Quadratic-Growth Geminoid Challenge

[dvgrn]

For late-night entertainment lately I've been making trivial adjustments to a glider synthesis of a Gemini spaceship, mostly just to get an official LifeWiki Did-You-Know statistic.

Running the Gemini again has been a reminder for me about what an impressive piece of engineering it is... and also of how much it could be improved nowadays!

The last several years' worth of Geminoid development has been an experimental foray into oversimplification. It was technically possible to build a universal constructor with only one construction arm, so I ended up doing that instead of solving the annoying encoding and signal-crossing problems that come along with running a two-arm U.C.

However, it seems pretty obvious that a two-arm U.C. will be much more efficient, so that the extra circuitry will easily pay for itself. And thanks to recent developments like simsim314's "armless" U.C. design, there really isn't that much circuitry needed. I would argue that the following device is a complete programmable two-armed U.C.:

Code: Select all

x = 912, y = 855, rule = B3/S23
648b2o$648b2o134$325b2o$2o323b2o$2o344bo$344b3o11bo$343bo14b3o$343b2o
16bo14bo$360b2o12b3o$373bo$373b2o3$372b2o$353b2o17b2o$353b2o2$315b2o$
315b2o3$356b2o$336b2o19bo$336bobo15b3o$338bo15bo$338b2o19b2o$360bo$
357b3o$357bo6$350b2o$351bo$351bobo15b2o$352b2o15b2o12$370b2o$370bobo$
372bo$372b2o9$360b2o$360b2o$348b2o$347bobo$347bo$346b2o2$371b2o$350b2o
19bo$351bo17bobo$351bobo15b2o$352b2o4bo$357bobo$357bobo$358bo10b2o$
369bobo$371bo$371b2o$356b2o$357bo$354b3o68bo$354bo68bobo$424b2o4$434b
3o2$432bo5bo$432bo5bo$432bo5bo2$434b3o2$443bo$442b2o$442bobo43$505b2o$
505b2o11$491b2o$490bobo$490bo$489b2o6$510b2o$510bo$511b3o$513bo4$494b
2o$493bobo$493bo$492b2o4$522bo34bo$522b3o32b3o$525bo34bo$502b2o20b2o
33b2o$502b2o7b2o56b2o$511bo57bo$509bobo55bobo$509b2o4b2o44b2o4b2o$493b
2o20bo44bo2bo$494bo18bobo45b2o$494bobo16b2o34b2o$495b2o52b2o8$524b2o
32b2o3b2o$524b2o11b2o20bo3bo$537bo18b3o5b3o$501b2o35b3o15bo9bo$497b2o
2b2o37bo$496bobo$496bo23b2o$495b2o23bo$521b3o$523bo24$533b2o$533b2o11$
519b2o$518bobo$518bo$517b2o6$538b2o$538bo$539b3o$541bo4$522b2o$521bobo
$521bo$520b2o4$550bo34bo$550b3o32b3o$553bo34bo$530b2o20b2o33b2o$530b2o
7b2o56b2o$539bo57bo$537bobo55bobo$537b2o4b2o44b2o4b2o$521b2o20bo44bo2b
o$522bo18bobo45b2o$522bobo16b2o34b2o$523b2o52b2o8$552b2o32b2o3b2o$552b
2o11b2o20bo3bo$565bo18b3o5b3o$529b2o35b3o15bo9bo$525b2o2b2o37bo$524bob
o$524bo23b2o$523b2o23bo$549b3o$551bo59$528b2o$528b2o9$513b2o$513b2o10$
533b2o$533bo$534b3o$536bo11$545bo34bo$545b3o32b3o$548bo34bo$525b2o20b
2o33b2o$525b2o7b2o56b2o$534bo57bo$532bobo55bobo$532b2o4b2o44b2o4b2o$
516b2o20bo44bo2bo$517bo18bobo45b2o$517bobo16b2o34b2o$518b2o52b2o8$547b
2o32b2o3b2o$547b2o11b2o20bo3bo$560bo18b3o5b3o$524b2o35b3o15bo9bo$520b
2o2b2o37bo$519bobo$519bo23b2o$518b2o23bo$544b3o$546bo9$738b2o$737b2o$
739bo8$464bo$462b2o$463b2o4$456b3o2$454bo5bo$454bo5bo$454bo5bo2$456b3o
7$448b3o$450bo$449bo6$361b2o$361b2o9$346b2o$346b2o10$366b2o$366bo$367b
3o$369bo4$350b2o$349bobo$349bo$348b2o4$378bo34bo$378b3o32b3o$381bo34bo
$358b2o20b2o33b2o$358b2o7b2o56b2o$367bo57bo$365bobo55bobo$365b2o4b2o
44b2o4b2o$349b2o20bo44bo2bo$350bo18bobo45b2o$350bobo16b2o34b2o$351b2o
52b2o8$380b2o32b2o3b2o$380b2o11b2o20bo3bo$393bo18b3o5b3o$357b2o35b3o
15bo9bo$353b2o2b2o37bo$352bobo$352bo23b2o$351b2o23bo$377b3o$379bo4$
457b2o$457b2o7$910bo$909b2o$909bobo2$443b2o$442bobo$442bo$441b2o6$462b
2o$462bo$463b3o$465bo4$446b2o$445bobo$445bo$444b2o4$474bo34bo$474b3o
32b3o$477bo34bo$454b2o20b2o33b2o$454b2o7b2o56b2o$463bo57bo$461bobo55bo
bo$461b2o4b2o44b2o4b2o$445b2o20bo44bo2bo$446bo18bobo45b2o$446bobo16b2o
34b2o$447b2o52b2o8$476b2o32b2o3b2o$476b2o11b2o20bo3bo$489bo18b3o5b3o$
453b2o35b3o15bo9bo$449b2o2b2o37bo$448bobo$448bo23b2o$447b2o23bo$473b3o
301b2o$475bo300b2o$778bo130$662b2o$661b2o$663bo!

This design would need slow elbows, as shown, to produce intersecting gliders to the north -- which would slow down construction by quite a bit, of course. So maybe armless U.C.s aren't the way to go. Here's a version with two 10hd glider-pair construction arms instead, with an implied construction zone to the west this time:

Code: Select all

x = 710, y = 838, rule = B3/S23
84b2o$84b2o175$233b2o$218bo15bo$216b3o15bobo$203bo11bo19b2o$203b3o9b2o
$206bo$193b2o10b2o$194bo61b2o$194bobo59b2o$180b2o13b2o$180b2o36b2o$
218b2o2$174b2o$174b2o$178b2o$178b2o2$228b2o$209b2o18bo$173b2o34bo16b3o
$173b2o35b3o13bo$212bo33b2o$246b2o9$180b2o$181bo$178b3o$178bo$193b2o$
193bobo$195bo$195b2o6$329b2o$185b2o142b2o$176b2o7b2o$177bo$177bobo$
178b2o3$196b2o$196bo$194bobo$194b2o$315b2o$314bobo$180b2o132bo$179bobo
131b2o$179bo$178b2o4$334b2o$334bo$193b2o140b3o$183b2o8bo143bo$184bo6b
3o$181b3o$181bo$318b2o$317bobo$317bo$316b2o3$187b2o$187b2o4b2o151bo34b
o$193b2o151b3o32b3o$349bo34bo$326b2o20b2o33b2o$326b2o7b2o56b2o$192b2o
141bo57bo$188b2o2b2o139bobo55bobo$187bobo143b2o4b2o44b2o4b2o$187bo12b
2o115b2o20bo44bo2bo$186b2o11bobo116bo18bobo45b2o$199bo118bobo16b2o34b
2o$198b2o119b2o52b2o5$200b2o$199bobo$199bo$198b2o148b2o32b2o3b2o$348b
2o11b2o20bo3bo$361bo18b3o5b3o$325b2o35b3o15bo9bo$263bo57b2o2b2o37bo$
263b3o54bobo$266bo53bo23b2o$208b2o55b2o52b2o23bo$208b2o7b2o56b2o68b3o$
217bo57bo71bo$215bobo55bobo$215b2o4b2o44b2o4b2o$199b2o20bo44bo2bo$200b
o18bobo45b2o$200bobo16b2o34b2o$201b2o52b2o8$230b2o32b2o3b2o$230b2o11b
2o20bo3bo$243bo18b3o5b3o$207b2o35b3o15bo9bo$203b2o2b2o37bo$202bobo$
202bo23b2o$201b2o23bo$227b3o$229bo57$215bo$215b3o$218bo$217b2o6b2o$
224bobo$225bo3$212b2o$212b2o6b2o$220b2o2$229b2o$229b2o2$214b2o$213bobo
$213bo$212b2o53$183b2o$183b2o9$198b2o106b2o$198b2o106b2o10$178b2o$179b
o112b2o$176b3o112bobo$176bo114bo$290b2o6$182b2o127b2o$182b2o4b2o121bo$
188b2o122b3o$314bo3$187b2o$183b2o2b2o106b2o$182bobo109bobo$182bo12b2o
97bo$181b2o11bobo96b2o$194bo$193b2o2$323bo34bo$323b3o32b3o$326bo34bo$
195b2o106b2o20b2o33b2o$194bobo106b2o7b2o56b2o$194bo117bo57bo$193b2o
115bobo55bobo$310b2o4b2o44b2o4b2o$294b2o20bo44bo2bo$295bo18bobo45b2o$
258bo36bobo16b2o34b2o$258b3o35b2o52b2o$261bo$203b2o55b2o$203b2o7b2o56b
2o$212bo57bo$210bobo55bobo$210b2o4b2o44b2o4b2o$194b2o20bo44bo2bo$195bo
18bobo45b2o61b2o32b2o3b2o$195bobo16b2o34b2o73b2o11b2o20bo3bo$196b2o52b
2o86bo18b3o5b3o$302b2o35b3o15bo9bo$298b2o2b2o37bo$297bobo$297bo23b2o$
296b2o23bo$322b3o160b2o$324bo160bobo$225b2o32b2o3b2o219bo$225b2o11b2o
20bo3bo$238bo18b3o5b3o$202b2o35b3o15bo9bo$198b2o2b2o37bo$197bobo$197bo
23b2o$196b2o23bo$222b3o$224bo3$640b2o$640bobo$640bo83$2o$2o100$579b2o$
579bobo$579bo109$580b2o$580bobo$580bo15$707b2o$707bobo$707bo!

I threw in a semi-Snark as an experiment -- they could certainly cut down on the amount of circuitry, but at the cost of doubling the number of gliders coming in on the circuit and slowing down the repeat time from ~500 to ~1000.

We may want to go in the opposite direction, and build a 10hd U.C. that uses spark-coil Herschel transmitters and receivers, similar to the ones in the parallel HBK gun. [But we can't pack signals quite that close because we don't want to have to build 7x9 eaters.]

I've been stopped from investigating that so far by the continued lack of a really good signal splitter. Spartan Herschel fanout devices can be built, but they're just awkward enough to be discouraging to work with -- by the time you're done correcting for chirality problems and so on, it ends up seeming easier to stick with plain old gliders and live with the p497 or p575 repeat time.

There are unavoidable signal crossings in this design (about which more in a future post). One advantage of not reworking the circuitry to pack signals more tightly, is that more attenuated streams have a much lower risk of interfering with each other at these crossing points.

It's also worth thinking about whether a hybrid design with one armless U.C. and one 10hd U.C. would turn out to be more efficient. Or even a three-U.C. design, maybe two 10hd arms and a very wide armless shotgun between them. Lots of permutations to consider here in the early design stages...!

[simsim314]

How about making two arms in the same way you did your previous linear replicator, with single stream - it uses 4G to generate G2 anyway, so you can just attach another "interpretation unit" for the later two glider to "program" the second arm.

I would also suggest for starters to generate some rule which will allow the quadratic replicator "sketching" using particles. Similar to geminoid particles rule - I think it really helps to visualize and catch the major issues of the design in very early stage.

----

On some other front: I was thinking to use LifeAPI to see if all collisions between 3-4 SL and glider can yield more complex SLs, so we could add them into out circuitry. Unfortunately having more complex SLs is not so promoting Herschel conduits as one could hope - spartan circuitry is still one of the best circuitry there is on its own right.

[dvgrn]

Okay, I haven't really justified the title of this thread yet. A working two-arm universal constructor will be a good step along the way, but a lot more problems will have to be solved before we can program a 2armUC to achieve quadratic growth. Here's my list of goals so far:

• Design a diamond-shaped Geminoid replicator that never allows a recipe glider stream to double back on itself. (This is just so that the replicator will run quickly in Golly. In a sense this makes it a slightly silly and arbitrary goal, but it is a lot nicer when a pattern can be simulated efficiently.)
• Include enough adjustability to allow replicators to make copies of themselves in exactly 2^N ticks, with spatial offsets that are also exact multiples of two. (Same arbitrary reason as above.)
• Build child replicators at least one replicator-width away from the parent replicator, so that parent and child glider streams won't be traveling in opposite directions very close to each other (yet again to keep Hashlife happy.)
  
  If the green diamond is the original replicator loop, the white dotted diamonds mark the locations of the new child loops. Red lines show the paths that gliders and *WSSes must travel to set up the initial elbows needed for the actual construction:
  

