of blocks that are suitable as Pi-maker for
gliders in this iteration. i.e. one lane lower down than the Pi-maker
for the previous iteration.

The SW glider meets some NW gliders and eventually kills the Snark.

More NW gliders arrive that turn the previous Snark into an elbow block.
This happens one lane lower down than in the previous iteration.

An off-axis glider travels NE. This is intended to be made from the
recently produced elbow.

A NE glider destroys the elbow. This is only to facillitate the example
and should not happen in the real pattern.

More NE gliders arrive to turn the already-damaged-Snark into an elbow.
The NE gliders are 3 lanes away from the lane in the previous iteration.
This same salvo (and the orthogonal damage-making glider) should be
possible to use for the not-shown Snark in the SW.

[dvgrn]

It seems that dvgrn and I disagree on the relative positions of these Snarks that need to be cleaned up.

"Disagree" may be too strong a term. It's more likely to be just "dvgrn is still confused"...!

Also I have an idea that instead of adding extra still lifes around the Snarks they can be dam..aged by cheap orthogonal gliders until they end up being lumps of junk that behave themselves better.

Sounds good, as long as there's a cheap no-delay place for these orthogonal gliders to come from. Zero-degree gliders might also be used in some cases to convert an offset Snark to an elbow, in preparation for the zero-degree Snarkmaker recipe.

I'm going to try to build some more detailed diagrams of the stages this knightship will have to go through, with all the distances shortened down but everything actually lined up as it will have to be in the final pattern. Here's a first draft of the initial three phases; please feel free to improve on them!

