Eater 3 synthesized with 42 gliders!

[Extrementhusiast]

This should explain itself:

Code: Select all

x = 333, y = 34, rule = LifeHistory
266.A$265.A$261.A3.3A$262.2A7.A$261.2A6.2A$18.A215.A35.2A$16.2A204.2A
10.A.A$17.2A201.A.A.A9.2A$105.A112.A.A.A$106.A60.A.A49.2A15.2A30.2D
29.2C21.2C$104.3A61.2A44.2A2.D16.A.A3.A20.A5.2D29.2C21.2C$8.A6.A92.A
59.A46.2AD.D17.A.DA.C20.A5.A2.C30.C22.C$9.2A5.2A90.A.A103.A3.2D19.2D
2C18.3A4.D4C16.A9.5C18.5C$8.2A5.2A8.A.A25.A54.2A56.2A100.D21.2A7.C22.
C$25.2A24.A.A113.2A2.2D19.2C24.2C21.2C28.2C16.2A11.2C21.2C$7.A12.D5.A
25.2A6.C85.2C.2C15.A4.DAC.2C15.C.C.2C20.C.C.2C17.C.C.2C11.A.A10.C.C.
2C25.C.C.2C17.C.C.2C$6.2A8.2D.D.D26.A7.2C.C.C83.D.C.C.C19.A.C.C.C16.C
.C.C21.C.C.C18.C.C.C11.2A12.C.C.C16.A4.D4.C.C.C13.C4.C.C.C$6.A.A7.2D.
D2.D26.A2.A2.DAC.C2.C51.2A24.A4.C.C.C2.C18.ADC.C2.C14.2C.C2.C19.2C.C
2.C16.2C.C2.C10.A12.2C.C2.C16.A2.D.D2.2C.C2.C11.C.C2.2C.C2.C$19.D.2D
24.3A2.2A.2D2.C.2C41.2D.DC5.A.A21.A.A4.AC2.C.2C19.A2.C.2C17.C.2C22.C.
2C19.C.2C26.C.2C14.3A2.D2.D4.C.2C11.C2.C4.C.2C$19.D31.A.A5.C44.AC.C.C
4.A24.2A8.C25.C20.C25.C22.C29.C23.2D5.C15.2C5.C$18.2D38.2C43.C.C.C2.C
37.2C16.2A6.2C18.DAC23.C.C20.C.C14.3A10.C.C28.C.C20.C.C$103.2C2.C.2C
30.3A21.A.A23.A2.2D5.A18.2C21.2C17.A10.2C17.3A9.2C21.2C$31.A75.C35.A
23.A24.2A5.2A60.A32.A$31.A.A72.2C34.A19.2A8.2A17.2A7.2A91.A$24.3A4.2A
128.A.A8.A.A139.3C$12.3A9.A138.A8.A26.A116.C$3A11.A10.A172.2A115.C$2.
A10.A176.3A5.A.A$.A188.A120.3C$191.A121.C$10.A301.C$10.2A4.A$9.A.A4.
2A$15.A.A!

[mniemiec]

This should explain itself:

Very nice! I had previously written eater-3 off into the "don't hold your breath" category, since it didn't seem like one could grow the pre-block from one arm, or vice versa. I hadn't considered using a different stator form. I hadn't seen the bookend version before.

[Sokwe]

Here is a slight reduction of one of the steps:

Code: Select all

x = 22, y = 20, rule = B3/S23
2bo$obo$b2o12bo$14bo$14b3o8$2bo$2b2o$bobo6bo$6b2obobo8bo$5bobobo2bo6b
2o$5b2o2bob2o6bobo$9bo$8b2o!

[Extrementhusiast]

Main post has been updated.

[Sphenocorona]

This new discovery got me wondering how close we are to synthesizing the original form with current techniques. Of course this is not possible at this time, maybe at some point it will be. In the mean time here is the construction plan so far, with the two consecutive question marks where gaps need to be filled:

Code: Select all

x = 141, y = 154, rule = LifeHistory
112.A$113.2A$112.2A3.A$99.A.A7.A7.A.A$100.2A5.A.A7.2A$21.A78.A7.2A$
19.A.A$20.2A76.2A$27.A69.A.A$27.A.A69.A$27.2A95.2A.2A$43.2A3.2A13.2A
3.2A13.2A3.2A11.A6.2A3.2A9.2A.A3.2A$28.A15.A2.A.A14.A2.A.A14.A2.A.A
11.2A6.A2.A.A12.A2.A.A$18.2A8.2A3.A10.A.A.A15.A.A.A15.A.A13.A.A6.A.A
15.A.A$19.2A6.A.A3.A.A9.A.A17.A.A17.A24.A17.A$18.A14.2A11.A19.A2.2A$
69.A.A$65.2A2.A$64.A.A$66.A10$95.A$96.A$94.3A2$101.A$99.A.A$100.2A$
26.A$27.A$25.3A$81.A2.A17.A4.A$85.A15.2A4.A.A25.2A$81.A3.A15.A.A3.2A
27.A$82.4A49.A$48.2A84.A$47.A2.A17.2A28.2A33.A$47.A2.A16.A2.A26.A.A
32.A$16.2A.2A9.2A5.2A.2A6.2A17.A2.A25.A34.A$16.2A.A3.2A4.2A6.2A.A3.2A
11.2A.2A6.2A17.2A.2A3.A34.A$19.A2.A.A6.A8.A2.A.A11.2A.A3.2A21.2A.A3.A
26.2A.2A3.A$19.A.A18.A.A17.A2.A.A11.A12.A2.A27.2A.A3.A$20.A20.A18.A.A
13.2A12.A.A31.A2.A$61.A14.A.A12.A32.A.A$109.2A14.A$109.A.A$109.A$64.
2A$65.2A6.2A21.3D$64.A7.2A21.D3.D$68.3A3.A20.D3.D$70.A27.D$69.A27.D$
97.D2$97.D3$97.D$97.D$97.D$97.D$97.D$97.D$97.D$94.7D$95.5D$96.3D$97.D
7.A$105.2A$14.2A16.2A32.2A36.A33.3B$15.A17.A33.A35.A34.3B$14.A17.A33.
A35.A33.5B$13.A17.A33.A10.3D22.A34.3B$12.A17.A33.A10.D3.D20.A33.5B$
11.A17.A33.A11.D3.D13.2D4.A34.3B$10.A17.A33.A15.D11.CA.CA3.A33.5B$9.A
17.A33.A15.D11.DAC.C3.A29.2A3.3B$2A.2A3.A9.2A.2A3.A25.2A.2A3.A16.D12.
D2.C2.A27.C2.C2.5B$2A.A3.A10.2A.A3.A26.2A.A3.A33.C.A27.A.C.C2.A2B$3.A
2.A14.A2.A30.A2.A18.D16.C3.AD24.A2.C.ABAB$3.A.A4.A10.A.A31.A.A37.4CD
27.C.2A$4.A4.A12.A33.A71.C4.A$9.3A11.3A31.3A37.CA30.4CA$25.A33.A36.DA
C$97.D33.C$14.A115.A.C$6.2A6.A.A114.A$5.2A7.2A$7.A3.2A$10.2A73.2D19.D
$12.A72.D20.D2.D$85.2D.D.D2.D3.D.D3.D2.D.D.D$85.D3.D2.D.D.D.D.D.D.D.D
.2D$85.2D.D.D2.2D.D.D.D.2D2.D.D$102.D6.2D4$92.2D6.D$91.D2.D5.D.D.D$
91.D2.D.2D2.D.D.D$91.D2.D.D.D.D2.2D$92.2D2.D.D.D3.D$103.D20$35.A$36.A
$34.3A87.A$65.2A56.A$62.C2.C57.3A$32.2A27.A.C.C22.A$29.C2.C29.A2.C.2A
20.A$28.A.C.C2.A7.2A20.C2.A18.3A$29.A2.C.ABA6.A.A20.C4.A46.2A$32.C.2A
7.A23.4CA41.2A2.A2.A$33.C4.A46.2A23.C2.C4.A.A$34.4CA30.C12.C2.C23.A.C
.C5.A$68.A.C10.A.C.C10.2A12.A2.C.2A$36.C32.A12.A2.C.2A7.A.A14.C2.A$
35.A.C47.C2.A7.A17.C4.A$36.A49.C4.A23.4CA$87.4CA$117.C$89.C26.A.C$88.
A.C26.A$89.A!

The problem here is synchronizing the diagonal wick with building out the arms, and finding out how to build the arms further in the first place.

It's really cool to see that an alternate form of the eater 3 now has a synthesis, allowing (for example) the rectifier to be glider constructed, which means it could be used in a geminoid spaceship if needed or desired.

[mniemiec]

Two slight improvements to the variant eater-3 synthesis:

Step 3: can be reduced by 2 gliders (now 1, after Sokwe's improvement) by using 3 gliders to directly produce a line-of-3 spark that leaves a spurious bit on only one side, rather than using 2 extra gliders to remove one side from a similar spark that leaves a bit on both sides.

