ConwayLife.com

Posted: **April 26th, 2014, 5:49 pm**

Calcyman sent me a four-trails-to-six front end over a week ago now, and I haven't had much time to work on it since then. I'm convinced that some creative use of the minimal side-puffer table can shorten this construction down quite a bit -- but the math changes a little when you're missing two block trails out of the normal set.

Another thing I want to look at is how to start with just one or two of those four initial block trails, and produce the other trails with the minimum number of supporting glider streams. Reverse lateral forward glider streams can be generated starting from an LWSS upship stream colliding with a forward glider stream. I don't know yet what the optimal recipe will turn out to be -- but I'm pretty sure that the fewer times it has to be done, the better.

Anyway, the mostly unimproved (and for all I know unimprovable) four-trails-to-six end pattern is attached. I took out a few blank rows of blocks, but that's about all so far. Anyone want to try rigging up a shorter 4->6 solution?

Posted: **April 27th, 2014, 6:33 am**

Dave Greene: Calcyman is Adam P. Goucher, don't you know?

Posted: **April 27th, 2014, 1:16 pm**

Freywa wrote:Dave Greene: Calcyman is Adam P. Goucher, don't you know?

It would be a little surprising if I didn't; we've been corresponding about Conway's Life since mid-2008, well before conwaylife.com showed up, and collaborating on LifeNews articles and so on.

But on this forum, "calcyman" still seems like the right handle to do a user search on, so that's the name I generally use.

Posted: **May 21st, 2014, 1:49 pm**

A lot of the recent development on the 31c/240 caterpillar spaceship has been chronicled over on the thread for oblique's sscs search program. Short summary: the various details are slowly getting worked out, and it's now much more efficient to build side-puffers for various small objects, in exactly the locations where they're needed.

The idea of bootstrapping an upship stream with a Heisenburped glider probably doesn't make sense any more -- it seems likely to be cheaper to build an initial target directly in the best possible location, or possibly to build an entire *WSS seed one object at a time in some cases.

Anyway, attached is an attempt at a new front end for the spaceship -- a variation on a new two-trails-to-six idea from Calcyman, mixed with his previous four-trails-to-six spaceship front. He's planning to put together his own two-trails-to-six design, so I'm hoping that will show up eventually, and maybe it will be clear which design is better. Meanwhile, this shows what it looks like to use a kickback to recycle a backrake stream from the two-trail front of the ship.

31c240-alternate-front.rle.gz: experimental front end for 31c/240 spaceship; (26.26 KiB) Downloaded 352 times

(It's pretty ugly. Look at the big triangles on the left side. It doesn't seem to be possible to move the kickback point very much closer to the block trails, though no doubt it could move in a few hundred cells.)

Timing isn't much of a problem -- there are lots of adjustable pieces in the various rakes -- but rephasing the block trails is still downright ugly; there are no shortcuts, unlike with the rakes where every lane is now reachable within just seven rephasers.

Quick overview: from the top --

MWSS collisions generate two block trails.
Two pairs of Herschels generate two backrake streams in each direction.
The two backrakes on the right are used to build trails #3 and #4, with help from some reversed forward streams (not yet hooked up to anything -- these will be connected to LWSS upship streams most likely.)
Incomplete rakes running on four trails support each other and help build block trail #5.
One of the backrakes on the left is destroyed; the other is kicked back to support the construction of block trail #6.
An unfortunately long chain of four-trail rephasers move the right four trails two cells down relative to trails #5 and #6.
Finally we can use six-trail rakes to produce a forward stream on the correct lane to produce a good kickback.

There are all sorts of things I haven't investigated yet, such as:

-- are there other forerakes and backrakes that can be supported on just four trails?
-- is there a way to avoid the annoying support stream halfway down on the right?
-- can an earlier forerake stream be used for the kickback on the left? (I convinced myself this wasn't possible, but now I think I must have missed something. The gliders will return on the same lanes no matter which lane is used to kick them back. There's a big section of empty four-trail track that could be shortened, if this can be made to work.) (EDIT: see next posting for several improvements.)
-- can trails #3 and #4 be constructed with fewer support streams from the right?
-- can regular six-trail rakes be adapted for use on a track where the left two trails are offset by two cells? Should be possible, but I haven't spent much time looking at it, and there may well be annoying problems with permeability.

I'm not sure yet (or I've forgotten) whether the MWSS trick can be made to work for the two trails at the nose of the ship. It would make the whole spaceship look like a huge inverted triangle, or rather a slightly indented quadrilateral -- a Penrose dart shape. Just as well, I suppose; was getting tired of spaceships that look like long skinny straight lines, anyway.

Posted: **May 21st, 2014, 3:02 pm**

dvgrn wrote: a variation on a new two-trails-to-six idea

Two ideas:

1. All the "upcoming" gliders can come from "2 trails down shoots" that collide with "6 trails upper shoots", so all the trails can be built with this "triangular construction" as for the left most trail in the current "front".

2. One can use the same triangular structure to create 1->2 trail reaction. There is a small issue cleaning the debris block from the first single trail. So actually there is a "2 single trail Hs" one is shoot and cleaned from the left, and second is cleaned from the right (the cleaning mechanism is made with the usual "large triangle" that come from much lower 6 trails). This constellation creates two "glider shoots" from both direction that can allow the construction of the second trail.

Posted: **May 21st, 2014, 3:41 pm**

simsim314 wrote:
dvgrn wrote: a variation on a new two-trails-to-six idea
Two ideas:

Oh, good! I'm definitely looking for new ideas. Seems as if this front-end design should be significantly simpler somehow.

simsim314 wrote:1. All the "upcoming" gliders can come from "2 trails down shoots" that collide with "6 trails upper shoots", so all the trails can be built with this "triangular construction" as for the left most trail in the current "front".

Yes, this is clearly an option. I'm not sure yet whether this method will end up being more expensive than "simply" building an *WSS upship stream to reflect each upcoming glider stream.

Another alternative is to start from a single LWSS stream and use a forerake slow salvo to multiply the initial G+LWSS junk and convert it into several gliders on nearby tracks. (I think this last is doable, but it's going to be a little tricky to avoid collisions between input gliders, output gliders, intermediate targets, and the LWSS stream.)

simsim314 wrote:2. One can use the same triangular structure to create 1->2 trail reaction. There is a small issue cleaning the debris block from the first single trail. So actually there is a "2 single trail Hs" one is shoot and cleaned from the left, and second is cleaned from the right (the cleaning mechanism is made with the usual "large triangle" that come from much lower 6 trails). This constellation creates two "glider shoots" from both direction that can allow the construction of the second trail.

I think that should work to build the initial two trails from a single trail -- but the single trail is going to have to be pretty long to leave room for the large triangle. At this stage I'm collecting alternatives that look workable, to go with codeholic's original front end. For all I know, that front end may still be the best way to go, now that *WSS recipes are getting cheaper -- but we'd have to rebuild all the rakes to work on 90:234:90:234:90 block trails, and unfortunately most of the 116:110:90 designs aren't compatible with other trail spacings.

Posted: **May 21st, 2014, 6:02 pm**

dvgrn wrote:I'm not sure yet whether this method will end up being more expensive than "simply" building an *WSS upship stream

Well I'm thinking here of two "extremes". If WSS's are cheap, and it looks like they are (but yet again, with correct timing + correct placing etc. they might be not so cheap), we can build all the 6 trails with forward glider reflecting from "WSS couple", directly creating all the 6 trails (that costs 24 WSS's which is not that high price). The advantage of this method is the unified "API" for all constructions, just have a function that can manage the timing and placing of the WSS's reflected glider, and you will have all the six trails, with the same "function". This is probably the simplest designing approach, because writing such API shouldn't be too much of a headache, and it allows enough of freedom to built a lot of combinations, so the details should work out.

Another extreme is to built it all with gliders, using only one "WSS couple" for the front end. I do agree it's probably more expensive solution, but it has it's own beauty, minimizing the usage of unnecessary WSS's.

Your solution is somewhere "in between" approach, it's probably will be better optimized but it's harder to develop, than "unified WSS" approach, and on the other hand it requires more WSS's so it lacks the "elegance" of single WSS pair.

It would be nice to see already some not perfectly optimized, caterpillars in action, we are very close to it.

Posted: **May 21st, 2014, 11:04 pm**

simsim314 wrote:Another extreme is to built it all with gliders, using only one "WSS couple" for the front end. I do agree it's probably more expensive solution, but it has it's own beauty, minimizing the usage of unnecessary WSS's.

Your solution is somewhere "in between" approach, it's probably will be better optimized but it's harder to develop, than "unified WSS" approach, and on the other hand it requires more WSS's so it lacks the "elegance" of single WSS pair.

Well, I don't really have a solution yet. Seems like a good idea to have a quick look at what different construction methods will look like, then decide on a plan. I am kind of leaning toward the "unified WSS" approach at the moment.

simsim314 wrote:It would be nice to see already some not perfectly optimized, caterpillars in action, we are very close to it.

True enough. I'll build one if you'll build one...!

EDIT: I was probably wrong about the kickback triangle being irreducible in my last sample spaceship front. There are a lot more options for the lane doing the kickback than I thought. The attached version has the extraneous cleanup stream removed from halfway down the right side:

31c240-alternate-front2.rle.gz: Revised partial front end. One support stream removed, another temporarily disconnected.; (20.88 KiB) Downloaded 339 times

I'll be traveling for the next couple of weeks -- anyone care to figure out a good way to hook up the lower edge of the kickback triangle to some kind of glider source in the four-trail rephasers? It might require adding a Herschel-pair climber or two to the two trails on the left side, to let a glider escape on the correct lane.

EDIT 2: Found time on my travels to reconnect the kickback triangle to a convenient forward glider stream. As I thought, pretty much any forward stream will work, except for a few unlucky ones that cause crossing problems at the top (and even those could be fixed by shooting down the first backward stream later, or preferably just using it for something, like making an initial target for the upship stream recipe on that side.)

31c240-alternate-front6.rle.gz: Kickback stream connected to first available glider from four-trail rephasers. Further optimization is possible.; (21.68 KiB) Downloaded 341 times

The next question is whether block trails #3 and #4 can be generated somehow with less than five reversed forward support streams. No doubt more kickback triangles could be arranged on that side. I found the triangle on the left to be plenty enough trouble -- I'm not particularly looking forward to dealing with multiple kickback triangles with crossing streams... That must mean it's time to write some helper scripts to do the crossing analysis for me (but I'm not really looking forward to that task either!)

Posted: **May 29th, 2014, 5:24 pm**

I had the following design in mind for quite a while, but I've drawn it only now. I wonder how feasible it is. It seems hardly possible to find its solution without computer assistance, but unfortunately I'm not so deep into 31c/240 arithmetics to make a program on my own.

https://www.dropbox.com/s/jv4jmj2d80mo4zn/31c240.png

Block trails are red, gliders are green, spaceships are blue.

Once you have these six trails, you can build the next, narrower set to make things faster.

Posted: **May 29th, 2014, 7:15 pm**

What about having kinks in the lines, by using the other block? That would still allow for the normal 31c/240 progression, while potentially allowing some easy adjustments.

Posted: **May 30th, 2014, 3:19 am**

Do you mean shifting block trails, as proposed by Dave?

Code: Select all

x = 63, y = 255, rule = LifeHistory
53.2C$53.2C11$2C$2C18$53.2C$53.2C11$2C$2C18$53.2C$53.2C11$2C$2C18$53.
2C$53.2C11$2C$2C18$53.2C$53.2C11$2C$2C18$53.2C$53.2C11$2C$2C18$53.2C$
53.2C11$2C$2C18$53.2C$53.2C11$2C$2C10$60.3A$61.A$59.3A10$7.3A$8.A$6.
3A!

