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:

Code: Select all

`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:

Code: Select all

`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 (!).