super breeders?

[wintersolstice]

Hello I'm new here (first post!) anyway I had an idea for a type of patturn that I call a super breeder, but I'm not if they've already been discovered or proven non-existent (I haven't found any info on them nor have I found any myself)

basically (if you exclude patturns that behave chaotiacally and/or need time to stabilise) then there are two main types of patturn: (at level 1 anway)

Stationary patturns (oscilators that end up in the same location) - S
Moving ocilators (oscilators that translate after an oscilation) - M

at level 2 there are three

Puffer - MS
Gun - SM
Rake - MM

at level 3 (a breeder)

Gun that spits out rakes - SMM
Puffer that spits out guns - MSM
Rake that spits out puffers - MMS
Rake that spits out rakes - MMM

at level 4 (this is the super breeder!)

Gun that spits out rakes that spits out rakes - SMMM
Puffer that spits out guns that spits out rakes - MSMM
Rake that spits out puffers that spits out guns - MMSM
Rake that spits out rakes that spits out puffers - MMMS
Rake that spits out rakes that spits out rakes - MMMM

basically it involves a primary patturn that gives birth to a secondary patturn that gives birth to a tertiary patturn that gives birth to a quaternary patturns

Does anyone know if these have been studied or proved non existent?

I also deduced there can be at mosty one stationary patturn

I also though about exending it beyond level 4 and even "infinity breeders"

I've only just found a program to investigate the Conway's game of life

[Paul Tooke]

wintersolstice wrote:

Hello I'm new here

Hello. Welcome.

I had an idea for a type of patturn that I call a super breeder

The kind of pattern that you describe doesn't seem realistic to implement in 2-Dimensional CA, which is what most people on this forum study. Have you tried producing a diagram of how such a pattern would grow? It seems to me that you've run out of directions for things to travel in once you've reached the tertiary stage. It would in any case imply exceeding quadratic growth. The "speed of light" in the usual 2-Dimensional CA neighbourhoods restricts the expansion of the bounding box of any pattern to one cell per tick in any direction. The growth of any pattern can thus be quadratic at best. Your "super breeder" pattern idea implies cubic expansion. This may well be possible in 3 or more dimensions (in fact there is scope for super-super-breeders etc.) but I think that many of us find that two dimensions is enough to deal with. Which CA were you thinking of implementing this in?

[calcyman]

Your "super breeder" pattern idea implies cubic expansion.

You've made the assumption that the patterns emit other patterns at a linear rate. Using logarithmic rakes it may be possible to engineer such a pattern.


Furthermore, cubic (and higher, up to exponential) growth is still possible in two dimensions, if you use the hyperbolic plane.

This may well be possible in 3 or more dimensions

Yes, cubic growth is possible in 3-dimensional Euclidean space, quartic growth in 4 dimensions, etc. In Leech Lattice Life (my favourite!), you could have a super-super-super- ... -breeder with O(t^24) growth!

I also deduced there can be at most one stationary pattern

So you're saying that a SSM breeder is impossible, in other words? It may surprise you to know that one already exists (slide-breeder).

[wintersolstice]

I am a complete beginner at this (although I have known about the game of life for a couple of years and have read a lot about configurarations) But I've never studied any patturn, because I've never had the resources to So my ideas are only based on guess work.

The idea that a "breeder" can have only one "stationary" patturn comes from something I read somewhere about the four types of breeders (the ones I mentioned)

You see I'm talking about a "patturn giving birth" over and over for eternity, if a S patturn gave birth to another S patturn the the next one would be blocked first (the one created by the primary) so similarly for more patturns, I think it depends on the definition of a "patturn giving birth" patturns that grow unbounded (apart from breeders) are in three types MM(rake), MS(puffer) and SM(gun) SS doesn't exist (yes patturns like that exist but can't grow unbounded, or at least I can't see how they can) patturns sometimes need time to stabilise (which is when S gives birth to S)

So you're saying that a SSM breeder is impossible, in other words? It may surprise you to know that one already exists (slide-breeder).

BTW can you describe a "Slider breeder" to me?

here's where I read of 4 breeders (only one stationary patturn)
http://en.wikipedia.org/wiki/Breeder_(c ... automaton)

I don't know if "super breeders can exist or if they've been studied that why I was asking"
are there any strategies for studying specific patturns apart from just scattering random squares and seeing what happens

PS My computer doesn't support Java so I can't use the features of the home page any ideas?

[Extrementhusiast]

PS My computer doesn't support Java so I can't use the features of the home page any ideas?

You could download Golly (a free, open-source, cross-platform, and in my opinion, excellent Life program which also runs many different types of rules) here: http://golly.sourceforge.net/

[calcyman]

BTW can you describe a "Slider breeder" to me?

It's included in Golly, as 'Breeders/slide-breeder.rle'. A configuration of 12 shotguns sends spaceships upward, which shift blocks whilst generating gliders to the south-east and north-east. These gliders collide and form Gosper glider guns, which then produce gliders ad infinitum.

Are there any strategies for studying specific patt[e]rns apart from just scattering random squares and seeing what happens?

Yes. On 22 January 1993, Dean Hickerson wrote:

There are basically 4 methods that have been used to produce Life
patterns:

(0) We try random patterns and wait till we find something nice.
Achim Flammenkamp has been the most systematic about this. He
wrote a program that runs random patterns on a 32x32 torus until
they finish and then records what they contain. During several
million runs, it produced 467 different still lifes and 17
different oscillators (plus a couple that depended on the size of
the torus). Inspired by Achim's results, I ran some random torus
experiments a few months ago, but used initial patterns that had
some type of symmetry, and thereby found glider syntheses of some
still lifes and oscillators. (I'll send some of these with my
next batch of patterns.)

(1) We stare in awe at the oscillators found by Bob Wainwright and
David Buckingham and wonder how they came up with them. (Bob
does most of his work on Life by hand!) And we stare in awe at
some of David Buckingham's glider syntheses. (I'll send some of
those too.)

(2) We build large constructions out of things we already know about.
Most of the ones that you've seen are probably pretty self-
explanatory. The fun part is figuring out a design for something;
after that we search for all the reactions needed to make it work,
and then put the pieces together.

(3) We use search programs to find low period oscillators and
spaceships. I'm sending a description of my program that I wrote
in 1989. The program is written in 6502 assembly language for an
Apple II , so it probably wouldn't be of much use to you. David
Bell's is written in c; contact him if you want a copy.

Dean Hickerson

My favourite option is (2), which is how all of the manageably large constructions (up to and including my stable telegraph) were built. Even larger constructions (such as Wade's Gemini, my Pi calculator, the Caterpillar and all of Golly's meta-patterns) required the help of computer programs to assemble them.

are in three types MM(rake), MS(puffer) and SM(gun) SS doesn't exist

SS does exist -- the following pattern demonstrates unbounded growth where a stationary pattern (a bilaterally symmetric configuration of two slide-guns) generates pairs of blocks (again, stationary patterns) forever:

Code: Select all

x = 244, y = 291, rule = B3/S23
156bo$155bobo$155bobbo$156boo$155bobo$155bobo$154boobo$149bob3o4bobboo
$149bo4boboobbobbo$149boobobbo5boo$151bo4b3o$157boo$$150bo11boo$148bob
o10bobo$149boo12bo12$130bo$130boo$129bobo3$125bo$125boo$124bobo$$139b
oo$80boo5boo49bobo$80boo5boo51bo4$173bo$171bobo$172boo$$27boo5boo$27b
oo5boo$$81bo5bo$80b3o3b3o18bo$27b3o3b3o43booboobooboo17boo$26bobbo3bo
bbo41b3o7b3o15bobo$30bobo$26boo7boo43bo7bo$26boo7boo65bo$29bo3bo68boo$
29booboo67bobo$27b3o3b3o$27boo5boo45bo34boo$27bo7bo44b3o32bobo$79bobbo
34bo$79bobobo$80b3o$81bo5boo$87boo$65bo3bo$53boo9bo5bo$53boo15bo$65bo
3boo$66b3o$196bo$66b3o125bobo$65bo3boo13bo110boo$53boo15bo13boo$35bo
17boo9bo5bo12bobo$36boo27bo3bo$35boo$79bo$79boo$24boo5boo45bobo$23bobb
o3bobbo$24bobbobobbo60boo$27bobo62bobo$25b3ob3o62bo$23b3o5b3o$23boo7b
oo$23boo7boo12bobo$24bobooboobo14boo$24b3o5bo14bo$23b3obbo5b3o$22boo4b
o4bobbo4boo$23bo6booboo6bo$20b3o19b3o$20bo5bo11bo5bo$27bo9bo$29bobobob
o$29bobobobo65boo$30booboo65boo$27bobbo3bobbo64bo$28boo5boo182bo$56bo
160bobo$56boo160boo$55bobo$$71boo$70boobo$73bo$72bo13bo3b3o$68bo16bobo
bb5o3boo$69boo14bo3boo3boobboo$86bobbo3boo$87b3o3bo$28boo5boo$28boo5b
oo50b3o3bo$86bobbo3boo$71boo12bo3boo3boobboo$71boo12bobobb5o3boo$86bo
3b3o19boo$113bo$47boo64bobo8boo$47bo66boo7boo$45bobo77bo$45boo$33bo$
33boo64b3o3bo$32bobo57boo3b5obbobo32boobbobo$57bo34boobboo3boo3bo31b3o
bo3bo12boo$57boo8boo28boo3bobbo31boo6bo13boo$oo14boo40boo7boo29bo3b3o
26boobo3bob5o97bo$oo15boo34boobboo67b3obboobbo3b3o98bobo$13b5o80bo3b3o
22boo6bo105boo$13b4o13b3o64boo3bobbo22b3o3boo3b3o$30bo3bo57boobboo3boo
3bo22bo3bo4bob5o$13b4o13bo4bo17boobboo33boo3b5obbobo30boo6bo13boo$13b
5o13bo3bo22boo7boo30b3o3bo23bo3bo4b3obo3bo12boo$oo15boo38boo8boo59b3o
3boo3boobbobo$oo14boo13bo3bo21bo69boo6bo$30bo4bo90b3obboobbo$30bo3bo
79boo15boobo$30b3o80bobo$45boo66bo92boo10boo10boo10boo$45bobo64boo92b
oo10boo10boo10boo$47bo$47boo$$47boo$47bo$45bobo64boo92boo10boo10boo10b
oo$45boo66bo92boo10boo10boo10boo$30b3o80bobo$30bo3bo79boo15boobo$30bo
4bo90b3obboobbo$oo14boo13bo3bo21bo69boo6bo$oo15boo38boo8boo59b3o3boo3b
oobbobo$13b5o13bo3bo22boo7boo30b3o3bo23bo3bo4b3obo3bo12boo$13b4o13bo4b
o17boobboo33boo3b5obbobo30boo6bo13boo$30bo3bo57boobboo3boo3bo22bo3bo4b
ob5o$13b4o13b3o64boo3bobbo22b3o3boo3b3o$13b5o80bo3b3o22boo6bo105boo$oo
15boo34boobboo67b3obboobbo3b3o98bobo$oo14boo40boo7boo29bo3b3o26boobo3b
ob5o97bo$57boo8boo28boo3bobbo31boo6bo13boo$57bo34boobboo3boo3bo31b3obo
3bo12boo$32bobo57boo3b5obbobo32boobbobo$33boo64b3o3bo$33bo$45boo$45bob
o77bo$47bo66boo7boo$47boo64bobo8boo$113bo$86bo3b3o19boo$71boo12bobobb
5o3boo$71boo12bo3boo3boobboo$86bobbo3boo$28boo5boo50b3o3bo$28boo5boo$
87b3o3bo$86bobbo3boo$69boo14bo3boo3boobboo$68bo16bobobb5o3boo$72bo13bo
3b3o$73bo$70boobo$71boo$$55bobo$56boo160boo$56bo160bobo$28boo5boo182bo
$27bobbo3bobbo64bo$30booboo65boo$29bobobobo65boo$29bobobobo$27bo9bo$
20bo5bo11bo5bo$20b3o19b3o$23bo6booboo6bo$22boo4bo4bobbo4boo$23b3obbo5b
3o$24b3o5bo14bo$24bobooboobo14boo$23boo7boo12bobo$23boo7boo$23b3o5b3o$
25b3ob3o62bo$27bobo62bobo$24bobbobobbo60boo$23bobbo3bobbo$24boo5boo45b
obo$79boo$79bo$35boo$36boo27bo3bo$35bo17boo9bo5bo12bobo$53boo15bo13boo
$65bo3boo13bo110boo$66b3o125bobo$196bo$66b3o$65bo3boo$53boo15bo$53boo
9bo5bo$65bo3bo$87boo$81bo5boo$80b3o$79bobobo$79bobbo34bo$27bo7bo44b3o
32bobo$27boo5boo45bo34boo$27b3o3b3o$29booboo67bobo$29bo3bo68boo$26boo
7boo65bo$26boo7boo43bo7bo$30bobo$26bobbo3bobbo41b3o7b3o15bobo$27b3o3b
3o43booboobooboo17boo$80b3o3b3o18bo$81bo5bo$$27boo5boo$27boo5boo$$172b
oo$171bobo$173bo4$80boo5boo51bo$80boo5boo49bobo$139boo$$124bobo$125boo
$125bo3$129bobo$130boo$130bo12$149boo12bo$148bobo10bobo$150bo11boo$$
157boo$151bo4b3o$149boobobbo5boo$149bo4boboobbobbo$149bob3o4bobboo$
154boobo$155bobo$155bobo$156boo$155bobbo$155bobo$156bo!

The same principle can be used to produce a SSS breeder, but it is likely to be very large.

[Paul Tooke]

Calcyman wrote:

SS does exist -- the following pattern demonstrates unbounded growth where a stationary pattern (a bilaterally symmetric configuration of two slide-guns) generates pairs of blocks (again, stationary patterns) forever:

Nice. Here's a slight variation of that pattern which extends a line of blocks diagonally. This has the advantage that the construction arms and line of blocks occupy a diagonal line of bounded width so that multiple copies can be placed side by side: [EDIT: my original post had a corrupted slide gun. This works]

Code: Select all

x = 414, y = 402, rule = B3/S23
37$196b4o$195bob2o$190b2o4b2o$189bo$190bo9$191bo$189bobo$190b2o4$171bo
$171b2o$170bobo3$166bo$166b2o$165bobo2$180b2o$179bobo$181bo12$108b2o5b
2o31bo65bo$108b2o5b2o31b2o62bobo$147bobo63b2o3$143bo$143b2o$142bobo2$
55b2o5b2o45bo5bo41b2o$54bobo5bobo43b3o3b3o39bobo$53b3o7b3o41b2obo3bob
2o40bo$53b2ob3ob3ob2o$54b5ob5o$56bo5bo47bo3bo$57b2ob2o48bo3bo4$56bo5bo
$55b2o5b2o45bo$54bob2o3b2obo43bobo$54bob2o3b2obo42b2ob2o$55b3o3b3o43bo
3bo13bo$55b3o3b3o42b3ob3o12b2o$107bo3bo12bobo$107bo3bo$108bobo4b2o$
109bo5b2o3bo113bo$98b2o20b2o112bo$81b2o14b2ob2o17bobo$81b2o15bo2bo$98b
o2bo32b2o96b2o$99b2o32bobo96b2o$135bo$99b2o128b2o$98bo2bo127b2o$81b2o
15bo2bo$81b2o14b2ob2o124b2o$98b2o126b2o$64bobo$53bo5bo5b2o156b2o$52bob
o3bobo4bo157b2o$51bo3bobo3bo$51bo3bobo3bo$51bo9bo2$52b2o5b2o55b2o$115b
2o$117bo2$97bo$63b2o32b2o$96bobo162b2o$50b2o17b2o189b2o$51bo17bo41b2o
149bo$48b3o19b3o37bobo$48bo23bo39bo3$56bo7bo2$54b3o7b3o$55b2ob2ob2ob2o
21bobo$56b3o3b3o23b2o$57bo5bo24bo5$123bo2bo12b2o$113b3o7bo14b2o$112bo
4bo9bo12bo$111bo5bo8b2o$74bo37bo8bo$74b2o37b2o8b2o$56b2o5b2o8bobo214b
2o$56b2o5b2o48b2o8b2o164b2o$112bo8bo169bo$99b2o10bo5bo8b2o$99b2o11bo4b
o9bo$113b3o7bo16b2o$123bo2bo14bo11bo$75b2o64bobo4b2ob3o$75bo66b2o4bobo
bo$73bobo74bo$62b2o9b2o74b2o$63b2o2b3o51bo2bo$62bo4bo56bo7b3o$68bo15bo
35bo9bo4bo36b2o$84bo2b2o31b2o8bo5bo34bo2bo12b2o$44b4o35bo5bo5b2o29bo8b
o35bo2b2o11b2o145bo$28b2o14bo2b2o35bobo2b2o4b2o26b2o8b2o20b2o14bo2bo
157b2o$28b2o15bo2b2o8b2o24bo3b2o63b2o2bo4b2o9bo158bo$45bo2bo7b5o25b3o
34b2o8b2o18b6o2b2o168bo$46b2o7bo4bo65bo8bo17b4o6bo9bo158b2o$55bo2b3o
25b3o31b2o8bo5bo34bo2bo$46b2o7b2o2bo24bo3b2o30bo9bo4bo35bo2b2o11b2o$
45bo2bo8b2o25bobo2b2o4b2o27bo7b3o36bo2bo12b2o$28b2o15bo2b2o33bo5bo5b2o
24bo2bo28b4o15b2o145b2o7bob2o$28b2o14bo2b2o8b2o25bo2b2o64b6o6bo152b2o
9b3o$44b4o7b2o2bo24bo68b2o2bo7bo154bo$55bo2b3o81b2o11b2o7bo28b2o5b2o$
55bo4bo80bobo49b2o5b2o$56b5o12b2o66bo$58b2o13bobo64b2o$75bo$75b2o2$
303b2o$304b2o$303bo5$193b3o3b3o$193bo2bobo2bo$193b2obobob2o110b2o$193b
2o5b2o109bobo$313bo3$307b2o$306bobo$190b2o116bo$189bo2bo3b2o$190bo8bo$
196bobo$197bo3$280b2o$190b3o3b3o82b2o$189bo9bo80bo$189bo3bobo3bo$190b
3o3b3o9bo$191bo5bo10bo$207b2o2$205b3o$206bobo80b2o$207b2o79bobo$290bo
3$284b2o$188b2o17b2o74bobo$189bo17bo77bo$186b3o19b3o9bo$186bo23bo10bo$
219b3o4$194b3o3b3o54b2o$194b3o3b3o55b2o$193bob2o3b2obo53bo$193bob2o3b
2obo$194b2o5b2o$195bo5bo3$211b2o5b2o$196b2ob2o9bobo5bobo45b2o$195bo5bo
7b3o7b3o43bobo$193b5ob5o5b2ob3ob3ob2o45bo$192b2ob3ob3ob2o5b5ob5o$192b
3o7b3o7bo5bo$193bobo5bobo9b2ob2o43b2o$194b2o5b2o57bobo$262bo$243bo$
212bo5bo25bo$211b2o5b2o22b3o18b2o14b3o8b2o$210bob2o3b2obo42b2o12bo3bo
8b2o$210bob2o3b2obo55bo4bo$211b3o3b3o56bo3bo$211b3o3b3o14b2o$235b2o29b
3o7bo3bo$234bo29b2obob2o5bo4bo$264b2o5bo5bo3bo8b2o$264b2obob2o8b3o8b2o
$266b3o6$254bo5bo$211b2o40b3o3b3o$211b2o39bo2b2ob2o2bo$238b2o12b3o5b3o
$237bobo$192b2o5b2o38bo$192b2o5b2o6$192b3o3b3o26b2o$191bo2bo3bo2bo25bo
bo$191bo3bobo3bo25bo$190b2obobobobob2o$190b2ob2o3b2ob2o$191b3o5b3o2$
253b2o5b2o$253b2o5b2o5$184bo23bo$184b3o19b3o6b2o$187bo17bo8bobo$186b2o
17b2o9bo$234b2o$235bo$235bob2o$202bobo31bo$203b2o$203bo$250b2o$228b3o
19bobo$214b2o11bo4bo6b2o9bo18b2o7b4o$203b3o8b2o10bo5bo5bo29bo2bo6bo3bo
$205bo21bo39b2o2bo10bo$204bo23b2o16b2o20bo2bo4bob2obo$187b2o7b2o47bo2b
2o19bo6b3o$187bob2o3b2obo30b2o14b6o$187bo3bobo3bo29bo18b4o19bo6b3o$
187b2o2bobo2b2o16b2o10bo5bo35bo2bo4bob2obo$188b3o3b3o17b2o11bo4bo34b2o
2bo10bo$189bo5bo32b3o37bo2bo6bo3bo$246b4o19b2o7b4o$244b6o$245bo2b2o$
236b2o8b2o$235bobo$235bo$191b3o3b3o34b2o$191bo2bobo2bo$190bo3bobo3bo$
190b4o3b4o$191bo7bo15$191b2o5b2o$191b2o5b2o!