  Code: Select all

  #C [[ VIEWONLY ZOOM 1.45 ]]
x = 411, y = 273, rule = LifeHistory
68.D.C269.C$67.C2D271.2DC$68.D.D.C265.C.D.D$65.C2.D2.D267.D2.D2.C$68.
D3.D.C261.C.D3.D$63.C4.D4.D263.D4.D4.C$68.D5.D.C257.C.D5.D$61.C6.D6.D
259.D6.D6.C$68.D7.D.C253.C.D7.D$59.C8.D8.D255.D8.D8.C$68.D9.D.C249.C.
D9.D$57.C10.D10.D251.D10.D10.C$68.D11.D.C245.C.D11.D$55.C12.D12.D247.
D12.D12.C$68.D13.D.C241.C.D13.D$53.C14.D14.D243.D14.D14.C$68.D15.D.C
237.C.D15.D$51.C16.D16.D239.D16.D16.C$68.D17.D.C233.C.D17.D$49.C18.D
18.D235.D18.D18.C$68.D19.D.C229.C.D19.D$47.C20.D20.D231.D20.D20.C$68.
D21.D.C225.C.D21.D$45.C22.D22.D227.D22.D22.C$68.D23.D.C211.C.C.C.C.C.
C.D23.D$33.C.C.C.C.C.C24.D24.D223.D24.D24.C$68.D25.D.C217.C.C25.D$41.
C.C24.D26.D219.D26.D26.C$68.D27.D.C213.C.D.C25.D$39.C3.C24.D28.D215.D
28.D28.C$68.D29.D.C209.C.D3.C25.D$37.C5.C24.D30.D211.D30.D30.C$68.D
31.D.C9.C195.C.D5.C25.D$35.C7.C24.D32.6D197.6D32.D32.C9.C$68.D32.2D.C
7.C193.C.2D6.C25.D$33.C9.C24.D32.D.D203.D.D32.D34.C7.C$68.D32.D2.D.C
5.C191.C.D2.D32.D$31.C36.D32.D3.D199.D3.D32.D36.C5.C$68.D32.D4.D.C3.C
189.C.D4.D32.D$29.C38.D38.D195.D38.D38.C3.C$68.D39.D.C.C187.C.D39.D$
27.C40.D40.D191.D40.D40.C.C$68.D33.C.C.C.C.C.C185.C.D41.D$25.C42.D42.
D187.D42.D32.C.C.C.C.C.C$68.D43.D.C181.C.D43.D$23.C44.D44.D183.D44.D
44.C$68.D45.D.C177.C.D45.D$21.C46.D46.D179.D46.D46.C$68.D47.D.C173.C.
D47.D$19.C48.D48.D175.D48.D48.C$68.D49.D.C169.C.D49.D$17.C50.D50.D
171.D50.D50.C$68.D51.D.C165.C.D51.D$15.C52.D52.D167.D52.D52.C$68.D53.
D.C161.C.D53.D$13.C54.D54.D163.D54.D54.C$68.D55.D.C157.C.D55.D$11.C
56.D56.D159.D56.D56.C$68.D57.D.C153.C.D57.D$9.C58.D58.D155.D58.D58.C$
68.D59.D.C149.C.D59.D$7.C60.D60.D151.D60.D60.C$68.D61.D.C145.C.D61.D$
5.C62.D62.D147.D62.D62.C$68.D21.D41.D.C141.C.D41.D21.D$3.C64.D20.D43.
D143.D43.D20.D64.C$68.D19.D45.D.C137.C.D45.D19.D$.C66.D18.D47.D139.D
47.D18.D66.C$.136D137.137D$.D66.D18.D47.C2D135.2DC47.D18.D66.D$C.D65.
D19.D47.D.D133.D.D47.D19.D65.D.C$3.D64.D20.D43.C2.D2.D131.D2.D2.C43.D
20.D64.D$2.C.D63.D21.D45.D3.D129.D3.D45.D21.D63.D.C$5.D62.D62.C4.D4.D
127.D4.D4.C62.D62.D$4.C.D61.D67.D5.D125.D5.D67.D61.D.C$7.D60.D60.C6.D
6.D123.D6.D6.C60.D60.D$6.C.D59.D67.D7.D121.D7.D67.D59.D.C$9.D58.D58.C
8.D8.D119.D8.D8.C58.D58.D$8.C.D57.D67.D9.D117.D9.D67.D57.D.C$11.D56.D
56.C10.D10.D115.D10.D10.C56.D56.D$10.C.D55.D67.D11.D113.D11.D67.D55.D
.C$13.D54.D54.C12.D12.D111.D12.D12.C54.D54.D$12.C.D53.D67.D13.D109.D
13.D67.D53.D.C$15.D52.D52.C14.D14.D107.D14.D14.C52.D52.D$14.C.D51.D
67.D15.D105.D15.D67.D51.D.C$17.D50.D50.C16.D16.D103.D16.D16.C50.D50.D
$16.C.D49.D67.D17.D101.D17.D67.D49.D.C$19.D47.3D47.C18.D18.D99.D18.D
18.C47.3D47.D$18.C.D45.D.D.D65.D19.D97.D19.D65.D.D.D45.D.C$21.D43.D2.
D2.D43.C20.D20.D95.D20.D20.C43.D2.D2.D43.D$20.C.D41.D3.D3.D63.D21.D
93.D21.D63.D3.D3.D41.D.C$23.D44.D44.C22.D22.D91.D22.D22.C44.D44.D$22.
C.D43.D67.D23.D89.D23.D67.D43.D.C$25.D42.D42.C24.D24.D87.D24.D24.C.C.
C.C.C.C32.D42.D$24.C.C.C.C.C.C33.D67.D25.D85.D25.D67.D41.D.C$27.D40.D
40.C26.D26.D83.D26.D24.C.C40.D40.D$24.C.C.D39.D67.D27.D81.D27.D67.D
39.D.C$29.D38.D38.C28.D28.D79.D28.D24.C3.C38.D38.D$24.C3.C.D37.D67.D
29.D77.D29.D67.D37.D.C$31.D36.D36.C30.D30.D75.D30.D24.C5.C36.D36.D$
24.C5.C.D35.D67.D31.D73.D31.D67.D35.D.C$33.6D29.D24.C9.C32.D32.6D61.
6D32.D24.C7.C34.D29.6D$24.C7.C2D33.D67.D32.2D69.2D32.D67.D25.C7.2DC$
33.D.D32.D24.C7.C34.D32.D.D67.D.D32.D24.C9.C32.D32.D.D$24.C8.DC.D31.D
67.D32.D2.D65.D2.D32.D67.D25.C5.D.CD$33.D3.D30.D24.C5.C36.D32.D3.D63.
D3.D32.D36.C30.D30.D3.D$33.D2.C.D29.D67.D32.D4.D61.D4.D32.D67.D25.C3.
D.C2.D$39.D28.D24.C3.C38.D38.D59.D38.D38.C28.D28.D$38.C.D27.D67.D39.D
57.D39.D67.D25.C.D.C$41.D26.D24.C.C40.D40.D55.D40.D40.C26.D26.D$40.C.
D25.D67.D41.D53.D41.D67.D25.C.C$43.D24.D24.C.C.C.C.C.C32.D42.D51.D42.
D42.C24.D24.D$42.C.D23.D67.D43.D49.D43.D67.D23.D.C.C.C.C.C.C$45.D22.D
22.C44.D44.D47.D44.D44.C22.D22.D$44.C.D21.D67.D45.D45.D45.D67.D21.D.C
$47.D20.D20.C46.D46.D43.D46.D46.C20.D20.D$46.C.D19.D67.D47.D41.D47.D
67.D19.D.C$49.D18.D18.C48.D48.D39.D48.D48.C18.D18.D$48.C.D17.D67.D49.
D37.D49.D67.D17.D.C$51.D16.D16.C50.D50.D35.D50.D50.C16.D16.D$50.C.D
15.D67.D51.D33.D51.D67.D15.D.C$53.D14.D14.C52.D52.D31.D52.D52.C14.D
14.D$52.C.D13.D67.D53.D29.D53.D67.D13.D.C$55.D12.D12.C54.D54.D27.D54.
D54.C12.D12.D$54.C.D11.D67.D55.D25.D55.D67.D11.D.C$57.D10.D10.C56.D
56.D23.D56.D56.C10.D10.D$56.C.D9.D67.D57.D21.D57.D67.D9.D.C$59.D8.D8.
C58.D58.D19.D58.D58.C8.D8.D$58.C.D7.D67.D59.D17.D59.D67.D7.D.C$61.D6.
D6.C60.D60.D15.D60.D60.C6.D6.D$60.C.D5.D67.D61.D13.D61.D67.D5.D.C$63.
D4.D4.C62.D62.D11.D62.D62.C4.D4.D$62.C.D3.D67.D21.D41.D4B.4BD41.D21.D
67.D3.D.C$65.D2.D2.C64.D20.D42.BD7BDB42.D20.D64.C2.D2.D$64.C.D.D67.D
19.D42.3BD5BD3B42.D19.D67.D.D.C$67.2DC66.D18.D43.4BD3BD4B43.D18.D66.C
2D$66.C.137DB137D.C$69.D66.D18.D43.13B43.D18.D66.D$70.D65.D19.D43.4BA
BA4B43.D19.D65.D$71.D64.D20.D43.2BAB.BA2B43.D20.D64.D$72.D63.D21.D43.
A5.A43.D21.D63.D$73.D62.D64.A7.A64.D62.D$74.D61.D63.A9.A63.D61.D$75.D
60.D62.A11.A62.D60.D$76.D59.D61.A13.A61.D59.D$77.D58.D60.A15.A60.D58.
D$78.D57.D59.A17.A59.D57.D$79.D56.D58.A19.A58.D56.D$80.D55.D57.A21.A
57.D55.D$81.D54.D56.A23.A56.D54.D$82.D53.D55.A25.A55.D53.D$83.D52.D
54.A27.A54.D52.D$84.D51.D53.A29.A53.D51.D$85.D50.D52.A31.A52.D50.D$
86.D49.D51.A33.A51.D49.D$87.D47.3D49.A35.A49.3D47.D$88.D45.D.D.D47.A
37.A47.D.D.D45.D$89.D43.D2.D2.D45.A39.A45.D2.D2.D43.D$90.D41.D3.D3.D
43.A41.A43.D3.D3.D41.D$91.D44.D46.A43.A46.D44.D$92.D43.D45.A45.A45.D
43.D$93.D42.D44.A47.A44.D42.D$94.D41.D43.A49.A43.D41.D$95.D40.D42.A
51.A42.D40.D$96.D39.D41.A53.A41.D39.D$97.D38.D40.A55.A40.D38.D$98.D
37.D39.A57.A39.D37.D$99.D36.D38.A59.A38.D36.D$100.D35.D37.A61.A4.A32.
D35.D$101.6D29.D31.6A63.A3.A32.D29.6D$101.2D33.D35.2A64.A2.A32.D33.2D
$101.D.D32.D34.A.A65.A.A32.D32.D.D$101.D2.D31.D33.A2.A66.2A32.D31.D2.
D$101.D3.D30.D32.A3.A62.6A32.D30.D3.D$101.D4.D29.D31.A4.A68.A31.D29.D
4.D$107.D28.D30.A75.A30.D28.D$108.D27.D29.A77.A29.D27.D$109.D26.D28.A
79.A28.D26.D$110.D25.D27.A81.A27.D25.D$111.D24.D26.A83.A26.D24.D$112.
D23.D25.A85.A25.D23.D$113.D22.D24.A87.A24.D22.D$114.D21.D23.A89.A23.D
21.D$115.D20.D22.A91.A22.D20.D$116.D19.D21.A93.A21.D19.D$117.D18.D20.
A95.A20.D18.D$118.D17.D19.A97.A19.D17.D$119.D16.D18.A99.A18.D16.D$
120.D15.D17.A101.A17.D15.D$121.D14.D16.A103.A16.D14.D$122.D13.D15.A
105.A15.D13.D$123.D12.D14.A107.A14.D12.D$124.D11.D13.A109.A13.D11.D$
125.D10.D12.A111.A12.D10.D$126.D9.D11.A113.A11.D9.D$127.D8.D10.A115.A
10.D8.D$128.D7.D9.A117.A9.D7.D$129.D6.D8.A119.A8.D6.D$130.D5.D7.A121.
A7.D5.D$131.D2.2BDB5.A123.A5.BD2B2.D$132.D3BD2B3.A125.A3.2BD3BD$132.B
D2BD3B.A127.A.3BD2BDB$132.2BDBD3BA129.A3BDBD2B$132.3B2D2BA131.A2B2D3B
$132.4BDBAB131.BABD4B$133.6B133.6B$134.4BA133.A4B$139.A131.A$140.A
129.A$141.A127.A$142.A125.A$143.A123.A$144.A121.A$145.A119.A$146.A
117.A$147.A115.A$148.A113.A$149.A111.A$150.A109.A$151.A107.A$152.A
105.A$153.A103.A$154.A101.A$155.A99.A$156.A97.A$157.A95.A$158.A93.A$
159.A91.A$160.A89.A$161.A87.A$162.A85.A$163.A83.A$164.A81.A$165.A79.A
$166.A77.A$167.A75.A$168.A68.A4.A$169.6A62.A3.A$169.2A66.A2.A$169.A.A
65.A.A$169.A2.A64.2A$169.A3.A63.6A$169.A4.A61.A$175.A59.A$176.A57.A$
177.A55.A$178.A53.A$179.A51.A$180.A49.A$181.A47.A$182.A45.A$183.A43.A
$184.A41.A$185.A39.A$186.A37.A$187.A35.A$188.A33.A$189.A31.A$190.A29.
A$191.A27.A$192.A25.A$193.A23.A$194.A21.A$195.A19.A$196.A17.A$197.A
15.A$198.A13.A$199.A11.A$200.A9.A$201.A7.A$202.A5.A$203.A3.A$204.A.A!
• Work out a 2armUC design that will make it easy to use Calcyman's existing synthesise-pattern2.py script to generate construction recipes for arbitrary Spartan stable circuitry.
• Put two exact copies of the 2armUC at two corners of the replicator loop, so that a single pass of a glider recipe through the circuitry will generate two identical child replicators 90 degrees apart.
• Design one-time turners and signal splitters that can be constructed near the corners of the replicator loop, that can be triggered to quickly produce multiple elbow blocks (one for each arm of each 2armUC) very far away.
• It will be necessary to trigger these one-time circuits simultaneously at two or more corners of the replicator, because the creation of faraway elbow blocks requires colliding gliders from one corner with *WSSes from an adjacent corner.
• The first set of elbow blocks may have to be used as scaffolding to build a second set of elbow blocks even farther away. The first set would be the two near corners of a child replicator, and the second set would be the two far corners. Again this can be accomplished by creating a glider and a *WSS simultaneously at each near-child-corner, and allowing each of the four to collide with its opposite type from the other corner.
• Glider-pair operations can be sent to the construction arms almost immediately after the elbow-building one-time circuits have been triggered, because the faraway elbow blocks will have been constructed successfully by the time the glider pairs reach them.

There's an apparently endless array of tricky little problems that will have to be solved to get this blueprint working. Just for example:

For a 2armUC we need four streams of input gliders. But to copy the full recipe to the child replicators, it would be much easier to have just one single long stream of gliders.

Four streams can be encoded into one stream in a couple of ways: in parallel -- four gliders following each other on one path, copied and directed successively into four different circuits... or in series -- all gliders for circuit #1 are sent, then all gliders for circuit #2, then #3, then #4.

In the parallel case, every instruction must contain four gliders -- so both construction arms have to be doing something whether there's something for them to do or not. This isn't impossible to arrange, I think, just annoying.

In the series case, the single stream would have to be reflected around the loop three times, and then three output circuits would have to be opened simultaneously to get the U.C. going. Very similar to the current Demonoid design, but with two more circuits.

Sending recipes in series has the advantage that the much more efficient singleton-glider 10hd elbow-op library can be used -- but the disadvantages that A) it's four times as slow, and B) extra circuitry has to be added to keep the four subrecipes' relative timings the same between the two UCs at adjacent corners of the replicator.

A third option may well make sense: four simultaneous streams, just as in the serial case, but there's dedicated circuitry to copy each of them, as well as the timing-adjustment circuitry that would have to be done anyway for the serial case.

Other ideas, comments, questions, and/or competing diagrams are all welcome as usual.

[dvgrn]

Another quick for-example difficulty: these replicator loops will be very large, but it would still be difficult (as towerator and others have pointed out) to store enough enough instructions in the loop to move an elbow from one corner of a child loop to another corner.

So one of the items in the last post is that construction elbows will need to be pre-built at each of the four corners, so that construction can be done efficiently. Unfortunately, with a 2armUC design, the near-corner construction will get in the way of completing the far-corner construction. So the far-corner construction has to be done first... but then we need a special trick to pop up an elbow at the near corner just when we need it, without having to wait around for a glider or LWSS to come from far, far away to trigger the reaction.

Waiting around could potentially use up a large fraction of the recipe storage space in the loop, so I'm trying to avoid that. It's certainly possible to design switching systems that allow for huge delays, where part of a recipe is read on its first trip around the replicator loop, but another part is kept "turned off" and not expressed until the second trip around the loop. But that adds up to a lot of extra complex circuitry, and I'd rather avoid that as well.

Some of this has been described fairly thoroughly in a previous thread, so I won't duplicate it in detail here. I'm looking for a really good way to use armless UC technology to work around this Construction Obstruction problem, but haven't quite found it yet...!

The "diamond Geminoid" idea from the above link was potentially a somewhat less ambitious project. Building a diamond Geminoid spaceship is a relatively easy trick, especially with 2armUCs: just encode four separate recipes for complete UCs at the four corners of the diamond. Each corner is responsible for replicating itself at a small offset and destroying its predecessor, after which the construction-instruction glider stream flows naturally into the new copies -- all exactly like in the original Gemini, except for the shape. Oddly enough, doubling the number of replicator units will allow Golly to simulate the spaceship enormously faster.

[towerator]

I would like to put back on table my old idea to use a slow spaceship to be "thrown and caught" to create easily far away objects. While my old idea of using corderships and gliders is obviously impratical, being both slow and extremely expensive, the recent syntheses of several new spaceships updated the idea.

Think about is: a LWSS only gains 1 cell to a dart every 6 generations. So if I shoot a dart and then a LWSS 500 generations later, the encounter will be 3000 cells away!

I chose 4 speed which each have their pros, but also their cons.

* c/7 orthogonal
Candidate: loafer
Pros: extremely cheap synthesis, with only 8 gliders

Cons: Slow (the ratio between the shooting interval and the distance gained is 6:1) Also, it isn't diagonal, which could cause some griefs.

Code: Select all

x = 28, y = 58, rule = B3/S23
19$12bo$11bobo$10bo2bo$11b2o2$7bo5bo$6bobo3bo$5bo2bo3b2o$5bo2b2o3bo15$
14b3o$13bo2bo$16bo$16bo$15bo!

* c/3 orthogonal
Candidates: dart; 25P3H1V0.2

Pros: good ratio (1:6); the dart is fast and cheap to create. Many recipes known.

Cons: Not diagonal. Also, LWSS/MWSS + dart are messy, I used a HWSS.

Code: Select all

x = 31, y = 95, rule = B3/S23
23$12bo$11bobo$10bo3bo$11b3o2$9b2o3b2o$7bo3bobo3bo$6b2o3bobo3b2o$5bo5b
obo5bo$6bob2obobob2obo31$8b3o$7bo2bo$10bo$10bo$10bo$10bo$9bo!

* 2c/5 orthogonal
Candidate: 30P5H2V0

Pros: excellent ratio (1:10!), rather compact

Cons: expensive, and again, not diagonal.

Code: Select all

x = 62, y = 115, rule = B3/S23
20$26bo$25b3o$24b2ob2o2$23bobobobo2bo$22b2o3bo3b3o$22b2o3bo6bo$32bobo$
30bobo$31bo2bo$34bo33$20b3o$19bo2bo$22bo$22bo$21bo!

* c/5 diagonal
Candidate: 58P5H1V1

Pros: Excellent ratio (1:20!), can create blocks mid -way without being destroyed, and can even turn a glider 90°. Also, diagonal.

Cons: 58P5H1V1 is a sturdy ships creating tons of sparks destroying any gliding threat. It, however, has a sweet spot at it's center, in which it creates a rather clean constellation. Also, it's recipe is unknown.

Code: Select all

x = 75, y = 67, rule = B3/S23
6$24b2o$24b2o$23bo2bo$20b2obo2bo$26bo$18b2o3bo2bo$18b2o5bo$19bob5o$20b
o3$17b3o$17bo$15b2o$9b2o4bo$9b3o3bo$7bo4bo$7bo3bo$11bo$6b2obobo$4b2o5b
o$4b2o4b2o$6b4o12$26b3o$26bo$27bo26b3o$54bo$55bo4$47b3o$47bo$48bo!

IMO, c/5d would be the best candidate if we had a recipe. In our actual state of knowledge, c/3 seems the best.

[simsim314]

For the loop size problem, there is a solution using snake container. while building snake container takes linear time it can contain quadratic size loop.

Also in replicator the construction size is measured in SLs not gliders. This is important nuance - 8 gliders for example can translate into ~ 250 SLs.

As for using armless design - each corner of the replicator needs only "local" glider adjustments - this is where armless is strongest. And I'm not sure why dvgrn decided that two arms is the best solution, but on the long and far away axis we can use 10hd design, while on the short axis we can use the armless.

In general armless alone can provide slow salvo constructions on its own, but if we insist on using two arms I see no good reason to use "slider" design on the short axis.

[dvgrn]

For the loop size problem, there is a solution using snake container. while building snake container takes linear time it can contain quadratic size loop.

True enough -- I'm just not at all sure that there is a loop size problem. It seems to me that a fairly reasonable sized chain reaction, set off at the right time, could build the near-corner and then far-corner elbows or target objects, by colliding gliders with *WSS as my diagram above suggests.

Once the freeze-dried salvos are available to create those G+*WSS collisions, I don't see why a full construction recipe wouldn't fit into half or even a quarter of a diamond-shaped loop. The size can be increased as necessary without changing the recipe or construction mechanism at all.

Also in replicator the construction size is measured in SLs not gliders. This is important nuance - 8 gliders for example can translate into ~ 250 SLs.

No argument there. The two-stage G+LWSS seeds would end up being very expensive to build. But I still think they'll be extraordinarily cheap... compared to building a snake-shaped container with enough folds to hold the elbow moves needed to reach a full replicator diameter away.

There's also a big practical problem with packing a long glider recipe into a compact 2D space: quite simply, Golly can't possibly run it efficiently. There's no way to avoid an exponential explosion in the number of hashtiles needed, as gliders pass each other in close proximity. Even if it's a spiral instead of a back-and-forth folded loop, Golly will have to garbage-collect constantly.