Posted: **May 30th, 2014, 4:46 am**

codeholic wrote:I had the following design in mind for quite a while, but I've drawn it only now...

I forgot to mention, that rephasers are not shown. The main idea is to build forward glider streams in that part of the front where fully functional rephasers and forward rakes are already possible, so that all four streams from two pairs of Herschels, running on two initial trails, are used to build other four trails, and there are no escaping gliders, that you'd need to clean up later.

Posted: **May 30th, 2014, 9:58 pm**

codeholic wrote:I had the following design in mind for quite a while, but I've drawn it only now. I wonder how feasible it is. It seems hardly possible to find its solution without computer assistance, but unfortunately I'm not so deep into 31c/240 arithmetics to make a program on my own.

I think you're right that a custom search program would be really handy, either for completing your design, or for finding useful ways to put kinks in the block trails as Extrementhusiast suggested.

The easiest way to bend a block trail is with a (2,1) block pull. Simple Herschel-pair climbers work on [54..59]+31N, with some weird options for [60,61]+31N... and for some of these distances, they work even if the block trails aren't exactly aligned, so it might be possible to (2,1) block-pull them back and forth, and still have them work -- i.e., it would be possible to send Herschel pairs up the block trails both before and after the adjustment:

Code: Select all

#C 54-spaced block trails turning rather awkwardly into 56-spaced trails
x = 951, y = 482, rule = LifeHistory
445.2C52.2C$445.2C52.2C30$445.2C52.2C$445.2C52.2C30$445.2C52.2C$445.
2C52.2C30$445.2C52.2C$445.2C52.2C30$445.2C52.2C$445.2C52.2C30$445.2C
52.2C$445.2C52.2C18$449.2A$447.2A.A$447.2A$449.2A$451.2A38.3A$492.A$
450.A.A39.3A$451.A5$445.2D52.2D$445.2D52.2D2$501.2A$453.2A36.2A8.2A$
453.2A36.2A5$503.A$502.A.A$501.A3.A$501.A3.A$501.A$502.3A7$445.2A52.
2A$445.2A52.2A8$445.2D52.2D$445.2D52.2D3$453.2A36.2A$453.2A36.2A16$
420.2A$421.2A131.A$420.A131.A.A$444.2A54.2A51.2A$444.2A54.2A$528.3A$
386.A.A139.A$386.2A141.A$387.A$383.2A$384.2A$383.A3$565.3A$565.A$566.
A10$438.A.A$438.2A$439.A$360.2A$361.2A148.A$360.A151.A$510.3A2$444.2A
54.2A86.3A$444.2A54.2A86.A$589.A2$323.2A$324.2A$323.A3$625.3A$625.A$
626.A13$300.2A$301.2A$300.A3$648.3A$648.A$444.2A54.2A147.A$444.2A54.
2A$263.2A$264.2A$263.A3$685.3A$685.A$686.A13$240.2A$241.2A$240.A3$
708.3A$708.A$709.A2$203.2A239.2A54.2A$204.2A238.2A54.2A$203.A3$745.3A
$745.A$746.A13$180.2A$181.2A$180.A3$768.3A$768.A$769.A2$143.2A$144.2A
$143.A300.2A54.2A$444.2A54.2A2$805.3A$805.A$806.A13$120.2A$121.2A$
120.A3$828.3A$828.A$829.A2$83.2A$84.2A$83.A2$444.2A54.2A$444.2A54.2A
363.3A$865.A$866.A13$60.2A$61.2A$60.A3$888.3A$888.A$889.A2$23.2A$24.
2A$23.A3$925.3A$444.2A54.2A423.A$444.2A54.2A424.A13$2A$.2A$A3$448.2A
498.3A$446.2A.A498.A$446.2A501.A$448.2A$450.2A40.3A$493.A$449.A.A41.
3A$450.A9$452.2A38.2A$452.2A38.2A17$444.2A54.2A$444.2A54.2A!

This might end up being the basis for more new rakes, come to think of it (arrrgh). But it doesn't seem to work as well when you shoot down the "main block" and leave the "spare block"; the offset is too big, so I haven't come up with any before-and-after spacings that do anything particularly useful yet. Maybe there's a way to get a pair of trails to drift gradually closer to another pair of trails, though, using (2,1) block pulls -- I'll investigate that a little more. A back-and-forth (2,1) or (1,2) drift would reset the phase by +/-2 or +/-4, which could also be very useful -- it takes a lot of rephasers to do that... Then again, it will take a dozen precisely-aimed gliders to do that for a full six-trail track, so probably the rephasers will be more efficient!

There are other trail separations that work only if the trails are not precisely aligned, but usually those fail to clean up one spare block or the other on one of the trails, and produce an extra output glider instead. So things get complicated very quickly. A brute-force search utility might do about as good a job at digging up new combinations as my slow and imperfect half-theoretical half-experimental approach...!

No doubt there are more complex arrangements of block trails where three or four or five trails with various offsets cooperate to clean up each other's spare blocks, just not in simple pairs. There's probably even a four- or five-trail setup that can support forward and backward rakes somehow -- just nobody has found it yet.

codeholic wrote:Once you have these six trails, you can build the next, narrower set to make things faster.

Somehow I suspect that the shortest possible 31c/240 spaceship will build just six block trails, and use those to support whatever rakes can be supported. Once you have six trails, there's not much point in wasting spaceship length by building more -- unless they're very very widely spaced, I suppose. But it seems as if we might just as well build reasonably closely spaced trails to start out, and be done with it.

As usual, I'll be very happy to be proved wrong about this, but probably won't spend much time or effort trying to prove myself wrong...!

The 116:110:90 trail spacing, which supports most of the currently known rakes, was a fairly arbitrary choice. There are definitely good arguments for other spacings, including arrangements where not all of the trails are aligned. Many of the known rakes could no doubt be adapted to work on other spacings.

In particular, a nice simple standard 116-spacing still has a lot going for it -- you can run climbers up any pair of adjacent trails, add as many more trails as you want with the same tools, and so on. I haven't dared to go back with our current collected knowledge and seriously investigate how much easier the 116x5 spacing would be -- don't really want to rebuild piles of rakes for the new spacing.

Posted: **May 31st, 2014, 9:56 pm**

dvgrn wrote:I haven't dared to go back with our current collected knowledge and seriously investigate how much easier the 116x5 spacing would be -- don't really want to rebuild piles of rakes for the new spacing.

Well, how about better rakes (assuming I haven't missed anything)?

Code: Select all

x = 1632, y = 2087, rule = B3/S23
771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b
2o414b2o17$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o
414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o
302b2o$593b2o414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b2o10$649b2o
302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b
2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o17$771b2o58b2o
$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o17$
771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b
2o414b2o17$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o
414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o
302b2o$593b2o414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b2o10$649b2o
302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b
2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o17$771b2o58b2o
$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o17$
771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b
2o414b2o17$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o
414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o
302b2o$593b2o414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b2o10$649b2o
302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o14$1630b2o$1629bobo$1631b
o$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$
593b2o414b2o12$1570b2o$1569bobo$1571bo3$771b2o58b2o$771b2o58b2o10$649b
2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o10$1510b2o$1509bobo$
1511bo5$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o414b
2o$593b2o414b2o8$1450b2o$1449bobo$1451bo7$771b2o58b2o$771b2o58b2o10$
649b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o6$1390b2o$1389bobo$
1391bo9$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o414b
2o$593b2o414b2o4$1330b2o$1329bobo$1331bo11$771b2o58b2o$771b2o58b2o10$
649b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o2$1270b2o$1269bobo$
1271bo13$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o
414b2o$593b2o414b2o199b2o$1209bobo$1211bo15$771b2o58b2o$771b2o58b2o10$
649b2o302b2o$649b2o302b2o195b2o$593b2o414b2o138bobo$593b2o414b2o140bo
17$771b2o58b2o$771b2o58b2o9$1090b2o$649b2o302b2o134bobo$649b2o302b2o
136bo$593b2o414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b2o7$1030b2o$
1029bobo$1031bo$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o17$
771b2o58b2o$771b2o58b2o5$970b2o$969bobo$971bo3$649b2o302b2o$649b2o302b
2o$593b2o414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b2o3$910b2o$909bobo
$911bo5$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o17$771b2o
58b2o$771b2o58b2o$850b2o$849bobo$851bo7$649b2o302b2o$649b2o302b2o$593b
2o414b2o$593b2o414b2o17$771b2o17b2o39b2o$771b2o16bobo39b2o$791bo9$649b
2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o15$730b2o$729bobo$731bo
39b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o
414b2o13$670b2o$669bobo$671bo2$771b2o58b2o$771b2o58b2o5$600b3o$599bo3b
o2$598bo$599b5o$602bo46b2o302b2o$649b2o302b2o$1001b3o$1000bo2bo$1000b
2obo$591b2o418b2o$591b2o8b2o408b2o$601b2o3$1011bo$1009bobo$591bo418b2o
$590bobo$592b2o16b2o34bo$589b2obo16bobo33b3o$589bo2bo18bo32b2o2bo364b
2o$590b2o56b2o363b2o$645b3ob2o$646bo2b2o309bobo$645b3o123b2o58b2o126bo
2bo$648b2o121b2o58b2o125b2o3bo$648b2o313bo2$593b2o363b3o2bo45b2o$593b
2o46bo320b2o45b2o$641bobo315b3o$641b2o316b3o7$951b2o$641b2o308b2o8b2o$
641b2o308bo9b2o$601b2o347bo50b2o$601b2o347b2o49b2o$950b3o$951b2o$946bo
2$550b2o$549bobo$551bo6$771b2o58b2o$771b2o58b2o$649b2o302b2o$649b2o
302b2o$593b2o414b2o$593b2o414b2o12$601b2o398b2o$601b2o398b2o2$596b2o$
595b2o$597bo3$1001b3o$1003bo$1002bo4$771b2o58b2o$771b2o58b2o$649b2o
302b2o$649b2o302b2o$593b2o302bo111b2o$593b2o301bo112b2o$896b3o3$710bo$
711b2o$710b2o7$656b2o$655b2o$657bo3$941b3o$943bo$942bo5$763b3o71bo$
763bo2bo70bo$762bo3bo70bo$649b2o111b4o187b2o$649b2o112bo9b2o54b2o7bo2b
o111b2o$593b2o178b2o54b2o3bobo2b2o168b2o$593b2o239b2o3bo169b2o$835bo2$
773bo$774bo$772b3o4$775b2o50b2o$775b2o50b2o$716b2o$715b2o$717bo3$881b
3o$771b2o58b2o50bo$771b2o58b2o49bo10$649b2o302b2o$649b2o302b2o$593b2o
168b2o74b2o168b2o$593b2o168b2o74b2o168b2o8$786bo$786bobo$786b2o3$820bo
bo$821b2o$821bo2$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$
593b2o168b2o74b2o168b2o$593b2o168b2o74b2o168b2o17$771b2o58b2o$771b2o
58b2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o17$771b2o
58b2o$771b2o58b2o5$600b3o$599bo3bo2$598bo$599b5o$602bo46b2o302b2o$649b
2o302b2o$1001b3o$1000bo2bo$1000b2obo$591b2o418b2o$591b2o8b2o408b2o$
601b2o3$1011bo$1009bobo$591bo54bo363b2o$590bobo52bobo$592b2o50b2ob2o$
589b2obo52bob2o$589bo2bo49b2o2b3o364b2o$590b2o55bo365b2o$646bo$645b2o
313bobo$650b2o119b2o58b2o126bo2bo$650b2o119b2o58b2o125b2o3bo$649b2o
312bo$649bo$593b2o363b3o2bo45b2o$593b2o367b2o45b2o$640bo318b3o$640bobo
316b3o$640b2o6$951b2o$641b2o308b2o8b2o$641b2o308bo9b2o$601b2o347bo50b
2o$601b2o347b2o49b2o$950b3o$951b2o$946bo10$771b2o58b2o$771b2o58b2o$
649b2o302b2o$540bo108b2o302b2o$540bobo50b2o414b2o$540b2o51b2o414b2o12$
601b2o398b2o$601b2o398b2o7$1001b3o$1003bo$1002bo4$771b2o58b2o$771b2o
58b2o$649b2o302b2o$649b2o302b2o$593b2o302bo111b2o$593b2o301bo112b2o$
896b3o4$711bo$712b2o$711b2o11$941b3o$943bo$942bo5$763b3o71bo$763bo2bo
70bo$762bo3bo70bo$649b2o111b4o187b2o$649b2o112bo9b2o54b2o7bo2bo111b2o$
593b2o178b2o54b2o3bobo2b2o168b2o$593b2o239b2o3bo169b2o$835bo2$773bo$
774bo$772b3o4$775b2o50b2o$775b2o50b2o6$881b3o$771b2o58b2o50bo$771b2o
58b2o49bo9$480bo$480bobo166b2o302b2o$480b2o167b2o302b2o$593b2o168b2o
74b2o168b2o$593b2o168b2o74b2o168b2o8$786bo$786bobo$786b2o3$820bobo$
821b2o$821bo2$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b
2o168b2o74b2o168b2o$593b2o168b2o74b2o168b2o17$771b2o58b2o$771b2o58b2o
10$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o17$771b2o58b2o$
771b2o58b2o4$600b3o$601bo$599b3o$420bo$420bobo$420b2o$649b2o302b2o$
649b2o302b2o$1001b3o$1000bo2bo$1000b2obo$591b2o418b2o$591b2o8b2o408b2o
$601b2o3$1011bo$1009bobo$590bo419b2o$589bobo$588bo3bo53bo$588bo3bo52b
3o$592bo51b2o2bo364b2o$589b3o56b2o363b2o$645b3ob2o$646bo2b2o309bobo$
645b3o123b2o58b2o126bo2bo$648b2o121b2o58b2o125b2o3bo$648b2o313bo2$593b
2o363b3o2bo45b2o$593b2o46bo320b2o45b2o$641bobo315b3o$641b2o316b3o7$
951b2o$641b2o308b2o8b2o$641b2o308bo9b2o$601b2o347bo50b2o$601b2o347b2o
49b2o$950b3o$951b2o$946bo10$771b2o58b2o$771b2o58b2o$649b2o302b2o$649b
2o302b2o$593b2o414b2o$593b2o414b2o12$601b2o398b2o$601b2o398b2o2$596b2o
$595b2o$597bo3$1001b3o$1003bo$1002bo4$771b2o58b2o$771b2o58b2o$649b2o
302b2o$649b2o302b2o$593b2o302bo111b2o$593b2o301bo112b2o$360bo535b3o$
360bobo$360b2o$710bo$711b2o$710b2o7$656b2o$655b2o$657bo3$941b3o$943bo$
942bo5$763b3o71bo$763bo2bo70bo$762bo3bo70bo$649b2o111b4o187b2o$649b2o
112bo9b2o54b2o7bo2bo111b2o$593b2o178b2o54b2o3bobo2b2o168b2o$593b2o239b
2o3bo169b2o$835bo2$773bo$774bo$772b3o4$775b2o50b2o$775b2o50b2o$716b2o$
715b2o$717bo3$881b3o$771b2o58b2o50bo$771b2o58b2o49bo10$649b2o302b2o$
649b2o302b2o$593b2o168b2o74b2o168b2o$593b2o168b2o74b2o168b2o8$786bo$
786bobo$786b2o3$820bobo$821b2o$821bo2$771b2o58b2o$771b2o58b2o10$649b2o
302b2o$649b2o302b2o$300bo292b2o168b2o74b2o168b2o$300bobo290b2o168b2o
74b2o168b2o$300b2o16$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b
2o$593b2o414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b2o10$649b2o302b2o$
649b2o302b2o$593b2o414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b2o10$
240bo408b2o302b2o$240bobo406b2o302b2o$240b2o351b2o414b2o$593b2o414b2o
17$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$
593b2o414b2o17$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$
593b2o414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b2o8$180bo$180bobo$
180b2o467b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o17$771b2o58b
2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o
17$771b2o58b2o$771b2o58b2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$
593b2o414b2o17$771b2o58b2o$771b2o58b2o6$120bo$120bobo$120b2o2$649b2o
302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o17$771b2o58b2o$771b2o58b
2o10$649b2o302b2o$649b2o302b2o$593b2o414b2o$593b2o414b2o53$60bo$60bobo
$60b2o89$o$obo$2o!

