Funny, I thought I had figured out that that didn't work for some reason. It certainly looks good now!Sokwe wrote:The classical way to solve this is with Buckingham's B->r, giving a new R421 conduit...
A strange and useless coincidence: there's a known R421 with a different output Herschel location. This might be the first case where the output orientation and timing isn't sufficient to identify a Herschel conduit:
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#C R421+4N 421+4N 43+N -43-N 202 DMG 4 Dec 2002 x = 88, y = 95, rule = B3/S23 14bo$13bobo$14bo3$8boo$8boo23boo$oo31bo$bo29bobo$bobo27boo$bboo4boo$8b oo$$42boo$oo40bo$o39bobo$bboboo34boo$booboo$22boo$booboo16boo$bbobo$bb obo$3bo8$29boo$29boo4$29boo$29boo$$23boo$24bo$24bobo$25boo3$76boo$76b oo$81bo$79b3o$25bo52bo$25bobo22boo26boo$25b3o22bo5boo$27bo23b3obboo$ 53bo$$42boo$42boo$$68boo$68boo$82boo$82boo$86boo$86boo$$37boo$37bo$38b 3o$40bo23boo$63bobbo$64bobo$65bo16$59bo$59b3o$62bo$61bobo$62bo$$69b3o$ 63boo4bo$63boo3b3o!
One of the old standard ways of proving usefulness was to use the conduit successfully in a period-N gun from Jason Summers' gun collection. In point of fact, the new R421 is quite useful for building compact guns, especially higher-period guns, because the Herschel travels unusually slowly. Here's the old p485 gun, for example:Sokwe wrote:Unfortunately, it might not be very useful due to its size and high repeat time.
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#C p00485 found using Karel Suhajda's Hersrch program #C Scot Ellison - 4 November 2003 #C Reduced by 16 columns with smaller P5 - Scot Ellison 4 May 2007 x = 179, y = 58, rule = B3/S23 41bob2ob2o17b2o6b2o16bob2ob2o$41b2obobobo16b2o4bo2bo16b2obobobo$47bo 23b2obob2o19bo$74bobobo$28bo20b3o19b2obo3bo42bo$28b3o18bo21b2o2bo2b3o 38b3o13bo25bo$31bo18bo23b2o5bo36bo16b3o21b3o$14b2o14b2o11b2o35b2o11b2o 23b2o18bo19bo9bo$14b2o27b2o20b3o25b2o42b2o19b2o6b5o$64bo2bo97bo5bo$64b 2obo97bob2o2bo$8b2o58bo95b2obobob3obo$8b2o57bo2bo98bo4b2o$12b2o48bo3bo bobo97b2ob2o$12b2o47bo4bob2o96b2obobob5o$62bo4bo59b2o36bobobo8bo$127b 2o35b2ob2ob4o3b2o$55b2o47b2o58bo3bo5bo$7b2o47bo46bobo58bo7b2o$7b2o44b 3o47bo60bo7b2o$53bo48b2o10b2o48bo3bo5bo$27bo3b2o82bo48b2ob2ob4o3b2o$ 26bobo3bo39b2o38b3o9b2o39bobobo8bo$26b2o3bo12b2o27bo20b2o16bo11bo41b2o bobob5o$30bo13bobo23b3o21bobo28bo42b2ob2o$26b5obo13bo23bo25bo27b2o43bo 4b2o$26bo4b2o13b2o48b2o66b2obobob3obo$27b3o135bob2o2bo$29bob2o132bo5bo $30bobo8b2o123b5o$42bo25bo99bo$10bo31bobo21b3o$8b5o30b2o20bo80bobo$7bo 5bo51b2o79b2obo$7bo2b2obo135b3o$3bob3obobob2o70bo45b2o13b2o4bo$3b2o4bo 73b3o17b2o27bo13bob5o$6b2ob2o71bo20bo28bobo13bo$b5obobob2o56b2o11b2o 20bo11bo16b2o12bo3b2o$o8bobobo55b2o32b2o9b3o29bo3bobo$2o3b4ob2ob2o98bo 32b2o3bo$4bo5bo3bo98b2o10b2o$5b2o7bo110bo44b2o$5b2o7bo108bobo44b2o$4bo 5bo3bo108b2o$2o3b4ob2ob2o85b2o$o8bobobo86b2o9bo3b2o$b5obobob2o31b2o64b 3ob4o47b2o$6b2ob2o33b2o11b2o50b2o6bo47b2o$3b2o4bo47bo50b3o5bo52b2o$3bo b3obobob2o43b3o49bo4bo53b2o$7bo2b2obo46bo50bo$7bo5bo100bo$8b5o6b2o19b 2o48b2o17bo3bo20b2o27b2o$10bo9bo19bo27b2o20bo18bo24b2o11b2o14b2o$17b3o 21b3o23bobo21b3o16bo17bo18bo$17bo25bo23bo25bo13b3o19bo18b3o$66b2o39bo 19b3o20bo!