A Gemini gun or similar large open loop may actually be several orders of magnitude larger than a tightly folded loop like the double-spiral period-2^23 loafer gun, but it will run well at much higher step sizes. The first thing on my priority list is for the replicator to run really well in Golly. It should be able to complete a construction cycle a lot faster than the Gemini or the linear GoL propagator can.

As for using armless design - each corner of the replicator needs only "local" glider adjustments - this is where armless is strongest. And I'm not sure why dvgrn decided that two arms is the best solution, but on the long and far away axis we can use 10hd design, while on the short axis we can use the armless.

Well, I certainly haven't concluded that 2-arm UCs are necessarily best.

At the moment I'm inclined to think that a 2-arm design will result in a much smaller replicator size overall. Considering how inefficient the original Gemini's construction arms were, it's really impressive to watch how quickly it can get things done. And there's a decent 2armUC compiler already written, too, which is more than I can say for 1armUCs...!

That said, the spiral-growth pattern can do its construction very quickly with only one arm -- again because the gliders never double back. It's quite possible that two arms will create significantly more hashtiles than a single arm, and Golly might end up running slower.

-- So I'm certainly prepared to be convinced to go with a one-arm or armless design instead. This is still definitely still the early-exploration stage, and I'd like to build a few trial designs and see which one seems most worth focusing on.

[dvgrn]

I would like to put back on table my old idea to use a slow spaceship to be "thrown and caught" to create easily far away objects.

These look like good options, and I'd like to look them over pretty closely before settling down to work on any particular design.

In particular, I'm not sure if it's such a disadvantage to have a target that's far away orthogonally. Thanks to chris_c's work on 10hd construction, some time ago on the Demonoid thread, we could actually try doing one-arm constructions with slow LWSSes, at a fairly reasonable cost.

We could send enough LWSSes to build a 90-degree LWSS turner, anyway, and then hit that output LWSS with a glider to get a diagonally very-far-away block. What's more, the same 10hd1armUC could be used to fire all of the LWSSes and the glider -- no extra circuitry needed (!).

Or we could see if it would work to build the entire replicator with slow LWSSes, I suppose -- that's hardly been investigated at all, ever, as far as I know, but quite likely it would work just as well as slow gliders.

On the other hand, simsim314's point applies here, too. To get any of these leader-and-chaser spaceship pairs off the ground, we'll need to construct a seed for the leader. So we might need 250 still lifes to build a constellation that synchronizes 8 gliders -- and that's just for a loafer, not the more ambitious c/3 ships.

-- Actually, that's a bit of an overestimate, though. The loafer gun in Golly's Patterns/Hashlife needed only 81 blocks to synchronize 8 gliders, and that was a highly constrained trial run. If we relax the Blockic requirement and use any still lifes we want, we can probably build a 40sL loafer seed.

(Somebody should definitely do that. I'm glad I already took my turn.)

In any case, it's not clear to me yet that a dart plus long-delay-mechanism plus HWSS, or a loafer plus long-delay-mechanism plus LWSS, is really going to be any cheaper when you add everything up. A few simple LWSS+G seeds and freeze-dried slow salvos, with no (I think) delay mechanism needed, still look competitive to me.

[dvgrn]

Last thing for tonight: here's a test run for one of the designs I was going on about -- a diamond-shaped replicator loop designed to run two construction arms at each of two corners.

Code: Select all

#C 4-channel replicator loop,
#C showing sample switching mechanisms for a single-use loop
#C that's capable of constructing and programming two child loops.
#C ... No viewer option for *this* pattern!
x = 44047, y = 47193, rule = B3/S23
3346bo$3345bobo$3345b2o149$3747b2o$3747b2o2$3715bo$3713b3o$3697bo14bo$
3697b3o12b2o$3700bo$3699b2o3$3700b2o$3700b2o17b2o$3719b2o2$3757b2o$
3757b2o3$3716b2o$3716bo19b2o$3717b3o15bobo$3719bo15bo$3713b2o19b2o$
3713bo$3714b3o$3716bo6$3722b2o$3722bo$3703b2o15bobo$3703b2o15b2o$3691b
2o$3690bobo$3690bo$3689b2o8$3702b2o$3701bobo$3701bo$3700b2o9$3712b2o$
3712b2o$3724b2o$3724bobo$3726bo$3726b2o2$3651bo49b2o$3650bobo49bo19b2o
$3651b2o49bobo17bo$3703b2o15bobo$3715bo4b2o$3714bobo$3714bobo$3703b2o
10bo$3702bobo$3702bo$3701b2o$3716b2o$3716bo$3717b3o$3719bo3$3667bo$
3666bobo$3666bobo$3667bo5$3661b2o$3660bo2bo$3661bobo5bo$3662bo5bobo$
3669b2o25$3577bo$3576bobo$3577b2o6$3747b2o$3747b2o2$3715bo$3713b3o$
3697bo14bo$3631b2o64b3o12b2o$3631b2o67bo$3699b2o$3593bo$3592bobo$3578b
2o12bobo40b2o63b2o$3579bo13bo41b2o63b2o17b2o$3576b3o140b2o$3576bo33b2o
$3611bo145b2o$3611bobo143b2o$3587b2o23b2o$3586bo2bo$3587bobo5bo120b2o$
3588bo5bobo119bo19b2o$3595b2o120b3o15bobo$3719bo15bo$3713b2o19b2o$
3713bo$3597b2o29b2o84b3o$3597b2o29b2o86bo6$3622b2o98b2o$3622b2o98bo$
3703b2o15bobo$3703b2o15b2o$3691b2o$3690bobo$3623b2o65bo$3623b2o64b2o7$
3503bo$3502bobo197b2o$3503b2o196bobo$3701bo$3700b2o9$3712b2o$3712b2o3$
3519bo$3518bobo$3504b2o12bobo$3505bo13bo181b2o$3502b3o197bo19b2o$3502b
o199bobo17bo$3703b2o15bobo$3715bo4b2o$3513b2o199bobo$3512bo2bo198bobo$
3513bobo5bo19b2o160b2o10bo$3514bo5bobo19bo159bobo$3521b2o19bobo157bo$
3543b2o156b2o$3716b2o$3716bo$3523b2o192b3o$3523b2o194bo$3402b2o$3402b
2o2$3559b2o$3407b2o150b2o$3407b2o5$3553b2o$3553b2o5$3554b2o$3554b2o19$
3445bo$3444bobo$3430b2o12bobo$3431bo13bo$3428b3o$3428bo3$3439b2o$3438b
o2bo$3439bobo5bo$3440bo5bobo298b2o$3447b2o298b2o2$3715bo$3472b2o239b3o
$3449b2o22bo223bo14bo$3449b2o22bobo221b3o12b2o$3474b2o224bo$3699b2o3$
3700b2o$3700b2o17b2o$3719b2o2$3490b2o265b2o$3490b2o265b2o3$3716b2o$
3716bo19b2o$3717b3o15bobo$3484b2o233bo15bo$3484b2o227b2o19b2o$3453b2o
258bo$3452bobo259b3o$3453bo262bo2$3485b2o$3485b2o3$3722b2o$3722bo$
3703b2o15bobo$3703b2o15b2o$3691b2o$3690bobo$3690bo$3689b2o8$3702b2o$
3701bobo$3701bo$3700b2o9$3712b2o$3712b2o6$3701b2o$3702bo19b2o$3702bobo
17bo$3703b2o15bobo$3715bo4b2o$3714bobo$3714bobo$3703b2o10bo$3512b2o
188bobo$3512bobo187bo$3513bo187b2o$3716b2o$3716bo$3717b3o$3719bo48$
3747b2o$3747b2o2$3715bo$3713b3o$3697bo14bo$3697b3o12b2o$3700bo$3699b2o
3$3700b2o$3700b2o17b2o$3719b2o2$3757b2o$3757b2o3$3716b2o$3716bo19b2o$
3717b3o15bobo$3719bo15bo$3713b2o19b2o$3713bo$3714b3o$3716bo6$3722b2o$
3722bo$3703b2o15bobo$3703b2o15b2o$3691b2o$3690bobo$3690bo$3689b2o8$
3702b2o$3701bobo$3701bo$3700b2o9$3712b2o$3712b2o6$3701b2o$3702bo19b2o$
3702bobo17bo$3703b2o15bobo$3715bo4b2o$3714bobo$3714bobo$3703b2o10bo$
3702bobo$3702bo$3701b2o$3716b2o$3716bo$3717b3o$3719bo48$3747b2o$3747b
2o2$3715bo$3713b3o$3697bo14bo$3697b3o12b2o$3700bo$3699b2o3$3700b2o$
3700b2o17b2o$3719b2o2$3757b2o$3757b2o3$3716b2o$3716bo19b2o$3717b3o15bo
bo$3719bo15bo$3713b2o19b2o$3713bo$3714b3o$3716bo6$3722b2o$3722bo$3703b
2o15bobo$3703b2o15b2o$3691b2o$3690bobo$3690bo$3689b2o8$3702b2o$3701bob
o$3701bo$3700b2o9$3712b2o$3712b2o3$3507bo$3506bobo$3507b2o$3701b2o$
3702bo19b2o$3702bobo17bo$3703b2o15bobo$3715bo4b2o$3714bobo$3714bobo$
3703b2o10bo$3702bobo$3702bo$3701b2o$3716b2o$3716bo$3717b3o$3719bo2506$
605b2o$605b2o9$590b2o$590b2o10$610b2o$610bo$611b3o$613bo11$622bo34bo$
622b3o32b3o$625bo34bo$602b2o20b2o33b2o$602b2o7b2o56b2o$611bo57bo$609bo
bo55bobo$609b2o4b2o44b2o4b2o$593b2o20bo44bo2bo$594bo18bobo45b2o$594bob
o16b2o34b2o$595b2o52b2o8$624b2o32b2o3b2o$624b2o11b2o20bo3bo$637bo18b3o
5b3o$601b2o35b3o15bo9bo$597b2o2b2o37bo$596bobo$596bo$595b2o5$626b2o$
626bo$627b3o$629bo34$2o$2o4$4b2o$4b2o19$605b2o$605b2o6210bo$6817b3o$
6820bo$6819b2o5$6850b2o$590b2o6258bo$590b2o6256bobo$6806bo37b2o2b2o$
6780bo9bo15b3o35b2o$6780b3o5b3o18bo$6783bo3bo20b2o11b2o$6782b2o3b2o32b
2o5$610b2o$610bo$611b3o$613bo6182b2o52b2o$6796b2o34b2o16bobo$6784b2o
45bobo18bo$6783bo2bo44bo20b2o$6778b2o4b2o44b2o4b2o$6777bobo55bobo$
6777bo57bo$6776b2o56b2o7b2o$6786b2o33b2o20b2o$6786bo34bo$6787b3o32b3o$
622bo34bo6131bo34bo$622b3o32b3o$625bo34bo$602b2o20b2o33b2o$602b2o7b2o
56b2o6182b2o$611bo57bo6183bo$609bobo55bobo6181bobo$609b2o4b2o44b2o4b2o
6182b2o$593b2o20bo44bo2bo$594bo18bobo45b2o$594bobo16b2o34b2o$595b2o52b
2o6182bo$6833b3o$6836bo$6835b2o5$624b2o32b2o3b2o$624b2o11b2o20bo3bo$
637bo18b3o5b3o$601b2o35b3o15bo9bo$597b2o2b2o37bo$596bobo6256b2o$596bo
6258b2o$595b2o5$626b2o$626bo$627b3o$629bo6210b2o$6840b2o58$605b2o$605b
2o6210bo$6817b3o$6820bo$6819b2o5$6850b2o$590b2o6258bo$590b2o6256bobo$
6806bo37b2o2b2o$6780bo9bo15b3o35b2o$6780b3o5b3o18bo$6783bo3bo20b2o11b
2o$6782b2o3b2o32b2o5$610b2o$610bo$611b3o$613bo6182b2o52b2o$6796b2o34b
2o16bobo$6784b2o45bobo18bo$6783bo2bo44bo20b2o$6778b2o4b2o44b2o4b2o$
6777bobo55bobo$6777bo57bo$6776b2o56b2o7b2o$6786b2o33b2o20b2o$6786bo34b
o$6787b3o32b3o$622bo34bo6131bo34bo$622b3o32b3o$625bo34bo$602b2o20b2o
33b2o$212b2o388b2o7b2o56b2o6182b2o$211bobo397bo57bo6183bo$212bo396bobo
55bobo6181bobo$609b2o4b2o44b2o4b2o6182b2o$593b2o20bo44bo2bo$594bo18bob
o45b2o$594bobo16b2o34b2o$595b2o52b2o6182bo$6833b3o$6836bo$6835b2o5$
624b2o32b2o3b2o$624b2o11b2o20bo3bo$637bo18b3o5b3o$601b2o35b3o15bo9bo$
597b2o2b2o37bo$596bobo6256b2o$596bo6258b2o$595b2o8$6840b2o$6840b2o19$
649b2o$648bobo$649bo3$391b2o261b2o$391b2o261bo$655b3o$657bo2$387b2o$
387b2o28$605b2o$605b2o6210bo$6817b3o$339b2o6479bo$339b2o6478b2o4$337b
2o$330bo5bobo6511b2o$329bobo5bo252b2o6258bo$328bo2bo258b2o6256bobo$
329b2o6475bo37b2o2b2o$6780bo9bo15b3o35b2o$6780b3o5b3o18bo$318bo6464bo
3bo20b2o11b2o$318b3o6461b2o3b2o32b2o$321bo13bo$320b2o12bobo$334bobo$
335bo$610b2o$610bo$611b3o$613bo6182b2o52b2o$6796b2o34b2o16bobo$6784b2o
45bobo18bo$6783bo2bo44bo20b2o$6778b2o4b2o44b2o4b2o$6777bobo55bobo$458b
2o6317bo57bo$458b2o6316b2o56b2o7b2o$6786b2o33b2o20b2o$6786bo34bo$6787b
3o32b3o$471b2o149bo34bo6131bo34bo$318b2o145b2o4b2o149b3o32b3o$317bobo
145b2o158bo34bo$318bo283b2o20b2o33b2o$602b2o7b2o56b2o6182b2o$611bo57bo
6183bo$609bobo55bobo6181bobo$609b2o4b2o44b2o4b2o6182b2o$593b2o20bo44bo
2bo$594bo18bobo45b2o$594bobo16b2o34b2o$449b2o144b2o52b2o6182bo$450bo
6382b3o$447b3o6386bo$447bo6387b2o5$624b2o32b2o3b2o$624b2o11b2o20bo3bo$
637bo18b3o5b3o$413b2o186b2o35b3o15bo9bo$413b2o182b2o2b2o37bo$596bobo
6256b2o$596bo6258b2o$595b2o$411b2o$404bo5bobo$403bobo5bo$402bo2bo$403b
2o221b2o$626bo$627b3o$392bo236bo6210b2o$392b3o6445b2o$395bo13bo$394b2o
12bobo$408bobo$409bo15$393b2o$392bobo$393bo8$517b2o$517b2o4$530b2o$
524b2o4b2o$524b2o5$487b2o$487b2o3$508b2o$485b2o22bo$478bo5bobo19b3o$
477bobo5bo20bo$476bo2bo$477b2o5$483bo$482bobo$482bobo$483bo121b2o$605b
2o6210bo$6817b3o$6820bo$6819b2o5$6850b2o$590b2o5953bo304bo$590b2o5952b
obo301bobo$6544b2o260bo37b2o2b2o$6780bo9bo15b3o35b2o$6780b3o5b3o18bo$
467b2o6314bo3bo20b2o11b2o$466bobo6313b2o3b2o32b2o$467bo4$610b2o$610bo$
611b3o$613bo6182b2o52b2o$446b2o6348b2o34b2o16bobo$446bobo6335b2o45bobo
18bo$447bo6335bo2bo44bo20b2o$6778b2o4b2o44b2o4b2o$6777bobo55bobo$6777b
o57bo$6776b2o56b2o7b2o$6786b2o33b2o20b2o$6786bo34bo$6787b3o32b3o$622bo
34bo6131bo34bo$622b3o32b3o$625bo34bo$602b2o20b2o33b2o$602b2o7b2o56b2o
6182b2o$576b2o33bo57bo6183bo$576b2o31bobo55bobo6181bobo$609b2o4b2o44b
2o4b2o6182b2o$593b2o20bo44bo2bo$594bo18bobo45b2o$589b2o3bobo16b2o34b2o
$583b2o4b2o4b2o52b2o6182bo$583b2o6248b3o$6836bo$6835b2o5$624b2o32b2o3b
2o$624b2o11b2o20bo3bo$567b2o68bo18b3o5b3o$568bo32b2o35b3o15bo9bo$565b
3o29b2o2b2o37bo$565bo30bobo6256b2o$596bo6258b2o$595b2o8$6840b2o$630b2o
6208b2o$630bo$631b3o$633bo2567$3791bo$3791b3o$3794bo$3793b2o$3808b2o$
3808bo$3806bobo$3795bo10b2o$3794bobo$3794bobo$3789b2o4bo$3788bobo15b2o
$3788bo17bobo$3787b2o19bo$3808b2o6$3797b2o$3797b2o9$3809b2o$3809bo$
3807bobo$3807b2o8$3820b2o$3820bo$3818bobo$3818b2o$3789b2o15b2o$3788bob
o15b2o$3788bo$3787b2o6$3794bo$3794b3o$3797bo$3775b2o19b2o$3775bo15bo$
3773bobo15b3o$3773b2o19bo$3793b2o3$3752b2o$3752b2o2$3790b2o$3790b2o17b
2o$3809b2o3$3810b2o$3810bo$3797b2o12b3o$3780b2o16bo14bo$3780bo14b3o$
3781b3o11bo$3783bo$3762b2o$3762b2o48$3791bo$3791b3o$3794bo$3793b2o$
3808b2o$3808bo$3806bobo$3795bo10b2o$3794bobo$3794bobo$3789b2o4bo$3788b
obo15b2o$3788bo17bobo$3787b2o19bo$3808b2o6$3797b2o$3797b2o9$3809b2o$
3809bo$3807bobo$3807b2o8$3820b2o$3820bo$3818bobo$3818b2o$3789b2o15b2o$
3788bobo15b2o$3788bo$3787b2o6$3794bo$3794b3o$3797bo$3775b2o19b2o$3775b
o15bo$3773bobo15b3o$3773b2o19bo$3793b2o3$3752b2o$3752b2o2$3790b2o$
3790b2o17b2o$3809b2o3$3810b2o$3810bo$3797b2o12b3o$3780b2o16bo14bo$
3780bo14b3o$3781b3o11bo$3783bo$3762b2o$3762b2o48$3791bo$3791b3o$3794bo
$3793b2o$3808b2o$3808bo$3806bobo$3795bo10b2o$3794bobo$3794bobo$3789b2o
4bo$3788bobo15b2o$3788bo17bobo$3787b2o19bo$3808b2o6$3797b2o$3797b2o9$
3809b2o$3809bo$3807bobo$3807b2o8$3820b2o$3820bo$3818bobo$3818b2o$3789b
2o15b2o$3788bobo15b2o$3788bo$3787b2o6$3794bo$3794b3o$3797bo$3775b2o19b
2o$3775bo15bo$3773bobo15b3o$3773b2o19bo$3793b2o3$3752b2o$3752b2o2$
3790b2o$3790b2o17b2o$3809b2o3$3810b2o$3810bo$3797b2o12b3o$3780b2o16bo
14bo$3780bo14b3o$3781b3o11bo$3783bo$3762b2o$3762b2o37$3527b2o$3527b2o
3$3532b2o$3532b2o6$3791bo$3791b3o$3794bo$3793b2o$3808b2o$3808bo$3806bo
bo$3795bo10b2o$3794bobo$3794bobo$3789b2o4bo$3788bobo15b2o$3788bo17bobo
$3787b2o19bo$3808b2o6$3797b2o$3797b2o9$3809b2o$3809bo$3807bobo$3807b2o
8$3820b2o$3820bo$3818bobo$3818b2o$3789b2o15b2o$3788bobo15b2o$3788bo$
3787b2o6$3794bo$3794b3o$3797bo$3775b2o19b2o$3775bo15bo$3773bobo15b3o$
3773b2o19bo$3793b2o3$3752b2o$3752b2o2$3790b2o$3790b2o17b2o$3809b2o3$
3810b2o$3810bo$3797b2o12b3o$3780b2o16bo14bo$3780bo14b3o$3781b3o11bo$
3783bo$3762b2o$3762b2o1610$5330b2o$5329b2o$5331bo510$5842b2o$5841b2o$
5843bo510$6354b2o$6353b2o$6355bo510$6866b2o$6865b2o$6867bo10891$17760b
o$17759b2o$17759bobo510$18272bo$18271b2o$18271bobo510$18784bo$18783b2o
$18783bobo510$19296bo$19295b2o$19295bobo10817$30114b2o$30113b2o$30115b
o510$30626b2o$30625b2o$30627bo510$31138b2o$31137b2o$31139bo510$31650b
2o$31649b2o$31651bo10857$42508b3o$42508bo$42509bo510$43020b3o$43020bo$
43021bo510$43532b3o$43532bo$43533bo510$44044b3o$44044bo$44045bo!