EDIT: I did miss something: dvgrn's very similar rake from the previous page. This one is slightly more compatible with a backwards kickback, but fails at the fifth block. No combination that I have tried would allow it to pass all six blocks.

Posted: **June 2nd, 2014, 12:03 pm**

Extrementhusiast wrote:EDIT: I did miss something: dvgrn's very similar rake from the previous page. This one is slightly more compatible with a backwards kickback, but fails at the fifth block. No combination that I have tried would allow it to pass all six blocks.

I think this could work if the fifth and sixth blocks were moved up by 9 cells. So there might be a way to combine a backwards kickback with a rephaser that moves the edge trails as early as possible and the center trails as late as possible.

It would work if the block trails were "properly" lined up, anyway:

Code: Select all

#C 2R backward kickback using trails from Extrementhusiast's rake
x = 472, y = 1082, rule = B3/S23
205b2o58b2o$205b2o58b2o10$83b2o302b2o$83b2o302b2o$27b2o414b2o$27b2o
414b2o17$205b2o58b2o$205b2o58b2o10$83b2o302b2o$83b2o302b2o$27b2o414b2o
$27b2o414b2o17$205b2o58b2o$205b2o58b2o10$83b2o302b2o$83b2o302b2o$27b2o
414b2o$27b2o414b2o17$205b2o58b2o$205b2o58b2o10$83b2o302b2o$83b2o302b2o
$27b2o414b2o$27b2o414b2o17$205b2o58b2o$205b2o58b2o10$83b2o302b2o$83b2o
302b2o$27b2o414b2o$27b2o414b2o17$205b2o58b2o$205b2o58b2o10$83b2o302b2o
$83b2o302b2o$27b2o414b2o$27b2o414b2o17$205b2o58b2o$205b2o58b2o10$83b2o
302b2o$83b2o302b2o$27b2o414b2o$27b2o414b2o17$205b2o58b2o$205b2o58b2o
10$83b2o302b2o$83b2o302b2o$27b2o414b2o$27b2o414b2o17$205b2o58b2o$205b
2o58b2o10$83b2o302b2o$83b2o302b2o$27b2o414b2o$27b2o414b2o17$205b2o58b
2o$205b2o58b2o10$83b2o302b2o$83b2o302b2o$27b2o414b2o$27b2o414b2o17$
205b2o58b2o$205b2o58b2o10$83b2o302b2o$83b2o302b2o54b2o$442bo$26b3o413b
o$26b2ob2o3b2o$28b2o2bob2o406b2ob2o$26bo2bob4o408b2ob2o$25bobobobob2o
405bo3bo2bo$25bobobob2o406b2o2b3obo$26bo3bo407b2o2bo4b2o$439b3obob3o$
440b4ob2o$43b3o397b2o$42bo3bo$42bo3bo$22b2o19b3o$15bo5bo2bo422b2o$14bo
3bob3obo422b2o$18b3ob2o$15bo$17b5o183b2o58b2o$18b5o182b2o58b2o3$27b2o
414b2o$3bobo21b2o414b2o$3b2o$4bo465bo$471bo$83bob3o300bo80b3o$82b3o3bo
298bo$81b3obo302bo$80b2o2b2ob2o298b3o$80bo3b5o298b2o$80bobo302b2ob2o$
81b4ob2o297bo$83b2ob2o296bo2bo3bo$35b2o38bo8bobo297bob2o2bobo42b2o$35b
2o38bo9bo297b2o3bo4bo41b2o$75bo309b2o3bobo$386bob2obo$387bo4$87b2o294b
2o$87b2o294b2o3$58bo$59bo$57b3o145b2o58b2o$205b2o58b2o144bo$83b2o302b
2o20b2o$83b2o302b2o21b2o$27b2o414b2o$27b2o333bo80b2o$360b2o$361b2o3$
115bo$113bobo$114b2o3$75b2o318b2o$75b2o318b2o$35b2o398b2o$35b2o398b2o
3$2o$obo$o3$465b2o$466b2o$465bo2$421bo$205b2o58b2o152bobo$205b2o58b2o
153b2o$83b2o302b2o$83b2o302b2o$27b2o16bobo395b2o$27b2o16b2o396b2o$46bo
11$35b2o398b2o$35b2o398b2o$60b2o$60bobo$60bo3$405b2o$406b2o$405bo5$
205b2o58b2o$205b2o58b2o$83b2o302b2o$83b2o122b3o177b2o$27b2o172b2o3b6o
231b2o13bo$27b2o171b3ob2obobo2bo230b2o11b2o$198b2o3bobo2bobobo52bo191b
2o$197bo2b3ob2ob2o2bo52bobob3o$199b2o2bo3b2o48b3o3b2ob4o$188bo3b3o7b2o
11bo41b5o2bo$188bo4bo8b2o8bo3bo44bo3bo3b2o3b2o$188bo5bo8bo7bo44b5o4bo
5bobo2bo3b3o$194bo6bob2o9b2obo38bo11b3o6bo2bo$196b2o4bo7bob3ob2o39bobo
10bo3b3o2b2obo$199bo8b3o6bo32bobo5b2o11b3o3bob2obo$197b3o8bo2bob2obo
33b2o20bo4b2obo$198bo9bo3b2obo35bo23bo$120b2o76bo10bo3bo61bo2b3o$120bo
bo76bo10bobo12bo53bo4bo$120bo105bo52bo4bo$224b3o53bo2bo2$205b2o58b2o
78b2o$205b2o58b2o79b2o$345bo9$83b2o302b2o$83b2o217bo84b2o$27b2o168b2o
74b2o25b2o141b2o$27b2o168b2o74b2o26b2o140b2o2$287bo$175bo112bo$173bobo
110b3o$174b2o2$180bo$178b2o$179b2o8$205b2o58b2o$205b2o58b2o10$83b2o
302b2o$83b2o302b2o$27b2o168b2o74b2o168b2o$27b2o168b2o74b2o168b2o17$
205b2o58b2o$205b2o58b2o10$83b2o302b2o9bo$83b2o302b2o7b2o$27b2o368b2o
44b2o$27b2o414b2o17$205b2o58b2o$205b2o58b2o10$83b2o302b2o$83b2o302b2o$
27b2o414b2o$27b2o414b2o17$205b2o58b2o$205b2o58b2o10$83b2o302b2o$83b2o
302b2o$27b2o414b2o$27b2o414b2o17$205b2o58b2o$205b2o58b2o8$338bo$336b2o
$83b2o252b2o48b2o$83b2o302b2o$27b2o414b2o$27b2o414b2o17$205b2o58b2o$
205b2o58b2o10$83b2o302b2o$83b2o302b2o$27b2o414b2o$27b2o414b2o17$205b2o
58b2o$205b2o58b2o10$83b2o302b2o$83b2o302b2o$27b2o414b2o$27b2o414b2o17$
205b2o58b2o$205b2o58b2o6$278bo$276b2o$277b2o2$83b2o302b2o$83b2o302b2o$
27b2o414b2o$27b2o414b2o17$205b2o58b2o$205b2o58b2o10$83b2o302b2o$83b2o
302b2o$443b2o$26b3o414b2o$26b2ob2o3b2o$28b2o2bob2o$26bo2bob4o409bo$25b
obobobob2o403b2o3bob5o$25bobobob2o404bo2b4o2b4ob2o$26bo3bo405bobob2o2b
3o$432b2ob2o$426bo4b4o3b3o$43b3o380bo4bo8bo11b3o$42bo3bo379bo5bobob2o
13b2o3bo$42bo3bo386bobo2b4o7b2o3bobo$22b2o19b3o394b2o6bobo5bo$15bo5bo
2bo412b3o7bo4b3o$14bo3bob3obo409b2o2b2o6bo6bo$18b3ob2o412bobo8bo$15bo
420b3o9b4o$17b5o183b2o58b2o196bo$18b5o182b2o58b2o194bobo$462b2o2$27b2o
414b2o$3bobo21b2o414b2o$3b2o$4bo2$83bob3o300bo$82b3o3bo298bo$81b3obo
302bo$80b2o2b2ob2o298b3o$80bo3b5o298b2o$80bobo302b2ob2o$81b4ob2o297bo$
83b2ob2o296bo2bo3bo$35b2o38bo8bobo297bob2o2bobo42b2o$35b2o38bo9bo297b
2o3bo4bo41b2o$75bo309b2o3bobo$386bob2obo$387bo4$87b2o294b2o32bobo$87b
2o294b2o32b2o$418bo2$58bo$59bo$57b3o145b2o58b2o$205b2o58b2o$83b2o302b
2o$83b2o302b2o$27b2o414b2o$27b2o189bo143bo80b2o$216b2o142b2o$217b2o
142b2o3$115bo$113bobo$114b2o3$75b2o318b2o$75b2o318b2o$35b2o398b2o$35b
2o398b2o3$2o$obo$o3$465b2o$466b2o$465bo2$421bo$205b2o58b2o152bobo$205b
2o58b2o153b2o$83b2o302b2o$83b2o302b2o$27b2o16bobo395b2o$27b2o16b2o396b
2o$46bo11$35b2o398b2o$35b2o398b2o$60b2o$60bobo$60bo3$405b2o$406b2o$
405bo5$205b2o58b2o$205b2o58b2o$83b2o302b2o$83b2o122b3o177b2o$27b2o172b
2o3b6o231b2o$27b2o171b3ob2obobo2bo230b2o$198b2o3bobo2bobobo52bo$197bo
2b3ob2ob2o2bo52bobob3o$199b2o2bo3b2o48b3o3b2ob4o$188bo3b3o7b2o11bo41b
5o2bo$188bo4bo8b2o8bo3bo44bo3bo3b2o3b2o$188bo5bo8bo7bo44b5o4bo5bobo2bo
3b3o$194bo6bob2o9b2obo38bo11b3o6bo2bo$196b2o4bo7bob3ob2o39bobo10bo3b3o
2b2obo$199bo8b3o6bo32bobo5b2o11b3o3bob2obo$197b3o8bo2bob2obo33b2o20bo
4b2obo$198bo9bo3b2obo35bo23bo$120b2o76bo10bo3bo61bo2b3o$120bobo76bo10b
obo12bo53bo4bo$120bo105bo52bo4bo$224b3o53bo2bo2$205b2o58b2o78b2o$205b
2o58b2o79b2o$345bo9$83b2o302b2o$83b2o73bo143bo84b2o$27b2o127b2o39b2o
74b2o25b2o141b2o$27b2o128b2o38b2o74b2o26b2o140b2o2$287bo$175bo112bo$
173bobo110b3o$174b2o2$180bo$178b2o$179b2o8$205b2o58b2o$205b2o58b2o10$
83b2o302b2o$83b2o302b2o$27b2o168b2o74b2o168b2o$27b2o168b2o74b2o168b2o
17$205b2o58b2o$205b2o58b2o10$83b2o302b2o$83b2o302b2o$27b2o414b2o$27b2o
414b2o17$205b2o58b2o$205b2o58b2o9$98bo$83b2o11b2o289b2o$83b2o12b2o288b
2o$27b2o414b2o$27b2o414b2o17$205b2o58b2o$205b2o58b2o10$83b2o302b2o$83b
2o302b2o$27b2o414b2o$27b2o414b2o17$205b2o58b2o$205b2o58b2o10$83b2o302b
2o$83b2o302b2o$27b2o414b2o$27b2o414b2o17$205b2o58b2o$205b2o58b2o7$38bo
$36b2o$37b2o$83b2o302b2o$83b2o302b2o$27b2o414b2o$27b2o414b2o!

