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Spiral Growth Geminoid Challenge

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

Spiral Growth Geminoid Challenge

Postby dvgrn » December 10th, 2013, 12:39 pm

It's now fairly straightforward to use Geminoid technology to put together a spiral-growth Life pattern. I can think of a couple of obvious designs:

1) Start with four pre-built spiral corners plus just one glider-stream-encoded recipe. Each spiral corner consists of a 90-degree stable reflector attached to a Geminoid universal constructor. The UC will use the recipe to build a copy of itself one step farther from the center of the spiral; at the same time, it will reflect the recipe to the next UC in the spiral. If the spiral is big enough, the fifth UC corner will be complete in time to accept the incoming glider stream after its trip around the first four corners.

The cycle will continue indefinitely, in at least a somewhat space-filling fashion -- it won't exercise every cell in the Life plane or anything like that, but at least any chosen location will eventually be no more than a few hundred cells away from a live cell.

2) Start with a high-period salvo shotgun that repeatedly emits the above glider-stream recipe. As before, each spiral corner will construct an offset copy of itself. However, the 90-degree output will be blocked until the end of the construction process, when a one-time-turner chain will remove the output-blocking eater and also block off the universal-constructor part of the circuitry, leaving only a stable reflector. The next recipe from the salvo gun will then activate the UC at the next corner.

The salvo gun can be folded into a relatively small two-dimensional space, which allows for an initial pattern with a much smaller bounding box. In absolute terms the population increase will be much slower, but it will get to all the same places eventually.

Here's a 62-still-life 9hd Geminoid universal constructor that Calcyman put together a while back:

x = 400, y = 272, rule = LifeHistory
110.2A194.2E$80.2A28.2A194.E$80.2A222.E.E$304.2E$92.A19.2A$90.3A19.2A
$89.A35.2A$89.2A34.A$123.A.A$123.2A$127.2A$127.2A3$63.2A$62.A2.A$63.
2A2$114.2A$114.2A$58.2A$57.A.A$57.2A$95.A$66.2A26.A.A$66.2A27.2A5$
121.2A$121.2A2$66.2A$67.A$2A65.A.A$2A66.2A3$82.2A$82.A.A$84.A$84.2A3$
66.2A$65.A.A$65.A$64.2A7.2A$73.2A5$172.2A$172.2A11$152.2A4.2A$93.2A
57.A4.A.A$86.2A5.2A16.A38.A.A4.A$86.2A21.3A29.2A7.2A4.2A$108.A11.A20.
2A$108.2A10.3A$88.2A33.A$88.2A32.2A$82.2A$70.2A10.2A93.2A$69.A2.A104.
A$70.2A85.2A19.3A$157.2A21.A$119.2A$119.2A25.2A$146.2A2$150.A$150.3A$
153.A$126.2A24.2A$79.A47.A12.2A$79.3A42.3A6.A6.2A$82.A41.A7.A.A54.A
34.A$81.2A50.A55.3A32.3A$192.A34.A$169.2A20.2A33.2A$169.2A7.2A56.2A$
178.A57.A$176.A.A55.A.A$176.2A4.2A44.2A4.2A$119.2A39.2A20.A44.A2.A$
119.A41.A18.A.A45.2A$120.3A38.A.A16.2A34.2A$101.2A19.A39.2A52.2A$101.
2A126.3A$229.A$230.A5$191.2A32.2A3.2A$191.2A11.2A20.A3.A$86.2A116.A
18.3A5.3A$86.2A80.2A35.3A15.A9.A$164.2A2.2A37.A$163.A.A$163.A23.2A$
162.2A23.A$188.3A$190.A23$92.2A$93.A$93.A.A$94.2A2$109.2A$109.2A3$92.
2A$92.2A5.2A$99.2A2$105.A$104.A.A$97.2A6.2A$98.A$95.3A$95.A111$397.3A
$397.A$398.A!

This would finally make some use of some of Guam's impressive Herschel technology from a few years back -- the 4hd transceiver and the R126 turn.