The same principle can be used to produce a SSS breeder, but it is likely to be very large.

Ooh, would it be soo hard to program a static universal constructor to produce a line of these?

[Lewis]

Here's a slight variation of that pattern which extends a line of blocks diagonally. This has the advantage that the construction arms and line of blocks occupy a diagonal line of bounded width so that multiple copies can be placed side by side:

I think there's a mistake with the RLE file you posted. The pattern self destructs when run.

[Paul Tooke]

Lewis wrote:

I think there's a mistake with the RLE file you posted. The pattern self destructs when run.

Yes: a careless cut and paste job. I normally check patterns I post before hitting "submit". This time I forgot. I have posted a working version now.

[Macbi]

I applied some repairs.

Code: Select all

x = 296, y = 319, rule = B3/S23
154bo$153bobo$153bobo$154bo2$149b2o7b2o$148bo2bo5bo2bo$149b2o7b2o2$
154bo$153bobo$153bobo$154bo5$135b3o$137bo$136bo3$130b3o$132bo$131bo$
145bo$145b2o7bobo$144bobo8b2o$155bo4$80b2o5b2o$80b2o5b2o7$112b3o$27b2o
5b2o78bo$27b2o5b2o77bo$80bo7bo2$78b3o7b3o16b3o$79b2ob2ob2ob2o19bo$80b
3o3b3o19bo$81bo5bo34bo$122b2o$121bobo5$27bo7bo141bobo$27b2o5b2o142b2o$
27b3o3b3o142bo$29b2ob2o$29bo3bo53b2o$26b2o7b2o50b2o$26b2o7b2o28bo3bo$
30bobo20b2o9bo5bo$26bo2bo3bo2bo16b2o9bo24b3o$27b3o3b3o28b2o3bo9bo11bo$
25bo5bo34b3o5b2o4bo9bo$24b3o3b3o42b3o$24bob2ob2obo33b3o10b2o$23b2o7b2o
30b2o3bo5b2o2bo4b3o$23b2o7b2o19b2o9bo9bo4bo6bo$23b3o5b3o19b2o9bo5bo4bo
bobo5bo$25b3ob3o33bo3bo5bob2o20bo$27bobo69b2o$24bo2bobo2bo65bobo$23bo
2bo3bo2bo$24b2o5b2o$42bo$40bobo$40bobo$39bobo147b2o$41b2o146b2o$40bo$
186b2o$186b2o2$183b2o$22b2o17b2o52b2o86b2o$23bo17bo11bo41bobo$20b3o19b
3o9bo40bo84b2o$20bo23bo7b3o125b2o2$61b3o113b2o$63bo113b2o31b2o$62bo
147bobo$76bo97b2o34bo$28b2o5b2o39b2o96b2o$27bo2bo3bo2bo37bobo$30b2ob2o
136b2o$29bobobobo135b2o$29bobobobo$27bo9bo$26bo11bo2$30b2ob2o43b3o3bo$
28bo2bobo2bo39b5o2bobo12b2o$28b3o3b3o38b2o3b2o3bo12b2o$76b2o3bo2bo$77b
o3b3o$28b2o5b2o$28b2o5b2o40bo3b3o34b2o$76b2o3bo2bo33bobo$71b2o2b2o3b2o
3bo12b2o18bo$71b2o3b5o2bobo12b2o$78b3o3bo27b2o$38b3o72bo$40bo6b2o64bob
o123b2o$39bo7bo66b2o123bobo$45bobo191bo$45b2o2$107bo3b3o$92b2o12bobo2b
5o13b3o15bobo2b2o$51bo40b2o12bo3b2o3b2o12bo16bo3bob3o4b2o$50b2o15b2o
38bo2bo3b2o14bo16bo6b2o3b2o$2o9b2o36b2o16b2o39b3o3bo3bob2o26b5obo$2o8b
2o15b2o21b2o2b2o61bo2b2o2b3o24b3o$11b5o10bobo79b3o3bo2bo6b2o$12b4o12bo
7b3o68bo2bo3b5o3b3o26b3o$34bo3bo53b2o12bo3b2o3b2o2bo3bo24b5obo$12b4o
17bo4bo11b2o2b2o36b2o12bobo2b5o31bo6b2o3b2o$11b5o17bo3bo11b2o16b2o38bo
3b3o5bo3bo22bo3bob3o4b2o$2o8b2o38b2o15b2o48b2o3b3o22bobo2b2o$2o9b2o20b
o3bo13bo65bo6b2o$33bo4bo78bo2b2o2b3o$34bo3bo75b2o2bob2o167bo$36b3o74bo
bo172bobo$45b2o66bo174bobo$45bobo64b2o175bo$47bo220b2o$47b2o219bobo13b
2o7b2o$268bo14bo2bo5bo2bo$284b2o7b2o2$289bo$288bobo$288bobo$289bo2$
268b2o$267bobo$269bo7$277bo$141b2o5b2o127b2o$141b2o5b2o126bobo3$141b3o
3b3o122bo$141bo2bobo2bo122b2o$143b2ob2o123bobo2$139bo11bo$140bo9bo$
142bobobobo$142bobobobo$143b2ob2o$140bo2bo3bo2bo94b2o$141b2o5b2o94bobo
$246bo7$254bo$254b2o$253bobo3$249bo$249b2o$248bobo$149bobo$150b2o$150b
o2$138b2o5b2o$138bob2ob2obo$139bobobobo76b2o$139bobobobo75bobo$138bo7b
o76bo3$161bo$141b2o3bo15b2o$142bo4bob2o10b2o$141bob2o5bo$136b2o12bo4b
2o74bo$137bo8bobo6bo75b2o$134b3o10bo8b3o71bobo$134bo23bo2$226bo$142b2o
5b2o75b2o$142b2obobob2o74bobo$142bo2bobo2bo$142b3o3b3o5$199b2o$198bobo
$159b2o5b2o32bo$159b2o5b2o2$184bo$185b2o$184b2o$142b2o5b2o$142b2o5b2o
57bo$208b2o$207bobo$223bo3bo$211b2o9bo5bo9b2o$203bo7b2o9bo15b2o$203b2o
17b2o3bo$159b3o3b3o34bobo19b3o$159bo2bobo2bo$159b2obobob2o56b3o$159b2o
5b2o54b2o3bo$222bo15b2o$201b2o19bo5bo9b2o$200b3o20bo3bo$176b2o22bobobo
$161b2ob2o9bobo21bo3b4o$159bo2bobo2bo9bo25bob2o$159bobo3bobo35b2o$159b
3o3b3o33b2o2bo$159b2o44bo$159b2o$159b2o3$140b2o5b2o54bo3bo$140b2o5b2o
54bo3bo3$180bo19b2obo3bob2o$180b2o19b3o3b3o$179bobo20bo5bo7$182bo$181b
2o18b2o5b2o$181bobo17b2o5b2o$140bo7bo$139b4o3b4o$139bo3bobo3bo$140bo2b
obo2bo$132bo7b3o3b3o7bo$132b3o19b3o$135bo17bo$134b2o17b2o$182b2o$183bo
7bo3bo$183bobo4bo4bo$157bo26b2o4bo4bo$137bo5bo13b2o32b3o$136b3o3b3o11b
obo$135bo2b2ob2o2bo$135b3o5b3o17b4o7b2o$162bo3bo6bo2bo$162bo10bo2b2o
34bo2b2o12b2o$163bob2obo4bo2bo29bo6b2obo12b2o$166b3o6bo39bo$196b4o4b2o
7b3o$166b3o6bo20bob2o4b4o$163bob2obo4bo2bo19bo7bo8b3o$145b2o15bo10bo2b
2o19b2o16bo$146b2o14bo3bo6bo2bo36b2obo12b2o$145bo17b4o7b2o21b2o13bo2b
2o12b2o$196bo8bo$196bob2o6b2o$196b4o5b3o$184b2o$183bobo$183bo$182b2o9$
138b2obo3bob2o$138bo2bo3bo2bo$139b3o3b3o8$139b2o5b2o$139b2o5b2o!

[wintersolstice]

Thanks for the codes, but they're useless to me! What do you do with them? If they're for the home page i can't use them you might have to do something else sorry

[Macbi]

They paste into Golly, the program that Extrementhusiast linked to up the page. If you need a hand getting it to work, feel free to ask. It might not be work if your computer is really old though.