So I haven't figured out what the advantage would be of the not-quite-lined-up block trails in your sample rake. The reason I posted that 116x5 block-trail example was that it was really easy to build six trails from two at that spacing, with everything lined up more or less automatically, no expensive adjustments needed.

Even the first two trails could be built with reversed forward glider streams at 116x5. At a spacing of 90 the trails get in the way of each other's construction gliders, which makes the MWSS support system look better. The advantage of 116:110:90 was that it was easy to make 1R double forward rakes -- a glider stream could cross all six block trails at that spacing, and that allows for a lot of other nice tricks to make forerakes and backrakes on alternate lanes.

With all this new rake-building experience, I should probably go back to 116x5 (or possibly 85x5 or 54x5?) and see how many different forerake and backrake output lanes can be easily produced. If it's really just as efficient as 116:110:90, that would bring the upship construction problem back down to just one or two LWSSes on each side, I think.

Posted: **June 2nd, 2014, 7:06 pm**

Question: Is symmetry of the block trails along the direction of travel a necessity, or just the ability to produce gliders in all four directions from the same track?

In other news, I have been looking at these two reflection reactions:

Code: Select all

x = 148, y = 657, rule = B3/S23
32b2o102b2o$32b2o102b2o30$32b2o102b2o$32b2o102b2o30$32b2o102b2o$32b2o
102b2o30$32b2o102b2o$32b2o102b2o30$32b2o102b2o$32b2o102b2o30$32b2o102b
2o$32b2o102b2o30$32b2o102b2o$32b2o102b2o30$32b2o102b2o$32b2o102b2o30$
32b2o102b2o$32b2o102b2o30$32b2o102b2o$32b2o102b2o30$32b2o102b2o$32b2o
102b2o30$32b2o102b2o$32b2o102b2o30$32b2o102b2o$32b2o102b2o30$31b3o102b
2o$26b2o3bo2b2o100b2o$25bo3bob2o$26bob4obo2bo$18bo7bo4b3ob2o$16bobo8bo
bobobob2o$17b2o8bo3bobobo$29b2o3bo83bo17b2o$16bo99bobo16bo$16bo100b2o
16b3o$15b3o102bo13b3o7b3o$119bo2bo10bo10b3o$123bo6bob2o3bo4bo4bo$15b3o
100bo4bo5bo7bo4bo3b2o$16bo19b2o84b2o5bo6bo9bo$16bo19bo2b2obo87bo11bo2b
o$37bob3obo75b3o10b3o3b2o3bo$40bo97b2o$37bo6bo93bo$37bo2bobo$40bo$39b
2o$32b2o102b2o$32b2o23bo78b2o$58bo$56b3o9$119bo$24b2o92bo9b2o$24b2o92b
3o7b2o12$2bo$2o$b2o3$32b2o102b2o$32b2o102b2o12$24b2o102b2o$24b2o102b2o
17$32b2o102b2o$32b2o102b2o12$24b2o102b2o$24b2o102b2o17$32b2o102b2o$32b
2o102b2o12$24b2o102b2o$24b2o102b2o17$32b2o102b2o$32b2o102b2o12$24b2o
102b2o$24b2o102b2o17$32b2o102b2o$32b2o102b2o12$24b2o102b2o$24b2o102b2o
17$32b2o102b2o$32b2o102b2o12$24b2o102b2o$24b2o102b2o17$32b2o102b2o$32b
2o102b2o12$24b2o102b2o$24b2o102b2o!

Posted: **June 2nd, 2014, 9:58 pm**

Extrementhusiast wrote:Question: Is symmetry of the block trails along the direction of travel a necessity, or just the ability to produce gliders in all four directions from the same track?

Definitely not a necessity, just a convenience; otherwise you have to build different rakes for the right and left sides, and do separate sscs searches to build a left-side LWSS vs. a right-side LWSS. But if it turned out to be really convenient for other reasons, asymmetry would be fine.

Extrementhusiast wrote:In other news, I have been looking at these two reflection reactions:
[block trails 104 cells apart, with Herschel climbers in the same orientation]

These are the [42,43]+31N Herschel pairs I was talking about a few pages back in this thread. The main problem with them is that you can't easily kick a glider forward from the left side, because that Herschel is in the opposite orientation from normal, so the backrake glider is on a bad lane for the post-rake block trail. Even if you rephase the trails again before the kickback glider gets there, I think something still gets in the way.

I've been thinking it's probably possible to make a universal set of forerakes and backrakes and rephasers using just four block trails, along the lines of the four-trail rakes in Calcyman's front-end experiment. Seems as if you could carefully drop objects on one side that could suppress multiple gliders, and then point the "leaky" side of a four-trail rake at those objects while setting up a regular rephaser/rake column on the other side:

Code: Select all

#C four trails with 116x3 spacing
x = 440, y = 4766, rule = B3/S23
43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o30$43b2o114b2o114b2o
114b2o$43b2o114b2o114b2o114b2o30$43b2o114b2o114b2o114b2o$43b2o114b2o
114b2o114b2o30$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o30$43b2o
114b2o114b2o114b2o$43b2o114b2o114b2o114b2o27$438b2o$438b2o2$43b2o114b
2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o
12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$
438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$
43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o
2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b
2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o
114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b
2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b
2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$
438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o
114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b
2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$
438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b
2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o
114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$
438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o
8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o
114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b
2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o
12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$
438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$
43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o
2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b
2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o
114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b
2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b
2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$
438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o
114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b
2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$
438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b
2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o
114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$
438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o
8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o
114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b
2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o
12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$
438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$
43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o
2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b
2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o
114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b
2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b
2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$
438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o
114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b
2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$
438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b
2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o
114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$
438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o
8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o
114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b
2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o
12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$
438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$
43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o
2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b
2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o
114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b
2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b
2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$
438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o
114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b
2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$
438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b
2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o
114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$
438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o
8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o
114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b
2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o
12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$
438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$
43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o
2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b
2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o
114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b
2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b
2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$
438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o
114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b
2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$
438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b
2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o
114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$
438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o
8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o
114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b
2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o
12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$
438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$
43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o
2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b
2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o
114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b
2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o12$438b
2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$
438b2o8$438b2o$438b2o12$438b2o$438b2o2$43b2o114b2o114b2o114b2o$43b2o
114b2o114b2o114b2o5$438b2o$438b2o8$438b2o$438b2o7$51bo$50b3o$50b3o2$
49b4o$49b5o384b2o$50bob2o384b2o2$159b2o114b2o114b2o$159b2o114b2o114b2o
2$41b2o$41b2o8b2o$51b2o$438b2o$438b2o3$41bo$42b2o$39b2ob2o$39b2obo$39b
o2bo$40b2o396b2o$438b2o6$43b2o$43b2o5$438b2o$438b2o2$159b2o114b2o114b
2o$159b2o114b2o114b2o3$51b2o$6b2o43b2o$6b2o2b2o426b2o$10b2o147b2o277b
2o$160bo2$159bo5bo2bo$158bo6bo2bo$143bo13b2o4bo5bo$141b2ob2o6b2o3bo5bo
bob2o$142bo2bo6b2o2bob2obobo4bo$143b2o11bobob8o270b2o$157b9o272b2o$
164bo$54bo$53b2o$53bobo2$43b2o114b2o$43b2o114b2o5$438b2o$438b2o2$275b
2o114b2o$275b2o114b2o$143bo$142bo$51b2o89b3o6b2o$6b2o43b2o98b2o$6b2o2b
2o426b2o$10b2o426b2o8$104bo333b2o$102bobo9bo323b2o$103b2o8b2o$113bobo
4$43b2o114b2o$43b2o114b2o5$438b2o$438b2o2$280b3o$279bo3bo100b2o$279bo
104bobo$273b2o9bo100b2o6b2o$51b2o98b2o120b2o5b2ob2o100b2o6b2o$6b2o43b
2o98b2o127bo100bobobo$6b2o2b2o370b2o54b2o$10b2o370bob2o4bobo45b2o$391b
2o$391bo3$284bo$282b3o$174bo96b2o9b3o110b2o$173b2o96b2o122b2o41b2o$
173bobo262b2o6$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o
$438b2o6$51b2o98b2o130b2o98b2o$6b2o43b2o98b2o130b2o98b2o$6b2o2b2o426b
2o$10b2o216bobo207b2o$229b2o$229bo2$232bo$232bobo$232b2o9$43b2o114b2o
114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$438b2o2$83bo$82bo$82b3o2$
51b2o230b2o98b2o$6b2o43b2o230b2o39bobo56b2o$6b2o2b2o313b2o111b2o$10b2o
313bo112b2o3$336bobo$336b2o$337bo10$43b2o114b2o114b2o114b2o$43b2o114b
2o114b2o114b2o5$438b2o$438b2o6$51b2o230b2o98b2o$6b2o43b2o230b2o98b2o$
6b2o2b2o426b2o$10b2o426b2o15$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o
114b2o5$438b2o$438b2o6$283b2o98b2o$6b2o275b2o98b2o$6b2o2b2o426b2o$10b
2o426b2o15$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b2o$
438b2o2$383bo$382bobo$381bo3bo$381bo3bo$381bo$6b2o374b3o$6b2o2b2o426b
2o$10b2o426b2o15$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o5$438b
2o$438b2o7$6b2o$6b2o2b2o426b2o$10b2o426b2o7$51bo$50b3o$50b3o2$49b4o$
49b5o$50bob2o2$159b2o114b2o114b2o$159b2o114b2o114b2o2$41b2o$41b2o8b2o$
51b2o$438b2o$438b2o3$41bo$42b2o$39b2ob2o$39b2obo$6b2o31bo2bo$6b2o2b2o
28b2o396b2o$10b2o426b2o6$43b2o$43b2o8$159b2o114b2o114b2o$159b2o114b2o
114b2o3$51b2o$6b2o43b2o$6b2o2b2o426b2o$10b2o147b2o277b2o$160bo2$159bo
5bo2bo$158bo6bo2bo$143bo13b2o4bo5bo$141b2ob2o6b2o3bo5bobob2o$6b2o134bo
2bo6b2o2bob2obobo4bo$6b2o2b2o131b2o11bobob8o270b2o$10b2o145b9o272b2o$
164bo$54bo$53b2o$53bobo2$43b2o114b2o$43b2o114b2o8$275b2o114b2o$275b2o
114b2o$143bo$142bo$51b2o89b3o6b2o$6b2o43b2o98b2o$6b2o2b2o426b2o$10b2o
426b2o7$6b2o$6b2o2b2o92bo333b2o$10b2o90bobo9bo323b2o$103b2o8b2o$113bob
o4$43b2o114b2o$43b2o114b2o8$280b3o$279bo3bo100b2o$279bo104bobo$273b2o
9bo100b2o6b2o$51b2o98b2o120b2o5b2ob2o100b2o6b2o$6b2o43b2o98b2o127bo
100bobobo$6b2o2b2o370b2o54b2o$10b2o370bob2o4bobo45b2o$391b2o$391bo3$
284bo$282b3o$6b2o166bo96b2o9b3o110b2o$6b2o2b2o161b2o96b2o122b2o41b2o$
10b2o161bobo262b2o6$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o12$
51b2o98b2o130b2o98b2o$6b2o43b2o98b2o130b2o98b2o$6b2o2b2o426b2o$10b2o
216bobo207b2o$229b2o$229bo2$232bo$232bobo$232b2o$6b2o$6b2o2b2o$10b2o6$
43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o8$83bo$82bo$82b3o2$51b
2o230b2o98b2o$6b2o43b2o230b2o39bobo56b2o$6b2o2b2o313b2o111b2o$10b2o
313bo112b2o3$336bobo$336b2o$337bo2$6b2o$6b2o2b2o$10b2o6$43b2o114b2o
114b2o114b2o$43b2o114b2o114b2o114b2o12$51b2o230b2o98b2o$6b2o43b2o230b
2o98b2o$6b2o2b2o426b2o$10b2o426b2o7$6b2o$6b2o2b2o$10b2o6$43b2o114b2o
114b2o114b2o$43b2o114b2o114b2o114b2o12$283b2o98b2o$6b2o275b2o98b2o$6b
2o2b2o426b2o$10b2o426b2o7$6b2o$6b2o2b2o$10b2o6$43b2o114b2o114b2o114b2o
$43b2o114b2o114b2o114b2o8$383bo$382bobo$381bo3bo$381bo3bo$381bo$6b2o
374b3o$6b2o2b2o426b2o$10b2o426b2o7$6b2o$6b2o2b2o$10b2o6$43b2o114b2o
114b2o114b2o$43b2o114b2o114b2o114b2o13$6b2o$6b2o2b2o426b2o$10b2o426b2o
7$6b2o43bo$6b2o2b2o38b3o$10b2o38b3o2$49b4o$49b5o$50bob2o2$159b2o114b2o
114b2o$159b2o114b2o114b2o2$41b2o$41b2o8b2o$51b2o5$41bo$42b2o$39b2ob2o$
39b2obo$6b2o31bo2bo$6b2o2b2o28b2o396b2o$10b2o426b2o6$43b2o$6b2o35b2o$
6b2o2b2o$10b2o6$159b2o114b2o114b2o$159b2o114b2o114b2o3$51b2o$6b2o43b2o