Code: Select all

x = 1015, y = 325, rule = LifeHistory
95.3D5.D31.3D213.3D5.D32.D214.3D5.D31.3D213.3D5.D31.3D$94.D3.D4.D30.D
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D125.D16.A9.4B90.2D7.D125.D16.A9.4B90.2D7.D$45.D14.A10.4B91.2D7.D125.
D14.A10.4B91.2D7.D125.D14.A10.4B91.2D7.D125.D14.A10.4B91.2D7.D$45.D
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8D5.2A.A.B3.10B$61.A8.8B239.A8.8B239.A8.8B6.4D229.A8.8B$61.2A7.9B238.
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4B3.D3.D68.B170.3B2.4B76.B$69.5B3.4B74.2B168.5B3.4B74.2B168.5B3.4B3.
3D.D66.2B168.5B3.4B74.2B$69.2A7.3B73.3B168.2A7.3B73.3B168.2A7.3B73.3B
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4B$67.3A2B8.B15.2B54.4B167.3A2B8.B15.2A54.4B167.3A2B8.B2C13.2D54.4B
167.3A2B8.B15.2D54.4B$67.A3.B23.B.B53.4B168.A3.B23.A.A9.6D38.4B168.A
3.B9.C.C11.D.D9.6D38.4B168.A3.B11.B11.D.D9.6D38.4B$68.3B18.2B4.B5.6D
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2B4.2D4.D11.D5.D36.4B$68.B18.B2.B2.2B.4B.D5.D41.4B171.B18.A2.A2.2A.4A
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6.D34.4B$87.2B.B.B.B.B2.B.D6.D39.4B191.2A.A.A.A.A2.A7.D6.D33.4B189.2B
2D.D.D.D.D2.D7.D6.D33.4B187.4B2D.D.D.D.D2.D7.D6.D33.4B$90.B.B.3B4.D6.
D38.4B195.A.ABABAB9.D6.D32.4B190.3B2.D.DBDBDB9.D6.D32.4B189.4B2.D.DBD
BDB9.D6.D32.4B$90.B.B.2B5.D6.D37.4B196.A.AB2AB10.D6.D31.4B191.4B.D.DB
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13B29.2B6.4B202.13B29.2B6.4B202.13B29.2B6.4B202.13B29.2B6.4B$88.14B
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6B31.2B2.4B$85.3B4.9B30.2B.4B202.4B4.9B30.2B.4B202.4B4.2A7B30.2B.4B
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4B5.3D7.4B27.4B202.4B5.3D7.4B27.4B$90.B10.4B27.9B195.4B6.A10.4B27.9B
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21.4B$104.4B46.D178.4B23.4B46.D178.4B23.4B46.D178.4B23.4B46.D$105.4B
45.3D175.4B25.4B45.3D175.4B25.4B45.3D175.4B25.4B45.3D$106.4B35.D9.A.D
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2AB6.4B11.ADA21.A7.11B2D129.D10.D16.4B20.B2AB.B2AB6.4B11.ADA21.A7.11B
2D157.4B20.B2AB.B2AB6.4B11.ADA21.A7.11B2D157.4B20.B2AB.B2AB6.4B11.ADA
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B5.11B156.4B14.2D6.2B2.3B3.B4.4B12.A20.2A3.B5.11B$89.D7.3B.3B.4B3.4B
11.2A19.8B2.11B2A128.D10.D14.4B16.D7.3B.3B.4B3.4B11.2A19.8B2.11B2A
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2A19.8B2.11B2A$89.2AD4.7B.13B11.B21.19B2A128.D24.4B17.2AD4.7B.13B11.B
21.19B2A153.4B17.2AD4.7B.13B11.B21.19B2A153.4B17.2AD4.7B.13B11.B21.
19B2A$90.AD4.23B9.3B19.20B129.D23.4B19.AD4.23B9.3B19.20B153.4B19.AD4.
23B9.3B19.20B153.4B19.AD4.23B9.3B19.20B$90.A.AB.19B.8B4.6B16.20B130.D
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20.A.AB.19B.8B4.6B16.20B$91.2AB.29B2.10B11.21B131.2D3.D16.4B22.2AB.
29B2.10B11.21B153.4B22.2AB.29B2.10B11.21B153.4B22.2AB.29B2.10B11.21B$
93.44B3.2B2.25B130.D5.D14.4B25.44B3.2B2.25B151.4B25.44B3.2B2.25B151.
4B25.44B3.2B2.25B$93.37B2A15BD14B4.4B129.D5.D.2D10.4B26.37B2A15BD14B
4.4B149.4B26.37B2A15BD14B4.4B149.4B26.37B2A15BD14B4.4B$93.37B2A15BDBD
4B.6BD5.4B128.2D3.D4.D8.BD2B27.37B2A15BDBD4B.6BD5.4B147.4B27.37B2A15B
DBD4B.6BD5.4B147.4B27.37B2A15BDBD4B.6BD5.4B$94.53B3D4B2.B.5B5.4B127.D
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53B3D4B2.B.5B5.4B$93.2D.53BD4B7.2AD5.4B134.D8.BD2B29.2D.53BD4B7.2AD5.
4B143.4B29.2D.53BD4B7.2AD5.4B143.4B29.2D.53BD4B7.2AD5.4B$94.59B8.A.D
6.4B133.3D5.4B31.59B8.A.D6.2BDB141.4B31.59B8.A.D6.2BDB141.4B31.59B8.A
.D6.4B$91.3D2A3.25B4.13B.4B16.3A6.4B139.BD2B29.3D2A3.25B4.13B.4B16.3A
6.4B139.4B29.3D2A3.25B4.13B.4B16.3A6.4B139.4B29.3D2A3.25B4.13B.4B16.
3A6.4B$91.D3.A3.20B4.B4.7B.B2.2D.3B19.A7.4B137.4B30.D3.A3.20B4.B4.7B.
B2.2D.3B19.A7.2BDB137.4B30.D3.A3.20B4.B4.7B.B2.2D.3B19.A7.2BDB137.4B
30.D3.A3.20B4.B4.7B.B2.2D.3B19.A7.4B$92.3A6.15B4.3D2A15.4B29.4B135.BD
2B32.3A6.15B4.3D2A15.4B29.4B135.4B32.3A6.15B4.3D2A15.4B29.4B135.4B32.
3A6.15B4.3D2A15.4B29.4B$92.A8.11B8.D3.A12.3D2A32.4B133.4B33.A8.11B8.D
3.A12.3D2A32.2BDB133.4B33.A8.11B8.D3.A12.3D2A32.2BDB133.4B33.A8.11B8.
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4B131.4B42.13B8.3A13.D3.A33.4B131.4B42.13B8.3A13.D3.A33.4B$99.15B7.A
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4B42.15B7.A16.3A35.4B$99.16B23.A38.4B120.D6.BD2B43.16B23.A38.4B127.4B
43.16B23.A38.4B127.4B43.16B23.A38.4B$99.17B62.4B125.4B44.17B62.2BDB6.
D118.4B44.17B62.2BDB6.D118.4B44.17B62.4B$99.16B14.2D48.4B118.D4.BD2B
45.16B14.2D48.4B123.4B45.16B14.2D48.4B123.4B45.16B14.2D48.4B$101.13B
15.2D49.4B121.4B48.13B15.2D36.D12.2BDB4.D116.4B48.13B15.2D36.D12.2BDB
4.D116.4B48.13B15.2D49.4B$98.2D.3B.2B2A5B14.4D49.4B116.D2.BD2B46.2D.
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2B3D3B14.2D2.2D51.4B$97.3A5.3BD4B13.2D4.2D51.4B112.DBD.D.D.D43.3A5.3B
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D7.7B12.2D6.2D32.2D3.D14.4B107.4B50.D.D7.7B12.2D6.2D32.2D3.D14.4B107.
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4B.D4.4B90.4B8.D$17.2B11.4B63.2D8.3BA5.B3A18.D71.4B7.3D49.2B11.4B63.
2D8.3BA99.4B7.3D49.2A10.4B64.2D8.3BA99.4B7.3D49.2A10.4B64.2D8.3BA99.
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D61.4B63.2D9.BA.A99.4B7.A.D61.4B63.2D9.BA.A99.4B7.A.D$98.2D9.ADAD5.A
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A.A128.2D10.3A100.4B6.A.A$99.2D12.A9.D.D.D.D.D6.D64.4D8.4B5.A.AB127.
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127.2D12.A101.4B5.A.AB$100.2D36.D.3D59.D3.D9.4B5.A3B127.2D114.4B5.A3B
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8B.4BDB235.4B2.8B.4BDB$103.D19.D5.D8.D.3D66.3D9.17B.B2A54.4B59.D19.D
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11B66.BD2B3.D52.D3.D24.D81.2DA.AB2.11B66.4B56.D3.D106.2DA.AB2.11B$47.
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8.2D10.7B3.B2AB3A41.D18.D.D.D.DBD2B85.D60.2D8.2D10.7B3.B2AB3A67.4B
146.2D8.2D10.7B3.B2AB3A$53.4B145.2D7.3D10.6B5.DBD3.A67.4B145.2D7.3D
10.6B5.DBD3.A40.D.3D22.4B145.2D7.3D10.6B5.DBD3.A67.4B145.2D7.3D10.6B
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3.D22.4B144.2D6.3D12.6B4.2AD3A69.4B144.2D6.3D12.6B4.2AD3A$55.4B143.
10D13.5B6.A.A72.4B143.10D13.5B6.A.A43.D5.D22.4B143.10D13.5B6.A.A72.4B
143.10D13.5B6.A.A$56.4B85.D.D.D.D.D6.3D39.10D12.6B6.A.A73.4B142.10D
12.6B6.A.A43.D5.D.2D20.4B142.10D12.6B6.A.A73.4B142.10D12.6B6.A.A$57.
4B98.D3.D38.2D6.3D11.6B7.A75.4B141.2D6.3D11.6B7.A44.2D3.D4.D20.4B141.
2D6.3D11.6B7.A75.4B141.2D6.3D11.6B7.A$58.4B83.D.D15.D38.2D7.3D9.7B5.
3D76.4B140.2D7.3D9.7B5.3D44.D.3D3.2D22.4B140.2D7.3D9.7B5.3D76.4B140.
2D7.3D9.7B5.3D$59.4B97.4D38.2D8.2D9.2B3D2B4.D3.A76.4B139.2D8.2D9.2B3D
2B4.D3.A53.D22.4B139.2D8.2D9.2B3D2B4.D3.A76.4B139.2D8.2D9.2B3D2B4.D3.
A$60.4B81.D3.D9.D3.D38.2D8.2D9.4BD3B3.2D3A77.4B138.2D8.2D9.4BD3B3.2D
3A51.2D24.4B138.2D8.2D9.4BD3B3.2D3A77.4B138.2D8.2D9.4BD3B3.2D3A$61.4B
94.D3.D2.D35.2D8.2D9.3B3D2B4.A81.4B137.2D8.2D9.3B3D2B4.A81.4B137.2D8.
2D9.3B3D2B4.A81.4B137.2D8.2D9.3B3D2B4.A$62.4B79.D5.D8.3D.D.D35.2D7.3D
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7.3D10.8B3.2A$63.4B99.D35.2D6.3D11.3B2A2B2.4B82.4B135.2D6.3D11.3B2A2B
2.4B82.4B135.2D6.3D11.3B2A2B2.4B82.4B135.2D6.3D11.3B2A2B2.4B$64.4B77.
D7.D12.D35.10D10.5B2A2B.3B85.4B134.10D10.5B2A2B.3B85.4B134.10D10.5B2A
2B.3B85.4B134.10D10.5B2A2B.3B$65.4B133.9D11.13B86.4B133.9D11.13B86.4B
133.9D11.13B86.4B133.9D11.13B$66.4B85.B40.D24.16B85.4B126.D24.16B85.
4B126.D24.16B85.4B126.D24.16B$67.4B84.2B37.3D16.D6.17B86.4B84.2B37.3D
16.D6.17B86.4B84.2B37.3D16.D6.17B86.4B84.2B37.3D16.D6.17B$68.4B83.3B
12.D11.D10.D3.A13.3D7.16B87.4B83.3B12.D11.D10.D3.A13.3D7.16B87.4B83.
3B12.D11.D10.D3.A13.3D7.16B87.4B83.3B12.D11.D10.D3.A13.3D7.16B$69.4B
82.4B11.3D7.3D10.2D3A12.D3.A7.15B5.D82.4B82.4B11.3D7.3D10.2D3A12.D3.A
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10.2D3A12.D3.A7.15B5.D$70.4B82.4B11.A.D5.D3.A10.A15.2D3A8.13B4.3D83.
4B82.4B11.A.D5.D3.A10.A15.2D3A8.13B4.3D83.4B82.4B11.A.D5.D3.A10.A15.
2D3A8.13B4.3D83.4B82.4B11.A.D5.D3.A10.A15.2D3A8.13B4.3D$71.4B82.4B10.
3A5.2D3A10.2A15.A12.11B4.D3.A83.4B82.4B10.3A5.2D3A10.2A15.A12.11B4.D
3.A83.4B82.4B10.3A5.2D3A10.2A15.A12.11B4.D3.A83.4B82.4B10.3A5.2D3A10.
2A15.A12.11B4.D3.A$72.4B82.4B12.A5.A11.4B15.2A7.15B4.2D3A84.4B82.4B
12.A5.A11.4B15.2A7.15B4.2D3A84.4B82.4B12.A5.A11.4B15.2A7.15B4.2D3A84.
4B82.4B12.A5.A11.4B15.2A7.15B4.2D3A$73.4B82.4B10.2A4.B2A9.3B5.B.7B4.B
4.20B3.A88.4B82.4B10.2A4.B2A9.3B5.B.7B4.B4.20B3.A88.4B82.4B10.2A4.B2A
9.3B5.B.7B4.B4.20B3.A88.4B82.4B10.2A4.B2A9.3B5.B.7B4.B4.20B3.A$74.4B
82.4B9.9B8.4B.13B4.25B3.2A88.4B82.4B9.9B8.4B.13B4.25B3.2A88.4B82.4B9.
9B8.4B.13B4.25B3.2A88.4B82.4B9.9B8.4B.13B4.25B3.2A$75.4B82.4B10.5B3.
59B89.4B82.4B10.5B3.59B89.4B82.4B10.5B3.59B89.4B82.4B10.5B3.59B$76.4B
82.4B8.6B2.4BD53B92.4B82.4B8.6B2.4BD53B92.4B82.4B8.6B2.4BD53B92.4B82.
4B8.6B2.4BD53B$77.4B82.4B7.6B2.4B3D53B91.4B82.4B7.6B2.4B3D53B91.4B82.
4B7.6B2.4B3D53B91.4B82.4B7.6B2.4B3D53B$78.4B82.4B6.7B.4BDBD15B2A37B
91.4B82.4B6.7B.4BDBD15B2A37B91.4B82.4B6.7B.4BDBD15B2A37B91.4B82.4B6.
7B.4BDBD15B2A37B$79.4B82.4B4.15BD15B2A37BD91.4B82.4B4.15BD15B2A37BD
91.4B82.4B4.15BD15B2A37BD91.4B82.4B4.15BD15B2A37BD$80.4B82.4B2.20B2.
2B3.44B.D91.4B82.4B2.20B2.2B3.44B.D91.4B82.4B2.20B2.2B3.44B.D91.4B82.
4B2.20B2.2B3.44B.D$81.4B82.4B.17B11.10B2.29B.B2A92.4B82.4B.17B11.10B
2.29B.B2A92.4B82.4B.17B11.10B2.29B.B2A92.4B82.4B.17B11.10B2.29B.B2A$
82.4B82.19B16.6B4.8B.19B.BADA92.4B82.19B16.6B4.8B.19B.BADA92.4B82.19B
16.6B4.8B.19B.BADA92.4B82.19B16.6B4.8B.19B.BADA$83.4B82.17B19.3B9.23B
5.A93.4B82.17B19.3B9.23B5.A93.4B82.17B19.3B9.23B5.A93.4B82.17B19.3B9.
23B5.A$84.4B82.17BD19.B11.13B.7B5.2A93.4B82.17BD19.B11.13B.7B5.2A93.
4B82.17BD19.B11.13B.7B5.2A93.4B82.17BD19.B11.13B.7B5.2A$85.4B82.16B.D
15.3D2A11.3BD3.4B.3B.3B102.4B82.16B.D15.3D2A11.3BD3.4B.3B.3B102.4B82.
16B.D15.3D2A11.3BD3.4B.3B.3B102.4B82.16B.D15.3D2A11.3BD3.4B.3B.3B$86.
4B82.7B3.3B.B2A15.D3.A12.4B4.B2.D3B.D2B102.4B82.7B3.3B.B2A15.D3.A12.
4B4.B2.D3B.D2B102.4B82.7B3.3B.B2A15.D3.A12.4B4.B2.D3B.D2B102.4B82.7B
3.3B.B2A15.D3.A12.4B4.B2.D3B.D2B$87.4B82.6B7.BADA15.3A15.2AD6.B2AB.B
2AB102.4B82.6B7.BADA15.3A15.2AD6.B2AB.B2AB102.4B82.6B7.BADA15.3A15.2A
D6.B2AB.B2AB102.4B82.6B7.BADA15.3A15.2AD6.B2AB.B2AB$88.4B79.2D.4B11.A
15.A17.A.D7.2A3.2A104.4B79.2D.4B11.A15.A17.A.D7.2A3.2A104.4B79.2D.4B
11.A15.A17.A.D7.2A3.2A104.4B79.2D.4B11.A15.A17.A.D7.2A3.2A$89.4B79.5B
12.2A33.3A118.4B79.5B12.2A33.3A118.4B79.5B12.2A33.3A118.4B79.5B12.2A
33.3A$90.4B75.3D2A52.A119.4B75.3D2A52.A119.4B75.3D2A52.A119.4B75.3D2A
52.A$91.4B74.D3.A173.4B74.D3.A173.4B74.D3.A173.4B74.D3.A$92.4B74.3A
175.4B74.3A175.4B74.3A175.4B74.3A$93.4B73.A178.4B73.A178.4B73.A178.4B
73.A$94.4B252.4B252.4B252.4B$95.4B252.4B252.4B252.4B$96.4B78.10B164.
4B78.10B164.4B78.10B164.4B78.10B$97.4B77.10B165.4B77.10B165.4B77.10B
165.4B77.10B$98.4B81.5B166.4B81.5B166.4B81.5B166.4B81.5B$99.4B79.6B
167.4B79.6B167.4B79.6B167.4B79.6B$100.4B77.4B.2B168.4B77.4B.2B168.4B
77.4B.2B168.4B77.4B.2B$101.4B75.4B2.2B169.4B75.4B2.2B169.4B75.4B2.2B
169.4B75.4B2.2B$102.4B73.4B3.2B170.4B73.4B3.2B170.4B73.4B3.2B170.4B
73.4B3.2B$103.4B71.4B4.2B171.4B71.4B4.2B171.4B71.4B4.2B171.4B71.4B4.
2B$104.4B69.4B5.2B172.4B69.4B5.2B172.4B69.4B5.2B172.4B69.4B5.2B$105.
4B67.4B181.4B67.4B181.4B67.4B181.4B67.4B$106.4B65.4B183.4B65.4B183.4B
65.4B183.4B65.4B$107.4B63.4B185.4B63.4B185.4B63.4B185.4B63.4B$108.4B
61.4B187.4B61.4B187.4B61.4B187.4B61.4B$109.4B59.4B189.4B59.4B189.4B
59.4B189.4B59.4B$110.4B57.4B191.4B57.4B191.4B57.4B191.4B57.4B$111.4B
55.4B193.4B55.4B193.4B55.4B193.4B55.4B$112.4B53.4B195.4B53.4B195.4B
53.4B195.4B53.4B$113.4B51.4B197.4B51.3B198.4B51.3B198.4B51.3B$114.4B
49.4B199.4B49.4B199.4B49.4B199.4B49.4B$115.4B47.4B201.4B47.4B201.4B
47.4B201.4B47.4B$116.4B45.4B203.4B45.4B203.4B45.4B203.4B45.4B$117.4B
43.4B205.4B43.4B205.4B43.4B205.4B43.4B$118.4B41.4B207.4B41.4B207.4B
41.4B207.4B41.4B$119.4B39.4B209.4B39.4B209.4B39.4B209.4B39.4B$120.4B
37.4B211.4B37.4B211.4B37.4B211.4B37.4B$121.4B35.4B213.4B35.4B213.4B
35.4B213.4B35.4B$122.4B5.2B26.4B215.4B5.2B26.4B215.4B5.2B26.4B215.4B
5.2B26.4B$123.4B4.2B25.4B217.4B4.2B25.4B217.4B4.2B25.4B217.4B4.2B25.
4B$124.4B3.2B24.4B219.4B3.2B24.4B219.4B3.2B24.4B219.4B3.2B24.4B$125.
4B2.2B23.4B221.4B2.2B23.4B221.4B2.2B23.4B221.4B2.2B23.4B$126.4B.2B22.
4B223.4B.2B22.4B223.4B.2B22.4B223.4B.2B22.4B$127.6B21.4B225.6B21.4B
225.6B21.4B225.6B21.4B$128.5B20.4B227.5B20.4B227.5B20.4B227.5B20.4B$
129.4B19.4B229.4B19.4B229.4B19.4B229.4B19.4B$124.9B18.4B225.9B18.4B
225.9B18.4B225.9B18.4B$124.9B17.4B226.9B17.4B226.9B17.4B226.9B17.4B9$
139.2D254.2D254.2D254.2D$139.2D254.2D254.2D254.2D$140.2A254.2A254.2A
254.2A$140.2A254.2A254.2A254.2A5$137.D6.D248.D6.D248.D6.D248.D6.D$
137.D6.D248.D6.D248.D6.D248.D6.D$137.D6.D248.D6.D248.D6.D248.D6.D$
137.D6.D248.D6.D248.D6.D248.D6.D$137.D6.D248.D6.D248.D6.D248.D6.D$
137.8D248.8D248.8D248.8D$137.D6.D248.D6.D248.D6.D248.D6.D$137.D6.D
248.D6.D248.D6.D248.D6.D$137.D6.D248.D6.D248.D6.D248.D6.D$137.D6.D
248.D6.D248.D6.D248.D6.D$137.D6.D248.D6.D248.D6.D248.D6.D!

