In a 9 March 2003 LifeCA email, Dave Greene wrote:
Subject: Re: Improved-once-again pseudo p56 gun
--- In
LifeCA@yahoogroups.com, David Eppstein wrote:
> The pseudo-period only has to be a half-multiple, not a whole
> multiple, of the reflector period, right?
Right -- you could even do this with p4N periods, but you have to add four extra reflectors to the thickener to get the right elephant squares... P8 is annoying that way.
> So presumably a p6 version could be used for pseudo-57, which is
> currently missing from the collection (not that I have the
> patience to put it together).
Not quite -- with P6N you can only get four out of the eight possible phases/elephant squares out of the glider loop by adjusting the length of the path. P6N is annoying that way... It would work for anything relatively prime to 8, like p5N or p7N. See below for a sample of the problem at p6.
> The other advantage of your bootstrap construction is that uses
> open ended Herschel tracks instead of closed loops so no need to
> find a loop with the right period (114 is also missing).
That's odd -- I was sure I posted a p114, but now I can't find it in the archives [though I suppose it may possibly be buried somewhere in one of my more soporific long postings.] Anyway, it certainly never made it into the gun collection. Here's a reasonable-sized one:
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#C P114 gun Dave Greene 6 Sep 2002
x = 129, y = 63, rule = B3/S23
54boo$54boo$17bo12boo5boo$17b3o9bobbo5bo$20bo8bobobo4bobo$19boo7boobob
o5boo$30boboboo$6boo14bobboobboobobbo17b3o$6bobo12bobo7boboboboo14b3o$
8bo8boobboo5boobob3obbo12boo3bo28bo8bo12boo$4b4oboobboobboo10bobbo3boo
13bo3boo26b3o8b3o9bobbo$4bobbobobobbo14bob5o15bo3bo26bo14bo8bobobo$bb
oobbo4boo17bo4bo4boo10bobbo26boo12boo7boobobo$bobboobboobo19b4o4bobo
11b3o48bo4boboo$oboobboobobo21bo5bo14bobo42bo4boobobobbo$o3bo5bo24bobb
oo15boo10b3o28bobo3bo3boobboboo$b3obob3o24boo32b3o10bo12boobboo5boobbo
boobbo$3bobobo65boo5bobo11boo10bobobobboo$72bobbo4bobo23bob5o$4b3o21bo
bo42boo6bo4boo19bo4bo$29boo38boo15bobo19b4o$29bo29boo7bobo17bo6bo14bo$
6bo52bo8bo19boo5boo15bo$5bobo52b3o4boo25bobo14boo$6boo39bo14bo$bboo42b
o$bobo42b3o29bobo$bo5boo69bobo3boo$oo5boo70bo4bobo$84bo$$19bo$18boo29b
oo27b3o$18bobo28boo25boobbo$77b3o40boo5boo$78bo41boo5bo$125bobo$125boo
$66bo54boo$16boo42boo4b3o52bobo$16bo22boo19bo8bo52bo$18bo21bo17bobo7b
oo$17b4o19bobo15boo$16bo4bo19boo4bo64bobo$16b5obo23bobo63boo$14boo3bo
bbo10boo11bobo10bo53bo7b5o$13bobb3oboboo5boobboo12bo4boo4bobbo31boo24b
3obob3o$13boobobobo7bobo21bobo3bobbo27boobbo24bo4bo4bo$16bobboboobboo
bbo22bo7bo28bo5bo21boboobobboobo$16boobobo65bobo4b4o19bobo3boobbo$18bo
boboo7boo12boo40boo4bo4bo17boobobbobboo$18bobobo8bo14bo46b5obo14bobbob
o4bo$19bobbo9b3o8b3o45boobbobobo10boobboobboob4o$20boo12bo8bo16bobo27b
obboobobboo5boobboo8bo$61boo6bo20boobobboo3bo3bobo12bobo$61boo5bo24bo
bboboboo4bo14boo$93boobo4bo$66bo28boboboo7boo$65bobbo26bobobo8bo$65bob
o28bobbo9b3o$66bo25bo4boo12bo$73boo18bo$73boo16b3o!
