ConwayLife.com

Posted: **August 24th, 2016, 3:26 pm**

Advancing the bottom-left glider by N generations causes the pattern to emit N gliders at period-1024:

x = 308, y = 213, rule = B3/S23
178b2o$178bobo$180bo4b2o$176b4ob2o2bo2bo$176bo2bobobobob2o$179bobobobo
$180b2obobo$184bo2$170b2o$171bo7b2o$171bobo5b2o$172b2o4$243bo$243b3o$
246bo$182b2o61b2o$182bo$183b3o$185bo9$83b2o$83b2o3$287b2o$287bo$285bob
o$243bo37b2o2b2o$217bo9bo15b3o35b2o$217b3o5b3o18bo$68b2o150bo3bo20b2o
11b2o$68b2o149b2o3b2o32b2o8$233b2o52b2o16bo$233b2o34b2o16bobo13b3o$88b
2o131b2o45bobo18bo12bo$88bo131bo2bo44bo20b2o11b2o$89b3o123b2o4b2o44b2o
4b2o$91bo122bobo55bobo$214bo57bo$213b2o56b2o7b2o$223b2o33b2o20b2o$223b
o34bo$224b3o32b3o$226bo34bo4$178bo$100bo34bo42b3o$100b3o32b3o43bo$103b
o34bo41b2o6bo$80b2o20b2o33b2o48bobo$80b2o7b2o56b2o39bo$89bo57bo$87bobo
55bobo122bo$87b2o4b2o44b2o4b2o28b2o93b3o$71b2o20bo44bo2bo33b2o6b2o88bo
$72bo18bobo45b2o42b2o87b2o$72bobo16b2o34b2o$73b2o52b2o63b2o$192b2o2$
177b2o$176bobo$176bo$175b2o2$102b2o32b2o3b2o149b2o$102b2o11b2o20bo3bo
150b2o$115bo18b3o5b3o$79b2o35b3o15bo9bo$75b2o2b2o37bo$74bobo$74bo$73b
2o3$277b2o$277b2o5$150bo$150b3o$153bo44b2o$152b2o44bo$176bo22b3o$176b
3o22bo$144b2o33bo$115b2o27bo33b2o$115bo25b2obo$116b3o22bo2b3o4b2o$118b
o23b2o3bo3b2o$144b4o$144bo15b2o83bo$145b3o12bobo82b3o$148bo13bo25b2o
58bo$143b5o14b2o17b2o5bobo56b2o$143bo37b2o7bo$145bo44b2o$144b2o$177bo$
176bobob2o$176bobobobo$173b2obobobobo2bo$173bo2bo2b2ob4o$130b2o43b2o4b
o$131bo49bobo$131bobo48b2o$132b2o7$131b2o4b2o$131b2o4b2o2$189bo$187b3o
42bo$136b2o48bo43b3o$132b2o2b2o48b2o41bo$131bobo37b2o56b2o$131bo40bo$
130b2o40bob2o$173bo2bo$174b2o$189b2o13b2o$189b2o13b2o26b2o$232b2o2$
144b2o$143bobo$143bo$142b2o$192b2obo6b2o$192b2ob3o3bobo38b2o$92bo105bo
2bo41bo43b2o$93bo98b2ob3o2b2o25b2o11b3o44bo$91b3o99bobo31b2o11bo44bobo
$181b2o10bobo85b2o2b2o$152b2o27b2o11bo86b2o$152b2o7b2o50b2o$161bo52bo
43b2o$159bobo49b3o39b2o3b2o$159b2o50bo41b2o$223b2o$223bo15b2o$110b2o
112b3o13bo11b2o$110b2o114bo10b3o13bo4b2o$237bo12b3o5b2o$250bo$287b2o$
269b2o16bobo$136b2o130bobo18bo$136bobo129bo20b2o$137bo129b2o4$117b2o
36bo120b2o$93b2o22b2o35bobo119b2o$94bo59bobo$94bobo58bo$95b2o$99b2o$
98bo2bo44b2o$98bobo45b2o7b2o$99bo55b2o2$108b2o160b2o29b2o$107bobo161bo
29b2o$b2o104bo163bobo$obo103b2o164b2o$2bo93b2o21b2o$97bo21b2o$94b3o$
94bo$121b2o$121b2o177b2o2b2o$299bobo2bobo$300bo5bo$283bo22b2o$282bobo$
282b2o5$263b2o$264bo$261b3o$261bo!