I'm trying for

red = previous location of structure
red = labels
red = dotted-line arrows showing recipes, or pieces of recipes
blue = "foreshadowing" of future position of structure
blue = glider paths
(confusing, I know, but there aren't enough OFF colors in LifeHistory and I want this pattern to be runnable)

I added labels E, F, G, H just in case they come in handy. Maybe the boat location should have a separate label, but I think it's just part of G really.

A couple of new recipe labels have showed up so far --

b2' = the b recipe minus the initial Snarkmaker recipe (used up at D)
b3' = the b recipe minus the Snarkmaker recipe and the C-Snark-Shifter recipe (used up at C)

I'm out of time for tonight, so have left Stage 3 empty for now. Will get back to this tomorrow night, maybe, so anyone should feel free to add more stages to the diagram in the meantime.

-- And yes, I can see already that my diagram for C had the new gliders coming in on the wrong side of the channel. Will edit and fix that pattern in my previous post, once the other two Snarks have diagrams with the same level of detail.

EDIT: I didn't include the loop-with-boat trick in its proper places at Stage 0.01 and Stage 1.99, because I hadn't independently confirmed that the timing would really work out. Could the signal that disables the D Snark possibly just be bounced straight back from C? I guess the CD distance is probably too short -- if the signal comes from there then b3', the entire recipe for shooting down and reconstructing all of the B reflector, would have to be no more than twice as long as CD.

Maybe I have the a and b salvos reversed unnecessarily, though? Is there a way for the upper diamond to be larger, so that the a recipe is sent around first, and the very first signal returned from G is what creates the target at D? ... No, then we'd need a b-length gap in the middle of the a recipe. Technically I think that might be possible, but it makes the loop a lot longer. The boat trick will be better.

[chris_c]

I'm out of time for tonight, so have left Stage 3 empty for now. Will get back to this tomorrow night, maybe, so anyone should feel free to add more stages to the diagram in the meantime.