EDIT: Here's the 10hd version of Calcyman's universal constructor, with the same still-life count:

x = 395, y = 322, rule = LifeHistory
112.2A143.2E$82.2A28.2A143.E$82.2A171.E.E$255.2E$94.A19.2A$92.3A19.2A
$91.A35.2A$91.2A34.A$125.A.A$125.2A$129.2A$129.2A3$65.2A$64.A2.A$65.
2A2$116.2A$116.2A$60.2A$59.A.A$59.2A$97.A$68.2A26.A.A$68.2A27.2A5$
123.2A$123.2A2$68.2A$2E67.A$2E67.A.A$70.2A3$84.2A$84.A.A$86.A$86.2A3$
68.2A$67.A.A$67.A$66.2A7.2A$75.2A13$176.A$174.3A$152.2A19.A$93.2A57.A
20.2A$86.2A5.2A16.A38.A.A51.A$86.2A21.3A29.2A7.2A52.3A$108.A11.A20.2A
64.A14.A$108.2A10.3A83.2A12.3A$88.2A33.A95.A$88.2A32.2A95.2A$82.2A$
82.2A$218.2A$72.2A83.2A40.2A17.2A$71.A2.A82.2A40.2A$72.2A45.2A$119.2A
25.2A13.2A$146.2A13.2A2$150.A$150.3A49.2A$153.A28.2A19.A$126.2A24.2A
28.A.A15.3A$79.A47.A12.2A42.A15.A$79.3A42.3A6.A6.2A42.2A19.2A$82.A41.
A7.A.A71.A$81.2A50.A69.3A$203.A4$221.2A$221.A.A$119.2A75.2A25.A$119.A
77.A25.2A$120.3A74.A.A15.2A$101.2A19.A75.2A15.2A$101.2A9$86.2A$86.2A$
216.2A$216.A.A$218.A$218.2A9$206.2A$206.2A6$217.2A$196.2A19.A$197.A
17.A.A$197.A.A15.2A$198.2A4.A$203.A.A$203.A.A2.2C$204.A3.C.C4.2A$208.
C6.A.A$217.A$217.2A$202.2A$203.A$200.3A$200.A34$130.2A$131.A$131.A.A$
132.2A2$147.2A$147.2A3$130.2A$130.2A5.2C$137.2C2$143.A$142.A.A$135.2A
6.2A$136.A$133.3A$133.A124$393.C$392.2C$392.C.C!

The pieces don't fit together quite as tightly, but that has the nice side effect of allowing about twice as many different glider-pair timings for negative offsets, without any extra adjustment. By "negative offset" I mean the direction of adjustment that is eventually limited by the compression rating of the circuitry. In this kind of design, it's generally possible to have glider pairs with arbitrarily large positive offsets, just by delaying the second glider by the right amount.

As I mentioned on the old Geminoid Challenge thread, the jury is still officially out on whether 9hd or 10hd ultimately has a better set of elbow operations, but so far it looks like the 10hd toolkit is about thirty percent more efficient (!).
dvgrn
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Re: Spiral Growth Geminoid Challenge

Postby dvgrn » December 10th, 2013, 2:05 pm

Here's a more complete template for the spiral-growth pattern. Just imagine that the four quarters start out much farther apart, to leave room for a full encoded recipe stream. The copy of the corner in red at the far left has to be constructed by the universal constructor immediately to its right:

x = 919, y = 791, rule = LifeHistory
640.2A$640.2A56$654.2A$654.A.A$655.2A3$661.A$660.A.A$628.A31.A.A$628.
3A30.A$631.A11.A7.2A$630.2A9.3A7.2A$640.A$600.A39.2A$599.A.A$599.A.A$
600.A$627.2A$627.2A5$588.2A$588.A85.2A$586.A.A85.2A$586.2A13.2A33.2A$
601.2A34.A$634.3A$634.A$565.2A40.2A$565.2A40.2A$603.2A$603.2A64.2A$
669.A.A$671.A$526.2A8.A134.2A$526.2A6.3A71.2A$533.A74.2A42.A$518.2A
13.2A116.A.A$519.A131.2A$519.A.A$520.2A$525.2A$525.2A$575.2A$575.2A2$
522.A$521.A.A$521.2A2$605.2A$530.2A73.A.A$530.2A75.A67.2A$607.2A66.2A
$671.2A$671.2A$657.2A$657.2A4$578.2A16.2A$577.A.A16.2A7.2A$577.A27.A
39.2A$576.2A25.A.A39.2A$603.2A62.2A$587.2A78.A$588.A79.3A$588.A.A79.A
$589.2A74.2A$665.2A4$587.A$586.A.A$587.A6$588.2A$588.2A16.2A$606.2A4$
595.2A$595.2A3$592.2A13.2A$592.A14.A$590.A.A15.3A$590.2A18.A3$607.A$
598.2A7.3A$598.2A10.A$609.2A$579.A$577.3A$561.A14.A$561.3A12.2A$564.A
$563.2A3$564.2A$564.2A17.2A$583.2A2$621.2A$621.2A3$580.2A$580.A19.2A$
581.3A15.A.A$583.A15.A$577.2A19.2A$577.A$578.3A$580.A4$561.2A$560.A.A
$560.A25.2A$559.2A25.A$567.2A15.A.A$567.2A15.2A12$566.2A$565.A.A$565.
A$564.2A9$576.2A$576.2A6$565.2A$566.A19.2A$566.A.A17.A$567.2A15.A.A$
579.A4.2A$578.A.A$578.A.A$567.2A10.A$566.A.A$566.A$565.2A$580.2A$580.
A$581.3A$583.A5$110.2D254.2A$80.2D28.2D224.2A28.2A$80.2D254.2A2$92.D
19.2D234.A19.2A$90.3D19.2D232.3A19.2A$89.D35.2D218.A35.2A$89.2D34.D
219.2A34.A$123.D.D253.A.A$123.2D254.2A$127.2D254.2A$127.2D254.2A3$63.
2D254.2A$62.D2.D252.A2.A$63.2D254.2A2$114.2D254.2A$114.2D254.2A$58.2D
254.2A507.A$57.D.D253.A.A505.3A$57.2D254.2A505.A$95.D255.A460.2A6.2A$
66.2D26.D.D225.2A26.A.A459.A.A$66.2D27.2D225.2A27.2A460.A2$818.2A$
818.2A5.2A$825.2A$121.2D254.2A$121.2D254.2A$808.2A$66.2D254.2A484.2A$
67.D255.A$2D65.D.D186.2A65.A.A497.2A$2D66.2D186.2A66.2A497.A.A$825.A$
825.2A$82.2D254.2A$82.D.D253.A.A$84.D255.A$84.2D254.2A3$66.2D254.2A$
65.D.D253.A.A$65.D255.A$64.2D7.2D245.2A7.2A$73.2D254.2A5$172.2D254.2A
$172.2D254.2A6$728.A$728.3A$731.A23.2A$730.2A23.A$753.A.A$152.2D4.2D
248.2A4.2A295.A37.2A2.2A$93.2D57.D4.D.D189.2A57.A4.A.A269.A9.A15.3A
35.2A80.2A$86.2D5.2D16.D38.D.D4.D184.2A5.2A16.A38.A.A4.A271.3A5.3A18.
A116.2A$86.2D21.3D29.2D7.2D4.2D184.2A21.3A29.2A7.2A4.2A274.A3.A20.2A
11.2A$108.D11.D20.2D221.A11.A20.2A288.2A3.2A32.2A$108.2D10.3D241.2A
10.3A$88.2D33.D220.2A33.A$88.2D32.2D220.2A32.2A$82.2D254.2A$70.2D10.
2D93.2D147.2A10.2A93.2A$69.D2.D104.D147.A2.A104.A$70.2D85.2D19.3D145.
2A85.2A19.3A379.2A$157.2D21.D232.2A21.A264.2A52.2A39.A19.2A$119.2D
254.2A324.2A34.2A16.A.A38.3A$119.2D25.2D227.2A25.2A285.2A45.A.A18.A
41.A$146.2D254.2A284.A2.A44.A20.2A39.2A$683.2A4.2A44.2A4.2A$150.D255.
A275.A.A55.A.A$150.3D253.3A273.A57.A$153.D255.A271.2A56.2A7.2A$126.2D
24.2D228.2A24.2A281.2A33.2A20.2A$79.D47.D12.2D193.A47.A12.2A293.A34.A
$79.3D42.3D6.D6.2D193.3A42.3A6.A6.2A294.3A32.3A55.A50.2A$82.D41.D7.D.