Does anyone see a convenient way to simplify this (i.e. make it constructible in fewer gliders)?

Posted: **August 24th, 2016, 4:25 pm**

calcyman wrote:Advancing the bottom-left glider by N generations causes the pattern to emit N gliders at period-1024: ...
Does anyone see a convenient way to simplify this (i.e. make it constructible in fewer gliders)?

Seems as if the p1023 loop ignition could probably be cheaper.

For example, if the p1023 loop can be redesigned to include an NW31 edge shooter in the northwest, then the whole G-to-edge-shooter component in the southwest could be removed, because the ignition glider could be sent straight in to start up the p1023 loop.

Alternatively, is it allowable to start up the p1023 loop with a G0 glider pair instead of a single glider? It shouldn't be too painful to build a transparent G0 emitter, by starting with (say) a Fx77 conduit, and doubling back the Herschel to drop another glider on the same lane (with a transparent SW-2 H-to-G, maybe). Then you could start up the loop by shooting through the H-to-G0... right?

I'd have to beat my head against the Inconvenient Herschel Geometry Brick Wall for a while, but possibly similar tricks might be applied to the p1024 loop, to get rid of more of those constructible but still expensive Snarks.

Maybe it would be worth using an Lx200 instead of an F166 following the syringe in the p1023 loop, before the H-to-G0 component. The remaining 90-degree turn could be done with the semi-Snark -- assuming that the timing mod 8 can be made to work out, but we have a lot of conduit options to choose from these days.

EDIT: Sorry, that last doesn't work -- you don't get mod-8 timing adjustability unless there's a 180-degree reflector somewhere. Two semi-Snarks and a custom H-to-4-gliders-in-a-row, possibly? Can we get four gliders onto one lane in less than a thousand ticks?

EDIT2: Here's a half-baked idea: is there a way for the interaction of two Herschel signals, or a Herschel and a glider, to shut down both loops in a way similar to the 2G->loaf->nothing trick used in the current phase meter? Here are two Herschel-factory loops, both startable by a glider, one p1023 and one p1024:

Code: Select all

x = 325, y = 99, rule = LifeHistory
237.A$237.3A$240.A$239.2A$239.5B8.A$241.4B5.3A$239.7B3.A$238.9B2.2A$
197.A38.11B.3B2.B15.A11.2A$197.3A36.13B3.3B13.A.A9.B2AB$200.A22.A11.
2A18B13.A.A9.3B$60.A138.2A20.3A11.2A18B7.2A2.3A.2A9.B.B$60.3A136.4B
17.A15.B.18B6.A2.A4.B8.5B$63.A137.3B16.2A17.18B2.BA.A3.3AB2A6.6B$62.
2A136.4B14.4B15.20B2.B2A6.A.2A4.8B$62.5B8.A107.2B15.5B12.3B5.B.7B2.
24B10.13B$64.4B5.3A105.5B13.6B11.4B.13B2.24B12.13B$62.7B3.A107.7B12.
8B2.50B12.15B$61.9B2.2A106.8B10.14BD45B2.B10.15B$20.A38.11B.3B2.B15.A
11.2A73.9B11.13B3D48B5.B.17B$20.3A36.13B3.3B13.A.A9.B2AB71.10B12.7B.
4BDBD15B2A55B$23.A22.A11.2A18B13.A.A9.3B72.A8B12.15BD15B2A26B2A13B2A
13B$22.2A20.3A11.2A18B7.2A2.3A.2A9.B.B70.ABA8B11.19B2.2B3.11B.21B2A
13B2A14B$22.4B17.A15.B.18B6.A2.A4.B8.5B70.ABA10B8.17B11.10B2.46B3.B2A
$24.3B16.2A17.18B2.BA.A3.3AB2A6.6B70.BA14B2.2B.15B16.6B3.45B4.A2.A$
23.4B14.4B15.20B2.B2A6.A.2A4.8B71.11BD22B19.3B5.28B2.2B2.B3.6B5.2A.A$
6.2B15.5B12.3B5.B.7B2.24B10.13B72.9BDBD13B.9B20.B4.13B.7B2.4B13.6B7.A
$4.5B13.6B11.4B.13B2.24B12.13B72.7B3D9B2A2B3.8B19.2A3.13B2.6B17.9B6.
2A$3.7B12.8B2.50B12.15B71.7BD11B2A2B5.B3.2A20.A5.11B3.3B19.2A4.4B$3.
8B10.14BD45B2.B10.15B72.B2.18B10.A18.3A8.9B4.B21.A5.4B$2.9B11.13B3D
48B5.B.17B81.4B.3B.B12.3A15.A10.8B24.3A7.4B$.10B12.7B.4BDBD15B2A55B
82.4B19.A26.8B24.A10.4B$.A8B12.15BD15B2A26B2A13B2A13B82.4B47.6B36.4B$
ABA8B11.19B2.2B3.11B.21B2A13B2A14B82.4B46.5B38.4B$ABA10B8.17B11.10B2.
46B3.B2A82.4B47.3B39.4B$BA14B2.2B.15B16.6B3.45B4.A2.A82.4B89.4B$.11BD
22B19.3B5.28B2.2B2.B3.6B5.2A.A82.4B89.4B$.9BDBD13B.9B20.B4.13B.7B2.4B
13.6B7.A83.4B89.4B$3.7B3D9B2A2B3.8B19.2A3.13B2.6B17.9B6.2A83.4B89.4B$
3.7BD11B2A2B5.B3.2A20.A5.11B3.3B19.2A4.4B91.4B89.4B$4.B2.18B10.A18.3A
8.9B4.B21.A5.4B91.4B89.4B$14.4B.3B.B12.3A15.A10.8B24.3A7.4B91.4B89.4B
$15.4B19.A26.8B24.A10.4B91.4B89.4B$16.4B47.6B36.4B91.4B89.4B$17.4B46.
5B38.4B91.4B89.4B$18.4B47.3B39.4B91.4B89.4B$19.4B89.4B91.4B89.4B$20.
4B89.4B91.4B89.4B$21.4B89.4B91.4B89.4B$22.4B89.4B91.4B89.4B$23.4B89.
4B91.4B89.4B$24.4B89.4B91.4B89.4B$25.4B89.4B91.4B89.4B$26.4B89.4B91.
4B89.4B$27.4B89.4B91.4B89.4B$28.4B89.4B91.4B89.4B$29.4B89.4B91.4B89.
4B$30.4B89.4B91.4B89.4B$31.4B89.4B91.4B89.4B$32.4B89.4B91.4B89.4B$33.
4B89.4B91.4B88.4B$34.4B89.4B5.3B83.4B87.5B$35.4B89.4B4.4B83.4B85.9B$
36.4B89.12B.B81.4B84.9B$37.4B39.3B39.A7.12B2A81.4B39.3B41.9B$38.4B38.