$6b2o2b2o$10b2o147b2o$160bo2$159bo5bo2bo$158bo6bo2bo$143bo13b2o4bo5bo$
141b2ob2o6b2o3bo5bobob2o$6b2o134bo2bo6b2o2bob2obobo4bo$6b2o2b2o131b2o
11bobob8o270b2o$10b2o145b9o272b2o$164bo$54bo$53b2o$53bobo2$43b2o114b2o
$6b2o35b2o114b2o$6b2o2b2o$10b2o6$275b2o114b2o$275b2o114b2o$143bo$142bo
$51b2o89b3o6b2o$6b2o43b2o98b2o$6b2o2b2o$10b2o7$6b2o$6b2o2b2o92bo333b2o
$10b2o90bobo9bo323b2o$103b2o8b2o$113bobo4$43b2o114b2o$6b2o35b2o114b2o$
6b2o2b2o$10b2o6$280b3o$279bo3bo100b2o$279bo104bobo$273b2o9bo100b2o6b2o
$51b2o98b2o120b2o5b2ob2o100b2o6b2o$6b2o43b2o98b2o127bo100bobobo$6b2o2b
2o370b2o$10b2o370bob2o4bobo$391b2o$391bo3$284bo$282b3o$6b2o166bo96b2o
9b3o110b2o$6b2o2b2o161b2o96b2o122b2o41b2o$10b2o161bobo262b2o6$43b2o
114b2o114b2o114b2o$6b2o35b2o114b2o114b2o114b2o$6b2o2b2o$10b2o10$51b2o
98b2o130b2o98b2o$6b2o43b2o98b2o130b2o98b2o$6b2o2b2o$10b2o216bobo$229b
2o$229bo2$232bo$232bobo$232b2o$6b2o$6b2o2b2o$10b2o6$43b2o114b2o114b2o
114b2o$6b2o35b2o114b2o114b2o114b2o$6b2o2b2o$10b2o6$83bo$82bo$82b3o2$
51b2o230b2o98b2o$6b2o43b2o230b2o39bobo56b2o$6b2o2b2o313b2o$10b2o313bo
3$336bobo$336b2o$337bo2$6b2o$6b2o2b2o$10b2o6$43b2o114b2o114b2o114b2o$
6b2o35b2o114b2o114b2o114b2o$6b2o2b2o$10b2o10$51b2o230b2o98b2o$6b2o43b
2o230b2o98b2o$6b2o2b2o$10b2o7$6b2o$6b2o2b2o$10b2o6$43b2o114b2o114b2o
114b2o$6b2o35b2o114b2o114b2o114b2o$6b2o2b2o$10b2o10$283b2o98b2o$6b2o
275b2o98b2o$6b2o2b2o$10b2o7$6b2o$6b2o2b2o$10b2o6$43b2o114b2o114b2o114b
2o$6b2o35b2o114b2o114b2o114b2o$6b2o2b2o$10b2o6$383bo$382bobo$381bo3bo$
381bo3bo$381bo$6b2o374b3o$6b2o2b2o$10b2o7$6b2o$6b2o2b2o$10b2o6$43b2o
114b2o114b2o114b2o$6b2o35b2o114b2o114b2o114b2o$6b2o2b2o$10b2o11$6b2o$
6b2o2b2o$10b2o7$6b2o$6b2o2b2o$10b2o3$383b3o$383bo2bo$382bo3bo$43b2o
114b2o114b2o106bo2b2o$6b2o35b2o114b2o114b2o108bo$6b2o2b2o371b2o$10b2o
370b3o8b2o$382b3o8b2o5$394bo$395bo$393b3o3$6b2o387b2o$6b2o2b2o383b2o$
10b2o6$391b2o$6b2o383b2o$6b2o2b2o$10b2o6$43b2o114b2o114b2o$6b2o35b2o
114b2o114b2o$6b2o2b2o$10b2o$383b2o$383b2o2$275b2o$275bo2$267bo2bo5bo$
267bo2bo6bo$266bo5bo4b2o13bo$267b2obobo5bo3b2o6b2ob2o$6b2o259bo4bobob
2obo2b2o6bo2bo$6b2o2b2o256b8obobo11b2o$10b2o258b9o$271bo$381bo$381b2o$
380bobo2$275b2o114b2o$6b2o267b2o114b2o$6b2o2b2o$10b2o6$43b2o114b2o$6b
2o35b2o114b2o$6b2o2b2o280bo$10b2o281bo$283b2o6b3o89b2o$283b2o98b2o7$
334bo$333bo$6b2o325b3o$6b2o2b2o$10b2o309bo$321b2o$320bobo4$275b2o114b
2o$6b2o267b2o114b2o$6b2o2b2o$10b2o6$153b3o$6b2o42b2o100bo3bo$6b2o2b2o
37bobo104bo$10b2o29b2o6b2o100bo9b2o$41b2o6b2o100b2ob2o5b2o120b2o98b2o$
50bobobo100bo127b2o98b2o$52b2o$43bobo4b2obo$43b2o$44bo3$151bo$151b3o$
6b2o31b2o110b3o9b2o96bo$6b2o2b2o27b2o122b2o96b2o$10b2o248bobo6$43b2o
114b2o114b2o114b2o$6b2o35b2o114b2o114b2o114b2o$6b2o2b2o$10b2o7$6b2o$6b
2o2$51b2o98b2o130b2o98b2o$51b2o98b2o130b2o98b2o2$205bobo$205b2o$206bo
2$203bo$201bobo$202b2o$6b2o$6b2o2b2o$10b2o6$43b2o114b2o114b2o114b2o$6b
2o35b2o114b2o114b2o114b2o$6b2o2b2o$10b2o6$352bo$6b2o345bo$6b2o343b3o2$
51b2o98b2o230b2o$51b2o56bobo39b2o230b2o$109b2o$110bo3$97bobo$98b2o$98b
o2$6b2o$6b2o2b2o$10b2o6$43b2o114b2o114b2o114b2o$6b2o35b2o114b2o114b2o
114b2o$6b2o2b2o$10b2o7$6b2o$6b2o2$51b2o98b2o230b2o$51b2o98b2o230b2o9$
6b2o$6b2o2b2o$10b2o6$43b2o114b2o114b2o114b2o$6b2o35b2o114b2o114b2o114b
2o$6b2o2b2o$10b2o7$6b2o$6b2o2$51b2o98b2o$51b2o98b2o9$6b2o$6b2o2b2o$10b
2o6$43b2o114b2o114b2o114b2o$6b2o35b2o114b2o114b2o114b2o$6b2o2b2o$10b2o
6$52bo$6b2o43bobo$6b2o42bo3bo$50bo3bo$54bo$51b3o9$6b2o$6b2o2b2o$10b2o
6$43b2o114b2o114b2o114b2o$6b2o35b2o114b2o114b2o114b2o$6b2o2b2o$10b2o7$
6b2o$6b2o12$6b2o$6b2o2b2o$10b2o3$383b3o$383bo2bo$382bo3bo$43b2o114b2o
114b2o106bo2b2o$6b2o35b2o114b2o114b2o108bo$6b2o2b2o371b2o$10b2o370b3o
8b2o$382b3o8b2o5$394bo$6b2o387bo$6b2o385b3o3$395b2o$395b2o7$391b2o$6b
2o383b2o$6b2o2b2o$10b2o6$43b2o114b2o114b2o$6b2o35b2o114b2o114b2o$6b2o
2b2o$10b2o$383b2o$383b2o2$275b2o$275bo2$6b2o259bo2bo5bo$6b2o259bo2bo6b
o$266bo5bo4b2o13bo$267b2obobo5bo3b2o6b2ob2o$267bo4bobob2obo2b2o6bo2bo$
268b8obobo11b2o$270b9o$271bo$381bo$381b2o$380bobo2$275b2o114b2o$6b2o
267b2o114b2o$6b2o2b2o$10b2o6$43b2o114b2o$6b2o35b2o114b2o$6b2o2b2o280bo
$10b2o281bo$283b2o6b3o89b2o$283b2o98b2o5$6b2o$6b2o$334bo$333bo$333b3o
2$321bo$321b2o$320bobo4$275b2o114b2o$6b2o267b2o114b2o$6b2o2b2o$10b2o6$
153b3o$6b2o42b2o100bo3bo$6b2o2b2o37bobo104bo$10b2o29b2o6b2o100bo9b2o$
41b2o6b2o100b2ob2o5b2o120b2o98b2o$50bobobo100bo127b2o98b2o$52b2o$43bob
o4b2obo$43b2o$44bo$6b2o$6b2o$151bo$151b3o$39b2o110b3o9b2o96bo$39b2o
122b2o96b2o$260bobo6$43b2o114b2o114b2o114b2o$6b2o35b2o114b2o114b2o114b
2o$6b2o2b2o$10b2o7$6b2o$6b2o2$51b2o98b2o130b2o98b2o$51b2o98b2o130b2o
98b2o2$205bobo$205b2o$206bo$6b2o$6b2o195bo$201bobo$202b2o9$43b2o114b2o
114b2o114b2o$6b2o35b2o114b2o114b2o114b2o$6b2o2b2o$10b2o6$352bo$6b2o
345bo$6b2o343b3o2$51b2o98b2o230b2o$51b2o56bobo39b2o230b2o$109b2o$110bo
3$6b2o89bobo$6b2o90b2o$98bo10$43b2o114b2o114b2o114b2o$6b2o35b2o114b2o
114b2o114b2o$6b2o2b2o$10b2o7$6b2o$6b2o2$51b2o98b2o230b2o$51b2o98b2o
230b2o5$6b2o$6b2o11$43b2o114b2o114b2o114b2o$6b2o35b2o114b2o114b2o114b
2o$6b2o2b2o$10b2o7$6b2o$6b2o2$51b2o98b2o$51b2o98b2o5$6b2o$6b2o11$43b2o
114b2o114b2o114b2o$6b2o35b2o114b2o114b2o114b2o$6b2o2b2o$10b2o6$52bo$6b
2o43bobo$6b2o42bo3bo$50bo3bo$54bo$51b3o5$6b2o$6b2o11$43b2o114b2o114b2o
114b2o$6b2o35b2o114b2o114b2o114b2o$6b2o2b2o$10b2o7$6b2o$6b2o8$6b2o$6b
2o8$383b3o$383bo2bo$382bo3bo$43b2o114b2o114b2o106bo2b2o$6b2o35b2o114b
2o114b2o108bo$6b2o2b2o371b2o$10b2o370b3o8b2o$382b3o8b2o5$394bo$6b2o
387bo$6b2o385b3o3$395b2o$395b2o4$6b2o$6b2o2$391b2o$391b2o8$43b2o114b2o
114b2o$6b2o35b2o114b2o114b2o$6b2o2b2o$10b2o$383b2o$383b2o2$275b2o$275b
o2$6b2o259bo2bo5bo$6b2o259bo2bo6bo$266bo5bo4b2o13bo$267b2obobo5bo3b2o
6b2ob2o$267bo4bobob2obo2b2o6bo2bo$268b8obobo11b2o$270b9o$271bo$381bo$
6b2o373b2o$6b2o372bobo2$275b2o114b2o$275b2o114b2o8$43b2o114b2o$6b2o35b
2o114b2o$6b2o2b2o280bo$10b2o281bo$283b2o6b3o89b2o$283b2o98b2o5$6b2o$6b
2o$334bo$333bo$333b3o2$321bo$321b2o$320bobo$6b2o$6b2o2$275b2o114b2o$
275b2o114b2o8$153b3o$6b2o42b2o100bo3bo$6b2o2b2o37bobo104bo$10b2o29b2o
6b2o100bo9b2o$41b2o6b2o100b2ob2o5b2o120b2o98b2o$50bobobo100bo127b2o98b
2o$52b2o$43bobo4b2obo$43b2o$44bo$6b2o$6b2o$151bo$151b3o$39b2o110b3o9b
2o96bo$39b2o122b2o96b2o$260bobo3$6b2o$6b2o2$43b2o114b2o114b2o114b2o$
43b2o114b2o114b2o114b2o9$6b2o$6b2o2$51b2o98b2o130b2o98b2o$51b2o98b2o
130b2o98b2o2$205bobo$205b2o$206bo$6b2o$6b2o195bo$201bobo$202b2o6$6b2o$
6b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o8$352bo$6b2o345bo
$6b2o343b3o2$51b2o98b2o230b2o$51b2o56bobo39b2o230b2o$109b2o$110bo3$6b
2o89bobo$6b2o90b2o$98bo10$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o
114b2o9$6b2o$6b2o2$51b2o98b2o230b2o$51b2o98b2o230b2o5$6b2o$6b2o11$43b
2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o9$6b2o$6b2o2$51b2o98b2o$
51b2o98b2o5$6b2o$6b2o11$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b
2o8$52bo$6b2o43bobo$6b2o42bo3bo$50bo3bo$54bo$51b3o5$6b2o$6b2o11$43b2o
114b2o114b2o114b2o$43b2o114b2o114b2o114b2o9$6b2o$6b2o8$6b2o$6b2o8$383b
3o$383bo2bo$382bo3bo$43b2o114b2o114b2o106bo2b2o$43b2o114b2o114b2o108bo
$383b2o$382b3o8b2o$382b3o8b2o5$394bo$6b2o387bo$6b2o385b3o3$395b2o$395b
2o4$6b2o$6b2o2$391b2o$391b2o8$43b2o114b2o114b2o$43b2o114b2o114b2o3$
383b2o$383b2o2$275b2o$275bo2$6b2o259bo2bo5bo$6b2o259bo2bo6bo$266bo5bo
4b2o13bo$267b2obobo5bo3b2o6b2ob2o$267bo4bobob2obo2b2o6bo2bo$268b8obobo
11b2o$270b9o$271bo$381bo$6b2o373b2o$6b2o372bobo2$275b2o114b2o$275b2o
114b2o8$43b2o114b2o$43b2o114b2o$292bo$293bo$283b2o6b3o89b2o$283b2o98b
2o5$6b2o$6b2o$334bo$333bo$333b3o2$321bo$321b2o$320bobo$6b2o$6b2o2$275b
2o114b2o$275b2o114b2o8$153b3o$50b2o100bo3bo$49bobo104bo$41b2o6b2o100bo
9b2o$41b2o6b2o100b2ob2o5b2o120b2o98b2o$50bobobo100bo127b2o98b2o$52b2o$
43bobo4b2obo$43b2o$44bo$6b2o$6b2o$151bo$151b3o$39b2o110b3o9b2o96bo$39b
2o122b2o96b2o$260bobo3$6b2o$6b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o
114b2o114b2o9$6bo$5bobo$5bobo$6bo44b2o98b2o130b2o98b2o$51b2o98b2o130b
2o98b2o$b2o7b2o$o2bo5bo2bo192bobo$b2o7b2o193b2o$206bo$6bo$5bobo195bo$
5bobo193bobo$6bo195b2o6$6b2o$6b2o2$43b2o114b2o114b2o114b2o$43b2o114b2o
114b2o114b2o8$352bo$6bo346bo$5bobo343b3o$5bobo$6bo44b2o98b2o230b2o$51b
2o56bobo39b2o230b2o$b2o7b2o97b2o$o2bo5bo2bo97bo$b2o7b2o2$6bo90bobo$5bo
bo90b2o$5bobo90bo$6bo9$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o
9$6bo$5bobo$5bobo$6bo44b2o98b2o230b2o$51b2o98b2o230b2o$b2o7b2o$o2bo5bo
2bo$b2o7b2o2$6bo$5bobo$5bobo$6bo9$43b2o114b2o114b2o114b2o$43b2o114b2o
114b2o114b2o9$6bo$5bobo$5bobo$6bo44b2o98b2o$51b2o98b2o$b2o7b2o$o2bo5bo
2bo$b2o7b2o2$6bo$5bobo$5bobo$6bo9$43b2o114b2o114b2o114b2o$43b2o114b2o
114b2o114b2o8$52bo$6bo44bobo$5bobo42bo3bo$5bobo42bo3bo$6bo47bo$51b3o$b
2o7b2o$o2bo5bo2bo$b2o7b2o2$6bo$5bobo$5bobo$6bo9$43b2o114b2o114b2o114b
2o$43b2o114b2o114b2o114b2o9$6bo$5bobo$5bobo$6bo2$b2o7b2o$o2bo5bo2bo$b
2o7b2o2$6bo$5bobo$5bobo$6bo6$383b3o$383bo2bo$382bo3bo$43b2o114b2o114b
2o106bo2b2o$43b2o114b2o114b2o108bo$383b2o$382b3o8b2o$382b3o8b2o5$394bo
$6bo388bo$5bobo385b3o$5bobo$6bo$395b2o$b2o7b2o383b2o$o2bo5bo2bo$b2o7b
2o2$6bo$5bobo$5bobo$6bo384b2o$391b2o8$43b2o114b2o114b2o$43b2o114b2o
114b2o3$383b2o$383b2o2$275b2o$275bo2$6bo260bo2bo5bo$5bobo259bo2bo6bo$
5bobo258bo5bo4b2o13bo$6bo260b2obobo5bo3b2o6b2ob2o$267bo4bobob2obo2b2o
6bo2bo$b2o7b2o256b8obobo11b2o$o2bo5bo2bo257b9o$b2o7b2o259bo$381bo$6bo
374b2o$5bobo372bobo$5bobo$6bo268b2o114b2o$275b2o114b2o8$43b2o114b2o$
43b2o114b2o$292bo$293bo$283b2o6b3o89b2o$283b2o98b2o5$6bo$5bobo$5bobo
326bo$6bo326bo$333b3o$b2o7b2o$o2bo5bo2bo308bo$b2o7b2o309b2o$320bobo$6b
o$5bobo$5bobo$6bo268b2o114b2o$275b2o114b2o8$153b3o$50b2o100bo3bo$49bob
o104bo$41b2o6b2o100bo9b2o$41b2o6b2o100b2ob2o5b2o120b2o98b2o$50bobobo
100bo127b2o98b2o$52b2o$43bobo4b2obo$43b2o$44bo$6bo$5bobo$5bobo143bo$6b
o144b3o$39b2o110b3o9b2o96bo$b2o7b2o27b2o122b2o96b2o$o2bo5bo2bo247bobo$
b2o7b2o2$6bo$5bobo$5bobo$6bo36b2o114b2o114b2o114b2o$43b2o114b2o114b2o
114b2o12$51b2o98b2o130b2o98b2o$51b2o98b2o130b2o98b2o2$205bobo$205b2o$
206bo2$203bo$201bobo$202b2o2$b2o7b2o$o2bo5bo2bo$b2o7b2o2$6bo$5bobo$5bo
bo$6bo36b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o8$352bo$353bo$
351b3o2$51b2o98b2o230b2o$51b2o56bobo39b2o230b2o$109b2o$110bo3$97bobo$
98b2o$98bo10$43b2o114b2o114b2o114b2o$43b2o114b2o114b2o114b2o12$51b2o
98b2o230b2o$51b2o98b2o230b2o17$43b2o114b2o114b2o114b2o$43b2o114b2o114b
2o114b2o12$51b2o98b2o$51b2o98b2o17$43b2o114b2o114b2o114b2o$43b2o114b2o
114b2o114b2o!