Here is what I think Stage 3 should look like. The Snark at E has been shifted by (1,2) by Stage 2. The glider that hits the Snark at F makes the same kind of junk as at C in Stage 1:

Code: Select all

x = 247, y = 325, rule = LifeHistory
95.3D5.D31.3D$94.D3.D4.D30.D3.D$93.D5.D3.D29.D5.D$93.D7.5D33.D$94.D8.
D4.3D5.2D5.3D12.D$95.3D5.D3.D3.D3.D2.D3.D3.D8.3D$98.D4.D7.D2.D4.D2.D
3.D11.D$99.D3.D4.4D2.D4.D2.4D13.D$93.D5.D3.D3.D3.D2.D4.D2.D10.D5.D$
94.D3.D4.D3.D3.D3.D2.2D2.D3.D7.D3.D$95.3D5.D4.3D.D3.2D.D3.3D9.3D$119.
D$119.D$114.D3.D$115.3D12$112.8D$112.D$112.D$112.D$112.D$112.4D$112.D
$112.D$112.D$112.D$112.D4$113.2A$113.A.A$115.A4.2A$111.4A.2A2.A2.A$
111.A2.A.A.A.AB2A$113.BABABA.AB2.B$114.B2ABA.AB.2B$115.2B.BA.B$114.3B
3.B$105.2A6.4B$106.A6.B2A3B$106.A.AB3.B2A4B$107.2AB.10B$109.13B$109.
14B$109.15B$111.8B2.4B$111.6B5.4B$110.9B4.4B$109.4B4.2A5.3B$108.4B5.A
$107.4B7.3A$106.4B8.B.A$119.3B$121.B29$177.5D$77.4B95.D5.D$45.8D8.2D
13.4B95.D$45.D16.D12.4B87.2D7.D$45.D14.D.2A10.4B88.2D7.D$45.D14.3DAD
8.4B2.2D86.2A6.D$45.D15.A3.D6.4B3.D87.2A6.D3.4D$45.4D12.5A5.4B2.D.D2A
93.D6.D$45.D15.D4.A3.5B2.2D.A94.D6.D$45.D15.2D3AB2.7B.BA.A95.D5.D$45.
D13.2D.A.2B2.D7B.B2A97.5D$45.D12.D2.D4A12B$45.8D5.2D2A2.BA3B2A7B$59.A
.D3AB.2B2A7B$59.2ADA.B3.10B$62.A8.8B77.B$62.2A7.9B75.2B$69.2D.3B2.4B
73.3B$70.5B3.4B71.4B$67.3D2A7.3B14.2D54.4B$67.D3.A8.2B.B11.D.D9.6D38.
4B$68.3A10.B.2B4.2D4.D11.D5.D36.4B$68.A14.B2C.D2.D2.2D.4D7.D6.D34.4B$
83.BCBC2D.D.D.D.D2.D7.D6.D33.4B$84.C3B2.D.DBDBDB9.D6.D32.4B$85.4B.D.D
B2DB10.D6.D31.4B$86.4B.DB.2B11.D6.D30.4B$87.4B3.3B10.D6.D29.4B$88.4B
2.4B6.2D.D6.D28.4B$89.6B2DB6.D2.D5.D28.4B$90.5B2DB3.BD.D2.6D28.4B$90.
10B.B2D36.4B$89.13B29.2B6.4B$88.14B29.2B5.4B$87.15B29.2B4.4B$86.4B.2D
7B31.2B3.4B$85.4B2.2D.6B31.2B2.4B$84.4B4.2A7B30.2B.4B$83.4B5.2A4.4B
29.6B$82.4B7.D5.4B28.5B$81.4B5.3D7.4B27.4B$80.4B6.D10.4B27.9B$79.4B
19.4B26.9B$78.4B21.4B$77.4B23.4B46.D$76.4B25.4B45.3D$75.4B27.4B35.D9.
A.D$74.4B17.2D3.2D5.4B13.2D19.3D7.3A$73.4B18.2D3.2D6.4B12.D.D19.A.D9.
A$72.4B20.2A3.2A6.4B12.2A19.3A8.2A5.4B$71.4B20.B2AB.B2AB6.4B11.ADA21.
A7.11B2D$70.4B14.2D6.2B2.3B3.B4.4B12.A20.2A3.B5.11B$69.4B16.D7.3B.3B.
4B3.4B11.2A19.8B2.11B2A$68.4B17.2AD4.7B.13B11.B21.19B2A$67.4B19.AD4.
23B9.3B19.20B$66.4B20.A.AB.19B.8B4.6B16.20B$65.4B22.2AB.29B2.10B11.
21B$64.4B25.44B3.2B2.25B$63.4B26.37B2A15BD14B4.4B$62.4B27.37B2A15BDBD
4B.6BD5.4B$61.4B29.53B3D4B2.B.5B5.4B$60.4B29.2D.53BD4B7.2AD5.4B$59.4B
31.59B8.A.D6.4B$58.4B29.3D2A3.25B4.13B.4B16.3A6.4B$57.4B30.D3.A3.20B
4.B4.7B.B2.2D.3B19.A7.4B$56.4B32.3A6.15B4.3D2A15.4B29.4B$55.4B33.A8.
11B8.D3.A12.3D2A32.4B$54.4B42.13B8.3A13.D3.A33.4B$53.4B42.15B7.A16.3A
35.4B$52.4B43.16B23.A38.4B$51.4B44.17B62.4B$50.4B45.16B14.2D48.4B$49.
4B48.13B15.2D49.4B$48.4B46.2D.3B.2B2A5B14.4D49.4B$47.4B48.4B2.2B2A3B
16.4D50.4B$46.4B46.3D2A3.8B15.2D2.2D50.4B$45.4B47.D3.A4.2B3D3B14.2D2.
2D51.4B$44.4B49.3A5.3BD4B13.2D4.2D51.4B$43.4B50.A8.2B3D2B13.2D4.2D52.
4B$42.4B50.D.D7.7B12.2D6.2D52.4B$41.4B51.D.A7.6B13.2D6.2D53.4B$40.4B
50.3DADA6.6B12.12D53.4B$22.D16.4B50.D3.A.A6.5B13.12D54.4B$22.3D13.4B
52.D3AD2A4.6B13.2D8.2D55.4B$23.A.D11.4B53.A.D.DB6.6B12.2D8.2D56.4B$
23.3A10.4B55.3AB2AB3.7B12.2D8.2D57.4B$24.2BA8.4B58.A.2AB.8B13.2D8.2D
58.4B$25.2A7.4B63.10B4.2D7.2D8.2D59.4B$16.2D7.5B3.4B64.6B2A3B3.D8.2D
8.2D60.4B$2.5D9.D8.B.3B2.4B65.6B2A2B2.D.D2A79.4B$.D5.D5.2D.D2A3.13B
66.10B2.2D.A81.4B$D12.D2.DADB.2B2D9B66.11B2.BA.A82.4B$D13.2A.A5B2D8B
67.12B.B2A84.4B$D13.A.D3A4B2A7B66.15B87.4B$D14.2A.2BA3B2A6B2D59.2D3.
16B88.4B$D16.4A11BD.D58.2D2B.16B89.4B$D16.A.2B3.7B.B2A59.2A18B90.4B$D
14.3D3AB2.7B.BADA58.2AB.17B90.4B$.D5.D7.D5.A4.4B5.A59.2D4B.8B2.4B90.
4B$2.5D9.5A5.4B5.2A58.2D5.7B4.4B90.4B$16.AD9.4B65.2D5.6BD4.4B90.4B$
18.A9.4B64.2D7.4B.D4.4B90.4B8.D$17.2A10.4B64.2D8.3BA99.4B7.3D$30.4B
63.2D9.BA.A99.4B7.A.D$31.4B63.2D9.ADAD99.4B6.3AD$32.4B62.2D10.A.D100.
4B6.D.A$99.2D10.3A100.4B6.A.A$99.2D12.A101.4B5.A.AB$100.2D114.4B5.A3B
$100.2D115.4B6.4B$218.4B5.6B$102.D116.4B4.7B5.2D$220.4B2.8B.4BDB$103.
D117.17B.B2A$44.B177.18B2A$44.2B58.D117.16B.2B2D$44.3B172.2D.16B3.2D$
44.4B57.D5.D106.D.D.15B$45.4B169.D.2AB.12B$46.4B56.D3.D106.2DA.AB2.
11B$47.4B49.D101.9D8.A5.10B$48.4B50.D4.D.D92.10D6.2A5.2B2A6B$49.4B51.
D97.2D6.3D11.3B2A6BD.D$50.4B52.D.D93.2D7.3D11.10BD.3D$51.4B147.2D8.2D
11.8B.B2A.A.D$52.4B146.2D8.2D10.7B3.B2AB3A$53.4B145.2D7.3D10.6B5.DBD
3.A$54.4B144.2D6.3D12.6B4.2AD3A$55.4B143.10D13.5B6.A.A$56.4B142.10D
12.6B6.A.A$57.4B141.2D6.3D11.6B7.A$58.4B140.2D7.3D9.7B5.3D$59.4B139.
2D8.2D9.2B3D2B4.D3.A$60.4B138.2D8.2D9.4BD3B3.2D3A$61.4B137.2D8.2D9.3B
3D2B4.A$62.4B136.2D7.3D10.8B3.2A$63.4B135.2D6.3D11.3B2A2B2.4B$64.4B
134.10D10.5B2A2B.3B$65.4B133.9D11.13B$66.4B126.D24.16B$67.4B84.2B37.
3D16.D6.17B$68.4B83.3B12.D11.D10.D3.A13.3D7.16B$69.4B82.4B11.3D7.3D
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4B.13B4.25B3.2A$75.4B82.4B10.5B3.59B$76.4B82.4B8.6B2.4BD53B$77.4B82.
4B7.6B2.4B3D53B$78.4B82.4B6.7B.4BDBD15B2A37B$79.4B82.4B4.15BD15B2A37B
D$80.4B82.4B2.20B2.2B3.44B.D$81.4B82.4B.17B11.10B2.29B.B2A$82.4B82.
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A12.4B4.B2.D3B.D2B$87.4B82.6B7.BADA15.3A15.2AD6.B2AB.B2AB$88.4B79.2D.
4B11.A15.A17.A.D7.2A3.2A$89.4B79.5B12.2A33.3A$90.4B75.3D2A52.A$91.4B
74.D3.A$92.4B74.3A$93.4B73.A$94.4B$95.4B$96.4B78.10B$97.4B77.10B$98.
4B81.5B$99.4B79.6B$100.4B77.4B.2B$101.4B75.4B2.2B$102.4B73.4B3.2B$
103.4B71.4B4.2B$104.4B69.4B5.2B$105.4B67.4B$106.4B65.4B$107.4B63.4B$
108.4B61.4B$109.4B59.4B$110.4B57.4B$111.4B55.4B$112.4B53.4B$113.4B51.
3B$114.4B49.4B$115.4B47.4B$116.4B45.4B$117.4B43.4B$118.4B41.4B$119.4B
39.4B$120.4B37.4B$121.4B35.4B$122.4B5.2B26.4B$123.4B4.2B25.4B$124.4B
3.2B24.4B$125.4B2.2B23.4B$126.4B.2B22.4B$127.6B21.4B$128.5B20.4B$129.
4B19.4B$124.9B18.4B$124.9B17.4B9$139.2D$139.2D$140.2A$140.2A5$137.D6.
D$137.D6.D$137.D6.D$137.D6.D$137.D6.D$137.8D$137.D6.D$137.D6.D$137.D
6.D$137.D6.D$137.D6.D!