D54.D34.D113.A41.A7.A.A54.A34.A213.A34.A54.A.A7.A41.A$81.2D50.D55.3D
32.3D110.2A50.A55.3A32.3A294.2A6.A6.3A42.3A$192.D34.D220.A34.A293.2A
12.A47.A$169.2D20.2D33.2D197.2A20.2A33.2A281.2A24.2A$169.2D7.2D56.2D
187.2A7.2A56.2A271.A$178.D57.D197.A57.A273.3A$176.D.D55.D.D195.A.A55.
A.A275.A$176.2D4.2D44.2D4.2D196.2A4.2A44.2A4.2A$119.2D39.2D20.D44.D2.
D144.2A39.2A20.A44.A2.A284.2A$119.D41.D18.D.D45.2D145.A41.A18.A.A45.
2A285.2A25.2A$120.3D38.D.D16.2D34.2D158.3A38.A.A16.2A34.2A324.2A$101.
2D19.D39.2D52.2D139.2A19.A39.2A52.2A264.A21.2A$101.2D254.2A126.3A250.
3A19.2A85.2A$485.A255.A104.A2.A$486.A253.2A93.2A10.2A$835.2A$795.2A
32.2A$795.A33.2A$796.3A10.2A$191.2D32.2D3.2D215.2A32.2A3.2A288.2A20.A
11.A$191.2D11.2D20.D3.D216.2A11.2A20.A3.A274.2A4.2A7.2A29.3A21.2A$86.
2D116.D18.3D5.3D108.2A116.A18.3A5.3A271.A4.A.A38.A16.2A5.2A$86.2D80.
2D35.3D15.D9.D108.2A80.2A35.3A15.A9.A269.A.A4.A57.2A$164.2D2.2D37.D
212.2A2.2A37.A295.2A4.2A$163.D.D253.A.A$163.D23.2D230.A23.2A$162.2D
23.D230.2A23.A$188.3D253.3A$190.D255.A6$745.2A$745.2A5$844.2A$844.2A
7.2A$853.A$851.A.A$851.2A3$833.2A$834.A$834.A.A$835.2A$92.2D254.2A$
93.D255.A$93.D.D253.A.A497.2A66.2A$94.2D254.2A497.A.A65.2A$851.A$109.
2D254.2A484.2A$109.2D254.2A$796.2A$796.2A$92.2D254.2A$92.2D5.2D247.2A
5.2A$99.2D254.2A2$105.D255.A460.2A27.2A$104.D.D253.A.A459.A.A26.2A$
97.2D6.2D246.2A6.2A460.A$98.D255.A505.2A$95.3D253.3A505.A.A$95.D255.A
507.2A$803.2A$803.2A2$854.2A$853.A2.A$854.2A3$790.2A$790.2A$794.2A$
793.A.A$793.A34.2A$792.2A35.A$805.2A19.3A$805.2A19.A2$837.2A$807.2A
28.2A$807.2A91$653.3A$653.A$654.A40$463.A$463.3A$466.A$465.2A$480.2A$
480.A$478.A.A$467.A10.2A$466.A.A$466.A.A$461.2A4.A$460.A.A15.2A$460.A
17.A.A$459.2A19.A$480.2A6$469.2A$469.2A9$481.2A$481.A$479.A.A$479.2A
12$461.2A15.2A$460.A.A15.2A$460.A25.2A$459.2A25.A$484.A.A$484.2A4$
466.A$466.3A$469.A$447.2A19.2A$447.A15.A$445.A.A15.3A$445.2A19.A$465.
2A3$424.2A$424.2A2$462.2A$462.2A17.2A$481.2A3$482.2A$482.A$469.2A12.
3A$470.A14.A$467.3A$467.A$436.2A$436.A10.2A$437.3A7.2A$439.A3$436.A
18.2A$436.3A15.A.A$439.A14.A$438.2A13.2A3$450.2A$450.2A4$439.2A$439.
2A16.2A$457.2A6$459.A$458.A.A$459.A4$380.2A$380.2A74.2A$376.A79.A.A$
376.3A79.A$379.A78.2A$378.2A62.2A$400.2A39.A.A25.2A$400.2A39.A27.A$
440.2A7.2A16.A.A$449.2A16.2A4$388.2A$388.2A$374.2A$374.2A$370.2A66.2A
$370.2A67.A75.2A$439.A.A73.2A$440.2A2$524.2A$523.A.A$524.A2$470.2A$
470.2A$520.2A$520.2A$525.2A$525.A.A$394.2A131.A$393.A.A116.2A13.2A$
394.A42.2A74.A$437.2A71.3A6.2A$374.2A134.A8.2A$375.A$375.A.A$376.2A
64.2A$442.2A$438.2A40.2A$438.2A40.2A$412.A$410.3A$409.A34.2A$409.2A
33.2A13.2A$371.2A85.A.A$371.2A85.A$457.2A5$418.2A$418.2A$446.A$445.A.
A$445.A.A$405.2A39.A$406.A$394.2A7.3A9.2A$394.2A7.A11.A$385.A30.3A$
384.A.A31.A$384.A.A$385.A3$390.2A$390.A.A$391.2A56$405.2A$405.2A!