[calcyman]

Ooh, would it be soo hard to program a static universal constructor to produce a line of these?

It should be easy enough to program a UCC to build a line (no, that's too easy -- how about a parabola?) of Spartan (easily constructible still life) objects. And designing a Spartan analogue of your slide-printer should be trivial.

Objects of any desired complexity, such that they are composed of well-separated still lifes from the set {block, eater, boat, beehive, tub, loaf} can be constructed by my glider-synthesis script. I have explicit examples of functional components that fall into this category, including a two-dimensional unbounded memory store. In fact, these components are more than sufficient to build self-replicating machines in Life.

[wintersolstice]

They paste into Golly, the program that Extrementhusiast linked to up the page. If you need a hand getting it to work, feel free to ask. It might not be work if your computer is really old though.

I think I do need help actually the patturns seem to work to fast at such a small scale for me to work out how they work, there's thousands of instructions! and how do I enter the codes?

And back to my original question. Could there be "super breeders" in "2D Life" (I don't know that's why I was asking) and if there's a possiblilty where could I start searching for them?

[Paul Tooke]

Calcyman wrote:

It should be easy enough to program a UCC to build a line (no, that's too easy -- how about a parabola?)

Steady on! A line would suffice.

And designing a Spartan analogue of your slide-printer should be trivial

I had in mind a simplified version of the glider injections used by the Chapman-Greene construction arms. Obviously it would be a lot simpler than these because it only needs to fire one particular glider salvo. Two of these could be fed by a Herschel based gun or gun+duplicator combination with the gun employing a glider section involving the injection mechanism of the glider reflector receiving gliders from an edge-firing Herschel circuit. The whole construction could then be built as a static object and then activated by firing a single glider into the guns input.

Objects of any desired complexity, such that they are composed of well-separated still lifes from the set {block, eater, boat, beehive, tub, loaf} can be constructed by my glider-synthesis script.

Game on! (UK dialect)
So if I understand you correctly, all(!) that has to be done is for someone to produce a Spartan SS breeder and you could then produce a static constructor that could produce an unbounded sequence of copies it? That sounds like a plan.

[Axaj]

And back to my original question. Could there be "super breeders" in "2D Life" (I don't know that's why I was asking) and if there's a possiblilty where could I start searching for them?

I had an idea for a type of patturn that I call a super breeder

The kind of pattern that you describe doesn't seem realistic to implement in 2-Dimensional CA, which is what most people on this forum study. Have you tried producing a diagram of how such a pattern would grow? It seems to me that you've run out of directions for things to travel in once you've reached the tertiary stage. It would in any case imply exceeding quadratic growth. The "speed of light" in the usual 2-Dimensional CA neighbourhoods restricts the expansion of the bounding box of any pattern to one cell per tick in any direction. The growth of any pattern can thus be quadratic at best. Your "super breeder" pattern idea implies cubic expansion. This may well be possible in 3 or more dimensions (in fact there is scope for super-super-breeders etc.) but I think that many of us find that two dimensions is enough to deal with. Which CA were you thinking of implementing this in?

In short, if you did not catch the quote, no.

[calcyman]

So if I understand you correctly, all(!) that has to be done is for someone to produce a Spartan SS breeder and you could then produce a static constructor that could produce an unbounded sequence of copies it? That sounds like a plan.

Well, the Python script (at the moment) only outputs the glider synthesis in the form where you can then click on the 'Run' button in Golly and see the glider waves coalescing into the desired pattern.

It also outputs a file containing the positions of all of the still-lifes, and which recipe to use for each of them, in sequential order. That file could be read by another Python script to produce a Geminoid recipe, or something like that. But, yes, it is certainly possible.


A spaced-out version of the Chapman-Greene construction arm can be built by the script in all eight orientations.

[Paul Tooke]

Axaj wrote:

In short, if you did not catch the quote, no.

You may have missed Calcymans correction of my misplaced assumption: that each level of the breeder produces its offspring at a linear rate. Logarithmic growth patterns have been demonstrated which undermines my assertion that super breeders would have to exceed quadratic growth. So in short, the answer is maybe! Personally, I'm not entirely convinced because all of the sublinear growth patterns that I recall seeing use a combination of moving+moving or moving+stationary components, and so the gun itself is expanding spatially along with its output. This could make it tricky to incorporate into a superbreeder pattern because each level of breeder has to be able to grow indefinitely in some direction and there are only so many directions available.
BTW: Calcymans suggestion brought to my mind a picture of a gradually expanding fractal growth pattern of breeders producing breeders ad infinitum but I have no idea whether such a pattern is theoretically possible, let alone practically realisable.

Calcyman wote:

Well, the Python script (at the moment) only outputs the glider synthesis in the form where you can then click on the 'Run' button in Golly and see the glider waves coalescing into the desired pattern.

So I was perhaps getting a little carried away at thinking that an SSS breeder might be just around the corner. You wrote "glider synthesis script" and I rashly misinterpreted this as "UCC program". A glider recipe for a Spartan SS gun would be a big step forward though in terms of demonstrating the feasability of constructing SSS & MSS breeders. I stll think that this is a worthwhile project even though it doesn't fit comfortably within my area of expertise. I'm never quite satisfied with the theoretical arguments along the lines of "if you do this and that you'll have a pattern that does X". I'd greatly prefer to see a pattern that does X. Having said that I really ought to eat my own dog food and produce a Spartan SS gun.

[wintersolstice]

I think I may have proven that they don't exist! or at least not in 2D anyway

in 1D "semi breeders" (level 2) can exist (in theory)

in 2D you also have "breeders" (level 3) aswell

in 3D you also have "super breeders" (level 4) aswell

in 4D you also have "hyper-5 breeders" (level 5) aswell

etc...

possible prove this diagram



P,S,T represent primary secondary tertiary (patterns) in a typical breeder

P is 0D, S is 1D, T is 2D so Q (quaturnary) would have to 3D

I think that settles the matter

It seems to me that you've run out of directions for things to travel in once you've reached the tertiary stage.

It seems you were right!

[Axaj]

Axaj wrote:

In short, if you did not catch the quote, no.

You may have missed Calcymans correction of my misplaced assumption: that each level of the breeder produces its offspring at a linear rate. Logarithmic growth patterns have been demonstrated which undermines my assertion that super breeders would have to exceed quadratic growth. So in short, the answer is maybe! Personally, I'm not entirely convinced because all of the sublinear growth patterns that I recall seeing use a combination of moving+moving or moving+stationary components, and so the gun itself is expanding spatially along with its output. This could make it tricky to incorporate into a superbreeder pattern because each level of breeder has to be able to grow indefinitely in some direction and there are only so many directions available.
BTW: Calcymans suggestion brought to my mind a picture of a gradually expanding fractal growth pattern of breeders producing breeders ad infinitum but I have no idea whether such a pattern is theoretically possible, let alone practically realisable.

Ah, I misunderstood. I assumed it meant specifically exponential growth.

[Paul Tooke]

I wrote (a bit of a whinge about existance proofs) followed by:

... I really ought to eat my own dog food and produce a Spartan SS gun.

Well that shut me up for a while. After several false starts and some interesting experiments with Hersrch, I eventually opted for six independent guns using 'off-the-shelf' components with timing synchronised by an activation sequence using one-off still life glider duplicators/turners & destroyers. The whole thing consists of Spartan still lifes and is activated by a single glider arriving from the SW.