I cheated on the final signal that turns the UC construction-arm glider streams back off again -- it should really go the long way around the loop, just like everything else.

Short summary:

• A single long stream of gliders enters the loop.
• The gliders circle several times until all four channels are filled.
• A switching system removes the eaters blocking the output circuits.
• Sets of four gliders are sent into circuitry (not shown) that runs two construction arms.
• Complete child copies of the loop are constructed (definitely not shown).
• The switching system replaces the blocking eaters.
• The loop empties out again.
• Copies of the unaltered original recipe are sent in two directions, into the child loops.

The cycle can repeat indefinitely -- or at least until descendants start crashing into each other. But that's another story and will be told another time.

If a single 10hd1armUC turns out to be all that's needed at each corner, so much the better -- we only need half as many reflectors. Or we could send the recipe an extra time around and just use it to repeatedly trigger an INCn shotgun, to push an elbow far, far away.

Effectively we could get, for example, INC(n*GlidersInWholeRecipe/2), at some non-trivial but manageable cost in extra circuitry, and a 50% reduction in replication speed.

[chris_c]

Last thing for tonight: here's a test run for one of the designs I was going on about -- a diamond-shaped replicator loop designed to run two construction arms at each of two corners.

Already looking impressive. After some initial work on this project I have been trying to avoid getting sucked in too far because of just how much work there is to do. Anyway, here is an idea for how the far elbows could be made. I don't know why you want to make this stuff with "one-time turners and splitters", because it seems to me like most (if not all) of this junk could be built directly from the construction arms. Each MWSS has a timing dependence against 2 other gliders but that shouldn't be too hard to deal with if we have 4 arms altogether. (EDIT: Oh sorry, you can probably build from the construction arm for the elbows in the NW but for those in the NE it does look like you will need some frozen seeds)

Code: Select all

x = 288, y = 298, rule = B3/S23
251bo$249bo3bo$248bo$248bo4bo$232b4o12b5o$232bo3bo$232bo26b3o$233bo2bo
22bo$260bo22$285b3o$285bo$286bo2$234b3o$234bo$235bo8$247b3o$247bo$248b
o15$274b4o$274bo3bo$274bo$275bo2bo154$18b2o$18bobo$18bo11$28b2o$28bobo
$28bo21$61b3o$61bo2bo$61bo$61bo$62bobo6$4b3o$4bo2bo$4bo$4bo$5bobo7$22b
2o$22bobo$22bo3$2b3o$bo2bo$4bo$o3bo$4bo$bobo10$40b2o$40bobo$40bo!

When I first looked at this project I had the following design in mind:

Code: Select all

x = 124, y = 203, rule = B3/S23
59bo$58bobo$57bo3bo$56bo5bo$55bo7bo$54bo9bo$53bo11bo$52bo13bo$51bo15bo
$50bo17bo$49bo19bo$48bo21bo$47bo23bo$46bo25bo$45bo27bo$44bo29bo$43bo
31bo$42bo33bo$41bo35bo$40bo37bo$39bo39bo$38bo41bo$37bo43bo$36bo45bo$
35bo47bo$34bo49bo$33bo49bo$32bo49bo$31bo49bo$30bo49bo$29bo49bo$28bo49b
o11bo$27bo49bo11bobo$26bo49bo11bo3bo$25bo49bo11bo5bo$24bo49bo11bo7bo$
23bo49bo11bo9bo$22bo49bo11bo11bo$21bo49bo11bo13bo$20bo49bo11bo15bo$19b
o49bo11bo17bo$18bo49bo11bo19bo$17bo49bo11bo21bo$16bo49bo11bo23bo$15bo
49bo11bo25bo$14bo49bo11bo27bo$13bo49bo11bo29bo$12bo49bo11bo31bo$11bo
49bo11bo33bo$10bo49bo11bo35bo$9bo49bo11bo37bo$8bo49bo11bo39bo$b3o3bo
49bo11bo41bo$o7bo47bo11bo43bo$o8bo45bo11bo45bo$o9bo43bo11bo47bo$o10bo
41bo11bo49bo5b2o$b3o8bo39bo11bo49bo5bo2bo$13bo37bo11bo49bo6bo2bo$14bo
35bo11bo49bo7b4o$15bo33bo11bo49bo8bo2bo$16bo31bo11bo49bo9bo2bo$17bo29b
o11bo49bo$18bo27bo11bo49bo$19bo25bo11bo49bo$20bo23bo11bo49bo$21bo21bo
11bo49bo$22bo19bo11bo49bo$23bo17bo11bo49bo$24bo15bo11bo49bo$25bo13bo
11bo49bo$26bo11bo11bo49bo$27bo9bo11bo49bo$28bo7bo11bo49bo$29bo5bo11bo
49bo$30bo3bo11bo49bo$31bobo11bo49bo$32bo11bo49bo$43bo49bo$42bo49bo$41b
o49bo$40bo49bo$39bo49bo$38bo49bo$28b3o8bo47bo$28bo2bo8bo45bo$28bo2bo9b
o43bo$28b3o11bo41bo$28bo2bo11bo39bo$28bo2bo12bo37bo$28b3o14bo35bo$46bo
33bo$47bo31bo$48bo29bo$49bo27bo$50bo25bo$51bo23bo$52bo21bo$53bo19bo$
54bo17bo$55bo15bo$56bo13bo$57bo11bo$58bo9bo$59bo7bo$60bo5bo$61bo3bo$
62bobo$63bo9$58b3o9b3o$58b2o11b2o$58bobo9bobo$61bo7bo$62bo5bo$63bo3bo
3$65bo$64bobo$63bo3bo$62bo5bo$61bo7bo$60bo9bo$59bo11bo$58bo13bo$57bo
15bo$56bo17bo$55bo19bo$54bo21bo$53bo23bo$52bo25bo$51bo27bo$50bo29bo$
49bo31bo$48bo33bo$47bo35bo$46bo37bo$45bo39bo$44bo41bo$43bo43bo$42bo45b
o$41bo47bo$40bo49bo$39bo49bo$38bo49bo$37bo49bo$36bo49bo$35bo49bo$34bo
49bo$33bo49bo$32bo49bo$31bo49bo$30bo49bo$29bo49bo$28bo49bo$27bo49bo$
26bo49bo$25bo49bo$24bo49bo$23bo49bo$22bo49bo$21bo49bo$20bo49bo$19bo49b
o$18bo49bo$17bo49bo$16bo49bo$15bo49bo$14bo49bo$13bo49bo$14bo47bo$15bo
45bo$16bo43bo$17bo41bo$18bo39bo$19bo37bo$20bo35bo$21bo33bo$22bo31bo$
23bo29bo$24bo27bo$25bo25bo$26bo23bo$27bo21bo$28bo19bo$29bo17bo$30bo15b
o$31bo13bo$32bo11bo$33bo9bo$34bo7bo$35bo5bo$36bo3bo$37bobo$38bo!

There is just a single two arm constructor where the two small arrows point. Elbows at points A, B and C would be constructed by crashing a gliders into the back of Corderships. The glider loops are in proportion 2:1 so if the long side of the glider loop is increased by X then the length of the tape would increase by 3*X. This extra length should allow the Corderships to escape by a further 1.5 * X and so eventually there should be an X big enough so that the construction will work. I have no idea how this design would duplicate its tape --- that's what made me give up.

I did however, design the following 3 glider Cordership seed which looks fairly easy to build (the G + 2 Boat -> switch engine reaction does not appear in the Making Switch engines thread so maybe it is new?)

Code: Select all

x = 66, y = 77, rule = B3/S23
64bo$63bo$63b3o19$37bo$36bobo$37b2o$56bobo$56b2o$37bo19bo$36bobo$37b2o
12$55b2o$55b2o3$30bo$29bobo$30b2o3$30bo$29bobo$30b2o5$10bo4bo$9bobo2bo
bo$10b2o3b2o13$b2o$obo$2bo2$28b2o$28b2o!

[dvgrn]

I did however, design the following 3 glider Cordership seed which looks fairly easy to build (the G + 2 Boat -> switch engine reaction does not appear in the Making Switch engines thread so maybe it is new?)

New to me, anyway -- and very elegant indeed! I had no idea that it was possible to synchronize so few gliders and end up with a viable Cordership. Suddenly Cordership leaders and glider chasers don't seem so obviously impractical after all.

Here's an upper bound for the number of still lifes needed for a Cordership seed. 43 boats is very serious overkill, as a close inspection will show. The only splitters and turners used are ones that I could find in five minutes or less with the Seeds of Destruction Game... this is, shall we say, not exactly the last word in inexpensive OTTechnology. We should probably be looking for a seed constellation with no more than about 30 still lifes.

Code: Select all

#C 43 boats + 1 glider = Cordership!
#C Base synthesis by Chris Cain, 9 March 2015.
#C Dave Greene had nothing to do with adding all the other silly boats.
x = 148, y = 165, rule = B3/S23
134bo$133bobo$133b2o3$145b2o$145bobo$146bo36$98b2o$97bobo$98bo8$104bo
9bo$103bobo7bobo$103b2o9b2o$80bo$79bobo$80b2o2$100bo$80bo18bobo$79bobo
17b2o$80b2o8$124b2o16bo$109b2o13bobo14bobo$77bo30bobo14bo16b2o$76bobo
30bo$76b2o53b2o$131bobo$132bo2$73bo33b2o$72bobo32bobo$73b2o33bo$101b2o
$100bobo$73bo18b2o7bo$72bobo16bobo38bo$73b2o17bo38bobo$66b2o63b2o$65bo
bo$66bo2$53bo4bo$52bobo2bobo41bo16b2o$53b2o3b2o40bobo14bobo$92bo8b2o
15bo$91bobo$92b2o$66bo$65bobo$66b2o35b2o9b2o$103bobo7bobo$73bo30bo9bo$
72bobo$29bo16b2o25b2o$28bobo14bobo$28b2o16bo$143bo$39b2o101bobo$38bobo
101b2o$39bo79b2o$118bobo$119bo6$39bo84b2o$38bobo83bobo$39b2o84bo3$47b
2o9b2o7bo$47bobo7bobo6bobo$48bo9bo7b2o6$99bo$98bobo10b2o$98b2o11bobo$
111bo2$86b2o$86bobo$87bo4$b2o$obo$bo19$14b2o$14bobo$15bo!
#C [[ AUTOSTART THUMBNAIL THEME 4 ZOOM 2.7 LOOP 1600 ]]

[chris_c]

We should probably be looking for a seed constellation with no more than about 30 still lifes.

Here is a two-glider seed that should be really easy to make with a two arm constructor. The glider splitter was found by trawling simsim's collection; the reflector from blockish-and-blockic-seeds.rle in Golly. Also shown is a possible route for the Cordership destruction. Almost certainly the boat that appears in the junk can be made into an elbow. After that I imagine that all the junk can be deleted in at most 10 orthogonal glider pairs.

Code: Select all

x = 381, y = 429, rule = LifeHistory
89.2C$85.2C2.2C$85.2C4$77.2C$77.2C$88.2C$88.C.C$84.2C3.C.C$83.C.C4.C$
84.C$67.C$66.C.C$67.2C3$67.C$66.C.C$67.2C12$85.2C$85.2C3$60.C50.3A$
59.C.C49.A$60.2C50.A3$60.C$59.C.C$60.2C5$40.C4.C$39.C.C2.C.C$40.2C3.
2C17$58.2C$58.2C25$.2A$A.A$2.A130$221.2A$221.A.A$221.A166$348.3A$348.
A$349.A13$363.3A$363.A$364.A13$378.3A$378.A$379.A$372.2A$371.2A$373.A
!

[dvgrn]

We should probably be looking for a seed constellation with no more than about 30 still lifes.

Here is a two-glider seed that should be really easy to make with a two arm constructor.

Good gravy. It's fairly trivial even with a 1armUC -- down to 18 still lifes plus a glider, never mind my guess of 30sL, with a little more help from simsim314's splitter collection. It had kind of slipped my mind how good that collection was.

Code: Select all

x = 63, y = 67, rule = B3/S23
52b2o$48b2o2b2o$48b2o4$40b2o$40b2o$51b2o$34bo16bobo$33bobo11b2o3bobo$
34b2o10bobo4bo$47bo$60b2o$34bo25bobo$33bobo25bo$34b2o12$52b2o$52b2o3$
27bo11bo$26bobo9bobo$27b2o9b2o3$27bo4b2o$26bobo3bobo$27b2o4bo5$7bo4bo$
6bobo2bobo$7b2o3b2o4$50b3o$2o48bo$obo48bo$bobo$2bo9$15b2o8b2o$15bobo7b
2o$17bo$17b2o!
#C [[ AUTOSTART LOOP 900 ZOOM 5.4 THUMBNAIL ]]

There might even be an 18sL solution that's all boats, but it's silly to waste time on that I suppose. I also unnecessarily used up a lot of boats on the problem of cleaning up the trivial junk at the back, when of course it's much cheaper to take care of that by shooting it down directly with the construction arm after the seed is triggered.

I'll be curious to see if someone can find a cleaner chaser for the Cordership. What's the smallest amount of leftover junk if we allow two-glider synchronized salvos, for example?

[dvgrn]

Last thing for tonight: here's a test run for one of the designs I was going on about -- a diamond-shaped replicator loop designed to run two construction arms at each of two corners.

Already looking impressive...