Some trivial adjustment of the Herschel transceiver will almost certainly be needed, by the way, to allow a wider variety of glider-pair recipes to work. Moving the trombone-slide component in the NW by thirty or forty cells diagonally should be enough. Looks like that will mean increasing the offset to the new corner, maybe to 512 instead of 256 if we want to stick with powers of two for Hashlife's sake, but that's also a trivial change.

Can anyone come up with a significantly simpler design for a spiral-growth replicator unit?

I'd also be very interested in a more efficient universal constructor -- a two-arm design, for example, might allow for a much shorter total recipe stream. But I think it's someone else's turn to figure out the synchronization and programming details...!
dvgrn
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Re: Spiral Growth Geminoid Challenge

Postby towerator » December 10th, 2013, 5:00 pm

Those spirals UC are awesome, not because their function, but because they look like acutal cells. It is like a langton loop in GoL.
This is game of life, this is game of life!
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towerator
 
Posts: 323
Joined: September 2nd, 2013, 3:03 pm

Re: Spiral Growth Geminoid Challenge

Postby dvgrn » December 10th, 2013, 5:32 pm

towerator wrote:Those spirals UC are awesome, not because their function, but because they look like acutal cells. It is like a langton loop in GoL.

The best bet for a quadratic-growth spacefilling replicator in Conway's Life seems to be something along the lines of Langton's Loop. But nobody has seen one of those in action yet, and I'm afraid they'll mostly be empty space, so they'll just look like skinny diamonds.

You might be thinking of the loafer-seed gun variant with a double-spiral memory loop -- which is definitely fun to watch, but it doesn't necessarily have much to do with a spiral-growth universal constructor. The second design described in the original post could have a double-spiral memory loop in the center, to save space... but that object wouldn't get replicated out to the corner UCs in any recognizable form, so you wouldn't end up with anything resembling Langton's Loops.

Here are a few more experiments with 9hd and 10hd universal constructors that could be used in a spiral-growth pattern. Technically they're an improvement on Calcyman's design in terms of the number of still lifes -- these four are all about the same (I believe it's 55, 56, 57 and 58 still lifes). But they all require a semi-Snark pair quite a distance away:

x = 1102, y = 1177, rule = LifeHistory
304.2E$304.E$302.E.E$302.2E$724.2E$724.E$722.E.E$722.2E35$89.2A$82.2A
5.2A$82.2A3$84.2A17.2A8.2A$84.2A17.A9.2A$78.2A21.A.A$78.2A21.2A$119.
2A$119.2A$115.2A$115.2A4$120.2A$120.2A2$2E$2E73.A$75.3A$78.A$77.2A5$
504.A21.2A$502.3A21.2A$72.2A427.A35.2A$73.A427.2A34.A$73.A.A24.2A433.
A.A$74.2A23.A.A376.A56.2A$99.A370.A7.3A$98.2A370.3A8.A$88.2A16.2A365.
A6.2A$88.A.A15.2A17.2A345.2A$90.A34.2A384.2A11.2C12.2A$90.2A419.2A11.
2C12.A$70.2A464.A.A$70.A465.2A$71.3A$73.A$523.2A$79.2A387.2A44.2A6.A.
A$79.2A387.2A23.2A20.A6.A$95.A382.2D13.A18.3A6.2A$93.3A382.2D4.2A8.3A
15.A$92.A12.2A377.A11.A$92.2A10.A.A378.3A$104.A382.A$67.A35.2A$67.3A
455.2A$70.A453.A.A$69.2A453.A$401.2E120.2A$401.2E82.2A$485.A.A$487.A$
64.2A43.2A367.2A7.2A$65.A43.2A4.2A361.2A$65.A.A47.2A$66.2A$76.2A3.2A
446.2A$76.2A3.2A446.2A4.2A$114.2A350.2A67.2A$110.2A2.2A351.A$109.A.A
355.A.A$109.A12.2A344.2A$108.2A11.A.A410.2A$121.A408.2A2.2A$120.2A
407.A.A$91.2A244.3D46.3D140.A12.2A$91.2A189.2D26.6D19.5D44.5D139.2A
11.A.A$280.4D24.10D15.7D42.7D152.A$278.6D23.4D4.5D10.10D39.10D99.2A
50.2A$122.2A152.8D22.4D7.4D9.10D39.10D99.A$121.A.A150.10D21.4D8.4D13.
6D43.6D97.A.A$121.A155.7D20.4D10.4D12.6D43.6D97.2A$120.2A156.6D19.5D
10.5D11.6D43.6D$278.6D19.4D12.5D10.6D43.6D153.2A$279.5D18.5D12.5D10.
6D43.6D152.A.A$76.2A201.5D18.5D12.6D9.6D43.6D152.A$76.2A107.A93.5D17.
6D13.5D9.6D43.6D151.2A$185.3A91.5D17.5D14.5D9.6D43.6D$188.A90.5D17.5D
14.6D8.6D43.6D$130.2A55.2A90.5D16.6D14.6D8.6D43.6D$130.2A7.2A56.2A80.
5D16.6D14.6D8.6D6.6D21.7D3.6D216.A$139.A57.A81.5D16.6D14.6D8.6D4.9D
18.11D.6D216.3A$137.A.A55.A.A81.5D16.6D14.6D8.6D3.11D16.4D5.10D219.A$
137.2A4.2A44.2A4.2A82.5D16.6D14.7D7.6D2.13D13.5D7.9D79.2A15.2A63.2A
55.2A$121.2A20.A44.A2.A87.5D15.7D14.7D7.6D.3D5.6D12.5D9.8D78.A.A15.2A
63.2A7.2A56.2A$122.A18.A.A45.2A88.5D15.7D14.7D7.8D8.6D11.4D11.7D78.A
25.2A64.A57.A$122.A.A16.2A34.2A100.5D15.7D14.7D7.7D9.6D10.4D12.7D77.
2A25.A63.A.A55.A.A$123.2A52.2A100.5D15.7D14.7D7.6D11.5D9.5D13.6D102.A
.A63.2A4.2A44.2A4.2A$190.3C86.5D15.7D14.7D7.6D11.5D9.5D13.6D102.2A48.
2A20.A44.A2.A$190.C88.5D15.7D14.7D7.6D11.5D8.5D14.6D153.A18.A.A45.2A$
191.C87.5D15.7D14.7D7.6D11.5D8.5D14.6D153.A.A16.2A34.2A$279.5D15.7D
14.7D7.6D11.5D8.5D14.6D154.2A52.2A$279.5D15.7D14.7D7.6D11.5D8.5D14.6D
84.A136.3C$279.5D15.7D14.6D8.6D11.5D7.6D14.6D84.3A134.C$279.5D16.6D
14.6D8.6D11.5D7.6D14.6D87.A134.C$152.2A32.2A3.2A86.5D16.6D14.6D8.6D
11.5D7.6D14.6D86.2A$152.2A11.2A20.A3.A87.5D16.6D14.6D8.6D11.5D7.6D14.
6D$165.A18.3A5.3A84.5D16.6D14.6D8.6D11.5D7.6D14.6D$129.2A35.3A15.A9.A
84.5D17.5D14.5D9.6D11.5D7.6D14.6D$125.2A2.2A37.A110.5D17.5D14.5D9.6D
11.5D7.7D13.6D183.2A32.2A3.2A$124.A.A152.5D17.6D12.6D9.6D11.5D7.7D13.
6D183.2A11.2A20.A3.A$124.A154.5D18.5D12.5D10.6D11.5D8.6D13.6D196.A18.
3A5.3A$123.2A154.5D18.5D12.5D10.6D11.5D8.7D12.6D160.2A35.3A15.A9.A$
279.5D19.4D12.4D11.6D11.5D8.8D11.6D156.2A2.2A37.A$279.5D19.5D10.5D11.
6D11.5D9.7D11.6D155.A.A$279.5D20.4D10.4D12.6D11.6D8.9D8.7D106.2A47.A$
278.6D20.5D8.4D13.6D11.6D9.9D5.13D102.2A46.2A$278.6D21.5D6.5D13.6D11.
6D10.25D$277.9D20.5D4.4D13.9D8.9D10.14D.7D$273.16D19.10D12.14D2.15D8.
11D3.5D$310.6D56.6D5.3D5$480.2A$480.2A85$259.2A$259.2A3$268.2A$267.A.
A410.2A$268.A411.2A3$262.2C425.2A$262.2C2D422.A.A$264.2D423.A$269.2A$
269.A.A$271.A411.2C$256.2A13.2A410.2C2D$257.A427.2D$254.3A6.2A425.2A$
254.A8.2A425.A.A$692.A$677.2A13.2A$678.A$675.3A6.2A$675.A8.2A14$214.
2A$215.A$215.A.A$216.2A2$231.2A$231.2A2$222.2C$214.2A6.2C$214.2A5.2D$
221.2D2$227.A$226.A.A$219.2A6.2A$220.A$217.3A$217.A3$362.2C$362.C.C$
362.C3$784.C$783.2C$783.C.C3$609.2A$610.A$610.A.A$611.2A2$626.2A$626.