Lots of other List 1 and List 2 objects (and combinations) to try here, to see what can cleanly absorb the most gliders from the leaky side of a four-trail rephaser/rake column...

EDIT: Just because we can build a complete spaceship with only four block trails doesn't mean we should, of course -- no doubt it would be longer and have a higher total population, as well as being harder to build. Just might be useful to know how to effectively use four trails to make gliders to build trails #5 and #6.

EDIT 2: I've reviewed the reason for choosing 116 as the spacing. That seems to be the minimum width at which all List 1 and List 2 objects can be built a safe distance from the outermost block trails. Here's a sample pattern at 90x5, showing that any List 1 object can be safely constructed, but internal glider collisions cause problems for all but a few List 2 objects -- there's a vanish reaction and a not-very-useful backward kickback, but not much else:

Code: Select all

#C 90x5 spacing block-trail experiment.
#C List 1 collisions on the left (same glider color);
#C List 2 (different-color) collisions on the right.
#C Rightmost Herschel can be advanced 1-3 ticks, but can't be delayed.
#C 85x5, 87x5 and 89x5 seem to have glider color problems for the
#C   internal kickbacks; for 86x5 and 88x5 the kickbacks work, but
#C   there are more serious problems with internal glider collisions.
x = 508, y = 644, rule = B3/S23
49b2o88b2o88b2o88b2o88b2o88b2o$49b2o88b2o88b2o88b2o88b2o88b2o30$49b2o
88b2o88b2o88b2o88b2o88b2o$49b2o88b2o88b2o88b2o88b2o88b2o30$49b2o88b2o
88b2o88b2o88b2o88b2o$49b2o88b2o88b2o88b2o88b2o88b2o30$49b2o88b2o88b2o
88b2o88b2o88b2o$49b2o88b2o88b2o88b2o88b2o88b2o30$49b2o88b2o88b2o88b2o
88b2o88b2o$49b2o88b2o88b2o88b2o88b2o88b2o30$49b2o88b2o88b2o88b2o88b2o
88b2o$49b2o88b2o88b2o88b2o88b2o88b2o30$49b2o88b2o88b2o88b2o88b2o88b2o$
49b2o88b2o88b2o88b2o88b2o88b2o30$49b2o88b2o88b2o88b2o88b2o88b2o$49b2o
88b2o88b2o88b2o88b2o88b2o30$49b2o88b2o88b2o88b2o88b2o88b2o$49b2o88b2o
88b2o88b2o88b2o88b2o30$49b2o88b2o88b2o88b2o88b2o88b2o$49b2o88b2o88b2o
88b2o88b2o88b2o30$49b2o88b2o88b2o88b2o88b2o88b2o$49b2o88b2o88b2o88b2o
88b2o88b2o30$49b2o88b2o88b2o88b2o88b2o88b2o$49b2o88b2o88b2o88b2o88b2o
88b2o30$49b2o88b2o88b2o88b2o88b2o88b2o$49b2o88b2o88b2o88b2o88b2o88b2o
18$52b3o$51bo2bo$51bo2bo$52b4o$54b2o$56bo$55bo$55bo5$139b2o88b2o88b2o
88b2o88b2o$139b2o88b2o88b2o88b2o88b2o3$57b2o$57b2o3$499b3o$500b2o$486b
3o3b3o$484b6obob6o7b2o$484b2ob2o4b5obo5bobo$483bo3b2o4bo2bo2b4ob2obo$
484b6o3bo3b7o2bo$484b3o5bo4bo5b3o7$49b2o448b2o$49b2o448b2o8$139b2o88b
2o88b2o88b2o$139b2o88b2o88b2o88b2o73bo$483bo$483b3o$57b2o432b2o$57b2o
432b2o6$2b3o2$o5bo$o5bo$o5bo5$o5bo$o5bo$o5bo42b2o448b2o$49b2o448b2o$2b
3o5$504b2o$503bobo$229b2o88b2o184bo$138b2o89b2o88b2o$138b3obo269bo$
137bo2bob2o262b3o$50b2o5b2o78b3o272bobo76b2o$50bobo4b2o76b2ob3o2b2o
260bo3bo3b2o76b2o$50bo83bob5ob2o262bobo4bo4bo$133b2o2b2o2b4o262bo10bo$
134b2o7b2o273bo$138b2ob2o$140bo$140bo3$143b2o260b2o$143b2o260b2o6$114b
obo$49b2o64b2o22b2o268b2o88b2o$49b2o64bo23b2o268b2o88b2o3$167bo$165bob
o276b2o$166b2o275bobo$445bo2$229b2o88b2o$229b2o88b2o55bo$110b2o264bobo
$110bobo263b2o$57b2o51bo20b2o284b2o72b2o$57b2o72b2o284b2o72b2o3$318b2o
$316b4o$316bo2bo$310b2o3b2o4b2o$308b2o2bo3b3o3b2o$308bo2b3o2bob2ob2o$
308bo4bo4b4o$309b5o$233bo77b2o$232b3o$231bo2b2o$230b4obo$105bobo122bo
4bo$105b2o124b2o2bo$49b2o55bo32b2o91b2o85b2o88b2o88b2o$49b2o88b2o178b
2o88b2o88b2o$237bo$235bobo146b2o$236b2o145bobo62bobo$385bo63b2o$449bo
2$306bo117bo$170b2o134bobo114bo$170bobo133b2o115b3o$170bo2$57b2o178b2o
72b2o104b2o72b2o$57b2o178b2o72b2o104b2o72b2o17$49b2o88b2o88b2o88b2o88b
2o88b2o$49b2o88b2o88b2o88b2o88b2o88b2o12$57b2o178b2o72b2o178b2o$57b2o
178b2o72b2o178b2o17$49b2o88b2o88b2o88b2o88b2o88b2o$49b2o88b2o88b2o88b
2o88b2o88b2o12$237b2o72b2o$237b2o72b2o17$49b2o88b2o88b2o66bo21b2o88b2o
88b2o$49b2o88b2o88b2o64bobo21b2o88b2o88b2o$296b2o4$246bo$246bobo$246b
2o5$237b2o72b2o$237b2o72b2o17$49b2o88b2o88b2o88b2o88b2o88b2o$49b2o88b
2o88b2o88b2o88b2o88b2o!

The next little project will be to see what the two likely versions of a 116x5 front end would look like. After that I promise to go back to 116:110:90 and see what can be done to put a first complete spaceship together...!

Posted: **June 3rd, 2014, 3:52 pm**

I wonder, if the following or a similar reaction may be useful:

Code: Select all

x = 455, y = 646, rule = B3/S23
133b2o157b2o$133b2o157b2o30$133b2o157b2o$133b2o157b2o30$133b2o157b2o$
133b2o157b2o30$133b2o157b2o$133b2o157b2o30$133b2o157b2o$133b2o157b2o
30$133b2o157b2o$133b2o157b2o30$133b2o157b2o$133b2o157b2o30$133b2o157b
2o$133b2o157b2o30$133b2o157b2o$133b2o157b2o30$133b2o157b2o$133b2o157b
2o30$133b2o157b2o$133b2o157b2o30$133b2o157b2o$133b2o157b2o30$133b2o
157b2o$133b2o157b2o30$133b2o$133b2o3$297b2o$296bo2b2o$290bo5b2obo$135b
2o153bo6bo3b2o$132bo4bo152bo$126b2o4bo5bo$125bo2bo3bob2ob2o$121bo4bob
2o15b4o$120bo5bobo6bo8b2ob2o$120b3o2b3o7bo7b2o2bo2bo$125bo10bo7bo3b3o
137b2o$137b2o6bo2bo2bo136b2o$136bo12bobo$137b2o10b2o5$133b2o157b2o$
133b2o157b2o10$259bo$257b2o$141b2o115b2o40b2o$141b2o9bo147b2o$153b2o$
152b2o15$133b2o157b2o$133b2o157b2o4$334bo$332bobo$333b2o6$141b2o157b2o
$141b2o157b2o17$133b2o157b2o$133b2o157b2o12$141b2o157b2o$141b2o157b2o
4$61bo$60bo$60b3o11$133b2o157b2o$133b2o157b2o4$204b2o$204b2o7$141b2o
157b2o$141b2o157b2o17$133b2o157b2o$133b2o157b2o2$394bo$392bobo$204b2o
187b2o$204b2o7$141b2o157b2o$141b2o157b2o14$196b3o$197bo$197b3o$133b2o
157b2o$133b2o157b2o12$141b2o157b2o$141b2o157b2o2$bo$o$3o13$133b2o157b
2o$133b2o157b2o12$141b2o157b2o$141b2o157b2o17$133b2o157b2o$133b2o157b
2o160bo$452bobo$453b2o!