Yes, but is it the right design? Now I'm thinking that this setup is probably better:

Code: Select all

#C paired-glider diamond Geminoid
x = 11465, y = 14538, rule = B3/S23
3312b2o$3308b2o2b2o$3308b2o4$3300b2o$3300b2o$3311b2o$3294bo16bobo$
3293bobo11b2o3bobo$3294b2o10bobo4bo$3307bo$3320b2o$3294bo25bobo$3293bo
bo25bo$3294b2o12$3312b2o$3312b2o3$3287bo11bo$3286bobo9bobo$3287b2o9b2o
3$3287bo4b2o$3286bobo3bobo$3287b2o4bo$3323bo$3322bobo$3322b2o2$3267bo
4bo$3266bobo2bobo$3267b2o3b2o4$3339b2o$3260b2o77bobo$3260bobo77bo$
3261bobo$3262bo9$3275b2o8b2o$3275bobo7b2o$3277bo$3277b2o6$3341b2o$
3341bobo$3342bo3$3295b2o$3295bobo$3296bo20$3285bo$3284bobo$3285bobo$
3286b2o3$3280bo$3279bobo$3280b2o7$3248b2o$3249bo$3249bobo$3250b2o8$
3266b2o$3266b2o6$3260b2o$3260b2o2$3269b2o$3268bobo$3269bo$3261b2o$
3261b2o33b2o$3296b2o2$3264bo$3262b3o$3246bo14bo$3246b3o12b2o$3249bo$
3248b2o3$3249b2o$3249b2o17b2o$3268b2o2$3306b2o$3306b2o3$3265b2o$3265bo
19b2o$3266b3o15bobo$3268bo15bo$3262b2o19b2o$3262bo$3263b3o$3265bo6$
3271b2o$3271bo$3252b2o15bobo$3252b2o15b2o$3240b2o$3239bobo$3239bo$
3238b2o8$3251b2o$3250bobo$3250bo$3249b2o9$3261b2o$3261b2o6$3250b2o$
3251bo19b2o$3251bobo17bo$3252b2o15bobo$3264bo4b2o$3263bobo$3263bobo$
3252b2o10bo$3251bobo$3251bo$3250b2o$3265b2o$3265bo$3266b3o$3268bo65$
3230bo$3229bobo$3230b2o2915$73bo$52b2o18bobo$52bobo17b2o6303bo$53bobo
6320bobo$54bo6321b2o7$39bo$39b3o$42bo$41b2o7$14bo$13bobo$13b2o6$10bo$
2o7bobo16b2o$2o6bobo17b2o$8b2o2$b2o$b2o7b2o$10bobo141b2o$11bo142b2o
6210bo$6366b3o$79bo6289bo$77b3o6288b2o$76bo$6b2o68b2o$6b2o25bo$32bobo$
33b2o6364b2o$139b2o6258bo$139b2o6256bobo$10b2o3b2o6338bo37b2o2b2o$9bob
o2bobo21bo6290bo9bo15b3o35b2o$10bo4bo21bobo6289b3o5b3o18bo$37b2o6293bo
3bo20b2o11b2o$6331b2o3b2o32b2o3$33b2o3b2o$32bobo2bobo61b2o$33bo4bo24b
2o35bobo56b2o$63b2o34bobo57bo$100bo59b3o$162bo6182b2o52b2o$6345b2o34b
2o16bobo$106b2o6225b2o45bobo18bo$105bobo6224bo2bo44bo20b2o$106bo6220b
2o4b2o44b2o4b2o$66bo6259bobo55bobo$64b3o6259bo57bo$63bo6261b2o56b2o7b
2o$63b2o6270b2o33b2o20b2o$6335bo34bo$45b2o6289b3o32b3o$44bobo124bo34bo
6131bo34bo$45bo125b3o32b3o$135b2o37bo34bo$135bobo13b2o20b2o33b2o$45b2o
89bo14b2o7b2o56b2o6182b2o$44bobo78b2o33bo57bo6183bo$45bo79b2o31bobo55b
obo6181bobo$158b2o4b2o44b2o4b2o26b2o5972bo181b2o$142b2o20bo44bo2bo31b
2o5971bobo$53bo89bo18bobo45b2o6005b2o$52bobo83b2o3bobo16b2o34b2o$51bob
o78b2o4b2o4b2o52b2o39b2o6141bo$51b2o79b2o105b2o6141b3o$6385bo$6384b2o
5$173b2o32b2o3b2o18bo$173b2o11b2o20bo3bo18bobo14bo$116b2o68bo18b3o5b3o
16b2o13bobo$117bo32b2o35b3o15bo9bo31bo2bo$114b3o29b2o2b2o37bo58b2o$
114bo30bobo6256b2o$145bo6258b2o$144b2o94b2o$239bo2bo$240b2o8bo$249bobo
$250b2o4$6389b2o$6389b2o19$198b2o$197bobo$198bo3$203b2o$203bo$204b3o$
206bo2975$3263b2o$3263bobo$3264bo14$3276bo$3276b3o$3279bo$3154b2o122b
2o$3154b2o137b2o$3293bo$3291bobo$3159b2o119bo10b2o$3159b2o118bobo$
3279bobo$3274b2o4bo$3273bobo15b2o$3273bo17bobo$3272b2o19bo$3293b2o6$
3282b2o$3282b2o9$3294b2o$3294bo$3292bobo$3292b2o8$3305b2o$3305bo$3303b
obo$3303b2o$3274b2o15b2o$3273bobo15b2o$3273bo$3272b2o6$3279bo$3279b3o$
3282bo$3260b2o19b2o$3260bo15bo$3258bobo15b3o$3258b2o19bo$3278b2o3$
3237b2o$3237b2o2$3275b2o$3275b2o17b2o$3294b2o3$3295b2o$3295bo$3282b2o
12b3o$3265b2o16bo14bo$3265bo14b3o$3266b3o11bo$3268bo$3247b2o$3247b2o
1546$4879b2o$4878b2o$4880bo510$5391b2o$5390b2o$5392bo1510$6903b2o$
6902b2o$6904bo510$7415b2o$7414b2o$7416bo1510$8927b2o$8926b2o$8928bo
510$9439b2o$9438b2o$9440bo1510$10951b2o$10950b2o$10952bo510$11463b2o$
11462b2o$11464bo!

I threw in a couple of Cordership launches with the appropriate chasers this time too, because it's so easy now. It's very gratifying to watch the whole thing in action...!

Here again, the incoming construction data stream is duplicated and sent in two directions, and then the loop shuts down. This time it's just a single loop, so the data stream goes around the exact same circuits twice -- very efficient in terms of still-life count. The recipe could cycle three or more times just as easily if we wanted the Cordership to get farther away, but really it looks as if this might be plenty far enough already.

Let's call this the "paired-glider" diamond Geminoid design, where two or four channels of data are sent in parallel, encoded in a single glider stream. The previous design required four channels to be sent in series, one after another on the same stream, which means it's much slower to populate a new diamond with a recipe. At least that's true for the two-arm four-channel design; if there's only one arm it ends up about the same.

There are really only two nice things about that four-times-around serial-channel design. It allows the use of 10hd recipes with singleton gliders, which is a little more efficient. And we don't need to send NOP signals to Arm#2 when only Arm#1 is running, or vice versa.

With construction arm gliders coming in in pairs, or groups of four, all the signal crossing problems can be made to go away. It doesn't matter if we end up with one arm at each corner or two -- we can decode four channels just as easily as two, at the cost of a few more semi-Snarks.

But we can't use 10hd recipes with singleton gliders with this design -- at least, not without figuring out a way of encoding them as special cases, which will almost certainly take extra circuitry.

Now, we can hook these glider pairs up to armless UCs, where we have perfectly good efficient recipes with paired gliders and don't need singletons. Are armless UCs efficient enough to use for the entire construction process?

Seems as if, if we had a NW-facing and a NE-facing armless UC, each pointing to a faraway busted-up Cordership, we could build a child loop to the north: the child's N corner would be constructed first, via slow-elbow collaboration between the two armless UCs. Then the E and W corners would each be built by one armless UC, at the Cordership crash sites. And the S corner would be back home near the two armless UCs.

That makes for a different diagram than the original one I posted, I guess -- no G+*WSS collisions needed, just the Cordership launch-and-chase. Green for the parent loop, white for the child loops, red for the armless UC locations, blue for the Cordership crash sites:

Code: Select all

#C [[ VIEWONLY ZOOM 1.5 ]]
x = 295, y = 295, rule = LifeHistory
70.3D6.3D$71.2D6.2D$70.D.D6.D.D$69.D12.D$68.D14.D$67.D8.C7.D$66.D6.C
11.D$78.C$71.C$80.C$69.C$82.C$67.C$84.C$65.C$86.C$63.C$88.C$61.C$90.C
$59.C$92.C$57.C$94.C$55.C$96.C$53.C$98.C$51.C$100.C$39.C.C.C.C.C.C$
102.C$47.C.C$104.C$45.C3.C$106.C$43.C5.C$108.C9.C$41.C7.C$110.C7.C$
39.C9.C$112.C5.C$37.C$114.C3.C$35.C$116.C.C$33.C$108.C.C.C.C.C.C$31.C
$120.C$29.C$122.C$27.C$124.C$25.C$16.3D107.C6.3D$17.2D4.C109.2D$16.D.
D109.C4.D.D$15.D5.C114.D$14.D115.C6.D$13.D5.C118.D$12.D119.C6.D$17.C$
134.C$15.C$136.C$13.C126.6B$138.C8B$3.6B2.C126.10B$2.8B127.3BC8B$.8BC
B126.12B$12B125.5BC6B$7BC4B125.7B2A3B$3B2A7B125.7B2A3B$3B2A7B125.4BC
7B$6BC5B125.12B$12B126.BC8B$8BC3B127.8B$.10B126.C2.6B$2.8BC$3.6B126.C
$12.C$133.C$14.C$131.C$16.C$129.C$18.C$127.C$20.C$125.C$22.C$123.C$
24.C$121.C$26.C$119.C$28.C$117.C$30.C.C.C.C.C.C$115.C$30.C.C$113.C$
30.C3.C$111.C$30.C5.C$99.C9.C$30.C7.C$99.C7.C$30.C9.C$99.C5.C$42.C$
99.C3.C$44.C$99.C.C$46.C$99.C.C.C.C.C.C$48.C31.3D$65.3D13.2D14.C$50.C
14.2D13.D.D$65.D.D11.D3.3D9.C$52.C9.3D3.D9.D5.2D$62.2D5.D7.D5.D.D7.C$
54.C7.D.D5.D5.D5.D3.3D$59.3D3.D5.D9.D5.2D2.C$56.C2.2D5.D13.D5.D.D$59.
D.D5.D11.D5.D3.C$58.C3.D5.D15.D5.3D$55.3D5.D19.D3.C3.2D$55.2D3.C3.D
17.D7.D.D$55.D.D7.D19.C3.D3.3D$52.3D3.D3.C25.D5.2D$52.2D5.D23.C3.D5.D
.D42.B$52.D.D5.D3.C21.D5.D3.3D$49.3D3.D5.D19.C9.D5.2D$49.2D5.D9.C23.D
5.D.D$49.D.D5.D21.C9.D5.D$52.D5.D9.C25.D$53.D23.C15.D$54.D15.C21.D$
55.D19.C$72.C5$217.7B$216.9B$215.11B$214.6B2A5B$214.6B2A5B$214.13B$
214.5BC7B$73.A.A138.8BC4B$72.A3.A137.3BC9B$71.A5.A137.9BCB$70.A7.A
136.C9B$69.A9.A137.7B2.C$68.A11.A132.C19.D$67.A13.A146.C5.D$66.A15.A
128.C23.D$65.A17.A146.C5.D$64.A19.A124.C27.D.D$63.A21.A146.C5.2D$62.A
23.A120.C29.3D$61.A25.A146.C$60.A27.A116.C$59.A29.A146.C$58.A31.A112.
C$57.A33.A146.C$56.A35.A108.C$55.A37.A146.C$54.A39.A104.C$53.A41.A
146.C$52.A43.A100.C$51.A45.A146.C$50.A47.A86.C.C.C.C.C.C$49.A49.A146.
C$48.A51.A92.C.C$47.A53.A146.C$46.A55.A88.C3.C$45.A57.A146.C$44.A59.A
84.C5.C$43.A61.A4.A141.C$37.6A63.A3.A76.C7.C$41.2A64.A2.A143.C9.C$40.
A.A65.A.A74.C9.C$39.A2.A66.2A145.C7.C$38.A3.A62.6A72.C$37.A4.A68.A
146.C5.C$36.A75.A68.C$35.A77.A146.C3.C$34.A79.A64.C$33.A81.A146.C.C$
32.A83.A60.C$31.A85.A40.3D93.C.C.C.C.C.C$30.A87.A40.2D14.C$29.A89.A
38.D.D105.C$28.A91.A36.D3.3D9.C$27.A93.A34.D5.2D104.C$26.A95.A32.D5.D
.D7.C$25.A97.A30.D5.D3.3D103.C$24.A99.A34.D5.2D2.C$23.A101.A32.D5.D.D
105.C$22.A103.A30.D5.D3.C$21.A105.A34.D5.3D103.C$20.A107.A32.D3.C3.2D
$19.A109.A30.D7.D.D105.C$18.A111.A32.C3.D3.3D$17.A113.A34.D5.2D104.C$
16.A115.A28.C3.D5.D.D$15.A117.A30.D5.D3.3D103.C$14.A119.A24.C9.D5.2D
111.D$13.A121.A32.D5.D.D105.C6.D$12.A123.A20.C9.D5.D116.D$11.A125.A
34.D111.C6.D$10.A127.A16.C15.D120.D.D$9.A129.A30.D115.C6.2D$8.A131.A
12.C138.3D$7.A133.A146.C$6.A$7.A133.A12.C$8.A131.A30.D117.C$9.A129.A
16.C15.D$10.A127.A34.D113.C$11.A125.A20.C9.D5.D117.3D$12.A123.A32.D5.
D.D107.C7.2D$13.A121.A24.C9.D5.2D114.D.D$14.A119.A30.D5.D3.3D105.C7.D
$15.A117.A28.C3.D5.D.D115.D$16.A115.A34.D5.2D106.C7.D$17.A113.A32.C3.
D3.3D113.D$18.A111.A30.D7.D.D107.C$19.A109.A32.D3.C3.2D$20.A107.A34.D
5.3D105.C$21.A105.A30.D5.D3.C$22.A103.A32.D5.D.D107.C$23.A101.A34.D5.
2D2.C$24.A99.A30.D5.D3.3D105.C$25.A97.A32.D5.D.D7.C$26.A95.A34.D5.2D
106.C$27.A93.A36.D3.3D9.C$28.A91.A38.D.D107.C$29.A89.A40.2D14.C$30.A
87.A40.3D105.C$31.A85.A60.C.C.C.C.C.C$32.A83.A148.C$33.A81.A62.C.C$
34.A79.A148.C$35.A77.A64.C3.C$36.A75.A148.C$37.A68.A4.A66.C5.C$38.6A
62.A3.A148.C$38.2A66.A2.A68.C7.C$38.A.A65.A.A138.C9.C$38.A2.A64.2A70.
C9.C$38.A3.A63.6A135.C7.C$38.A4.A61.A84.C$44.A59.A142.C5.C$45.A57.A
88.C$46.A55.A144.C3.C$47.A53.A92.C$48.A51.A146.C.C$49.A49.A96.C$50.A
47.A148.C.C.C.C.C.C$51.A45.A100.C$52.A43.A148.C$53.A41.A104.C$54.A39.
A148.C$55.A37.A108.C$56.A35.A148.C$57.A33.A112.C$58.A31.A148.C$59.A
29.A116.C$60.A27.A148.C$61.A25.A120.C$62.A23.A148.C$63.A21.A124.C$64.
A19.A148.C$65.A17.A128.C24.3D$66.A15.A148.C6.2D$67.A13.A132.C22.D.D$
68.A11.A148.C6.D$69.A9.A136.C2.7B9.D$70.A7.A83.B55.9BC6.D$71.A5.A139.
BC9B5.D$72.A3.A139.9BC3B$73.A.A140.4BC8B$216.7BC5B$216.13B$216.5B2A6B
$216.5B2A6B$217.11B$218.9B$219.7B!

I'm not really good at thinking about these armless UCs yet, though. Better ideas are out there, no doubt...!

[dvgrn]

I really like the 18sL Cordership seed, but between the creation and the cleanup it's quite a bit of trouble. Still seems like the original blueprint will probably be more efficient. Here's a start at converting chris_c's multi-*WSS+G pattern into two fairly reasonable seeds:

Code: Select all

x = 426, y = 442, rule = LifeHistory
251.2A$251.2A37.2A$284.2A4.2A$245.2A37.2A$245.2A4$284.2A$284.2A$295.
2A$295.A$296.3A$298.A$253.2A$253.2A5$281.2A$281.A.A$282.A.A$283.A3$
276.2A$276.A.A$277.A3$267.2A$266.A.A$267.A103$372.3A$372.A$373.A31$
423.2A$423.A.A$423.A26$398.2A$398.A.A$398.A8$411.2A$411.A.A$411.A68$
3.2A$3.2A5$2A$2A$14.2A$14.2A12$32.A$31.A.A$31.2A8$26.2A$26.A.A$27.A3$
20.2A$20.A.A$21.A.A$2.2A4.2A12.A$2.2A4.2A5$.2A$.2A4$10.2A$10.A.A$12.A
$12.2A52$181.3A$181.A$182.A11$191.3A$191.A$192.A7$136.2A$136.A.A$136.
A33$185.3A$185.A$186.A!

I've left out the near-corner elbow and target for now. They have to be built much later anyway, so they don't get in the way. And I agree that those final glider and LWSS can be built one at a time, directly by the construction arms in the west and north.

It seems to make sense to build the two groups of three gliders and two *WSS with a stable seed, though, since they all have to get started at the same time. Am I missing anything obvious here?

The trigger signals for the two seeds will be a quarter-diamond away from each other in the recipe stream, no doubt leaving a huge gap. But that still leaves plenty of room to fit the whole construction recipe in the loop -- these corners can move as far as they need to away from each other with no extra cost.

[chris_c]

Here's a start at converting chris_c's multi-*WSS+G pattern into two fairly reasonable seeds

Just a few random points:

1. This might be a slightly cheaper way of making the LWSS + MWSS:

Code: Select all

x = 44, y = 97, rule = B3/S23
29b2o$6b2o21b2o$6b2o2$2o$2o$36b2o$18bo17b2o$17bobo$17b2o3$30b2o$30b2o
2$8b2o26b2o$8b2o12b2o12b2o$21bo2bo$21bobo$22bo18$35b3o$35bo$36bo41$30b
2o$29b2o$31bo12$42bo$41b2o$41bobo!

2. ... but do we really want to make the LWSS and the MWSS with a single glider anyway? The LWSS+G collision has no timing dependence with respect to the MWSS + 2G but constructing the LWSS and MWSS together will make all 5 objects timing dependent. What I'm trying to say is use timed gliders from the instruction tape wherever possible.

3. It is surely possible to lay some kind of elbow at the near points at the same time as making the 90 degree *WSS turn. Here is one example:

Code: Select all

x = 79, y = 55, rule = B3/S23
76b2o$76bobo$76bo5$54b5o$54bo4bo$31b2o21bo$30b4o21bo3bo$29b2ob2o23bo$
30b2o25$2o$obo$o13$18b3o$18bo$19bo!

I'm a bit hazy on the requirements for the elbows. Do they need to be precisely on a particular lane or can they be any old junk in a rough area?