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#C p00485 gun, 31 January 2015 x = 110, y = 57, rule = B3/S23 78bo$21b2o47bo5b3o$14b2o5b2o45b3o4bo$14b2o51bo7b2o$50b2o15b2o$50bo$16b 2o17b2o14bo38bo$16b2o17bo14b2o36b3o$10b2o21bobo45b2o4bo$10b2o21b2o46b 2o4b2o3$45bobo$37b2o5b2ob2o57b2o$36bo2bo7bo58bo$35b2o2bo4b2o57b2obo$ 36b2o2bo3b2o5bo52bob2o$37b4o4bo3bobo52bobo2bo$10b2o34bo56b2o3b2o$11bo 38bo51bo2bo$11bobo40b2o47b3o$7bo4b2o23b2o16bo$7b3o27bo14b3o6bo41b2obob 2o$10bo27b3o11bo7bobo40b2ob2obo$9b2o29bo20bo5b2o$32bo35bo7bob2o$31bobo 31b3o6b3ob2o$31bobo31bo7bo$30b2ob3o38b3ob2o$36bo7bo31bobo$30b2ob3o6b3o 31bobo$30b2obo7bo35bo$41b2o5bo20bo29b2o$ob2ob2o40bobo7bo11b3o27bo$2obo b2o41bo6b3o14bo27b3o$54bo16b2o29bo$4b3o47b2o$4bo2bo51bo$2o3b2o56bo$o2b obo52bobo3bo4b4o$2b2obo52bo5b2o3bo2b2o$3bob2o57b2o4bo2b2o$3bo58bo7bo2b o$2b2o57b2ob2o5b2o$62bobo3$21b2o4b2o46b2o21b2o9bo$22bo4b2o45bobo21b2o 7bobo$19b3o36b2o14bo17b2o14b2o$19bo38bo14b2o17b2o$59bo$41b2o15b2o$33b 2o7bo51b2o$34bo4b3o45b2o5b2o$31b3o5bo47b2o$31bo!
That means the R421 can potentially reduce quite a few existing higher-period guns that rely on length-N or length-2N or length-3N Herschel loops. (There are a lot of these -- in particular, most of the prime-period guns are Herschel loops, for obvious reasons.)
...So I guess it's time to roll out another version of Hersrch. What else has showed up since December 2012 that also ought to be included? Will have to reconstruct Extrementhusiast's Lx79p4, I suppose, as well as a few Snark-assisted conduits.
EDIT: The safe repeat rate for the conduit is 363 ticks, by the way. It would be much smaller if it weren't for the extra output glider that crosses the next Herschel's path rather late in the reaction. There seems to be definitely not enough room to catch that glider with a 7x9 eater, a boat-bit catch, or any other tricks I can think of, so I guess we'll just have to live with the high recovery time. There are a few lower periods like p300 where the glider is naturally suppressed by the following Herschel.