EDIT: I didn't include the loop-with-boat trick in its proper places at Stage 0.01 and Stage 1.99, because I hadn't independently confirmed that the timing would really work out. Could the signal that disables the D Snark possibly just be bounced straight back from C? I guess the CD distance is probably too short -- if the signal comes from there then b3', the entire recipe for shooting down and reconstructing all of the B reflector, would have to be no more than twice as long as CD.

I think that the distance CD is too long. If the lengths of recipe a and b are both approximately d then as per my calculations a few posts back I believe that the perimeter DEFG should be roughly d and the distance CD should be roughly d. Therefore the distance travelled bouncing a signal back from C is 2d.... which is too big. That's if all my math is correct of course...

Maybe I have the a and b salvos reversed unnecessarily, though? Is there a way for the upper diamond to be larger, so that the a recipe is sent around first, and the very first signal returned from G is what creates the target at D? ... No, then we'd need a b-length gap in the middle of the a recipe. Technically I think that might be possible, but it makes the loop a lot longer. The boat trick will be better.

I think I like the idea of swapping a and b over. The perimeter DEFG would need to be 2d in order to wait for both recipes to pass through A. CD and BH would need to have length d/2 in order for the back of recipe b to overtake the first construction glider produced by recipe b.

At the start of recipe a I would send a signal to G (I think the route is clear at that moment) that makes it back in time to meet the start of recipe b. For this to work the distance DG needs to be fixed at somewhere near d/2. After this we can vary the distances DE and DC in order to give long enough delay so that construction gliders do not interfere with recipe gliders.

If we go with this blueprint then we need to search for suitable debris to be left at G to facilitate the 180-degree reflection.

[dvgrn]

I think I like the idea of swapping a and b over... At the start of recipe a I would send a signal to G (I think the route is clear at that moment) that makes it back in time to meet the start of recipe b. For this to work the distance DG needs to be fixed at somewhere near d/2.

Seems to work quite nicely. There's no problem using up the NE/SW degree of freedom to get the timing of that single 180-degree bounce signal just right. We'll still have the NW/SE degree of freedom to do the rest of the timing adjustment. Time to start a competing blueprint for the ab-knightship, I guess, and see if it's really an improvement on the ba-knightship.

If we go with this blueprint then we need to search for suitable debris to be left at G to facilitate the 180-degree reflection.

That part seems like it will be pretty easy. In a pinch it could even be done with 0-degree gliders from F, as soon as the F Snark is constructed, building two blocks or a long boat or whatever near the SW edge of the available 0-degree lanes. That would put it safely out of the way of the following a single-channel recipe.

But that requires building a 0-degree elbow southeast of F, and really it shouldn't be necessary. The G elbow won't be doing anything at the point in time when the 180-degree signal has to get bounced back. It's probably pretty easy to find a state to leave the G elbow in, that will reflect a glider from the SW, leaving some remaining debris that can be cleaned back up into an elbow when the a recipe gets there.

EDIT:Maybe there's something even simpler than the ab-knightship, though. Here's a design that would work fine if an elbow would just magically appear at J, just when the a recipe is arriving there -- assuming the b recipe is sent first:

Code: Select all

x = 307, y = 296, rule = LifeHistory
115.3D5.D31.3D$114.D3.D4.D30.D3.D$113.D5.D3.D29.D5.D$113.D7.5D27.D5.D
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3.2D.D3.3D9.3D$139.D$139.D$134.D3.D$135.3D9$136.2A$135.A.A$129.2A4.A
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$157.D6.D!
#C [[ THUMBNAIL THUMBSIZE 2 ZOOM 1.5 ]]

It's possible to drop an extra target anywhere near C while that Snark is getting reconstructed. And that near-C target can get moved into elbow position by 180-degree gliders from H, which can be sent any time during the generation of the b slow salvo -- beginning, middle, end, wherever.

But distance CH is necessarily longer than d, so the minimum delay is going to be 2d-ish. Is there possibly a way to arrange the gap in the a-b-gap loop, such that the 180-degree return signal can do its work, and the a and b recipes can both do their destroy/rebuild work at a time when the A and B circuits are empty? The 180-degree signal could conceivably be a "fossil" signal left over from the previous cycle, so that at some points there might be two sets of 180-degree signals in existence simultaneously...?

[chris_c]

EDIT:Maybe there's something even simpler than the ab-knightship, though. Here's a design that would work fine if an elbow would just magically appear at J, just when the a recipe is arriving there -- assuming the b recipe is sent first:

...

It's possible to drop an extra target anywhere near C while that Snark is getting reconstructed. And that near-C target can get moved into elbow position by 180-degree gliders from H, which can be sent any time during the generation of the b slow salvo -- beginning, middle, end, wherever.

But distance CH is necessarily longer than d, so the minimum delay is going to be 2d-ish. Is there possibly a way to arrange the gap in the a-b-gap loop, such that the 180-degree return signal can do its work, and the a and b recipes can both do their destroy/rebuild work at a time when the A and B circuits are empty? The 180-degree signal could conceivably be a "fossil" signal left over from the previous cycle, so that at some points there might be two sets of 180-degree signals in existence simultaneously...?

Yes I think this might work. I am not going to assume that C is near to J because as far as I can tell the distances CJ and BH will need to controlled in order to avoid calamity at A and B. I haven't worked out what these distances are but I assume they are both non-zero multiples of d.

There would have to be some off-channel junk near to J that gets promoted into something elbow-like by a returning salvo from H. At the end of recipe a, the off-channel junk would need to be restored in the new position. So the next question is how and when the salvo from H is coded.

I think the answer is that the salvo should be coded at the end of recipe b. Let's imagine the point in time when the end of recipe b is at J. Since the length JH is the same as the length AB, the end of recipe b will travel to H and return to J in the same amount of time as one full period of the spaceship. In other words when the end of recipe b is at J the return salvo from the previous iteration will be arriving.