Code: Select all

x = 745, y = 750, rule = B3/S23
337b2o$337b2o9$322b2o$322b2o10$342b2o$342bo$343b3o$345bo4$326b2o$325bo
bo$325bo$324b2o60bo$384b3o$383bo$383b2o$354bo34bo$354b3o32b3o$357bo34b
o$334b2o20b2o33b2o$334b2o7b2o56b2o$343bo57bo$341bobo55bobo$341b2o4b2o
44b2o4b2o$325b2o20bo44bo2bo$326bo18bobo45b2o$326bobo16b2o34b2o$327b2o
52b2o8$356b2o32b2o3b2o$356b2o11b2o20bo3bo$369bo18b3o5b3o$333b2o35b3o
15bo9bo$329b2o2b2o37bo$328bobo$328bo$327b2o2$274b2o$274b2o9$259b2o$
259b2o10$279b2o$279bo$280b3o$282bo106bo$388bobo$389b2o2$263b2o$262bobo
$262bo$261b2o60bo$321b3o$320bo$320b2o$291bo34bo$291b3o32b3o$294bo34bo$
271b2o20b2o33b2o$271b2o7b2o56b2o$280bo57bo$278bobo55bobo$278b2o4b2o44b
2o4b2o$262b2o20bo44bo2bo$263bo18bobo45b2o$263bobo16b2o34b2o$264b2o52b
2o8$293b2o32b2o3b2o$293b2o11b2o20bo3bo$306bo18b3o5b3o$270b2o35b3o15bo
9bo$266b2o2b2o37bo$265bobo$265bo$264b2o7$504b2o$504bo$502bobo$21bo438b
o37b2o2b2o$20bobo411bo9bo15b3o35b2o$20b2o412b3o5b3o18bo$437bo3bo20b2o
11b2o$436b2o3b2o32b2o2$215b2o$215b2o5$450b2o52b2o$450b2o34b2o16bobo$
438b2o45bobo18bo$437bo2bo44bo20b2o$200b2o230b2o4b2o44b2o4b2o$200b2o
229bobo55bobo$431bo57bo$2o428b2o56b2o7b2o$2o438b2o33b2o20b2o$440bo34bo
$441b3o32b3o$443bo34bo$448b2o$2o447bo$2o444b3o$220b2o224bo60b2o$9b2o
209bo286bo$9b2o210b3o281bobo$223bo281b2o4$204b2o$203bobo281b2o$203bo
284bo$202b2o60bo223bobo$262b3o224b2o$261bo$261b2o282bo$232bo34bo276bob
o$232b3o32b3o274bobo$235bo34bo274bo$212b2o20b2o33b2o$212b2o7b2o56b2o
259b2o7b2o$221bo57bo259bo2bo5bo2bo$219bobo55bobo260b2o7b2o$219b2o4b2o
44b2o4b2o$203b2o20bo44bo2bo271bo$204bo18bobo45b2o217b2o15b2o35bobo$
204bobo16b2o34b2o229b2o15bobo34bobo$205b2o52b2o248bo35bo$509b2o5$368bo
$367bobo$234b2o32b2o3b2o93b2o71b2o39b2o$234b2o11b2o20bo3bo167bo41bo$
247bo18b3o5b3o162bobo28b2o11bobo$211b2o35b3o15bo9bo120bo37b2o2b2o30bo
12b2o$207b2o2b2o37bo120bo9bo15b3o35b2o34bobo90bo$206bobo162b3o5b3o18bo
71b2o2b2o40b2o43bobo$206bo167bo3bo20b2o11b2o62b2o40b2o43bobo$205b2o
166b2o3b2o32b2o150bo2$559b2o7b2o$477b2o34b2o43bo2bo5bo2bo$471b2o4b2o
34b2o44b2o7b2o$471b2o$564bo$563bobo$387b2o52b2o120bobo$387b2o34b2o16bo
bo120bo$375b2o45bobo18bo$374bo2bo44bo20b2o27b2o$369b2o4b2o44b2o4b2o42b
obo$368bobo55bobo42bo$368bo57bo43b2o$367b2o56b2o7b2o$311b2o64b2o33b2o
20b2o$311bobo63bo34bo$312bo65b3o32b3o$380bo34bo$385b2o$386bo$383b3o$
383bo60b2o$444bo$442bobo$442b2o3$544b2o$544b2o$424b2o$425bo$425bobo$
426b2o111b2o$539b2o3$557bo$557b3o$560bo22bo$559b2o20b3o11bo$580bo14b3o
$580b2o16bo14bo$597b2o12b3o$610bo$427b2o15b2o164b2o$427b2o15bobo$446bo
$446b2o161b2o$590b2o17b2o$590b2o5$419b2o$420bo138b2o32b2o$407b2o11bobo
136b2o11b2o20bo$408bo12b2o149bo18b3o$408bobo162b3o15bo$409b2o2b2o160bo
20b2o$413b2o182bo$547b2o45b3o$547bo46bo$548b3o$414b2o34b2o98bo$408b2o
4b2o34b2o$408b2o2$382b2o155b2o46b2o$382bo156b2o3b2o42bo$380bobo161b2o
42bobo15b2o$338bo37b2o2b2o207b2o15b2o$312bo9bo15b3o35b2o31b2o$312b3o5b
3o18bo66bobo120b2o12b2o$315bo3bo20b2o11b2o53bo123bo5b2o5bo$314b2o3b2o
32b2o52b2o120b3o6b2o6b3o$529bo18bo7$328b2o52b2o223b2o$167b2o159b2o34b
2o16bobo222bobo$166bo2bo146b2o45bobo18bo224bo$167b2o146bo2bo44bo20b2o
223b2o$310b2o4b2o44b2o4b2o$309bobo55bobo$309bo57bo$308b2o56b2o7b2o$
178bo139b2o33b2o20b2o$177bobo138bo34bo$177bobo139b3o32b3o$172b2o4bo
142bo34bo$160b2o10b2o152b2o148b2o119b2o$160b2o165bo148b2o119b2o$324b3o
258b2o$324bo60b2o197bobo$385bo108bo89bo$383bobo108b3o86b2o$383b2o112bo
22bo$170b2o324b2o20b3o11bo75b2o$169bo2bo344bo14b3o52b2o19bo$170b2o345b
2o16bo14bo37bo17bobo$534b2o12b3o37bobo15b2o$365b2o180bo41b2o4bo$366bo
180b2o45bobo$366bobo225bobo$367b2o226bo10b2o$546b2o58bobo$527b2o17b2o
60bo$527b2o79b2o$593b2o$594bo$591b3o$591bo2$496b2o32b2o$496b2o11b2o20b
o$509bo18b3o$368b2o15b2o123b3o15bo$368b2o15bobo124bo20b2o$387bo146bo$
387b2o95b2o45b3o$484bo46bo$485b3o$487bo3$136b2o3b2o$136b2o3b2o217b2o
114b2o46b2o$361bo114b2o3b2o42bo$348b2o11bobo117b2o42bobo15b2o$349bo12b
2o162b2o15b2o$349bobo$350b2o2b2o112b2o12b2o$354b2o113bo5b2o5bo$466b3o
6b2o6b3o$466bo18bo2$355b2o$137b2o210b2o4b2o$137b2o210b2o$705bo$703b3o$
187b2o355b2o156bo$186bobo355bobo155b2o$187bo358bo140b2o$350b2o194b2o
140bo$349bobo336bobo$349bo339b2o10bo$348b2o350bobo$700bobo$701bo4b2o$
689b2o15bobo$655b2o31bobo17bo$655bobo30bo19b2o$417bo116b2o120bo30b2o$
417b3o114b2o$420bo22bo78b2o188b2o$419b2o20b3o11bo65bobo188bo$440bo14b
3o63bo188bobo$440b2o16bo14bo46b2o188b2o$457b2o12b3o224b2o$470bo74b2o
151b2o$470b2o52b2o19bo$525bo17bobo$525bobo15b2o$469b2o55b2o4bo$450b2o
17b2o60bobo$450b2o79bobo$532bo10b2o$543bobo$545bo140b2o$545b2o140bo$
530b2o155bobo$419b2o32b2o76bo18b2o136b2o$419b2o11b2o20bo73b3o19bobo$
432bo18b3o74bo22bo$433b3o15bo$435bo20b2o$457bo$407b2o45b3o$407bo46bo$
408b3o$410bo3$689b2o15b2o$399b2o46b2o240b2o15bobo$399b2o3b2o42bo259bo$
404b2o42bobo15b2o240b2o$449b2o15b2o2$391b2o12b2o$392bo5b2o5bo$389b3o6b
2o6b3o$389bo18bo293bo$700b3o$699bo$39b2o658b2o19b2o$39b2o664bo15bo$
703b3o15bobo$702bo19b2o$467b2o233b2o$467bobo$469bo172bo$469b2o169b3o
100b2o$49b2o588bo103b2o$44b2o3b2o588b2o$44b2o578b2o79b2o$625bo60b2o17b
2o$625bobo58b2o$626b2o10bo$637bobo$637bobo45b2o$457b2o179bo4b2o41bo$
457b2o167b2o15bobo37b3o12b2o$445b2o178bobo17bo37bo14bo16b2o$444bobo
178bo19b2o52b3o14bo$444bo179b2o75bo11b3o$443b2o268bo$649b2o82b2o$468b
2o179bo83b2o$447b2o19bo178bobo$448bo17bobo178b2o$448bobo15b2o167b2o$
449b2o4bo179b2o$454bobo$454bobo$455bo10b2o$466bobo$468bo57bo$468b2o55b
obo$453b2o71b2o$454bo$451b3o169b2o$451bo172bo$624bobo$625b2o7$272b2o$
271bo2bo$272b2o3$626b2o15b2o$270b2o354b2o15bobo$270b2o373bo$262b2o381b
2o$262b2o2$279b2o$279b2o2$639bo$637b3o$636bo$636b2o19b2o$269b2o371bo
15bo$268bo2bo293bo74b3o15bobo$269b2o292b3o73bo19b2o$99b2o461bo76b2o$
98bobo461b2o$99bo447b2o$548bo131b2o$548bobo129b2o$549b2o10bo$560bobo
79b2o$560bobo60b2o17b2o$561bo4b2o55b2o$549b2o15bobo$548bobo17bo$548bo
19b2o52b2o$547b2o74bo$620b3o12b2o$572b2o46bo14bo16b2o$572bo63b3o14bo$
570bobo65bo11b3o$570b2o78bo$558b2o110b2o$558b2o110b2o9$546b2o$547bo$
547bobo$548b2o12$549b2o15b2o$549b2o15bobo$568bo$568b2o6$562bo$560b3o$
559bo$559b2o19b2o$565bo15bo$563b3o15bobo$562bo19b2o$562b2o3$603b2o$
603b2o$195b3o$197bo367b2o$196bo349b2o17b2o$546b2o3$545b2o$546bo$543b3o
12b2o$543bo14bo16b2o$559b3o14bo$561bo11b3o$573bo$593b2o$593b2o12$394b
2o$393bobo$394bo7$448b2o$447bo2bo$448b2o4$446b2o$438bo7b2o$437bobo$
437bobo$438bo17bo$455bobo$455bobo$456bo5$445b2o$445b2o6$425b2o$425b2o
3$426b2o$426b2o2$422b2o$422b2o3b2o$427b2o45$272b2o$271bobo$272bo48$
331b2o$331b2o4$330b2o$330b2o4$339b2o$339b2o17$609bo$608bobo$608b2o10$
581b2o$581b2o8$584b2o4b2o$584b2o4b2o!

Calcyman's glider synthesis script finds syntheses for this pattern in all 8 orientations. Here's the one for the pattern shown above, with a slightly delayed activation glider added to the end. This really needs Golly to run: it takes 271,080 generations to complete the construction. Activation starts just over a 1000 generations later with the blocks appearing at generation 276,616+1,086n.