[dvgrn]

... but do we really want to make the LWSS and the MWSS with a single glider anyway? The LWSS+G collision has no timing dependence with respect to the MWSS + 2G but constructing the LWSS and MWSS together will make all 5 objects timing dependent.

You're right, of course. Sometimes it takes me a while to absorb good new ideas, and the two *WSSes are close enough together that they looked like a salvo -- I actually never ran the pattern slow enough to see that they were timing-independent.

That really seems to make the *WSS+G method an easy win over the Cordership launch-and-chase. The only timing requirement is to synchronize the MWSS construction with the final glider from each corner -- just a matter of building a very slow MWSS seed, and then firing the last glider straight from the construction arm. Easy!

It is surely possible to lay some kind of elbow at the near points at the same time as making the 90 degree *WSS turn.
...
I'm a bit hazy on the requirements for the elbows. Do they need to be precisely on a particular lane or can they be any old junk in a rough area?

This is the haziest remaining piece of this design, actually. The answer will be clear as soon as the decision is made about exactly what kind of constructors are sitting at the corners of the diamond. For now let's assume we're talking about the first diagram in this thread, the one that needs the *WSS+G trick.

Do we put just one armless UC at each corner, like so?

Code: Select all

#C [[ VIEWONLY WIDTH 640 ZOOM 1.5 ]]
x = 444, y = 308, rule = LifeHistory
67.3C$68.2C$67.C.C$66.C3.3C$65.C5.2C$64.C5.C.C$63.C5.C3.3C$68.C5.2C$
67.C5.C.C$66.C5.C$71.C5.3C$70.C7.2C$69.C7.C.C$76.C3.3C$75.C5.2C$74.C
5.C.C$73.C5.C3.3C$78.C5.2C$77.C5.C.C$76.C5.C5.C$81.C3.C$80.C9.C$79.C
3.C$92.C$81.C$94.C239.3C$79.C255.2C$96.C237.C.C$77.C255.C3.3C$98.C
233.C5.2C$75.C255.C5.C.C6.2A$100.C229.C5.C3.3C3.2A$73.C261.C5.2C$102.
C231.C5.C.C$71.C261.C5.C$104.C233.C5.3C$69.C267.C7.2C$106.C229.C7.C.C
$67.C275.C3.3C$108.C233.C5.2C$65.C275.C5.C.C$110.C229.C5.C3.3C$63.C
281.C5.2C$112.C231.C5.C.C.C$51.C.C.C.C.C.C281.C5.C7.C$114.C233.C3.C$
59.C.C285.C11.C$116.C229.C3.C$57.C3.C299.C$118.C229.C$55.C5.C301.C$
120.C9.C215.C$53.C7.C303.C$122.C7.C213.C$51.C9.C305.C$124.C5.C211.C$
49.C319.C$126.C3.C209.C$47.C323.C$128.C.C207.C$45.C327.C$120.C.C.C.C.
C.C205.C$43.C331.C$132.C35.C165.C$41.C127.C207.C$134.C35.C161.C$39.C
125.C5.C207.C$136.C29.C5.C.C145.C.C.C.C.C.C$37.C129.C5.2C206.C$138.C
23.C5.C3.3C153.C.C$35.C127.C5.C.C211.C$140.C23.C5.2C154.C3.C$33.C131.
C3.3C213.C$142.C15.C7.C.C155.C5.C$31.C127.C7.2C218.C$144.C15.C5.3C
153.C7.C$29.C125.C5.C227.C9.C$146.C9.C5.C.C155.C9.C$27.C129.C5.2C226.
C7.C$148.C3.C5.C3.3C3.2A148.C$25.C127.C5.C.C6.2A223.C5.C$150.C3.C5.2C
154.C$23.C131.C3.3C233.C3.C$152.C3.C.C155.C$21.C135.2C238.C.C$154.C.
3C153.C$19.C369.C.C.C.C.C.C$310.C$153.C247.C35.C$18.C289.C129.C$151.C
251.C35.C$16.3C.C285.C127.C5.C$16.2C131.C255.C29.C5.C.C$16.C.C3.C281.
C131.C5.2C$13.3C3.C127.C259.C23.C5.C3.3C$13.2C5.C3.C277.C129.C5.C.C$
5.2A6.C.C5.C123.C263.C23.C5.2C$5.2A3.3C3.C5.C3.C273.C133.C3.3C$10.2C
5.C125.C267.C15.C7.C.C$10.C.C5.C9.C269.C129.C7.2C$13.C5.C121.C271.C
15.C5.3C$6.3C5.C15.C265.C127.C5.C$6.2C7.C123.C145.4C126.C9.C5.C.C$6.C
.C7.C15.C254.2C5.C131.C5.2C$3.3C3.C127.C148.C.C128.C3.C5.C3.3C$3.2C5.
C23.C250.C2.C3.C129.C5.C.C$3.C.C5.C123.C148.C134.C3.C5.2C$3C3.C5.C23.
C246.C6.C133.C3.3C$2C5.C125.C149.C137.C3.C.C$C.C5.C29.C244.C4.C137.2C
$3.C5.C121.C151.C.2A136.C.3C$4.C35.C242.C.2A$5.C123.C153.C5.C$6.C35.C
.C.C.C.C.C230.C140.C$127.C156.C6.C$42.C.C240.C136.C$125.C160.C6.C$42.
C3.C240.C132.C$123.C164.C6.C$42.C5.C369.C$111.C9.C175.C$42.C7.C365.C$
111.C7.C179.C$42.C9.C361.C$111.C5.C183.C$54.C357.C$111.C3.C187.C$56.C
353.C$111.C.C191.C$58.C349.C$111.C.C.C.C.C.C185.C$60.C345.C$109.C199.
C$62.C341.C$107.C203.C$64.C337.C$105.C207.C.C.C.C.C.C$66.C333.C$103.C
209.C.C$68.C329.C$101.C211.C3.C$70.C325.C$99.C213.C5.C$72.C321.C$97.C
215.C7.C$74.C307.C9.C$95.C54.B162.C9.C$76.C305.C7.C$93.C95.3D133.C$
78.C111.2D190.C5.C$91.C97.D.D135.C$80.C107.D3.3D187.C3.C$89.C97.D5.2D
134.C$82.C103.D5.D.D187.C.C$87.C97.D5.D3.3D133.C$77.4C3.C8.C96.D5.2D
184.C.C.C.C.C.C$77.2C13.C96.D5.D.D135.C$77.C.C5.2A4.C96.D5.D185.C$77.
C2.C4.2A3.C102.D5.3D133.C$81.C7.C102.D7.2D176.C$82.7C102.D7.D.D135.C$
198.D3.3D171.C$197.D5.2D134.C$196.D5.D.D169.C$195.D5.D3.3D133.C$200.D
5.2D164.C$199.D5.D.D.A133.C$198.D5.D3.A.A159.C$203.D3.A3.A133.C$202.D
3.A5.A155.C$201.D3.A7.A133.C$204.A9.A151.C$203.A11.A133.C$202.A13.A
147.C$201.A15.A133.C$200.A17.A78.B64.C$199.A19.A133.C$198.A21.A139.C
3.C$197.A23.A133.C7.C$196.A25.A135.C3.C$195.A27.A137.C5.C$194.A29.A
131.2AC.C5.C$193.A31.A130.2A2C5.C$192.A33.A131.3C3.C5.C$191.A35.A133.
C.C5.C$190.A37.A132.2C5.C$189.A39.A131.3C3.C$188.A41.A133.C.C7.C$187.
A43.A132.2C7.C$186.A45.A131.3C5.C$185.A47.A137.C5.C$184.A49.A133.C.C
5.C$183.A51.A132.2C5.C$182.A53.A131.3C3.C5.C$181.A55.A133.C.C5.C$180.
A57.A132.2C5.C$179.A59.A131.3C3.C$178.A61.A4.A128.C.C$172.6A63.A3.A
128.2C$176.2A64.A2.A128.3C$175.A.A65.A.A$174.A2.A66.2A$173.A3.A62.6A$
172.A4.A68.A$171.A75.A$170.A77.A$169.A79.A$168.A81.A$167.A83.A$166.A
85.A$165.A87.A35.D$164.A89.A35.D$163.A91.A35.D$162.A93.A29.D5.D$161.A
95.A29.D5.D.D$160.A97.A29.D5.2D$159.A99.A23.D5.D3.3D$158.A101.A23.D5.
D.D$157.A103.A23.D5.2D$156.A105.A23.D3.3D$155.A107.A15.D7.D.D$154.A
109.A15.D7.2D$153.A111.A15.D5.3D$152.A113.A9.D5.D$151.A115.A9.D5.D.D$
150.A117.A9.D5.2D$149.A119.A3.D5.D3.3D$148.A121.A3.D5.D.D$147.A123.A
3.D5.2D$146.A125.A3.D3.3D$145.A127.A3.D.D$144.A129.A3.2D$143.A131.A.
3D$142.A133.A$141.A135.A$142.A133.A$139.3D.A131.A$139.2D3.A129.A$139.
D.D3.A127.A$136.3D3.D3.A125.A$136.2D5.D3.A123.A$136.D.D5.D3.A121.A$
133.3D3.D5.D3.A119.A$133.2D5.D9.A117.A$133.D.D5.D9.A115.A$136.D5.D9.A
113.A$129.3D5.D15.A111.A$129.2D7.D15.A109.A$129.D.D7.D15.A107.A$126.
3D3.D23.A105.A$126.2D5.D23.A103.A$126.D.D5.D23.A101.A$123.3D3.D5.D23.
A99.A$123.2D5.D29.A97.A$123.D.D5.D29.A95.A$126.D5.D29.A93.A$127.D35.A
91.A$128.D35.A89.A$129.D35.A87.A$166.A85.A$167.A83.A$168.A81.A$169.A
79.A$170.A77.A$171.A75.A$172.A68.A4.A$173.6A62.A3.A$173.2A66.A2.A$
173.A.A65.A.A$173.A2.A64.2A$173.A3.A63.6A$173.A4.A61.A$179.A59.A$180.
A57.A$181.A55.A$182.A53.A$183.A51.A$184.A49.A$185.A47.A$186.A45.A$
187.A43.A$188.A41.A$189.A39.A$190.A37.A$191.A35.A$192.A33.A$193.A31.A
$194.A29.A$195.A27.A$196.A25.A$197.A23.A$198.A21.A$199.A19.A$200.A17.
A$201.A15.A$202.A13.A$203.A11.A$204.A9.A$205.A7.A$206.A5.A$207.A3.A$
208.A.A$201.4D4.A7.D$201.2D13.D$201.D.D11.D$201.D2.D9.D$205.D7.D$206.
7D!

I'm not sure about whether the diamonds should be offset as shown, or lined up exactly (which would make Hashlife a bit happier). There seem to be disadvantages either way. Some parts of the corners can be built with direct slow salvos from the armless UCs, but I don't see any way around building substantial parts of several corners with intersecting slow^2 glider pairs.

"Slow^2' means a slow salvo used to manipulate a "slow elbow" and fire occasional gliders at 90 degrees. It's pretty slow, but having slow^2 pairs available should make up for part of that anyway. It seems possible that the whole construction recipe could be made to fit into one quarter-diagonal, so that the UC on the north corner could be re-used for different purposes for the two child-loop constructions. Some switching circuitry would be needed in the west and east corners to prevent half-recipes from being sent to the wrong places.

I'd be most grateful if someone feels like taking a look at the armless-UC idea in detail, and maybe thinking about putting the UCs in different places or adding more UCs to solve some of the construction coverage problems. The ability to shoot slow salvos across a wide area seems really useful, and it's nice that armless UCs are so compatible with encoded streams of glider pairs -- but it seems really hard to get the geometry right. So I'm not going to look at that option again for a while, myself.

It seems worth having a look at a design with two simple 10hd construction arms at each corner, with quadruplets of gliders coming in to run the arms -- just to see what problems show up there:

Code: Select all

#C [[ VIEWONLY WIDTH 640 ZOOM 1.5 ]]
x = 429, y = 288, rule = LifeHistory
82.3C269.3C$83.2C270.2C$82.C.3C267.C.3C$81.C3.2C266.C3.2C$80.C3.C.C
265.C3.C.C$79.C3.C267.C3.C$78.C3.C267.C3.C$81.C271.C$77.2A.C4.C263.2A
.C4.C$77.2A7.C262.2A7.C$83.C3.C267.C3.C$84.C3.C267.C3.C$85.C3.C.C265.
C3.C.C$79.C6.C3.2C257.C8.C3.2C$76.C10.C.3C260.C6.C.3C$81.C6.2C257.C
12.2C$74.C12.3C264.C4.3C$83.C261.C$72.C283.C$85.C257.C$70.C287.C$87.C
253.C$68.C291.C$61.3D25.C3.3D243.C$62.2D2.C26.2D267.C$61.D.D27.C.D.D
241.C$60.D3.C31.D267.C$59.D33.C3.D237.C$58.D3.C35.D267.C$57.D37.C3.D
233.C$60.C307.C$97.C233.C$58.C311.C$99.C229.C$46.C.C.C.C.C.C315.C$
101.C225.C$54.C.C317.C$103.C211.C.C.C.C.C.C$52.C3.C319.C$105.C217.C.C
$50.C5.C321.C$107.C213.C3.C$48.C7.C323.C$109.C209.C5.C$46.C9.C325.C$
111.C9.C195.C7.C$44.C339.C9.C$113.C7.C193.C9.C$42.C343.C7.C$115.C5.C
191.C$40.C347.C5.C$117.C3.C189.C$38.C351.C3.C$119.C.C187.C$36.C355.C.
C$111.C.C.C.C.C.C185.C$34.C349.C.C.C.C.C.C$123.C181.C93.D$32.C363.C3.
D$125.C177.C97.D$30.C367.C3.D$127.C173.C101.D.D$28.C371.C3.2D$129.C
169.C103.3D$26.C375.C$12.3C116.C165.C$13.2C9.C379.C$12.C.3C116.C161.C
$11.C3.2C5.C383.C$10.C3.C.C118.C157.C$2.3C4.C3.C6.C387.C$2.2C4.C3.C
124.C153.C$3C.C6.C6.C257.4C130.C$2C3.C4.C128.C138.2C9.C$C.C3.C9.C134.
2C124.C.C132.C$3.C3.C133.C9.2C123.C2.C7.C$4.C3.C5.C260.C138.C$5.C137.
C130.C10.C133.2A$6.C.2A264.C144.2A.C$8.2A3.C131.C128.C8.C131.C7.C$
140.3D7.3D121.C3.2A140.C3.C$15.C125.2D7.2D122.C3.2A133.C7.C3.C$140.D.
D.C5.D.D121.C9.C137.C3.C.C$17.C121.D13.D120.C136.C6.C4.C3.2C$138.D3.C
11.D120.C10.C130.C6.C.3C$19.C117.D17.D120.C132.C6.C3.C4.2C$136.D3.C
15.D120.C10.C126.C3.C4.3C$21.C256.C128.C4.C.C3.C$138.C140.C10.C121.2C
3.C$23.C381.C6.3C.C$136.C155.C121.2C$25.C377.C10.3C$134.C159.C$27.C
373.C.3D$132.C163.C107.2D$29.C369.C3.D.D$130.C167.C103.D$31.C365.C3.D
$128.C171.C99.D$33.C361.C3.D$126.C175.C$35.C357.C$124.C179.C$37.C.C.C
.C.C.C343.C$122.C183.C$37.C.C349.C$120.C187.C.C.C.C.C.C$37.C3.C345.C$
118.C189.C.C$37.C5.C341.C$106.C9.C191.C3.C$37.C7.C327.C9.C$106.C7.C
193.C5.C$37.C9.C325.C7.C$106.C5.C195.C7.C$49.C323.C5.C$106.C3.C197.C
9.C$51.C321.C3.C$106.C.C211.C$53.C319.C.C$106.C.C.C.C.C.C205.C$55.C
317.C.C.C.C.C.C$104.C219.C$57.C313.C$102.C223.C$59.C309.C$100.C227.C$
61.C305.C$98.C231.C$63.C133.3D165.C$96.C100.2D133.C$65.C131.D.D163.C$
94.C105.D133.C$67.C133.D159.C$92.C109.D15.3D115.C$69.C133.D15.2D138.C
$90.C54.B72.D.3D115.C3.D$71.C145.D3.2D120.D13.C$88.C127.D3.D.D117.C3.
D$73.C141.D3.D125.D9.C$86.C121.2A4.D3.D123.C3.D.D$75.C132.2A7.D129.2D
4.C$84.C131.D4.D122.C.3D$77.C144.D128.C$82.C136.D3.D122.C$79.C140.D3.
D67.B56.C$214.A6.D3.D.D113.4C12.C$213.A.A6.D3.2D113.2C13.C$212.A3.A6.
D.3D113.C.C11.C$72.4C4.2A6.C122.A5.A6.2D115.C2.C9.C$72.2C6.2A5.C122.A
7.A4.3D119.C7.C$72.C.C11.C122.A9.A126.7C$72.C2.C9.C122.A11.A$76.C7.C
122.A13.A129.2C$77.7C122.A15.A128.2C$205.A17.A$204.A19.A115.3D$203.A
21.A115.2D$202.A23.A113.D.D$201.A25.A111.D$200.A27.A109.D$199.A29.A
107.D$198.A31.A105.D$197.A33.A$196.A35.A$195.A37.A$194.A39.A$193.A41.
A$192.A43.A$191.A45.A$190.A47.A$189.A49.A$188.A51.A$187.A53.A$186.A
55.A$185.A57.A$184.A59.A$183.A61.A4.A$177.6A63.A3.A$181.2A64.A2.A$
180.A.A65.A.A$179.A2.A66.2A$178.A3.A62.6A$177.A4.A68.A$176.A75.A$175.
A77.A$174.A79.A$173.A81.A$172.A83.A$171.A85.A$170.A87.A$169.A89.A$
168.A91.A$167.A93.A$166.A95.A$165.A97.A$164.A99.A$163.A101.A31.3D$
162.A103.A31.2D$161.A105.A29.D.D$160.A107.A27.D$146.3D10.A109.A25.D$
147.2D9.A111.A23.D$146.D.3D6.A113.A21.D$145.D3.2D5.A115.A$144.D3.D.D
4.A117.A$136.3D4.D3.D6.A119.A7.E$136.2D4.D3.D6.A121.A7.E$134.3D.D6.D
6.A123.A7.E2.2A$134.2D3.D4.D6.A125.A7.E.2A$134.D.D3.D9.A127.A7.E$137.
D3.D7.A129.A7.E$138.D3.D5.A131.A6.E$139.D7.A133.A5.E$140.D5.A135.A4.E
$147.A133.A5.E$148.A131.A6.E$149.A129.A7.E$150.A127.A7.E$151.A125.A4.
E2.E$152.A123.A5.E.E$153.A121.A6.2E$154.A119.A7.4E$155.A117.A$156.A
115.A$157.A113.A$158.A111.A$159.A109.A$160.A107.A$161.A105.A$162.A
103.A$163.A101.A$164.A99.A$165.A97.A$166.A95.A$167.A93.A$168.A91.A$
169.A89.A$170.A87.A$171.A85.A$172.A83.A$173.A81.A$174.A79.A$175.A77.A
$176.A75.A$177.A68.A4.A$178.6A62.A3.A$178.2A66.A2.A$178.A.A65.A.A$
178.A2.A64.2A$178.A3.A63.6A$178.A4.A61.A$184.A59.A$185.A57.A$186.A55.
A$187.A53.A$188.A51.A$189.A49.A$190.A47.A$191.A45.A$192.A43.A$193.A
41.A$194.A39.A$195.A37.A$196.A35.A$197.A33.A$198.A31.A$199.A29.A$200.
A27.A$201.A25.A$202.A23.A$203.A21.A$204.A19.A$205.A17.A$206.A15.A$
207.A13.A$208.A11.A$209.A9.A$210.A7.A$211.A5.A$212.A3.A$213.A.A$206.
4E4.A7.E$206.2E13.E$206.E.E11.E$206.E2.E9.E$210.E7.E$211.7E!