In the above paragraph "the same" should really be taken to mean "the same up to a constant". I guess that by making the distance JH slightly longer than AB we can make the return salvo come back to J just after the end of recipe b. Hopefullly....?

[dvgrn]

There would have to be some off-channel junk near to J that gets promoted into something elbow-like by a returning salvo from H. At the end of recipe a, the off-channel junk would need to be restored in the new position. So the next question is how and when the salvo from H is coded.

That seems like it should be reasonably simple. Eight gliders can do a simple block-splitting reaction, for example:

Code: Select all

x = 189, y = 157, rule = LifeHistory
B$2B$3B$4B$.4B$2.4B$3.4B$4.4B$5.4B$6.4B$7.4B$8.4B$9.4B$10.4B$11.4B$
12.4B16.2D$13.4B15.2D$14.4B15.2B$15.4B14.2B8.2C$16.4B23.2C$17.4B23.2D
$18.4B22.2D$19.4B.2D$20.4B2D$21.4B$22.4B$23.4B$24.4B29.2A$25.4B28.A.A
$26.4B27.A$27.4B$28.4B$29.4B$30.4B$31.4B$32.4B$33.4B$34.4B$35.4B$36.
4B$37.4B$38.4B31.2A$39.4B30.A.A$40.4B29.A$41.4B$42.4B$43.4B5$83.2A$
83.A.A$83.A11$93.2A$93.A.A$93.A22$113.2A$113.A.A$113.A19$139.2A$139.A
.A$139.A33$166.2A$166.A.A$166.A8$186.2A$186.A.A$186.A!

I'm pretty sure that narrow recipes can push that resulting elbow to a safe distance from the block. That link is kind of an out-of-date one with a traffic-light elbow -- I don't remember what the allowable clearance is on the elbow side of a block-elbow, but the sample pattern has enough clearance for the above recipe, and if that could be done with 153-tick minimum distance then we should be okay at 90 ticks.

I can't claim to have worked through the required distances yet, to be sure that the a and b recipes will both be able to hit A and B at times when the circuitry is empty. That still seems a little scary. But it doesn't seem as if the 180-degree return gliders will get in the way of anything.

[chris_c]

First some good news. I found a way of going from an elbow to a transparent lump of junk such that on the next iteration the junk is not transparent and can be easily turned back into an elbow. This means that we can run recipe a before recipe b and we don't need the trick with the reverse gliders:

Code: Select all

#C An elbow is made transparent but is turned back into an elbow
#C by the last three gliders that are one lane lower down.
x = 778, y = 781, rule = LifeHistory
.A$2.A$3A22$25.A$23.A.A$24.2A62$89.A$87.A.A$88.2A122$214.A$212.A.A$
213.2A137$353.A$351.A.A$352.2A62$416.A$417.2A$416.2A23$442.A$443.A$
441.3A62$506.A$507.A$505.3A21$529.A$530.A$528.3A63$592.A.A$593.2A$
593.A62$658.A$656.A.A$657.2A21$681.A$682.A$680.3A63$744.A.A$745.2A$
745.A25$773.A$771.A.A$772.2A6$776.2A$776.2A!

The bad news is that we have one fewer degree of freedom than I thought previously. Adjusting the length BH is irrelevant since it will adjust the timing of recipe a and recipe b by the same amount. The only degree of freedom we have is the length AD but I think that this means that we need a dead-space of length 2d in the design instead of just d in the previous model. Even though the new model only has one pair of Snarks I think it will need to be of higher period than the two pair version.

Going back to the two pair version here is an elbow-killing block to long boat followed by a recipe for converting an elbow block in this iteration into an elbow block suitable for the next iteration:

Code: Select all

x = 2142, y = 2177, rule = LifeHistory
41.2A$41.A.A$43.A4.2A$39.4A.2A2.A2.A$39.A2.A.A.A.A.2A$42.A.A.A.A$43.
2A.A.A$47.A2$33.2A$34.A7.2A$34.A.A5.2A$35.2A7$45.2A$45.A$46.3A$48.A3$
61.A$62.A$60.3A14$3.2A$4.A$2.A$2.5A14.2A$7.A13.A$4.3A12.A.A$3.A15.2A$
3.4A77.A$.2A3.A3.2A70.A.A$A2.3A4.2A71.2A$2A.A$3.A$3.2A3$11.2A$12.A$9.
3A$9.A53$148.A$149.A$147.3A21$171.A$169.A.A$170.2A62$235.A$236.A$234.
3A21$258.A$256.A.A$257.2A62$321.A$322.2A$321.2A21$345.A$346.A$344.3A
63$410.A$408.A.A$409.2A25$436.A$437.2A$436.2A215$654.A$655.A$653.3A
34$689.A$690.2A$689.2A62$753.A$754.2A$753.2A21$775.A.A$776.2A$776.A
62$841.A$839.A.A$840.2A25$868.A$866.A.A$867.2A62$932.A$933.A$931.3A
40$973.A$974.2A$973.2A62$1038.A$1039.A$1037.3A27$1066.A$1067.2A$1066.
2A62$1130.A$1131.2A$1130.2A36$1169.A$1167.A.A$1168.2A62$1232.A$1233.
2A$1232.2A27$1261.A$1262.2A$1261.2A62$1326.A$1327.A$1325.3A22$1348.A.
A$1349.2A$1349.A6$1353.2A$1353.2A17$1304.2C$1303.C.C$1304.C68$1441.2A
$1441.2A647$2023.2A$2023.A.A$2023.A18$2043.2A$2043.A.A$2043.A46$2091.
2A$2091.A.A$2091.A21$2113.3A$2113.A$2114.A23$2140.A$2139.2A$2139.A.A!

EDIT: Updated the second pattern to show how to turn the glider coming back from the long boat into a new elbow.

[dvgrn]

First some good news. I found a way of going from an elbow to a transparent lump of junk such that on the next iteration the junk is not transparent and can be easily turned back into an elbow. This means that we can run recipe a before recipe b and we don't need the trick with the reverse gliders...

Nice -- that costs basically nothing (compared to everything else that's going on, like Snarkmaking and universal-constructor rebuilding). I guess it's only good for the 2Snark model, though -- or can it be used in place of the boat on the NE side of the 4Snark? Start with those two blocks in place, convert to an elbow, shoot one sideways glider with the elbow, then convert the elbow back to the two-block transparent lump?

The bad news is that we have one fewer degree of freedom than I thought previously. Adjusting the length BH is irrelevant since it will adjust the timing of recipe a and recipe b by the same amount. The only degree of freedom we have is the length AD but I think that this means that we need a dead-space of length 2d in the design instead of just d in the previous model. Even though the new model only has one pair of Snarks I think it will need to be of higher period than the two pair version.

Yes, that matches my half-thunk thinks on the subject. With basically only the one construction arm, there seems to be no way to change the length of the path so that the b recipe hits the AB loop at a different point in the cycle. For example, if a comes first, and a hits during a length-d gap, then b is going to hit right after that same length-d gap -- which implies the gap has to be wider.

That said... there's nothing all that wrong with a 2d gap, especially since d will be a little smaller in the 2-Snark recipe. Quite possibly it will run significantly faster than the 4-Snark design, even if the period is higher -- because the recipe isn't always folded over on itself, the way it has to be if the AB loop length is only 3d instead of 4d. The three versions of the linear propagator make a good test case for this kind of thing.

Or we could compromise and use 3 Snarks:

Code: Select all

x = 368, y = 374, rule = LifeHistory
104.3D6.3D4.5D10.3D5.D31.3D$103.D3.D4.D3.D3.D4.D8.D3.D4.D30.D3.D$102.
D5.D2.D5.D2.D5.D6.D5.D3.D29.D5.D$108.D2.D8.D5.D6.D7.5D27.D5.D$107.D4.
D7.D4.D8.D8.D4.3D5.2D5.3D7.D5.D$104.3D6.3D4.5D10.3D5.D3.D3.D3.D2.D3.D
3.D6.D5.D$107.D8.D3.D17.D4.D7.D2.D4.D2.D3.D6.D5.D$108.D8.D2.D18.D3.D
4.4D2.D4.D2.4D7.D5.D$102.D5.D2.D5.D2.D12.D5.D3.D3.D3.D2.D4.D2.D10.D5.
D$103.D3.D4.D3.D3.D13.D3.D4.D3.D3.D3.D2.2D2.D3.D7.D3.D$104.3D6.3D4.D
14.3D5.D4.3D.D3.2D.D3.3D9.3D$159.D$159.D$154.D3.D$155.3D9$136.2A$135.
A.A$129.2A4.A12.6D$127.A2.A2.2A.4A8.D5.D$127.2A.A.A.A.A2.A8.D6.D$130.
A.ABABA4B7.D6.D$128.B.A.AB2A2B2.B7.D6.D$128.2B.AB.2B12.D6.D$134.3B11.
D6.D$134.4B6.2A2.D6.D$132.3B2AB6.A3.D6.D$131.4B2AB3.BA.A2B.D5.D$130.
10B.B2A.B2.6D$129.13B.B.B$128.14B.2B$127.15B$126.4B2.8B$125.4B5.6B$
124.4B4.9B$124.3B5.2A4.4B$124.2B7.A5.4B$124.B5.3A2B5.4B$130.A3.B6.4B$
131.3B8.4B$131.B11.4B$144.4B20$214.D$165.4B45.3D$166.4B35.D9.A.D$155.
2D3.2D5.4B13.2D19.3D7.3A$155.2D3.2D6.4B12.D.D19.A.D9.A$156.2A3.2A6.4B
12.2A19.3A8.2A5.4B$155.B2AB.B2AB6.4B11.ADA21.A7.11B2D$148.2D6.2B2.3B
3.B4.4B12.A20.2A3.B5.11B$149.D7.3B.3B.4B3.4B11.2A19.8B2.11B2A$149.2AD
4.7B.13B11.B21.19B2A$150.AD4.23B9.3B19.20B$150.A.AB.19B.8B4.6B16.20B$
151.2AB.29B2.10B11.21B$153.44B3.2B2.25B$153.37B2A15BD14B4.4B$153.37B
2A15BDBD4B.6BD5.4B$154.53B3D4B2.B.5B5.4B$153.2D.53BD4B7.2AD5.4B$154.
59B8.A.D6.4B$151.3D2A3.25B4.13B.4B16.3A6.4B$151.D3.A3.20B4.B4.7B.B2.
2D.3B19.A7.4B$152.3A6.15B4.3D2A15.4B29.4B$152.A8.11B8.D3.A12.3D2A32.
4B$160.13B8.3A13.D3.A33.4B$159.15B7.A16.3A35.4B$159.16B23.A38.4B$159.
17B62.4B$159.16B14.2D48.4B$161.13B15.2D49.4B$158.2D.3B.2B2A5B14.4D49.
4B$159.4B2.2B2A3B16.4D50.4B$156.3D2A3.8B15.2D2.2D50.4B$156.D3.A4.2B3D
3B14.2D2.2D51.4B$157.3A5.3BD4B13.2D4.2D51.4B$157.A8.2B3D2B13.2D4.2D
52.4B$156.D.D7.7B12.2D6.2D52.4B$156.D.A7.6B13.2D6.2D53.4B$154.3DADA6.
6B12.12D53.4B$153.D3.A.A6.5B13.12D54.4B$154.D3AD2A4.6B13.2D8.2D55.4B$
154.A.D.DB6.6B12.2D8.2D56.4B$155.3AB2AB3.7B12.2D8.2D57.4B$157.A.2AB.
8B13.2D8.2D58.4B$161.10B4.2D7.2D8.2D59.4B$161.6B2A3B3.D8.2D8.2D60.4B$
161.6B2A2B2.D.D2A79.4B$161.10B2.2D.A81.4B$160.11B2.BA.A82.4B$160.12B.
B2A84.4B$159.15B87.4B$153.2D3.16B88.4B$153.2D2B.16B89.4B$154.2A18B90.
4B$154.2AB.17B90.4B$155.2D4B.8B2.4B90.4B$155.2D5.7B4.4B90.4B$156.2D5.
6BD4.4B90.4B$156.2D7.4B.D4.4B90.4B8.D$22.A134.2D8.3BA5.B3A18.D71.4B7.
3D$22.3A10.B121.2D9.BA.A5.A2B18.D72.4B7.A.D$25.A8.2B122.2D9.ADAD5.A
19.D73.4B6.3AD$24.2A7.3B122.2D10.A.D25.D74.4B6.D.A$24.5B3.4B66.10B7.
10B5.10B15.2D10.3A24.D75.4B6.A.A$26.3B2.4B67.10B7.10B5.10B15.2D12.A9.
D.D.D.D.D6.D76.4B5.A.AB$16.2A7.9B73.5B12.5B10.5B16.2D36.D.3D73.4B5.A
3B$2.5D9.A8.8B73.6B11.6B9.6B16.2D21.D.D12.2D3.D73.4B6.4B$.D5.D5.2A.A.
B3.10B73.4B.2B10.4B.2B8.4B.2B54.D5.D73.4B5.6B$D12.A2.3AB.2B2A7B72.4B
2.2B9.4B2.2B7.4B2.2B18.D20.D3.D10.D5.D74.4B4.7B5.2D$D13.2A2.BA3B2A7B
71.4B3.2B8.4B3.2B6.4B3.2B54.2D3.D76.4B2.8B.4BDB$D15.4A12B70.4B4.2B7.
4B4.2B5.4B4.2B19.D19.D5.D8.D.3D78.17B.B2A$D15.A.2B3.7B.B2A67.4B5.2B6.
4B5.2B4.4B5.2B138.18B2A$D16.3AB2.7B.BA.A65.4B13.4B11.4B28.D18.D7.D90.
16B.2B2D$D19.A3.5B4.BA64.4B13.4B11.4B144.2D.16B3.2D$D14.5A5.4B4.B2A
62.4B13.4B11.4B31.D5.D21.D84.D.D.15B$.D5.D7.A5.B4.4B5.B61.4B13.4B11.
4B145.D.2AB.12B$2.5D10.A3B6.4B4.2B59.4B13.4B11.4B34.D3.D24.D81.2DA.AB
2.11B$16.2A10.4B63.4B13.4B11.4B29.D101.9D8.A5.10B$18.B10.4B61.4B13.4B
11.4B32.D4.D.D27.D64.10D6.2A5.2B2A6B$17.2B11.4B59.4B13.4B11.4B35.D97.
2D6.3D11.3B2A6BD.D$31.4B57.4B13.4B11.4B38.D.D30.D62.2D7.3D11.10BD.3D$
91.4B13.4B11.4B135.2D8.2D11.8B.B2A.A.D$90.4B13.4B11.4B75.D60.2D8.2D
10.7B3.B2AB3A$89.4B13.4B11.4B137.2D7.3D10.6B5.DBD3.A$88.4B13.4B11.4B
138.2D6.3D12.6B4.2AD3A$87.4B13.4B11.4B139.10D13.5B6.A.A$86.4B13.4B11.
4B83.D.D.D.D.D6.3D39.10D12.6B6.A.A$85.4B13.4B11.4B98.D3.D38.2D6.3D11.
6B7.A$84.4B13.4B11.4B85.D.D15.D38.2D7.3D9.7B5.3D$83.4B13.4B11.4B101.
4D38.2D8.2D9.2B3D2B4.D3.A$82.4B13.4B11.4B87.D3.D9.D3.D38.2D8.2D9.4BD
3B3.2D3A$81.4B13.4B11.4B102.D3.D38.2D8.2D9.3B3D2B4.A15.9B$80.4B13.4B
11.4B89.D5.D8.3D.D37.2D7.3D10.8B3.2A14.9B$79.4B13.4B11.4B147.2D6.3D
11.3B2A2B2.4B14.4B$78.4B13.4B11.4B91.D7.D48.10D10.5B2A2B.3B16.5B$77.
4B13.4B11.4B149.9D11.13B16.6B$76.4B13.4B11.4B103.D40.D24.16B14.2B.4B$
75.4B13.4B11.4B104.2B37.3D16.D6.17B14.2B2.4B$74.4B13.4B11.4B105.2BD
12.D11.D10.D3.A13.3D7.16B14.2B3.4B$215.4B11.3D7.3D10.2D3A12.D3.A7.15B
5.D8.2B4.4B$216.3BD11.A.D5.D3.A10.A15.2D3A8.13B4.3D8.2B5.4B$217.4B10.
3A5.2D3A10.2A15.A12.11B4.D3.A15.4B$76.6D136.3BD12.A5.A11.4B15.2A7.15B
4.2D3A16.4B$79.D139.4B10.2A4.B2A9.3B5.B.7B4.B4.20B3.A20.4B$79.D140.3B
D9.9B8.4B.13B4.25B3.2A20.4B$79.D141.4B10.5B3.59B21.4B$79.D142.4B8.6B
2.4BD53B11.9B4.4B$79.D143.4B7.6B2.4B3D53B9.9B5.4B$79.D144.4B6.7B.4BDB
D15B2A37B8.4B11.4B$79.D145.4B4.15BD15B2A37BD7.5B11.4B$79.D146.4B2.20B
2.2B3.44B.D6.6B11.4B$74.D3.D148.4B.17B11.10B2.29B.B2A6.2B.4B11.4B$75.
3D150.19B16.6B4.8B.19B.BADA5.2B2.4B11.4B$229.17B19.3B9.23B5.A5.2B3.4B
11.4B$230.17BD19.B11.13B.7B5.2A4.2B4.4B11.4B$71.2C158.16B.D15.3D2A11.
3BD3.4B.3B.3B12.2B5.4B11.4B$71.2C159.7B3.3B.B2A15.D3.A12.4B4.B2.D3B.D
2B19.4B11.4B$67.4B162.6B7.BADA15.3A15.2AD6.B2AB.B2AB19.4B11.4B$68.4B
159.2D.4B11.A15.A17.A.D7.2A3.2A21.4B11.4B$69.4B159.5B12.2A33.3A35.4B
11.4B$70.4B155.3D2A52.A36.4B11.4B$71.4B154.D3.A90.4B11.3B$72.4B154.3A
92.4B11.2B$73.4B153.A80.9B6.4B11.B$74.4B233.9B7.4B$75.4B232.4B13.4B$
76.4B231.5B13.4B$77.4B230.6B13.4B$78.4B229.2B.4B13.4B$79.4B228.2B2.4B
13.4B$80.4B227.2B3.4B13.4B$81.4B226.2B4.4B13.4B$82.4B225.2B5.4B13.4B$
83.4B232.4B13.4B$84.4B232.4B13.4B$85.4B232.4B13.4B$86.4B232.4B13.3B$
87.4B232.4B13.2B$88.4B232.4B13.B$89.4B232.4B$90.4B232.4B$91.4B232.4B$
92.4B232.4B$93.4B232.4B$94.4B232.4B$95.4B232.4B$96.4B232.4B19.2D$97.
4B232.4B18.2D$98.4B232.4B18.2A$99.4B232.4B17.2A$100.4B232.4B23.5D$
101.4B232.4B24.D$102.4B232.4B13.2B8.D$103.4B232.3B12.3B8.D$104.4B232.
2B11.4B8.D$105.4B232.B10.4B9.D$106.4B241.4B10.D$107.4B239.4B11.D$108.
4B237.4B12.D$109.4B235.4B13.D$110.4B233.4B12.5D$111.4B231.4B$112.4B
229.4B$113.4B227.4B$114.4B225.4B$115.4B223.4B$116.4B221.4B$117.4B219.
4B$118.4B217.4B$119.4B215.4B$120.4B213.4B$121.4B211.4B$122.4B209.4B$
123.4B207.4B$124.4B205.4B$125.4B203.4B$126.4B201.4B$127.4B199.4B$128.
4B197.4B$129.4B195.4B$130.4B193.4B$131.4B191.4B$132.4B189.4B$133.4B
187.4B$134.4B185.4B$135.4B183.4B$136.4B181.4B$137.4B179.4B$138.4B177.
4B$139.4B175.4B$140.4B173.4B$141.4B171.4B$142.4B169.4B$143.4B167.4B$
144.4B165.4B$145.4B163.4B$146.4B161.4B$147.4B159.4B$148.4B157.4B$149.
4B155.4B$150.4B153.4B$151.4B151.4B$152.4B149.4B$153.4B147.4B$154.4B
145.4B$155.4B143.4B$156.4B141.4B$157.4B139.4B$158.4B137.4B$159.4B135.
4B$160.4B133.4B$161.4B131.4B$162.4B129.4B$163.4B127.4B$164.4B125.4B$
165.4B123.4B$166.4B121.4B$167.4B119.4B$168.4B117.4B$169.4B115.4B$170.
4B113.4B$171.4B111.4B$172.4B109.4B$173.4B107.4B$174.4B105.4B$175.4B
103.4B$176.4B101.4B$177.4B99.4B$178.4B97.4B$179.4B95.4B$180.4B93.4B$
181.4B91.4B$182.4B89.4B$183.4B87.4B$184.4B85.4B$185.4B83.4B$186.4B81.
4B$187.4B79.4B$188.4B77.4B$189.4B75.4B$190.4B73.4B$191.4B71.4B$192.4B
69.4B$193.4B67.4B$194.4B65.4B$195.4B63.4B$196.4B61.4B$197.4B59.4B$
198.4B57.4B$199.4B55.4B$200.4B53.4B$201.4B51.4B$202.4B49.4B$203.4B47.
4B$204.4B45.4B$205.4B43.4B$206.4B41.4B$207.4B39.4B$208.4B37.4B$209.4B
35.4B$210.4B33.4B$211.4B31.4B$212.4B29.4B$213.4B27.4B$214.4B25.4B$
215.4B23.4B$216.4B21.4B$217.4B19.4B$218.4B10.A6.4B$219.4B7.3A5.4B$
220.4B5.A3.B3.4B$221.4B4.2A3B2.4B$222.9B4.4B$223.6B.2B2.4B$223.8B2.4B
$221.15B$221.14B$221.13B$219.2AB.10B$218.A.AB3.B2A4B$218.A.2B3.B2A3B$
217.2AB.B3.4B$219.B6.3B$218.2B7.2B.BA$226.B2ABA.A$225.BABABA.A$223.A
2.A.A.A.A.2A$223.4A.2A2.A2.A$227.A.B.B2A.2B$225.A.A.2B2.B2.B$225.2A.B
4.2B$226.B.B$226.2B4$226.D6.D$226.D6.D$226.D6.D$226.D6.D$226.D6.D$
226.8D$226.D6.D$226.D6.D$226.D6.D$226.D6.D$226.D6.D!