Code: Select all

x = 136112, y = 67754, rule = B3/S23
68856b3o$68856bo$68857bo$67315b3o$67317bo$67316bo205$69041b3o$69041bo$
69042bo$67100b3o$67102bo$67101bo231$66906bo2370b3o$66906b2o2369bo$
66905bobo2370bo28$66867b3o$66869bo$66868bo6$69315bo$69314b2o$69314bobo
149$66704b3o$66706bo$66705bo2740b2o$69445b2o$69447bo24$69469b3o$69469b
o$69470bo4$66683b2o$66682bobo$66684bo18$66663b2o$66662bobo$66664bo153$
69718b3o$69718bo$69719bo2$66555b2o$66554bobo$66556bo31$66524b2o$66525b
2o$66524bo4$69755b3o$69755bo$69756bo164$69860b3o$69860bo$69861bo$
66333b3o$66335bo$66334bo3$69888b3o$69888bo$66315b3o3571bo$66317bo$
66316bo17$66295bo$66295b2o$66294bobo2$69902b3o$69902bo$69903bo10$
66273b3o3653b3o$66275bo3653bo$66274bo3655bo153$70095b3o$70095bo$70096b
o$66168b3o$66170bo$66169bo3$70123b3o$70123bo$66150b3o3971bo$66152bo$
66151bo17$66130bo$66130b2o$66129bobo2$70137b3o$70137bo$70138bo10$
66108b3o4053b3o$66110bo4053bo$66109bo4055bo138$70253b3o$70253bo$70254b
o$65912b3o$65914bo$65913bo199$70463b3o$70463bo$65718b2o4744bo$65719b2o
$65718bo196$70721b3o$70721bo$65576b2o5144bo$65577b2o$65576bo199$70867b
3o$70867bo$65322b2o5544bo$65323b2o$65322bo199$71118b3o$71118bo$71119bo
$65166b3o$65168bo$65167bo193$64904b3o$64906bo$64905bo6344b2o$71249b2o$
71251bo195$71500b3o$71500bo$71501bo$64759b3o$64761bo$64760bo204$71675b
3o$71675bo$71676bo$64534b3o$64536bo$64535bo218$64355b3o$64357bo$64356b
o$71910b2o$71910bobo$71910bo15$71928b3o$71928bo$71929bo11$64323b3o$
64325bo$64324bo20$71983b3o$71983bo$71984bo$64288b3o$64290bo$64289bo
140$72129b3o$72129bo$72130bo$64175b2o$64174bobo$64176bo15$64156b3o$
64158bo$64157bo11$72161b3o$72161bo$72162bo20$64101b3o$64103bo$64102bo$
72196b3o$72196bo$72197bo143$63933bo8370b3o$63933b2o8369bo$63932bobo
8370bo28$63894b3o$63896bo$63895bo6$72342bo$72341b2o$72341bobo137$
72452b3o$72452bo$72453bo$63711b3o$63713bo$63712bo203$63507b3o$63509bo$
63508bo9140b2o$72648b2o$72650bo24$72672b3o$72672bo$72673bo4$63486b2o$
63485bobo$63487bo18$63466b2o$63465bobo$63467bo142$72793b3o$72793bo$
72794bo$63252b3o$63254bo$63253bo205$72978b3o$72978bo$72979bo$63037b3o$
63039bo$63038bo231$62843bo10370b3o$62843b2o10369bo$62842bobo10370bo28$
62804b3o$62806bo$62805bo6$73252bo$73251b2o$73251bobo138$62775b3o$
62777bo$62776bo$73506b3o$73506bo$73507bo36$62727b3o10818b3o$62729bo
10818bo$62728bo10820bo168$62441b3o$62443bo$62442bo11140b2o$73582b2o$
73584bo24$73606b3o$73606bo$73607bo4$62420b2o$62419bobo$62421bo18$
62400b2o$62399bobo$62401bo153$73855b3o$73855bo$73856bo2$62292b2o$
62291bobo$62293bo31$62261b2o$62262b2o$62261bo4$73892b3o$73892bo$73893b
o164$73997b3o$73997bo$73998bo$62070b3o$62072bo$62071bo3$74025b3o$
74025bo$62052b3o11971bo$62054bo$62053bo17$62032bo$62032b2o$62031bobo2$
74039b3o$74039bo$74040bo10$62010b3o12053b3o$62012bo12053bo$62011bo
12055bo153$74232b3o$74232bo$74233bo$61905b3o$61907bo$61906bo3$74260b3o
$74260bo$61887b3o12371bo$61889bo$61888bo17$61867bo$61867b2o$61866bobo
2$74274b3o$74274bo$74275bo10$61845b3o12453b3o$61847bo12453bo$61846bo
12455bo138$74390b3o$74390bo$74391bo$61649b3o$61651bo$61650bo199$74600b
3o$74600bo$61455b2o13144bo$61456b2o$61455bo196$74858b3o$74858bo$61313b
2o13544bo$61314b2o$61313bo199$75004b3o$75004bo$61059b2o13944bo$61060b
2o$61059bo199$75255b3o$75255bo$75256bo$60903b3o$60905bo$60904bo193$
60641b3o$60643bo$60642bo14744b2o$75386b2o$75388bo195$75637b3o$75637bo$
75638bo$60496b3o$60498bo$60497bo204$75812b3o$75812bo$75813bo$60271b3o$
60273bo$60272bo218$60092b3o$60094bo$60093bo$76047b2o$76047bobo$76047bo
15$76065b3o$76065bo$76066bo11$60060b3o$60062bo$60061bo20$76120b3o$
76120bo$76121bo$60025b3o$60027bo$60026bo140$76266b3o$76266bo$76267bo$
59912b2o$59911bobo$59913bo15$59893b3o$59895bo$59894bo11$76298b3o$
76298bo$76299bo20$59838b3o$59840bo$59839bo$76333b3o$76333bo$76334bo
143$59670bo16770b3o$59670b2o16769bo$59669bobo16770bo28$59631b3o$59633b
o$59632bo6$76479bo$76478b2o$76478bobo137$76589b3o$76589bo$76590bo$
59448b3o$59450bo$59449bo203$59244b3o$59246bo$59245bo17540b2o$76785b2o$
76787bo24$76809b3o$76809bo$76810bo4$59223b2o$59222bobo$59224bo18$
59203b2o$59202bobo$59204bo150$77224b3o$77224bo$59279b2o17944bo$59280b
2o$59279bo196$76933b3o$76933bo$76934bo$58602b3o$58604bo$58603bo36$
58560b3o18418b3o$58562bo18418bo$58561bo18420bo175$77566b3o$77566bo$
77567bo$58839b3o$58841bo$58840bo3$77594b3o$77594bo$58821b3o18771bo$
58823bo$58822bo17$58801bo$58801b2o$58800bobo2$77608b3o$77608bo$77609bo
10$58779b3o18853b3o$58781bo18853bo$58780bo18855bo135$58678b3o$58680bo$
58679bo$77819b3o$77819bo$77820bo214$77940b3o$77940bo$77941bo$58413b3o$
58415bo$58414bo3$77968b3o$77968bo$58395b3o19571bo$58397bo$58396bo17$
58375bo$58375b2o$58374bobo2$77982b3o$77982bo$77983bo10$58353b3o19653b
3o$58355bo19653bo$58354bo19655bo153$58236b3o$58238bo$58237bo$78163b3o$
78163bo$78164bo3$58208b3o$58210bo$58209bo19971b3o$78181bo$78182bo17$
78203bo$78202b2o$78202bobo2$58194b3o$58196bo$58195bo10$58167b3o20053b
3o$58169bo20053bo$58168bo20055bo137$78394b3o$78394bo$78395bo$58053b3o$
58055bo$58054bo198$78334b3o$78334bo$78335bo$57593b3o$57595bo$57594bo
201$78769b3o$78769bo$78770bo$57628b3o$57630bo$57629bo192$57486b3o$
57488bo$57487bo2$79012b2o$79012bobo$79012bo12$57468b3o$57470bo$57469bo
21560b2o$79029b2o$79031bo12$57454b3o$57456bo$57455bo27$57429b3o$57431b
o$57430bo18$57416b3o$57418bo$57417bo126$57264b3o$57266bo$57265bo21940b
2o$79205b2o$79207bo24$79229b3o$79229bo$79230bo4$57243b2o$57242bobo$
57244bo18$57223b2o$57222bobo$57224bo144$79363b3o$79363bo$79364bo$
57011b3o$57013bo$57012bo191$79319b3o$79319bo$79320bo$56578b3o$56580bo$
56579bo202$56610b3o$56612bo$56611bo23140b2o$79751b2o$79753bo24$79775b
3o$79775bo$79776bo4$56589b2o$56588bobo$56590bo18$56569b2o$56568bobo$
56570bo134$80007b3o$80007bo$80008bo2$56482b2o$56481bobo$56483bo12$
80025b3o$80025bo$56464b2o23560bo$56465b2o$56464bo12$80039b3o$80039bo$
80040bo27$80064b3o$80064bo$80065bo18$80077b3o$80077bo$80078bo121$
79719b3o$79719bo$79720bo$55778b3o$55780bo$55779bo195$80416b3o$80416bo$
80417bo$56075b3o$56077bo$56076bo221$55804bo24770b3o$55804b2o24769bo$
55803bobo24770bo28$55765b3o$55767bo$55766bo6$80613bo$80612b2o$80612bob
o160$55639bo25170b3o$55639b2o25169bo$55638bobo25170bo28$55600b3o$
55602bo$55601bo6$80848bo$80847b2o$80847bobo164$55412b3o25570bo$55414bo
25569b2o$55413bo25570bobo28$81022b3o$81022bo$81023bo6$55376bo$55376b2o
$55375bobo136$80719b3o$80719bo$80720bo$54778b3o$54780bo$54779bo222$
54784bo26370b3o$54784b2o26369bo$54783bobo26370bo28$54745b3o$54747bo$
54746bo6$81193bo$81192b2o$81192bobo138$81627b3o$81627bo$54882b2o26744b
o$54883b2o$54882bo194$81328b3o$81328bo$81329bo$54187b3o$54189bo$54188b