But if you want to add a p6 thickener to it, you're probably better off with the equivalent Herschel factory, which needs a somewhat longer glider loop:
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#C p114 Herschel factory Dave Greene 6 Sep 2002
x = 98, y = 138, rule = B3/S23
42bo12boo$42b3o9bobbo$45bo8bobobo$44boo7boobobo$53bo3boboo$47bo6boobo
bbo$30boo13boobobobbobboboboboo$30bobo9boo9boobobobobbo$32bo9bo7bo3bo
6boo$28b4oboobboo4boo9bob5o$28bobbo3bobbo6boobbo5bo4bo$26boo5boboo9b3o
7b4o$25bobb3o4bo22bo$24boboo4boobo24bo$24bo3bobo3bo24boo$25b3o3b3o$27b
obobo$28b3o$29bo3$30bo$29bobo$30boo$26boo39boo5boo$25bobo39boo5bo$25bo
5boo39bobo$24boo5boo39boo$68boo$68bobo$69bo3$70bo$69b3o$68bobobo$66b3o
3b3o$48b3o14bo3bobo3bo$48bo5bobo7boboo4boobo$44bo4bo4boo8bo4b3obbo4bo$
42b3o10bo7boobo5boo3b3o$41bo19bobbo3bobbo4bo$41boo18boobboob4o4boo$31b
oo34bo$32bo34bobo$32bobo33boo$33boo56boo$40b3o48boo$40b3obboo$40bo3bo
bbo3boo$41bo3b4obboo$39bo$39bo4bo$39b4o53boo$96boo$$87bo$87bobo$37boo
3boo32boo9b3o$39bobbo20boo11boo11bo$36bo6b3o18bo$37boo6bo15b3o$61bo9$
17b3o$19bo$18bo$$36bo$34b3o15bo7bo$33bo18b3o4boo$20boo11boo20bo3boo$
20boo32boo3bo4bobo$64boo$30boo33bo$29bobbo$oo27bobbo$oo27b5o$32booboo$
34bo$45boo$45boo$57boo$5boo49bobbo$5boo50boo4boo$28boo33bobo$28bobo34b
o$30bo34boo$20boo4b4oboobboo18boo$21bo4bo4bobobbo19bo$18b3o3boobboobob
oo18b3o$18bo4bobboo3bobo19bo$22boboobboobobo$22bo4bo4bo$23b3obob3o$25b
ooboo5$28bo$27bobo$28boo$24boo39boo5boo$23bobo10bo28boo5bo$23bo5boo4b
oo33bobo$22boo5boo4bobo23bobo6boo$62boobboo$62bo3bobo$67bo5$66booboo$
64b3obob3o$37boo24bo4bo4bo$37bo24boboboobboobo$39bo22bobo3boobbo$38b4o
19booboboobboo$37bo4bo16bobbobo4bo$37bobobobo15boobboob4o$35boo4bobo
10boo9bo$34bobboo4boo5boobboo9bobo$34boobobbobobbo3bobo14boo$37bobbo3b
3o3bo$37boobobobbo$39boboboo7boo$39bobobo8bo$40bobbo9b3o$41boo12bo!
I don't see an easy way to add the classic thickener loop to this, unless someone can provide a one-generation rephaser. The pattern below is about as close as you can get without some extra tricks -- you could get a few generations closer with a longer loop, but you'll never get exactly the right phase just by adding reflectors:
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#C P114 glider-pair gun; not quite a p57 gun due to p6 phase problem.