Technically I think there might be a way to keep H as a regular elbow. It "only" requires finding a slow-salvo recipe for B that uses slow *WSSes instead of slow gliders. That would add an additional HB-equivalent distance to the b recipe but not the a recipe... let's see, if AB is 1.5d, HB is 2d, and Recipe b goes first, then a' will arrive in the gap after a, but b' will hit halfway through b, which is pretty much the opposite of the right place.

-- Okay, never mind *WSSes; it's pretty definitely still not the right time to open that can of worms, anyway. And the other way to use them would be to replace the C elbow with a south-output G-to-MWSS... which would open two completely different cans of worms and wouldn't be worth all the extra construction effort in any case. We'll give MWSS signals some good exercise in the Orthogonoids instead.

[chris_c]

Or we could compromise and use 3 Snarks:

Yes, good idea. I think that would give the shortest period out of all designs so far. Let s be the length of a Snark recipe and a and b be the lengths of the construct/destroy portions of recipes a and b. Then the loop in the two Snark design would have length 2s + 2a + 2b and in the three Snark design it would have length 3s + a + b + max(a,b). The three Snark design would win provided s < min(a,b).

A minor optimisation to your latest blueprint would be that the Snark turns to the right at D. In the leftward version there is no way to turn the Snark into an elbow using only single-channel gliders so you would need an extra still life near the Snark or a temporary elbow near A.

With that in mind, the Snark at H flips over to the NE and here is a pattern that shows how to leave elbow I in a state suitable for the next iteration and turn Snark H into an elbow block:

Code: Select all

#C First 7 gliders from end of recipe b make elbow suitable for a stream 3 lanes further SE.
#C The next glider is an off-channel 0-degree glider from the end of recipe a.
#C The final gliders are from the start of recipe b, one lane lower down than the first 7.
x = 1138, y = 1307, rule = LifeHistory
.A$2.A$3A36$39.A$37.A.A$38.2A62$103.A$104.A$102.3A63$168.A$166.A.A$
167.2A21$189.A.A$190.2A$190.A62$255.A$253.A.A$254.2A27$282.A.A$283.2A
$283.A62$346.A.A$347.2A$347.A38$386.A.A$387.2A$387.A225$617.A$618.A$
616.3A210$828.A$826.A.A$827.2A62$891.A$892.2A$891.2A29$923.A$924.A$
922.3A63$986.A.A$987.2A$987.A21$1011.A$1012.A$1010.3A63$1074.A.A$
1075.2A$1075.A25$1103.A$1101.A.A$1102.2A9$1128.A$1126.3A$1125.A$1125.
2A3$1133.2A$1134.A$1134.A.2A$1126.2A4.3A2.A$1126.2A3.A3.2A$1131.4A$
1117.2A15.A$1116.A.A12.3A$1116.A13.A$1115.2A14.5A$1135.A$1133.A$1133.
2A175$941.2A$941.2A!

My calculations suggest that we could have roughly AB = 1.5 * d, AD = DC = 0.5 * d and BI = d. At certain times in the evolution of the spaceship there would be two copies of the construct/destroy gliders of recipe b in the path JHIB. I think this would make the bounding box slightly bigger than the 4-Snark version. Anyway, all versions are very similar in the first two Snarks and the construct/destroy at A so no need to decide yet.