5B37.3A6.9B.B2A82.4B38.5B38.10B$39.4B36.6B40.A4.10B2.B84.4B36.6B37.
12B$40.4B10.A24.8B25.2A10.2A3.12B87.4B10.A24.8B25.2A8.13B$41.4B7.3A
24.8B10.A15.A10.18B87.4B7.3A24.8B10.A15.A9.11B$42.4B5.A21.B4.9B8.3A
15.A.AB9.15B17.A71.4B5.A21.B4.9B8.3A15.A.AB4.12B$43.4B4.2A19.3B3.11B
5.A19.2AB.3B4.20B11.3A72.4B4.2A19.3B3.11B5.A19.2AB.15B$36.2A6.9B17.6B
2.13B3.2A20.7B.23B8.A68.2A6.9B17.6B2.13B3.2A20.17B$37.A7.6B13.4B2.7B.
13B4.B20.32B7.2A68.A7.6B13.4B2.7B.13B4.B20.17B$37.A.2A5.6B3.B2.2B2.
28B5.3B19.31B2.B.5B3.2A63.A.2A5.6B3.B2.2B2.28B5.3B19.17B.B$38.A2.A4.
45B3.6B16.32B.6B4.B2AB63.A2.A4.45B3.6B16.19B2A$39.2AB3.6BC39B2.10B11.
41B5.2B65.2AB3.6BC39B2.10B11.19B.B2A$40.9BCBC2B2A13B2A21B.11B3.2B2.
19B.26B.3B67.9BCBC2B2A13B2A21B.11B3.2B2.20B4.B$41.9B2C2B2A13B2A26B2A
15BD15B2.31B2.B63.9B2C2B2A13B2A26B2A15BD16B$42.55B2A15BDBD4B.7B4.30B.
B2A63.55B2A15BDBD4B.9B$42.17B.B5.48B3D4B2.7B3.32B2A63.17B.B5.48B3D4B
2.7B$43.15B10.B2.45BD4B4.2B2A4.2A4.24B.2B65.15B10.B2.45BD4B2.7B$43.
15B12.50B3.4B2A5.A4.24B68.15B12.50B4.6B$44.13B12.24B2.13B.4B10.2A6.3A
6.23B69.13B12.24B2.13B.4B10.7B$46.13B10.24B2.7B.B5.3B12.A6.A6.4B.16B.
4B70.13B10.24B2.7B.B5.3B12.6B$45.8B4.2A.A6.2AB2.20B15.4B10.3A14.2A3.
2B.12B3.B2A69.8B4.2A.A6.2AB2.20B15.4B13.7B$45.6B6.2AB3A3.A.AB2.18B17.
2A12.A17.A11.9B2.A70.6B6.2AB3A3.A.AB2.18B17.2A15.6B$45.5B8.B4.A2.A6.
18B.B15.A27.3A12.2A5.2A3.3A67.5B8.B4.A2.A6.18B.B15.A15.5B$45.B.B9.2A.
3A2.2A7.18B2A11.3A28.A15.A5.A6.A67.B.B9.2A.3A2.2A7.18B2A11.3A15.6B$
46.3B9.A.A13.18B2A11.A43.3A7.3A72.3B9.A.A13.18B2A11.A17.4B$45.B2AB9.A
.A13.3B3.13B56.A11.A71.B2AB9.A.A13.3B3.13B30.2B2AB$46.2A11.A15.B2.3B.
11B141.2A11.A15.B2.3B.11B32.2A$78.2A2.9B175.2A2.9B$79.A3.7B177.A3.7B$
76.3A5.4B176.3A5.4B$76.A8.5B174.A8.5B$88.2A186.2A$88.A187.A$89.3A185.
3A$91.A187.A!

Can someone find a way to overlap a glider lane in the p1023 with the Herschel output of the p1024, let's say, suitably modified if necessary, in such a way that the first touch of a gradually advancing glider will cleanly knock out both the Herschel and the glider?

Doesn't seem totally out of the question, but it's a long shot I suppose. Not sure how much extra junk I could add on to this idea before it would be just as expensive to construct as the existing phase meter.

ConwayLife.com

Phase meter

Phase meter

Re: Phase meter