o208$54182b3o$54184bo$54183bo27540b2o$81723b2o$81725bo24$81747b3o$
81747bo$81748bo4$54161b2o$54160bobo$54162bo18$54141b2o$54140bobo$
54142bo141$54266b3o$54268bo$54267bo27944b2o$82211b2o$82213bo208$82196b
3o$82196bo$82197bo2$53833b2o$53832bobo$53834bo31$53802b2o$53803b2o$
53802bo4$82233b3o$82233bo$82234bo152$82662b3o$82662bo$82663bo$53925b3o
$53927bo$53926bo15$82689b3o$82689bo$53902b2o28786bo$53903b2o$53902bo
188$82538b3o$82538bo$82539bo$53411b3o$53413bo$53412bo3$82566b3o$82566b
o$53393b3o29171bo$53395bo$53394bo17$53373bo$53373b2o$53372bobo2$82580b
3o$82580bo$82581bo10$53351b3o29253b3o$53353bo29253bo$53352bo29255bo
153$82773b3o$82773bo$82774bo$53246b3o$53248bo$53247bo3$82801b3o$82801b
o$53228b3o29571bo$53230bo$53229bo17$53208bo$53208b2o$53207bobo2$82815b
3o$82815bo$82816bo10$53186b3o29653b3o$53188bo29653bo$53187bo29655bo
138$82931b3o$82931bo$82932bo$52990b3o$52992bo$52991bo199$83141b3o$
83141bo$52796b2o30344bo$52797b2o$52796bo196$83399b3o$83399bo$52654b2o
30744bo$52655b2o$52654bo199$83865b3o$83865bo$83866bo$52713b3o$52715bo$
52714bo195$84074b3o$84074bo$84075bo$52522b3o$52524bo$52523bo195$83945b
3o$83945bo$52000b2o31944bo$52001b2o$52000bo199$84196b3o$84196bo$84197b
o$51844b3o$51846bo$51845bo193$51582b3o$51584bo$51583bo32744b2o$84327b
2o$84329bo200$84862b3o$84862bo$84863bo$51725b3o$51727bo$51726bo15$
84889b3o$84889bo$51702b2o33186bo$51703b2o$51702bo170$85009b3o$85009bo$
85010bo$51468b3o$51470bo$51469bo192$51289b3o$51291bo$51290bo2$85215b2o
$85215bobo$85215bo12$51271b3o$51273bo$51272bo33960b2o$85232b2o$85234bo
12$51257b3o$51259bo$51258bo27$51232b3o$51234bo$51233bo18$51219b3o$
51221bo$51220bo119$85178b3o$85178bo$85179bo$50837b3o$50839bo$50838bo
202$50754b3o$50756bo$50755bo$85485b3o$85485bo$85486bo36$50706b3o34818b
3o$50708bo34818bo$50707bo34820bo159$85553b3o$85553bo$85554bo$50412b3o$
50414bo$50413bo218$50233b3o$50235bo$50234bo$85788b2o$85788bobo$85788bo
15$85806b3o$85806bo$85807bo11$50201b3o$50203bo$50202bo20$85861b3o$
85861bo$85862bo$50166b3o$50168bo$50167bo140$86007b3o$86007bo$86008bo$
50053b2o$50052bobo$50054bo15$50034b3o$50036bo$50035bo11$86039b3o$
86039bo$86040bo20$49979b3o$49981bo$49980bo$86074b3o$86074bo$86075bo
120$86361b3o$86361bo$50016b2o36344bo$50017b2o$50016bo196$49861b3o$
49863bo$49862bo36744b2o$86606b2o$86608bo219$49411bo37170b3o$49411b2o
37169bo$49410bobo37170bo28$49372b3o$49374bo$49373bo6$86620bo$86619b2o$
86619bobo139$49449b3o$49451bo$49450bo37544b2o$86994b2o$86996bo194$
86930b3o$86930bo$86931bo$48989b3o$48991bo$48990bo213$87303b3o$87303bo$
87304bo$48976b3o$48978bo$48977bo3$87331b3o$87331bo$48958b3o38371bo$
48960bo$48959bo17$48938bo$48938b2o$48937bobo2$87345b3o$87345bo$87346bo
10$48916b3o38453b3o$48918bo38453bo$48917bo38455bo135$48815b3o$48817bo$
48816bo$87556b3o$87556bo$87557bo203$48385b3o$48387bo$48386bo39140b2o$
87526b2o$87528bo24$87550b3o$87550bo$87551bo4$48364b2o$48363bobo$48365b
o18$48344b2o$48343bobo$48345bo155$87877b3o$87877bo$87878bo$48350b3o$
48352bo$48351bo3$87905b3o$87905bo$48332b3o39571bo$48334bo$48333bo17$
48312bo$48312b2o$48311bobo2$87919b3o$87919bo$87920bo10$48290b3o39653b
3o$48292bo39653bo$48291bo39655bo153$48173b3o$48175bo$48174bo$88100b3o$
88100bo$88101bo3$48145b3o$48147bo$48146bo39971b3o$88118bo$88119bo17$
88140bo$88139b2o$88139bobo2$48131b3o$48133bo$48132bo10$48104b3o40053b
3o$48106bo40053bo$48105bo40055bo142$88481b3o$88481bo$88482bo$48144b3o$
48146bo$48145bo15$88508b3o$88508bo$48121b2o40386bo$48122b2o$48121bo
170$88595b3o$88595bo$88596bo$47854b3o$47856bo$47855bo195$88837b3o$
88837bo$88838bo$47696b3o$47698bo$47697bo196$88931b3o$88931bo$88932bo$
47390b3o$47392bo$47391bo204$89284b3o$89284bo$89285bo$47332b3o$47334bo$
47333bo195$89493b3o$89493bo$89494bo$47141b3o$47143bo$47142bo190$89596b
3o$89596bo$89597bo$46855b3o$46857bo$46856bo195$89832b3o$89832bo$89833b
o$46691b3o$46693bo$46692bo196$89990b3o$89990bo$89991bo$46449b3o$46451b
o$46450bo204$90281b3o$90281bo$90282bo$46344b3o$46346bo$46345bo15$
90308b3o$90308bo$46321b2o43986bo$46322b2o$46321bo171$90306b3o$90306bo$
90307bo$45965b3o$45967bo$45966bo192$45823b3o$45825bo$45824bo2$90549b2o
$90549bobo$90549bo12$45805b3o$45807bo$45806bo44760b2o$90566b2o$90568bo
12$45791b3o$45793bo$45792bo27$45766b3o$45768bo$45767bo18$45753b3o$
45755bo$45754bo126$45601b3o$45603bo$45602bo45140b2o$90742b2o$90744bo
24$90766b3o$90766bo$90767bo4$45580b2o$45579bobo$45581bo18$45560b2o$
45559bobo$45561bo144$90900b3o$90900bo$90901bo$45348b3o$45350bo$45349bo
197$45250b3o$45252bo$45251bo45940b2o$91191b2o$91193bo24$91215b3o$
91215bo$91216bo4$45229b2o$45228bobo$45230bo18$45209b2o$45208bobo$
45210bo145$44947b3o$44949bo$44948bo46340b2o$91288b2o$91290bo24$91312b
3o$91312bo$91313bo4$44926b2o$44925bobo$44927bo18$44906b2o$44905bobo$
44907bo134$91544b3o$91544bo$91545bo2$44819b2o$44818bobo$44820bo12$
91562b3o$91562bo$44801b2o46760bo$44802b2o$44801bo12$91576b3o$91576bo$
91577bo27$91601b3o$91601bo$91602bo18$91614b3o$91614bo$91615bo121$
91753b3o$91753bo$91754bo$44612b3o$44614bo$44613bo201$44293b3o$44295bo$
44294bo$91832b3o$91832bo$91833bo15$44266b3o$44268bo47585b3o$44267bo
47586bo$91855bo197$44141bo47970b3o$44141b2o47969bo$44140bobo47970bo28$
44102b3o$44104bo$44103bo6$92150bo$92149b2o$92149bobo160$43976bo48370b
3o$43976b2o48369bo$43975bobo48370bo28$43937b3o$43939bo$43938bo6$92385b
o$92384b2o$92384bobo164$43749b3o48770bo$43751bo48769b2o$43750bo48770bo
bo28$92559b3o$92559bo$92560bo6$43713bo$43713b2o$43712bobo141$92764b3o$
92764bo$43619b2o49144bo$43620b2o$43619bo199$93063b3o$93063bo$93064bo$
43522b3o$43524bo$43523bo200$43203b3o$43205bo$43204bo49944b2o$93148b2o$
93150bo196$93458b3o$93458bo$93459bo$43117b3o$43119bo$43118bo217$93663b
3o$93663bo$93664bo$42936b3o$42938bo$42937bo3$93691b3o$93691bo$42918b3o
50771bo$42920bo$42919bo17$42898bo$42898b2o$42897bobo2$93705b3o$93705bo
$93706bo10$42876b3o50853b3o$42878bo50853bo$42877bo50855bo150$93915b3o$
93915bo$93916bo2$42752b2o$42751bobo$42753bo31$42721b2o$42722b2o$42721b
o4$93952b3o$93952bo$93953bo161$94101b3o$94101bo$94102bo$42574b3o$
42576bo$42575bo3$94129b3o$94129bo$42556b3o51571bo$42558bo$42557bo17$
42536bo$42536b2o$42535bobo2$94143b3o$94143bo$94144bo10$42514b3o51653b
3o$42516bo51653bo$42515bo51655bo150$94345b3o$94345bo$94346bo2$42382b2o
$42381bobo$42383bo31$42351b2o$42352b2o$42351bo4$94382b3o$94382bo$
94383bo145$94346b3o$94346bo$94347bo$42005b3o$42007bo$42006bo192$41826b
3o$41828bo$41827bo2$94552b2o$94552bobo$94552bo12$41808b3o$41810bo$
41809bo52760b2o$94569b2o$94571bo12$41794b3o$41796bo$41795bo27$41769b3o
$41771bo$41770bo18$41756b3o$41758bo$41757bo121$94928b3o$94928bo$94929b