We'll have to use strict glider-pair recipes for the 10hd arms (red double arrows), but that's worked fine before. We actually only have to build two elbows at two corners of each child. The other construction arm's elbow stays close to the parent's N corner when it's building the child's N and E corners. So those two corners can be constructed Gemini-style with intersecting slow (but not slow^2) glider pairs. Those gliders are shown as single red arrows.

I'm not sure how to handle the construction of the child's W and then S corners. The biggest objects in the W corner are the two 10hd UC's, and they can't construct things that are lined up with them diagonally -- or not with Gemini-style slow glider pairs, anyway. Maybe switch over to a separate dedicated armless UC to get NWward gliders onto those key lanes -- or just build the W and S child corners with just one arm?

This implies that the 10hd construction arm parallel to the SW edge of the parent should use Fx119-based edge shooters, to allow the greatest possible distance for 10hd glider pairs to go past. Seems as if it should be possible to line up the child exactly diagonally from the parent, and make the offset an exact power of two.

Making the period an exact power of two should be a relatively trivial adjustment -- changing position or orientation on two or three Silver reflectors that we may need to have there anyway.

The two yellow curved arrows in this diagram can be simple 90-degree Silver reflectors. We could even use Snarks there, but only if we wanted to work out the painfully large seed constellation for them.

-- I'm sure I haven't followed through all the implications of these designs correctly yet, and there are many other geometries that might be worth looking at; these are definitely early draft blueprints. Corrections, comments and questions welcome as usual.

[dvgrn]

And now for something almost completely different.

A suggestion from Calcyman got me thinking about this pure-armless-UC architecture:

Code: Select all

#C [[ VIEWONLY ZOOM 1.2 ]]
x = 673, y = 671, rule = LifeHistory
343.2C$343.2C56$401.2C$401.2C17$283.2C$283.2C4$253.C$252.C$251.C3.C$
250.C8.C$249.C7.C.C$248.C10.C$247.B8.4C$246.B$245.B$244.B$243.B$242.B
$241.B$240.B$239.B$238.B$237.B$236.B$235.B$234.B$233.B$232.B$231.B$
230.B$229.B$228.B$227.B$226.B$225.B$224.B$223.B$222.B$221.B$220.B$
219.B$218.B$217.B$216.B108.2C$215.B109.2C$214.B$213.B$212.B$211.B$
210.B$209.B$208.B$207.B$206.B$205.B$204.B$203.B$202.B$201.B$192.2A6.B
$192.2A5.B4$197.C$194.C$199.C$192.C$201.C113.4C$190.C124.C$203.C111.C
.C$188.C126.C$205.C113.C$186.C$207.C113.C$184.C135.C$209.C109.C$182.C
135.C$211.C105.C$180.C135.C$213.C101.B$168.C.C.C.C.C.C135.B$215.C97.B
$176.C.C133.B$217.C93.B$174.C3.C131.B$219.C89.B$172.C5.C129.B$221.C
85.B$170.C7.C127.B$223.C81.B$168.C9.C125.B$225.C77.B$166.C135.B$227.C
73.B$164.C135.B$229.C9.C59.B$162.C135.B$231.C7.C57.B$160.C135.B$233.C
5.C55.B$158.C135.B$235.C3.C53.B$156.C135.B$237.C.C51.B$154.C135.B$
229.C.C.C.C.C.C49.B$152.C135.B$241.C45.B$150.C135.B$243.C41.B$148.C
135.B$245.C37.B$146.C135.B$247.C33.B$144.C135.B$249.C29.B$135.2A5.C
135.B$135.2A114.C25.B$140.C135.B$253.C21.B$274.B$139.C115.C17.B$272.B
$135.B5.C115.C13.B$134.B135.B$133.B9.C115.C9.B$132.B135.B$131.B13.C
115.C5.B$130.B$129.B17.C115.C$128.B$127.B21.C$126.B135.C$125.B25.C$
124.B127.2A6.C$123.B29.C98.2A$122.B135.C$121.B33.C$120.B135.C$119.B
37.C125.A$118.B135.C13.3D13.A$117.B41.C108.2D11.A3.A$116.B135.C15.D.D
6.A8.A$115.B45.C109.D5.A.A7.A$114.B135.C21.D4.A10.A$113.B49.C.C.C.C.C
.C99.D3.4A8.B$112.B135.C13.3D9.D15.B$111.B51.C.C96.2D27.B$110.B135.C
15.D.D27.B$109.B53.C3.C97.D27.B$108.B135.C21.D27.B$107.B55.C5.C97.D
27.B$106.B135.C25.D27.B$105.B57.C7.C125.B$104.B135.C57.B$103.B59.C9.C
125.B$102.B125.C9.C13.3D45.B$101.B73.C76.2D47.B$100.B127.C7.C15.D.D
47.B$99.B77.C77.D47.B$98.B129.C5.C21.D47.B$97.B81.C77.D47.B$96.B131.C
3.C25.D47.B$95.B85.C125.B$94.B133.C.C77.B$93.B89.C125.B$92.B135.C.C.C
.C.C.C3.3D65.B$91.B93.C56.2D67.B$90.B135.C15.D.D67.B$89.B97.C57.D67.B
$88.B135.C21.D67.B$87.B101.C57.D67.B$86.C135.C25.D67.B$85.C105.C125.B
$84.C135.C97.B$83.C109.C125.B$82.C127.2A6.C13.3D85.B$81.C113.C14.2A
20.2D87.B$216.C15.D.D87.B$83.C113.C37.D87.B$87.C126.C21.D87.B$85.C.C
111.C37.D87.B$87.C124.C25.D87.B$84.4C113.C125.B$210.C117.B$203.C125.B
$208.C13.3D46.B58.B$205.C16.2D107.B$222.D.D107.B$225.D107.B$226.D107.
B$203.B23.D107.B$202.B25.D107.B$201.B135.B$200.B13.3D$199.B14.2D397.
2C$198.B15.D.D123.A272.2C$197.B19.D121.A.A$196.B21.D119.A3.A$195.B23.
D117.A5.A$194.B25.D115.A7.A$193.B24.4A113.A9.A$192.B28.A112.A11.A$
191.B27.A.A111.A13.A$190.B30.A110.A15.A$189.B27.A113.A17.A$188.B141.A
19.A$76.2C109.B27.A113.A21.A$76.2C108.B29.A111.A23.A$185.B31.A109.A
25.A$184.B33.A107.A27.A$183.B35.A105.A29.A$182.B37.A103.A31.A$181.B
39.B101.A33.A$180.B41.B99.A35.A$179.B43.B97.A37.A$178.B45.B95.A39.A$
177.B47.B93.A41.A$176.B49.B91.A43.A$175.B51.B89.A45.A$174.B53.B87.A
47.A$173.B55.B85.A49.A$172.B57.B83.A51.A$171.B59.B81.A53.A4.A$170.B
61.B79.A55.A3.A$169.B63.B77.A57.A2.A$168.B65.B75.A59.A.A$167.B67.B73.
A61.2A$166.B69.B66.6A58.6A$165.B71.B69.2A64.A$164.B73.B67.A.A65.A$
163.B75.B65.A2.A66.A$162.B77.B63.A3.A67.A$161.B79.B61.A4.A68.A$160.B
81.B59.A75.A$159.B83.B57.A77.A$158.B85.B55.A79.A$157.B87.B53.A81.A$
156.B89.B51.A83.A$143.4C8.B91.B49.A85.A$143.C10.C93.B47.A87.A$143.C.C
7.C95.B45.A89.A$143.C8.C97.B43.A91.A$147.C3.C99.B41.A93.A$150.C101.B
39.A95.A$149.C103.B37.A97.A$254.B35.A99.A$255.B33.A101.A$256.B31.A
103.A$118.2C137.B29.A105.A$118.2C138.B27.A107.A$259.B25.A109.A$260.B
23.A111.A274.2C$261.B21.A113.A273.2C$262.B19.A115.A$263.B17.A117.A$
264.B15.A119.A$265.B13.A119.A$266.B11.A119.A$267.B9.A119.A5.B$268.B7.
A119.A7.B$269.B5.A119.A9.B$274.A119.A11.B$273.A119.A13.B$272.A119.A
15.B$273.A117.A17.B$274.A115.A19.B$2C273.A113.A21.B$2C274.A111.A23.B$
277.A109.A25.B$278.A107.A27.B138.2C$279.A105.A29.B137.2C$280.A103.A
31.B$281.A101.A33.B$282.A99.A35.B$283.A97.A37.B103.C$284.A95.A39.B
101.C$285.A93.A41.B99.C3.C$286.A91.A43.B97.C8.C$287.A89.A45.B95.C7.C.
C$288.A87.A47.B93.C10.C$289.A85.A49.B91.B8.4C$290.A83.A51.B89.B$291.A
81.A53.B87.B$292.A79.A55.B85.B$293.A77.A57.B83.B$294.A75.A59.B81.B$
295.A68.A4.A61.B79.B$296.A67.A3.A63.B77.B$297.A66.A2.A65.B75.B$298.A
65.A.A67.B73.B$299.A64.2A69.B71.B$300.6A58.6A66.B69.B$300.2A61.A73.B
67.B$300.A.A59.A75.B65.B$300.A2.A57.A77.B63.B$300.A3.A55.A79.B61.B$
300.A4.A53.A81.B59.B$306.A51.A83.B57.B$307.A49.A85.B55.B$308.A47.A87.
B53.B$309.A45.A89.B51.B$310.A43.A91.B49.B$311.A41.A93.B47.B$312.A39.A
95.B45.B$313.A37.A97.B43.B$314.A35.A99.B41.B$315.A33.A101.B39.B$316.A
31.A103.A37.B$317.A29.A105.A35.B$318.A27.A107.A33.B$319.A25.A109.A31.
B$320.A23.A111.A29.B108.2C$321.A21.A113.A27.B109.2C$322.A19.A141.B$
323.A17.A113.A27.B$324.A15.A110.A30.B$325.A13.A111.A.A27.B$326.A11.A
112.A28.B$327.A9.A113.4A24.B$328.A7.A115.D25.B$329.A5.A117.D23.B$330.
A3.A119.D21.B$331.A.A121.D19.B$58.2C272.A123.D.D15.B$58.2C397.2D14.B$
456.3D13.B$335.B135.B$336.B107.D25.B$337.B107.D23.B$338.B107.D$339.B
107.D$340.B107.D.D$341.B107.2D16.C$342.B58.B46.3D13.C$343.B125.C$344.
B117.C$345.B125.C113.4C$346.B87.D25.C124.C$347.B87.D37.C111.C.C$348.B
87.D21.C126.C$349.B87.D37.C113.C$350.B87.D.D15.C$351.B87.2D20.2A14.C
113.C$352.B85.3D13.C6.2A127.C$353.B125.C109.C$354.B97.C135.C$355.B
125.C105.C$356.B67.D25.C135.C$357.B67.D57.C101.B$358.B67.D21.C135.B$
359.B67.D57.C97.B$360.B67.D.D15.C135.B$361.B67.2D56.C93.B$362.B65.3D
3.C.C.C.C.C.C135.B$363.B125.C89.B$364.B77.C.C133.B$365.B125.C85.B$
366.B47.D25.C3.C131.B$367.B47.D77.C81.B$368.B47.D21.C5.C129.B$369.B
47.D77.C77.B$370.B47.D.D15.C7.C127.B$371.B47.2D76.C73.B$372.B45.3D13.
C9.C125.B$373.B125.C9.C59.B$374.B57.C135.B$375.B125.C7.C57.B$376.B27.
D25.C135.B$377.B27.D97.C5.C55.B$378.B27.D21.C135.B$379.B27.D97.C3.C
53.B$380.B27.D.D15.C135.B$381.B27.2D96.C.C51.B$382.B15.D9.3D13.C135.B
$383.B8.4A3.D99.C.C.C.C.C.C49.B$384.A10.A4.D21.C135.B$385.A7.A.A5.D
109.C45.B$386.A8.A6.D.D15.C135.B$387.A3.A11.2D108.C41.B$388.A13.3D13.
C135.B$389.A125.C37.B$416.C135.B$517.C33.B$414.C135.B$419.2A98.C29.B$
412.C6.2A127.B$521.C25.B$410.C135.B$523.C21.B$544.B$409.C115.C17.B$
542.B$405.B5.C115.C13.B$404.B135.B$403.B9.C115.C9.B$402.B135.B$401.B
13.C115.C5.B$400.B$399.B17.C115.C$398.B$397.B21.C$396.B135.C$395.B25.
C114.2A$394.B135.C5.2A$393.B29.C$392.B135.C$391.B33.C$390.B135.C$389.
B37.C$388.B135.C$387.B41.C$386.B135.C$385.B45.C$384.B135.C$383.B49.C.
C.C.C.C.C$382.B135.C$381.B51.C.C$380.B135.C$379.B53.C3.C$378.B135.C$
377.B55.C5.C$376.B135.C$375.B57.C7.C$374.B135.C$373.B59.C9.C$372.B
135.C$371.B73.C$370.B135.C$369.B77.C$368.B125.C9.C$367.B81.C$366.B
127.C7.C$365.B85.C$364.B129.C5.C$363.B89.C$362.B131.C3.C$361.B93.C$
360.B133.C.C$359.B97.C$358.B135.C.C.C.C.C.C$357.B101.C$356.C135.C$
355.C105.C$354.C135.C$353.C109.C$352.C135.C$351.C113.C$486.C$353.C
113.C$357.C126.C$355.C.C111.C$357.C124.C$354.4C113.C$480.C$473.C$478.
C$475.C4$473.B5.2A$472.B6.2A$471.B$470.B$469.B$468.B$467.B$466.B$465.
B$464.B$463.B$462.B$461.B$460.B$459.B$458.B$346.2C109.B$346.2C108.B$
455.B$454.B$453.B$452.B$451.B$450.B$449.B$448.B$447.B$446.B$445.B$
444.B$443.B$442.B$441.B$440.B$439.B$438.B$437.B$436.B$435.B$434.B$
433.B$432.B$431.B$430.B$429.B$428.B$427.B$426.B$413.4C8.B$413.C10.C$
413.C.C7.C$413.C8.C$417.C3.C$420.C$419.C4$388.2C$388.2C17$270.2C$270.
2C56$328.2C$328.2C!

The rest of this message is adapted from an email to Calcyman where I worked out some of the details (maybe successfully, maybe not):

Stage 1:

• Wait for a diamond-edge worth of glider travel time (a quarter loop) for the UC to load its recipe
• Build circuitry at two new corners (child N, then child E) with armless-UC slow salvos, using targets already in place, and using prebuilt parental semi-Snarks at child S and child E to collide the gliders.

Stage 2:

• Wait another quarter-loop for the armless-UC collision point to get back down to parent-W
• Build the circuitry at the last two corners (child W and child S).

Stage 3:

• Trigger seeds at all four corners that build target blocks at each corner of each grandchild of the child replicator.
• Most expensive: use freeze-dried slow salvos aimed at the near-corner target blocks, to construct the semi-Snarks that will be used to build each grandchild.

Stage 4:

• The original recipe gets to the other side of the loop and does exactly the same things there.
  
  (This still has to be a quadratic-growth replicator, but you can't do two 90-degree children with this model. The long sides have to be just slightly longer than the short sides to allow for the width of the semi-Snarks, and you can't put two long sides next to each other.)

The wait times for those varioius stages don't add up to anything even close to a full loop, so it all seems doable.

Unlike other replicator designs where only one loop will ever be trying to build in a particular blank space at a particular time, in this design the grandchildren will be trying to build great-grandchildren in overlapping spaces. I _think_ that one grandchild will always have a half-loop head start, which will probably be enough to allow a fairly trivial collision prevention mechanism, but I should probably run a few simulations to make sure.

If this timing issue turns out to be a problem, well, previous sample patterns have shown that a recipe can be cycled an extra time around the loop at insignificant extra expense. That should prevent one grandchild from starting a construction for 1.5 cycles, which is enough time for the other grandchild to finish construction and get suppression mechanisms into place.