2A2$617.2C$609.2A6.2C$609.2A5.2D$616.2D2$622.A$621.A.A$614.2A6.2A$
615.A$612.3A$612.A101$490.3C$490.C$491.C3$911.3C$911.C$912.C92$301.2E
$301.E$299.E.E$299.2E10$727.2E$727.E$725.E.E$725.2E13$618.3C$618.C$
619.C3$1039.3C$1039.C$1040.C$108.2A$101.2A5.2A$101.2A3$103.2A17.2A8.
2A$103.2A17.A9.2A$97.2A21.A.A$97.2A21.2A$138.2A$138.2A$134.2A$134.2A
4$139.2A$139.2A3$21.2E71.A$21.2E71.3A$97.A$96.2A7$91.2A$92.A$92.A.A
24.2A209.3D46.3D$93.2A23.A.A181.7D19.5D44.5D$118.A181.11D15.7D42.7D$
117.2A179.5D4.6D10.10D39.10D$107.2A16.2A170.4D8.5D9.10D39.10D$107.A.A
15.2A17.2A150.4D10.5D12.6D43.6D147.A21.2A$109.A34.2A150.3D12.5D11.6D
43.6D145.3A21.2A$109.2A184.4D12.5D11.6D43.6D144.A35.2A$89.2A203.5D13.
5D10.6D43.6D144.2A34.A$89.A204.4D14.5D10.6D43.6D178.A.A$90.3A200.5D
14.6D9.6D43.6D121.A56.2A$92.A200.5D15.5D9.6D43.6D113.A7.3A$293.5D15.
6D8.6D43.6D113.3A8.A$98.2A193.5D15.6D8.6D43.6D116.A6.2A$98.2A193.5D
15.6D8.6D43.6D115.2A$114.A177.6D15.6D8.6D6.6D21.7D3.6D154.2A11.2C12.
2A$112.3A177.6D15.6D8.6D4.9D18.11D.6D154.2A11.2C12.A$111.A12.2A167.5D
15.6D8.6D3.11D16.4D5.10D179.A.A$111.2A10.A.A167.6D14.6D8.6D2.13D13.5D
7.9D179.2A$123.A169.6D14.6D8.6D.3D5.6D12.5D9.8D$86.A35.2A169.6D14.6D
8.8D8.6D11.4D11.7D$86.3A204.7D13.6D8.7D9.6D10.4D12.7D166.2A$89.A204.
6D13.6D8.6D11.5D9.5D13.6D111.2A44.2A6.A.A$88.2A204.7D12.6D8.6D11.5D9.
5D13.6D111.2A23.2A20.A6.A$295.7D9.8D8.6D11.5D8.5D14.6D121.2D13.A18.3A
6.2A$296.8D5.10D8.6D11.5D8.5D14.6D121.2D4.2A8.3A15.A$297.14D.6D9.6D
11.5D8.5D14.6D127.A11.A$115.2A181.11D3.6D9.6D11.5D8.5D14.6D128.3A$83.
2A31.A183.7D4.7D9.6D11.5D7.6D14.6D130.A$84.A31.A.A15.2A175.6D10.6D11.
5D7.6D14.6D$84.A.A30.2A15.2A175.6D10.6D11.5D7.6D14.6D168.2A$85.2A223.
6D11.6D11.5D7.6D14.6D167.A.A$95.2A3.2A208.6D11.6D11.5D7.6D14.6D44.2A
121.A$95.2A3.2A207.6D12.6D11.5D7.6D14.6D44.2A120.2A$309.6D12.6D11.5D
7.7D13.6D128.2A$308.6D13.6D11.5D7.7D13.6D128.A.A$307.6D14.6D11.5D8.6D
13.6D130.A$307.5D15.6D11.5D8.7D12.6D121.2A7.2A$306.5D16.6D11.5D8.8D
11.6D121.2A$305.5D17.6D11.5D9.7D11.6D$304.5D18.6D11.6D8.9D8.7D159.2A$
110.2A191.5D19.6D11.6D9.9D5.13D156.A$110.2A23.2A165.4D21.6D11.6D10.
25D157.A.A15.2A$135.A.A162.5D20.9D8.9D10.14D.7D160.2A15.2A$137.A159.
6D20.14D2.15D8.11D3.5D$137.2A154.7D65.6D5.3D114.2A$494.A$494.A.A$495.
2A2$119.2A$95.2A21.A.A$95.2A21.A$117.2A394.2A$513.A$511.A.A47.2A$511.
2A48.A.A$147.A34.A380.A$147.3A32.3A378.2A$150.A34.A$127.2A20.2A33.2A$
127.2A7.2A56.2A$136.A57.A$134.A.A55.A.A350.2A$134.2A4.2A44.2A4.2A350.
A.A$118.2A20.A44.A2.A355.A$119.A18.A.A45.2A355.2A$119.A.A16.2A34.2A$
120.2A52.2A317.2A15.2A$187.3C302.A.A15.2A$187.C304.A25.2A53.A34.A$
188.C302.2A25.A54.3A32.3A$516.A.A57.A34.A$516.2A35.2A20.2A33.2A$553.
2A7.2A56.2A$562.A57.A$149.2A32.2A3.2A370.A.A55.A.A$149.2A11.2A20.A3.A
309.A61.2A4.2A44.2A4.2A$162.A18.3A5.3A306.3A43.2A20.A44.A2.A$126.2A
35.3A15.A9.A309.A43.A18.A.A45.2A$122.2A2.2A37.A334.2A43.A.A16.2A34.2A
$121.A.A422.2A52.2A$121.A491.3C$120.2A491.C$614.C5$575.2A32.2A3.2A$
520.2A53.2A11.2A20.A3.A$520.2A66.A18.3A5.3A$552.2A35.3A15.A9.A$548.2A
2.2A37.A$547.A.A$547.A$546.2A4$505.2A$505.2A81$256.2A$256.2A3$265.2A$
264.A.A$265.A3$259.2C$259.2C2D$261.2D$266.2A$266.A.A$268.A414.2A$253.
2A13.2A413.2A$254.A$251.3A6.2A$251.A8.2A430.2A$691.A.A$692.A3$225.2A
459.2C$226.A459.2C2D$226.A.A459.2D$227.2A464.2A$693.A.A$242.2A451.A$
242.2A436.2A13.2A$681.A$233.2C443.3A6.2A$225.2A6.2C443.A8.2A$225.2A5.
2D$232.2D2$238.A$237.A.A$230.2A6.2A$231.A$228.3A$228.A10$352.2C$352.C
.C$352.C10$626.2A$627.A$627.A.A150.C$628.2A149.2C$779.C.C$643.2A$643.
2A2$634.2C$626.2A6.2C$626.2A5.2D$633.2D2$639.A$638.A.A$631.2A6.2A$
632.A$629.3A$629.A130$511.3C$511.C$512.C13$939.3C$939.C$940.C143$671.
3C$671.C$672.C13$1099.3C$1099.C$1100.C!