Posted: **June 3rd, 2014, 8:49 pm**

I may not have been clear enough that they were supposed to be separate examples! I was thinking of something like this:

Code: Select all

x = 758, y = 674, rule = B3/S23
680b2o49b2o$680b2o49b2o16$8b2o56b2o$8b2o56b2o13$680b2o49b2o$680b2o49b
2o16$8b2o56b2o$8b2o56b2o13$680b2o49b2o$680b2o49b2o16$8b2o56b2o$8b2o56b
2o13$680b2o49b2o$680b2o49b2o16$8b2o56b2o$8b2o56b2o13$680b2o49b2o$680b
2o49b2o16$8b2o56b2o$8b2o56b2o13$680b2o49b2o$680b2o49b2o16$8b2o56b2o$8b
2o56b2o13$680b2o49b2o$680b2o49b2o16$8b2o56b2o$8b2o56b2o13$680b2o49b2o$
680b2o49b2o16$8b2o56b2o$8b2o56b2o13$680b2o49b2o$680b2o49b2o16$8b2o56b
2o$8b2o56b2o13$680b2o49b2o$680b2o49b2o16$8b2o56b2o$8b2o56b2o13$680b2o
49b2o$680b2o49b2o16$8b2o56b2o$8b2o56b2o13$680b2o49b2o$680b2o49b2o16$8b
2o56b2o$8b2o56b2o13$731b2o$731b2o4$677b3o$677bobo$677bobo2b3o$674b2ob
2o$675bobo$676bo4$684b2o$684b2o2$6bo59b2o$5bo60b2o$4b2obobo$6bobobo$
11bo$10bo669b2o$b3o676b2o$o2bo$3o3$5bo3$12b2o716b3o$12b2o711b2o3bo2b2o
$724bo3bob2o$725bob4obo2bo$672b2o43bo7bo4b3ob2o$672b2o41bobo8bobobobob
2o$716b2o8bo3bobobo$728b2o3bo$8b2o705bo$8b2o705bo$714b3o3$714b3o$715bo
19b2o$715bo19bo2b2obo$736bob3obo$66b2o671bo$66b2o668bo6bo$736bo2bobo$
739bo$2o736b2o$2o678b2o49b2o$680b2o49b2o23bo$48bo17b2o689bo$46bobo16bo
689b3o$47b2o16b3o$50bo13b3o7b3o$49bo2bo10bo10b3o$53bo6bob2o3bo4bo4bo
559bobo$48bo4bo5bo7bo4bo3b2o559b2o$52b2o5bo6bo9bo561bo$60bo11bo2bo$49b
3o10b3o3b2o3bo$68b2o$68bo603b2o49b2o$672b2o49b2o3$8b2o56b2o$8b2o56b2o
8$701bo$699b2o$700b2o$49bo$2o46bo9b2o$2o46b3o7b2o620b2o49b2o$680b2o49b
2o12$672b2o49b2o$672b2o49b2o3$8b2o56b2o$8b2o56b2o12$2o56b2o$2o56b2o
620b2o49b2o$680b2o49b2o12$672b2o49b2o$672b2o49b2o3$8b2o56b2o$8b2o56b2o
12$2o56b2o$2o56b2o620b2o49b2o$680b2o49b2o12$672b2o49b2o$672b2o49b2o3$
8b2o56b2o$8b2o56b2o12$2o56b2o$2o56b2o620b2o49b2o$680b2o49b2o12$672b2o
49b2o$672b2o49b2o3$8b2o56b2o$8b2o56b2o12$2o56b2o$2o56b2o620b2o49b2o$
680b2o49b2o12$672b2o49b2o$672b2o49b2o3$8b2o56b2o$8b2o56b2o12$2o56b2o$
2o56b2o620b2o49b2o$680b2o49b2o12$672b2o49b2o$672b2o49b2o3$8b2o56b2o$8b
2o56b2o12$2o56b2o$2o56b2o620b2o49b2o$680b2o49b2o12$672b2o49b2o$672b2o
49b2o3$8b2o56b2o$8b2o56b2o12$2o56b2o$2o56b2o!

The left one is a 58+31n track, while the right one is a 51+31n track.

Posted: **June 4th, 2014, 10:52 am**

There are more ways to perturb a glider:

Code: Select all

x = 518, y = 1122, rule = B3/S23
46b2o115b2o135b2o148b2o$46b2o115b2o135b2o148b2o22$53b3o114b3o134b3o
147b3o$54bo116bo136bo149bo$52b3o114b3o134b3o147b3o$315b2o$314b2o$316bo
9$2o$b2o491b2o$o492b2o$495bo8$150b3o$152bo$151bo100$2o148b2o148b2o148b
2o$2o148b2o148b2o148b2o22$7b3o147b3o147b3o147b3o$8bo149bo149bo149bo$6b
3o147b3o147b3o147b3o23$195b3o$195bo$196bo11$362b3o$362bo152b3o$363bo
151bo$516bo2$62b2o$61b2o$63bo82$2o148bo149bo149bo$2o149b2o148b2o148b2o
$150b2o148b2o148b2o21$7b3o$8bo$6b3o13$44bo$43b2o$43bobo150b2o$196b2o3$
346b2o$346b2o$500b2o$500b2o16$203b3o$204bo$202b3o2$353b3o$354bo$352b3o
152b3o$508bo$506b3o79$o150bo148bobo147bobo$b2o149bo148b2o148b2o$2o148b
3o148bo149bo17$343b2o$343b2o4$464b2o$464b2o2$163b2o$163b2o14$350b3o$
57b2o292bo$57b2o290b3o3$471b3o$472bo$470b3o$170b3o$171bo$169b3o14$64b
3o$65bo$63b3o82$obo182bo114b2o185bo$b2o182bobo112b2o183b2o$bo183b2o
299b2o8$450b2o$450b2o10$316bo$314b2o$307b3o5b2o$308bo$306b3o8$457b3o$
458bo$456b3o6$46b2o$46b2o2$150b2o$150b2o19$53b3o$54bo$52b3o$157b3o$
158bo$156b3o81$43bo154bo165bo133bo$41b2o153b2o164b2o133bo$42b2o153b2o
164b2o132b3o14$450b2o$450b2o5$2o148b2o$2o148b2o13$300b2o$300b2o2$457b
3o$458bo$456b3o4$7b3o147b3o$8bo149bo$6b3o147b3o12$307b3o$308bo$306b3o
89$47bo148bo153bo145bo$46bo148bo153bo145bo$46b3o146b3o151b3o143b3o19$
2o$2o298b2o$300b2o$150b2o$150b2o2$450b2o$450b2o16$7b3o$8bo298b3o$6b3o
299bo$157b3o146b3o$158bo$156b3o$457b3o$458bo$456b3o98$37bo162bo$36bo
162bo$36b3o160b3o39$150b2o$150b2o4$2o$2o17$157b3o$158bo$156b3o3$7b3o$
8bo$6b3o!

Posted: **June 4th, 2014, 11:19 am**

Extrementhusiast wrote:I may not have been clear enough that they were supposed to be separate examples! I was thinking of something like this... The left one is a 58+31n track, while the right one is a 51+31n track.

Oh. Yes. It's obvious enough now...!

I've played around with non-standard Herschel-pair climbers off and on, but no, I haven't tried anything with these reactions -- I'll add them to my collection of hopeful tools. Another thing I haven't tried is to put two pairs of block trails very close together and see if useful gliders can be produced by rubbing the Herschels' sparks together somehow.

58 is a standard spacing that can be used by mirror-image Herschels that clean up after each other. But in both of these reactions you have one of the Herschels reversed, so the cleanup doesn't work; you get lots of extra gliders, but you can't re-use the block trails until one pair of blocks is shot down (could be either pair).

At 51 spacing the interior gliders just move the spare blocks, so you'd definitely have to get more gliders from somewhere else to clean those up if you wanted to use the 51-trails again. If you think of the 51-offset trail as temporary, built for a single use to get a glider onto a particular lane, then to make the reaction useful you have to figure out how to build the block column and destroy it behind. There are all kinds of strange options for cleanup, like

Code: Select all

x = 87, y = 286, rule = B3/S23
8$15b2o49b2o$15b2o49b2o30$15b2o49b2o$15b2o49b2o30$15b2o49b2o$15b2o49b
2o30$15b2o49b2o$15b2o49b2o30$15b2o$15b2o4$68b3o$68bobo$63b3o2bobo$69b
2ob2o$70bobo$71bo4$62b2o$62b2o7$66b2o$66b2o12$10b2o18bo43b2o$8b2o2bo
17bobo41b2o$9bob2o5bo11b2o$6b2o3bo6bo$18bo6$19b2o$19b2o7$15b2o49b2o$
15b2o49b2o10$49bo$17b2o31b2o$7b2o8b2o30b2o23b2o$7b2o65b2o17$15b2o49b2o
$15b2o49b2o11$17b2o$7b2o8b2o55b2o$7b2o65b2o17$15b2o45bo$15b2o43bobo$
61b2o11$7b2o65b2o$7b2o65b2o!

(and then you can shoot down any two of the remaining blocks depending on where you want the other trail to end up.)

I've only briefly tried looking for triples or quadruples of Herschels that clean up each others' spare blocks in some way other than the simple pairing we've been concentrating on. I'm sure there are lots of clever ways of doing this kind of thing, somewhere out there, but it's a logistical nightmare to keep track of the glider lanes and offhand I can't see any great advantage over the standard model. (?)

I guess the short summary is that there are clearly a ridiculous number of clever ways to use Herschels and block trails, adjusting trail spacing or phase, building new trails, deleting trails, puffing temporary absorber objects, and so on. But there are so many possible tricks that it's hard to keep track of them all, let alone write a search program that can fit them together automatically without errors. So I've compromised by experimentally building rakes for 116:110:90; the way I prove that a given trick is useful is to use it in a complete new rake for a forward or backward glider lane [updated again just now], that's more efficient than any other way to reach that lane.

Posted: **June 4th, 2014, 12:28 pm**

codeholic wrote:There are more ways to perturb a glider...

I take it this was a simple gencols search for glider-in glider-out with nothing else changing -- you weren't looking for one-glider-in two-gliders-out, or one-glider-in *WSS-out or other interesting things?

It occurs to me that a useful trick for a perturbing glider would be to suppress the creation of the spare B-heptomino block. If you got a glider out of the suppression reaction and could free up the one that ordinarily destroys the block, you'd be a glider ahead for rake-producing kickbacks and that kind of thing.

Another more complicated search that I haven't tried is the case where the glider interacts with the Herschel to produce a stable object, and then the next Herschel on the same trail perturbs that object into a clean glider. Or I suppose it could be three or four Herschels later, when the active reaction returns to the same general vicinity again. It's an unlikely thing to look for, I suppose, but it would add a degree of freedom for the output glider which could be very useful, similar to the "throw and catch" reactions in the original Caterpillar.

This probably isn't much different from the idea of building one-time glider turners along the edges of the block trails, and triggering them with a forerake or backrake with whatever timing you want. There are a few cases that I should explore to see if a new rake shows up --

Posted: **June 4th, 2014, 1:31 pm**

dvgrn wrote:I take it this was a simple gencols search for glider-in glider-out with nothing else changing -- you weren't looking for one-glider-in two-gliders-out, or one-glider-in *WSS-out or other interesting things?

I found no G->*WSS or G->2G Herschel-catalysed reactions.

dvgrn wrote:It occurs to me that a useful trick for a perturbing glider would be to suppress the creation of the spare B-heptomino block. If you got a glider out of the suppression reaction and could free up the one that ordinarily destroys the block, you'd be a glider ahead for rake-producing kickbacks and that kind of thing.

I'll take a look for this one.

dvgrn wrote:Another more complicated search that I haven't tried is the case where the glider interacts with the Herschel to produce a stable object, and then the next Herschel on the same trail perturbs that object into a clean glider. Or I suppose it could be three or four Herschels later[...]

It sounds more like a task for a custom search script.

Posted: **June 4th, 2014, 1:47 pm**

dvgrn wrote:It occurs to me that a useful trick for a perturbing glider would be to suppress the creation of the spare B-heptomino block. If you got a glider out of the suppression reaction and could free up the one that ordinarily destroys the block, you'd be a glider ahead for rake-producing kickbacks and that kind of thing.

You can do that, but then another spare block is not being destroyed

Code: Select all

x = 202, y = 55, rule = B3/S23
39b2o109bo$39b2o110b2o$150b2o16$192b2o$192b2o4$46b3o$47bo$45b3o16$199b
3o$200bo$198b3o9$2o$b2o$o!

Posted: **June 4th, 2014, 3:11 pm**

codeholic wrote:
dvgrn wrote:It occurs to me that a useful trick for a perturbing glider would be to suppress the creation of the spare B-heptomino block. If you got a glider out of the suppression reaction and could free up the one that ordinarily destroys the block, you'd be a glider ahead for rake-producing kickbacks and that kind of thing.
You can do that, but then another spare block is not being destroyed :

That wasn't the B-heptomino block, though. That's one of the pair of blocks that are fortunately cleaned up by yet another glider coming out of the Herschel-climber reaction. I usually don't dare muck around with that part of the reaction, except occasionally to absorb a glider I don't want, or (just a couple of posts back) to release that glider to help with cleanup on another trail.

ConwayLife.com

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