One little detail is that if the semi-Snarks are close to parent-N and parent-W corners, Stage 2 gliders end up traveling SW in close proximity to NE-traveling gliders. That's no good, due to Hashlife limitations. One of the primary design goals is to build something that will run ridiculously fast in Golly.

Therefore, the above diagram assumes that the parent starts out with a semi-Snark already at child-S and child-E, pointed at each other to create an armless UC, and two elbows at child-N and child-W, as shown in the diagram. Colors are green for parent circuitry and white for child circuitry, as usual. Invert N<->S and E<->W for the second child, of course, but it's all the same geometry.

Part of the parent's construction job is to construct two sets of those semi-Snarks and two new elbows for *each* of its children, probably using seed constellations for the kinds of *WSS+G that Chris Cain has outlined. That way there are never any of those forbidden boustrophedonic glider streams at all.

It would be better to encode the construction of the semi-Snarks and elbows into the beginning of the recipe, so it can be done once for each child instead of twice -- but I don't quite see how to avoid boustrophedonic gliders in that case. Probably this is the biggest awkward part of this design: we have to pre-build *WSS+G and semi-Snark slow salvo seeds with different recipes at each corner.

That all seems a bit silly. In the ideal world where Golly can run everything equally well, it's much more efficient to keep the semi-Snarks right near parent-N and parent-W. But I'm really fairly determined to end up with something that real-world Golly has some chance of running away with.

Anyway, if someone can see a way to encode those *WSS+G+semi-Snark seeds into the beginning of the recipe, or can suggest other possible improvements, please do explain them! In general this design seems almost ridiculously simple. The base loop is just four Silver reflectors, there's only one UC for each child, and each UC consists of a matched pair of semi-Snarks.

We'll have to add some one-time circuitry and a few more reflectors to get the construction recipe copied to the two children at the right time, plus solve the *WSS+G+semi-Snark construction problem, plus figure out suppression details.

Suppression seems easy, though -- just build appropriate eaters for the initial *WSSes and Gs, and probably allow the semi-Snarks to be constructed but leave a one-time circuit to disable them as soon as they start to get used. Each of the two short sides of a diamond will only have to be defended against attempted construction once, and then it's safe.

[dvgrn]

* c/7 orthogonal
Candidate: loafer
Pros: extremely cheap synthesis, with only 8 gliders...

Or now only one glider, plus fourteen small still lifes, thanks to some black magic by Chris Cain:

Code: Select all

#C 14sL loafer seed, plus one glider
x = 71, y = 56, rule = B3/S23
67b2o$67bobo$68bobo$69bo3$25b2o$25bobo$26bobo$27bo4$3bo$2bobo$bobo$b2o
9$10bo$9bobo4bo$10b2o3bobo$14bobo$14b2o3$25b2o$20b2o3b2o$19bo2bo$bo17b
o2bo$obo17b2o26b2o$b2o44bobo$47b2o2$39b2o$21b2o16bobo$21bobo4b2o10bobo
$22bo5bobo10bo$29b2o$33b2o$33b2o3$22b2o$21bo2bo$21bo2bo$22b2o$58b3o$
58bo$59bo!
#C [[ AUTOSTART THUMBNAIL ZOOM 7.8 LOOP 600 ]]

The bounding box and the still-life count can probably be reduced further. Anyone care to give it a try?

It seems pretty clear that the Cordership seed could also be cut down a little more, using a similar split-then-reflect method. Then again, with a big enough collection of splitters and turners to choose from, there may well be something even more efficient than that.

I had somehow forgotten that simsim314 has already posted an an enormous list of 2sL 90-degree turners, already partially sorted by phase and output color, but not yet by actual timing -- and there are a lot of duplicates in there.

[towerator]

Or now only one glider, plus fourteen small still lifes, thanks to some black magic by Chris Cain:

Amazing! And how many does it takes to perform the "summoning ritual"(that's simply too temptating to call such a thing like this) of a dart? As I pointed out, the loafer thas the large sin to be slower than slow (which is also true for a cordership)

(It may be a lot, however, since the dart is synthetized usually with 4 big shotguns of gliders)

[dvgrn]

Amazing! And how many does it takes to perform the "summoning ritual" (that's simply too temptating to call such a thing like this) of a dart?

No idea. Less than a hundred still lifes, I expect, even if we have to actually produce all of the final 17 converging gliders -- six still lifes per glider on average should be way more than enough. (That's if we call the five initial still lifes good enough -- the snakes are really pretty sketchy, hard to build with Gemini glider pairs, let alone a slow salvo... but let's leave that aside for the moment.)

I can see some possible reductions, but I don't know enough to do a good job... and I'm off on a Spring Break driving trip for a week very soon, so I won't even try.

As I pointed out, the loafer thas the large sin to be slower than slow (which is also true for a cordership)

As the Cordership example showed, an extra trip around the replicator loop will make up for a lot of slowness. The downside I'm worried about for the Geminoid replicator project is the loafer's orthogonal travel direction. It's going to be so easy to just use *WSS+G pairings to get what we want, with no long delays needed at all, that it seems to me that all of these other beautiful ideas will just have to wait for a different project.

Anyway, another day and a fresh look produced an obvious bounding-box reduction for the loafer seed:

Code: Select all

#C smaller 14sL loafer seed, plus one glider
x = 46, y = 45, rule = B3/S23
13b2o$14bo$14bobo$15b2o2$3bo23bo$2bobo22bobo$bobo23b2o$b2o$14b2o$13bob
o$13b2o4$20b2o$19bobo$10bo9bo$9bobo4bo$10b2o3bobo$14bobo$14b2o2$45bo$
25b2o16b3o$20b2o3b2o15bo$19bo2bo19b2o$bo17bo2bo$obo17b2o$b2o4$21b2o$
21bobo4b2o$22bo5bobo$29b2o$33b2o$33b2o3$22b2o$21bo2bo$21bo2bo$22b2o!
#C [[ AUTOSTART THUMBNAIL ZOOM 8 LOOP 400 ]]

[chris_c]

And how many does it takes to perform the "summoning ritual"(that's simply too temptating to call such a thing like this) of a dart?

Yes, probably quite a lot. The front spark in the Dart synthesis is quite scary and I wouldn't dare to start touching it again. If you wanted to construct a Dart with a UC it's probably best to use this synthesis where the front spark requires 7 timed gliders all coming from the north.

Code: Select all

x = 39, y = 42, rule = B3/S23
30bo$28b2o$29b2o$7bo$8b2o$7b2o6bo3bo12bo$13bobo4b2o8b2o$14b2o3b2o10b2o
2$9bo$10bo17bobo$8b3o17b2o$29bo2$10b2o$5bo4b2o4bo16bo$3bobo9bobob2o12b
obo$4b2o10b2ob2o12b2o3$17b2ob2o$17bo3bo$18bobo$17b2ob2o$5b2o25b2o$4bob
o25bobo$6bo12bo12bo$18bobo$bo17bo17bo$b2o33b2o$obo33bobo2$9b2o17b2o$
10b2o15b2o$9bo19bo$22b2o$22bobo$22bo2$16b2o$15bobo$17bo!

After that I guess it would be possible to find a one glider seed for each wing and a one glider seed for the pi at the bottom. That still leaves 12 gliders for the ignition phase.

As for building the the bait still lifes, I guess the double snake can be built using two timed gliders. Probably something along these lines:

Code: Select all

x = 14, y = 19, rule = B3/S23
12bo$11bobo$12bo5$11bo$10b2o$10bobo$6b3o$8bo$7bo$bo$b2o$obo2$6b2o$6b2o
!

Also you would probably need two timed gliders for the boat + block combination.

So the Dart doesn't appear to be in the same league as far as ease of slow construction goes.

Are there any c/2 puffers that leave behind a fuse that can be cleanly burnt and which destroys the puffer when the fuse reaches the end? I couldn't find anything suitable with a quick browse of LifeWiki.

EDIT:

Anyway, another day and a fresh look produced an obvious bounding-box reduction for the loafer seed:

Nice!

[Scorbie]

Are there any c/2 puffers that leave behind a fuse that can be cleanly burnt and which destroys the puffer when the fuse reaches the end? I couldn't find anything suitable with a quick browse of LifeWiki.

Hartmut Holzwart was able to destroy the p8 blinker puffer but with a lot of mess. I think that blinker puffer is a likely candidate.

EDIT: Here's the link.
viewtopic.php?f=2&t=1448&p=14336#p14336

[dvgrn]

Here's a slow-salvo recipe for a semi-Snark, lifted unmodified from the linear GoL propagator. The lane list is back on my other laptop, and I haven't bothered to dig up my old script to extract lane numbers.

Code: Select all

x = 566307, y = 566345, rule = B3/S23
2o$2o12365$12370b3o$12370bo$12371bo13297$25672b3o$25672bo$25673bo6155$
31836b3o$31836bo$31837bo8189$40027bo$40026b2o$40026bobo9201$49225b3o$
49225bo$49226bo10252$59480b3o$59480bo$59481bo10225$69700b3o$69700bo$
69701bo4094$73793b2o$73792b2o$73794bo8190$81992b3o$81992bo$81993bo
6155$88156b3o$88156bo$88157bo11262$99420b3o$99420bo$99421bo8190$
107600b3o$107600bo$107601bo12286$119898b3o$119898bo$119899bo8182$
128058b3o$128058bo$128059bo3078$131130b3o$131130bo$131131bo12286$
143430b3o$143430bo$143431bo15357$158797bo$158796b2o$158796bobo6130$
164914b3o$164914bo$164915bo12286$177216b3o$177216bo$177217bo2059$
179270b3o$179270bo$179271bo13296$192575b3o$192575bo$192576bo10252$
202822b3o$202822bo$202823bo17393$220234b3o$220234bo$220235bo7165$
227387b3o$227387bo$227388bo11275$238675bo$238674b2o$238674bobo11262$
249939bo$249938b2o$249938bobo14322$264267b2o$264266b2o$264268bo5130$
269395bo$269394b2o$269394bobo8191$277582b3o$277582bo$277583bo8190$
285764b3o$285764bo$285765bo13297$299066b3o$299066bo$299067bo8190$
307258b3o$307258bo$307259bo6154$313421bo$313420b2o$313420bobo8191$
321610b3o$321610bo$321611bo11261$332867bo$332866b2o$332866bobo13298$
346168b3o$346168bo$346169bo6155$352330b3o$352330bo$352331bo9200$
361527b3o$361527bo$361528bo7180$368700b3o$368700bo$368701bo13296$
382009b3o$382009bo$382010bo12285$394308bo$394307b2o$394307bobo9216$
403518b3o$403518bo$403519bo8190$411698b3o$411698bo$411699bo3069$
414761b3o$414761bo$414762bo16381$431170bo$431169b2o$431169bobo8191$
439337b3o$439337bo$439338bo12287$451630b3o$451630bo$451631bo8190$
459822b3o$459822bo$459823bo6141$465959b3o$465959bo$465960bo12286$
478257b3o$478257bo$478258bo8189$486446bo$486445b2o$486445bobo7181$
493616b3o$493616bo$493617bo9199$502816bo$502815b2o$502815bobo8191$
511005b3o$511005bo$511006bo9215$520222b3o$520222bo$520223bo13323$
533562b3o$533562bo$533563bo8190$541742b3o$541742bo$541743bo10225$
551970b3o$551970bo$551971bo8190$560170b3o$560170bo$560171bo6147$
566304b3o$566304bo$566305bo!

EDIT: I checked the spiral-growth pattern, and it appears to have a recipe with exactly the same cost, 59 gliders (I calculated wrong in the original post when I said 74). The 60th glider above just kills a harmless beehive off to the side.

Code: Select all

x = 219151, y = 219152, rule = B3/S23
4b2o$2o2bobo$2o2bo1548$1556b3o$1556bo$1557bo3059$4625b2o$4625bobo$
4625bo3585$8211bo$8210b2o$8210bobo3082$11290b3o$11290bo$11291bo3564$
14857b3o$14857bo$14858bo4112$18964b3o$18964bo$18965bo3577$22541bo$
22540b2o$22540bobo4607$27156b3o$27156bo$27157bo3568$30733b3o$30733bo$
30734bo4094$34829b3o$34829bo$34830bo4612$39432b2o$39432bobo$39432bo
3576$43019b3o$43019bo$43020bo3070$46068b2o$46068bobo$46068bo3582$
49644b2o$49644bobo$49644bo4094$53752b2o$53752bobo$53752bo1537$55297b2o
$55296b2o$55298bo3081$58366b3o$58366bo$58367bo2571$60953b3o$60953bo$
60954bo4579$65527b3o$65527bo$65528bo5136$70672b3o$70672bo$70673bo3570$
74238b2o$74238bobo$74238bo4614$78870b3o$78870bo$78871bo1547$80405b3o$
80405bo$80406bo5090$85508bo$85507b2o$85507bobo4094$89604bo$89603b2o$
89603bobo5136$94747bo$94746b2o$94746bobo3053$97796b2o$97795b2o$97797bo
3588$101382b2o$101382bobo$101382bo3070$104444b2o$104444bobo$104444bo
3091$107539b3o$107539bo$107540bo5617$113158b3o$113158bo$113159bo4598$
117765bo$117764b2o$117764bobo3064$120827b3o$120827bo$120828bo2557$
123380bo$123379b2o$123379bobo5137$128520b3o$128520bo$128521bo3052$
131579b3o$131579bo$131580bo4624$136200b3o$136200bo$136201bo2543$
138737b2o$138737bobo$138737bo4621$143370b3o$143370bo$143371bo2557$
145941bo$145940b2o$145940bobo2043$147978b3o$147978bo$147979bo3569$
151538b2o$151538bobo$151538bo5656$157187b3o$157187bo$157188bo5617$
162806b3o$162806bo$162807bo3595$166407b3o$166407bo$166408bo5617$
172026b3o$172026bo$172027bo3083$175105b3o$175105bo$175106bo5621$
180738b3o$180738bo$180739bo3577$184315bo$184314b2o$184314bobo3057$
187361b3o$187361bo$187362bo4120$191482bo$191481b2o$191481bobo4598$
196078b3o$196078bo$196079bo3582$199662b3o$199662bo$199663bo4079$
203759b2o$203759bobo$203759bo4091$207840b2o$207840bobo$207840bo2073$
209915b3o$209915bo$209916bo5109$215034b3o$215034bo$215035bo4089$
219148b3o$219148bo$219149bo!

Anyone want to try their luck at finding a way to build a semi-Snark with significantly less than 59 slow-salvo gliders?

My current favorite quadratic-replicator blueprint would use two of these 59-glider salvos, freeze-dried into two ~120sL constellations. Definitely expensive -- oddly enough, there might only be about 130-150 still lifes in the entire rest of the circuitry. The freeze-dried constellations will easily be the majority of the construction cost.

It still seems definitely worth the expense, to be able to simplify the design so radically and still have a replicator pattern that Golly can run really efficiently. Can anyone see a way to dodge the freeze-drying expense without losing the simulation efficiency?

[simsim314]

@dvgrn
Just a small reminder that this one is also a semi-snark (and interesting to check whether this reduces or not the glider count for slow salvo - at least for some of the orientations):

Code: Select all

#C [[ THUMBNAIL ZOOM 12 ]]
x = 19, y = 19, rule = B3/S23
8b2o8bo$8b2o6b3o$15bo$2o13b2o$bo$bobo$2b2o$7b2o$7b2o4$4bo$3bobo$4bo3$
12b2o$12b2o!

EDIT Also I would suggest to consider my adjustable 4 engine cordership. As it probably can be constructed with two pairs of synchronized gliders - it might be more efficient on the total SL count:

Code: Select all

#C [[ THUMBNAIL ZOOM 2 AUTOSTART LOOP 1000 THEME 0 ]]
x = 125, y = 137, rule = B3/S23
28bo$27bobo$26b2ob2o$3b3o20b2ob2o$2bo3bo18b3o$bo4bo18b3o3bo12b2o$o3bo
20b3o4bo11b2o$o2bob3o18b2o5bo$o7bo17b3o$2bo3bobo18b2o$2bo3bob2o18b2o$
4b3ob2o33b2o$20b2o$20b2o6bo14b3o6b2o$27b3o13bobo6b2o$26bo3bo$4b2o24b2o
13bo$4b2o23b2o13b2o$5bo38b2o2$5bo22b2o13b2o$28b2o13b3o$41b3o$3bo5b3o
21b3o5bo$3bo7bo$3bo5bobo10b2o16b3o$9b2o10bo2bo15bo$20bo3bo15b3o$22b2o
35b2o$59b2o$16bo$14b2o$8b2o2b2o5bo$8b2o4b2o$18bo$15b4o$14bobo50b2o$13b
o2b2obo47b2o$14bo4bo$15bo$16bo2bo$16b2o3$75b2o$75b2o7$83b2o$83b2o7$91b
2o$91b2o7$99b2o$99b2o7$107b2o$107b2o7$115b2o$115b2o6$114b3o$113bo3bo5b
2o$112bo4bo5b2o$111bo3bo$111bo2bob3o$111bo7bo$113bo3bobo$113bo3bob2o$
115b3ob2o2$88bo6b2o$87bobo3bo3bo$86bo3bobo3b2o18bo$87bobo2bobob2o17bob
o$88bo3bo2b2o17bo$92bo4bo21bo$93bo2bo10b2o5b2o2b2o$95bo11b2o7bo$114b2o
bo$113bo3bo$112bo$111b2obob2o$111b2o3bo$112bo2b2o$113b3o$102bo11bo$91b
3o7bo2bo16bo$90bobob2o5bo3bo15bo$90bobob2o5bo3bo15bo$90bo3bo5b2o3bo4b
3o$91bobo7bo2bo4b2o2bo$92bo15bo3b2o$107bo2b3o$106bo2b2o$106bo2bo$107bo
2bo$95b2o13bo$95b2o11bobo2$106bo$104bob2o$103bo2b2o$104b2obo$104b2ob2o
$105bobo$106bo!