Code: Select all

x = 28, y = 16, rule = B3/S23
bbo$3bo$b3o$5bo$5bobo$5boo4$11boo$5bo5bobo7booboo$boobobo4bo10bobobo$o
bobobbo12bobobobbo$oobboboo12boobboboo$4bo19bo$3boo18boo!

Steps 7+8: Instead of using 5 gliders to add a long bookend, you can use 5 gliders to add a table to reduce the bit count by 2 (and streamline the northeast corner slightly as well). for the same cost.

[Freywa]

Instead of using 5 gliders to add a long bookend, you can use 5 gliders to add a table to reduce the bit count by 2 (and streamline the northeast corner slightly as well). for the same cost.

But the cheapest method listed on the Pentadecathlon catalogue uses 6 gliders. Where's the 5-glider synthesis?

[mniemiec]

Instead of using 5 gliders to add a long bookend, you can use 5 gliders to add a table to reduce the bit count by 2 (and streamline the northeast corner slightly as well). for the same cost.

But the cheapest method listed on the Pentadecathlon catalogue uses 6 gliders. Where's the 5-glider synthesis?

It's two steps: 3 to add a bot (using one of several long-known methods), plus 2 to turn the boat into a table. Buckinham had found several 3-glider methods long ago. I found a 2-glider method a few years ago, that ended up slightly improving many syntheses. Here they are in context:

Code: Select all

x = 72, y = 17, rule = B3/S23
37bo$8b2o27bobo$6bobobo26b2o$4bobobo$5b2o32b2o$2o22bo13bobo3bo$b2o20bo
bo14bo2bobo16bo2bo$o23b2o18b2o16b4o2$4b2o18b2o18b2o18b2o$4bobob2o14bob
ob2o14bobob2o14bobob2o$6bobobo15bobobo15bobobo15bobobo$5b2obo2bo13b2ob
o2bo13b2obo2bo13b2obo2bo$8bob2o16bob2o16bob2o16bob2o$8bo19bo19bo19bo$
6bobo17bobo17bobo17bobo$6b2o18b2o18b2o18b2o!

[Extrementhusiast]

Main post has been updated again.

I'm not surprised that I didn't find that 3-glider version of step 3, as the method I initially used was the first one I found. I was aiming more for a proof-of-concept rather than maximum efficiency. But I guess that that's how glider syntheses of large objects work.

(However, the old form, with the extra hook, is better in one category: glider destruction. One appropriately-placed glider can destroy the entirety of the eater, while the new form requires more than just a glider.)

The nice part about this synthesis is that it has some flexibility in terms of step ordering.

EDIT: Perhaps it is easier. Eight-block destruction of rectifier:

Code: Select all

x = 72, y = 85, rule = LifeHistory
71.B$70.2B$69.3B$68.4B$67.5B$66.5B$65.5B$64.5B$63.5B$62.5B$61.5B$60.
5B$59.5B$58.5B$57.5B$56.5B$55.5B$54.5B$53.5B$52.5B$51.5B$50.5B$49.5B$
48.5B$47.5B$46.5B$24.A20.5B$25.A18.5B$23.3A9.2A6.5B$35.2A5.5B$41.5B$
40.5B$39.5B$38.5B$37.5B$36.5B$35.5B6.2A$34.5B7.2A$33.5B$32.5B3.2A$31.
5B4.2A$12.2A16.5B9.A$12.2A15.5B6.5A$18.2A8.5B7.A$19.A7.6B9.B2A$19.A.A
B3.9B7.BA.A.2A$9.2A9.2AB.11B5.A4BA.A.A$9.2A3.2A6.13B4.ABA2B2A.A2.A$
14.2A5.14B4.A2BAB2.BA.2A$21.19B2AB4.A$9.2A9.20B5.A.A$10.A7.22B5.2A$
10.A.AB4.21B$11.2AB.24B$13.26B$13.16B2A8B$15.14B2A7B$14.24B$13.4B.19B
$12.4B3.14B2.B$11.4B5.12B$10.4B5.11B$9.4B5.12B$8.4B5.13B$7.4B5.14B$6.
4B5.15B$5.4B5.4B.10B$4.4B5.4B2.10B$3.4B5.4B2.2BA8B$2.4B5.4B2.2BABA6B$
.4B5.4B4.BABA4B$D3B5.4B5.2BA4B$DBD5.4B6.6B$2D5.4B7.5B$6.4B9.3B$5.4B
18.2A$4.4B19.2A$3.4B$2.4B$.2D2B28.2A$DBDB29.2A$.BD2$24.2A$24.2A!