It may be possible to tighten these up somehow by using different settings on the period quadruplers, but I don't think so. Also, Calcyman's design has a huge efficiency advantage: all of the input gliders code for construction-arm gliders. In the above designs, two gliders out of every group of four are non-coding -- they serve only to reset the semi-Snarks and the period quadrupler (or period doublers).

Is there any simpler way to get the right amount of delay between the input gliders, to allow a wide range of glider-pair outputs... but use only one semi-Snark or period doubler on each construction lane?
dvgrn
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Re: Spiral Growth Geminoid Challenge

Postby dvgrn » August 1st, 2014, 4:40 pm

Finally took some time off of other half-baked projects, and cleaned up the last few details of a 10hd Geminoid universal constructor. This makes it possible to complete a relatively compact spiral growth pattern... less than 1.6 million cells on a side (sheesh):

Spiral-growth-pattern.png
Spiral-growth pattern overview
Spiral-growth-pattern.png (2.92 KiB) Viewed 3951 times

Life-spiral.mc.gz
Four 10hd Geminoid universal constructors programmed for spiral growth
(45.32 KiB) Downloaded 233 times

"10hd" means that the pairs of gliders aimed at the construction elbow are spaced 10 half-diagonals apart, instead of 9hd as in the linear Life replicator. 10hd still appears to be significantly more efficient, but I haven't done a side-by-side compilation of two identical recipes yet.

Here's a minimal version of the spiral-growth pattern with the input gliders in a single stream:

Spiral-in-Life-straightline-min.mc.gz
B3/S23 spiral-growth pattern with straight-line input recipe
(16.77 KiB) Downloaded 191 times
dvgrn
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Re: Spiral Growth Geminoid Challenge

Postby simsim314 » August 4th, 2014, 12:51 pm

Nice this one is simpler than any Geminoid or replicator, but still an interesting construction.

I think the question is: how can we use this construction in some more complex constellation, say quadratic growth, or something of a kind.
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