#C p114 Herschel factory plus thickener Dave Greene 9 Mar 2003
x = 131, y = 138, rule = B3/S23
42bo12boo$42b3o9bobbo$45bo8bobobo$44boo7boobobo$53bo3boboo$46boo5b3obo
bbo$30boo14boo5bobboboboboo$30bobo9boo5bo3boo5bobbo$32bo9bobo9bobo4boo
$28b4oboobboo4b3o8bob5o$28bobbobobobbo5b3obo6bo4bo$26boobbo4boo8b4o7b
4o$25bobboobboobo11bo10bo$24boboobboobobo24bo$24bo3bo5bo24boo$25b3obob
3o$27bobobo$$28b3o3$30bo$29bobo$30boo$26boo39boo5boo$25bobo39boo5bo$
25bo5boo39bobo$24boo5boo39boo$68boo$68bobo$69bo3$69b3o$$68bobobo$49bo
16b3obob3o$48boo15bo5bo3bo$48bobo3bo9boboboobboobo34bo$44bo9bobo7boboo
bboobbo4bo28b3o$42b3o9boo7boo4bobboo3b3o27bo$41bo19bobbobobobbo4bo19bo
10boo$41boo18boobboob4o4boo17bobo$31boo34bo27bobo$32bo34bobo23b3oboo
20bo$32bobo33boo22bo24b3o9boo$33boo6bo44bo6b3oboo17bo11bobo$40bobo43b
3o6boboo17boo12bo$39bobbooboo42bo$40bobobo3bobboo35boo$40bo4b4obboo$
40bo4b3o66boo$38boobo71bobbo$39b3o74bo$40boo73bobbo$115bo3bo$88bo29bo$
86boobo24b4o$38bo3boo32boo9boboo23bo$37boo3bo20boo11boo11bo11boo$37boo
4b3o18bo36bo$37bo7bo15b3o38b3o$61bo42bo$$122boo5boo$122boo5bo$118bo8bo
bo$119boo6boo$118boo3boo$123bobo$18bo105bo$18boo$17bobo$124b3o$100b3o$
36bo65bo20bobobo$34b3o15bo6boo18boo20bo19b3obob3o$33bo18b3o6bo17bobo
38bo5bo3bo$20boo11boo20bobbo22bo37boboboobboobo$20boo32boo3boo3bo12b4o
boobboo31boboobboobbo$64bobo10bobbobobobbo30boo4bobboo$30boo32boo9boo
bbo4boo30bobbobobobbo$29bobbo41bobboobboobo31boobboob4o$oo26boo43boboo
bboobobo37bo$oo27boo3bo38bo3bo5bo38bobo$30bo4bo38b3obob3o40boo$33b3o
40bobobo$45boo$45boo30b3o$57boo$5boo49bobbo$5boo50boo4boo14bo$28boo33b
obo12bobo$28bobo34bo13boo$30bo34boo8boo16bo$20boo4b4oboobboo18boo17bob
o15bo$21bo4bo4bobobbo19bo17bo5boo10b3o$18b3o3boobbobboboo18b3o17boo5b
oo$18bo4bobboo3bobo19bo$22boboobboboobo46boo$22bo4bo4bo46bobbo$23b3obo
b3o46bobobo10boo$25b5o48boboboo5boobboo$76boobo3bo4bobo$76bobbob3o5bo$
73boobobobobbo$73bobbo5boo7boo$28bo45boo4bobo8bo$27bobo46b5obo9b3o$28b
oo46bo4bo12bo$24boo39boo5boo3b4o$23bobo9boo28boo5bo5bo$23bo5boo4bobo
32bobo3bo$22boo5boo4bo27bo6boo4boo$61bobobboo$62boobbobo$67bo5$66b5o$
64b3obob3o$37boo24bo4bo4bo$37bo24boboobobboobo$39bo22bobo3boobbo$38b4o
19boobobbobboo$37bo4bo16bobbobo4bo$37booboobo15boobboob4o$35boo3bobbo
10boo9bo$34bobboobboboo5boobboo9bobo$34boobobobo4bobbobo14boo$37bobbo
bboobo3bo$37boobobo3bo$39boboboo7boo$39bobobo8bo$40bobbo9b3o$41boo12bo!
But of course there's no reason you _have_ to use that extra output glider from the transparent-beehive inserter. I seem to recall that it's annoyingly hard to add extra conduits before the thickener, to produce a different glider with the right phase -- but it should be possible one way or another. Even if the extra glider can't be fed into the insertion mechanism directly, it can probably be used to rephase the inserter's extra glider some other way.
As in the p56 case, a pure bootstrap version might be a little smaller -- though p6 reflectors are a little bulkier than p8 ones, so it might not make much difference in the end.
Anyone want to tackle this one -- the pure-bootstrap version, and/or a new and improved glider to feed into the transparent-beehive inserter? I can guarantee that I won't be looking at it again for a while, myself: somebody must have reported my last posting. The men in white coats from the Life Addict Recovery Center say they'll let me out again in six months or so...