o$41787b3o$41789bo$41788bo196$95109b3o$95109bo$95110bo$41568b3o$41570b
o$41569bo204$41198b3o$41200bo$41199bo53944b2o$95143b2o$95145bo194$
95478b3o$95478bo$95479bo$41137b3o$41139bo$41138bo218$40958b3o$40960bo$
40959bo$95713b2o$95713bobo$95713bo15$95731b3o$95731bo$95732bo11$40926b
3o$40928bo$40927bo20$95786b3o$95786bo$95787bo$40891b3o$40893bo$40892bo
121$40586b3o$40588bo$40587bo55144b2o$95731b2o$95733bo218$40536bo55570b
3o$40536b2o55569bo$40535bobo55570bo28$40497b3o$40499bo$40498bo6$96145b
o$96144b2o$96144bobo138$96132b3o$96132bo$96133bo$40191b3o$40193bo$
40192bo220$40160b3o56370bo$40162bo56369b2o$40161bo56370bobo28$96570b3o
$96570bo$96571bo6$40124bo$40124b2o$40123bobo162$39911bo56770b3o$39911b
2o56769bo$39910bobo56770bo28$39872b3o$39874bo$39873bo6$96720bo$96719b
2o$96719bobo138$96733b3o$96733bo$96734bo$39592b3o$39594bo$39593bo195$
96969b3o$96969bo$96970bo$39428b3o$39430bo$39429bo196$97127b3o$97127bo$
97128bo$39186b3o$39188bo$39187bo201$97302b3o$97302bo$38957b2o58344bo$
38958b2o$38957bo193$97658b3o$97658bo$97659bo$38917b3o$38919bo$38918bo
198$38766b3o$38768bo$38767bo59144b2o$97911b2o$97913bo194$98063b3o$
98063bo$98064bo$38522b3o$38524bo$38523bo196$98325b3o$98325bo$98326bo$
38384b3o$38386bo$38385bo214$98244b3o$98244bo$98245bo$37917b3o$37919bo$
37918bo3$98272b3o$98272bo$37899b3o60371bo$37901bo$37900bo17$37879bo$
37879b2o$37878bobo2$98286b3o$98286bo$98287bo10$37857b3o60453b3o$37859b
o60453bo$37858bo60455bo135$37756b3o$37758bo$37757bo$98497b3o$98497bo$
98498bo214$98618b3o$98618bo$98619bo$37491b3o$37493bo$37492bo3$98646b3o
$98646bo$37473b3o61171bo$37475bo$37474bo17$37453bo$37453b2o$37452bobo
2$98660b3o$98660bo$98661bo10$37431b3o61253b3o$37433bo61253bo$37432bo
61255bo153$37314b3o$37316bo$37315bo$98841b3o$98841bo$98842bo3$37286b3o
$37288bo$37287bo61571b3o$98859bo$98860bo17$98881bo$98880b2o$98880bobo
2$37272b3o$37274bo$37273bo10$37245b3o61653b3o$37247bo61653bo$37246bo
61655bo142$37187b3o$37189bo$37188bo61940b2o$99128b2o$99130bo24$99152b
3o$99152bo$99153bo4$37166b2o$37165bobo$37167bo18$37146b2o$37145bobo$
37147bo161$37096b3o$37098bo$37097bo$99451b2o$99451bobo$99451bo15$
99469b3o$99469bo$99470bo11$37064b3o$37066bo$37065bo20$99524b3o$99524bo
$99525bo$37029b3o$37031bo$37030bo142$36909bo62770b3o$36909b2o62769bo$
36908bobo62770bo28$36870b3o$36872bo$36871bo6$99718bo$99717b2o$99717bob
o136$99672b3o$99672bo$99673bo$36531b3o$36533bo$36532bo195$100057b3o$
100057bo$100058bo$36516b3o$36518bo$36517bo204$100047b3o$100047bo$
100048bo$36106b3o$36108bo$36107bo192$35964b3o$35966bo$35965bo2$100290b
2o$100290bobo$100290bo12$35946b3o$35948bo$35947bo64360b2o$100307b2o$
100309bo12$35932b3o$35934bo$35933bo27$35907b3o$35909bo$35908bo18$
35894b3o$35896bo$35895bo115$35989b3o$35991bo$35990bo2$100715b2o$
100715bobo$100715bo12$35971b3o$35973bo$35972bo64760b2o$100732b2o$
100734bo12$35957b3o$35959bo$35958bo27$35932b3o$35934bo$35933bo18$
35919b3o$35921bo$35920bo125$100492b3o$100492bo$100493bo$35340b3o$
35342bo$35341bo196$35342b3o$35344bo$35343bo65540b2o$100883b2o$100885bo
24$100907b3o$100907bo$100908bo4$35321b2o$35320bobo$35322bo18$35301b2o$
35300bobo$35302bo144$101041b3o$101041bo$101042bo$35089b3o$35091bo$
35090bo198$34888b3o$34890bo$34889bo66340b2o$101229b2o$101231bo24$
101253b3o$101253bo$101254bo4$34867b2o$34866bobo$34868bo18$34847b2o$
34846bobo$34848bo134$101485b3o$101485bo$101486bo2$34760b2o$34759bobo$
34761bo12$101503b3o$101503bo$34742b2o66760bo$34743b2o$34742bo12$
101517b3o$101517bo$101518bo27$101542b3o$101542bo$101543bo18$101555b3o$
101555bo$101556bo121$101694b3o$101694bo$101695bo$34553b3o$34555bo$
34554bo203$101695b3o$101695bo$101696bo$34158b3o$34160bo$34159bo15$
101722b3o$101722bo$34135b2o67586bo$34136b2o$34135bo194$34082bo67970b3o
$34082b2o67969bo$34081bobo67970bo28$34043b3o$34045bo$34044bo6$102091bo
$102090b2o$102090bobo160$33917bo68370b3o$33917b2o68369bo$33916bobo
68370bo28$33878b3o$33880bo$33879bo6$102326bo$102325b2o$102325bobo138$
102291b3o$102291bo$102292bo$33550b3o$33552bo$33551bo196$102479b3o$
102479bo$102480bo$33338b3o$33340bo$33339bo220$33290b3o69570bo$33292bo
69569b2o$33291bo69570bobo28$102900b3o$102900bo$102901bo6$33254bo$
33254b2o$33253bobo135$103195b3o$103195bo$103196bo$33254b3o$33256bo$
33255bo195$103516b3o$103516bo$103517bo$33175b3o$33177bo$33176bo204$
32963b3o$32965bo$32964bo70740b2o$103704b2o$103706bo24$103728b3o$
103728bo$103729bo4$32942b2o$32941bobo$32943bo18$32922b2o$32921bobo$
32923bo141$103705b3o$103705bo$32560b2o71144bo$32561b2o$32560bo212$
104000b3o$104000bo$104001bo$32473b3o$32475bo$32474bo3$104028b3o$
104028bo$32455b3o71571bo$32457bo$32456bo17$32435bo$32435b2o$32434bobo
2$104042b3o$104042bo$104043bo10$32413b3o71653b3o$32415bo71653bo$32414b
o71655bo150$104252b3o$104252bo$104253bo2$32289b2o$32288bobo$32290bo31$
32258b2o$32259b2o$32258bo4$104289b3o$104289bo$104290bo149$104095b3o$
104095bo$104096bo$31743b3o$31745bo$31744bo207$104638b3o$104638bo$
104639bo$31911b3o$31913bo$31912bo3$104666b3o$104666bo$31893b3o72771bo$
31895bo$31894bo17$31873bo$31873b2o$31872bobo2$104680b3o$104680bo$
104681bo10$31851b3o72853b3o$31853bo72853bo$31852bo72855bo138$104928b3o
$104928bo$31783b2o73144bo$31784b2o$31783bo197$31566b3o$31568bo$31567bo
73544b2o$105111b2o$105113bo207$105282b3o$105282bo$105283bo2$31319b2o$
31318bobo$31320bo31$31288b2o$31289b2o$31288bo4$105319b3o$105319bo$
105320bo147$30944b3o$30946bo$30945bo74344b2o$105289b2o$105291bo200$
105712b3o$105712bo$105713bo$30975b3o$30977bo$30976bo15$105739b3o$
105739bo$30952b2o74786bo$30953b2o$30952bo169$30788b3o$30790bo$30789bo
2$105914b2o$105914bobo$105914bo12$30770b3o$30772bo$30771bo75160b2o$
105931b2o$105933bo12$30756b3o$30758bo$30757bo27$30731b3o$30733bo$
30732bo18$30718b3o$30720bo$30719bo119$106065b3o$106065bo$106066bo$
30524b3o$30526bo$30525bo196$106246b3o$106246bo$106247bo$30305b3o$
30307bo$30306bo220$30158b3o$30160bo$30159bo$106513b2o$106513bobo$
106513bo15$106531b3o$106531bo$106532bo11$30126b3o$30128bo$30127bo20$
106586b3o$106586bo$106587bo$30091b3o$30093bo$30092bo122$106615b3o$
106615bo$106616bo$29874b3o$29876bo$29875bo218$29695b3o$29697bo$29696bo
$106850b2o$106850bobo$106850bo15$106868b3o$106868bo$106869bo11$29663b
3o$29665bo$29664bo20$106923b3o$106923bo$106924bo$29628b3o$29630bo$
29629bo143$29473bo77570b3o$29473b2o77569bo$29472bobo77570bo28$29434b3o
$29436bo$29435bo6$107082bo$107081b2o$107081bobo137$107087b3o$107087bo$
107088bo$29146b3o$29148bo$29147bo192$28967b3o$28969bo$28968bo2$107293b
2o$107293bobo$107293bo12$28949b3o$28951bo$28950bo78360b2o$107310b2o$
107312bo12$28935b3o$28937bo$28936bo27$28910b3o$28912bo$28911bo18$
28897b3o$28899bo$28898bo144$28897b3o78770bo$28899bo78769b2o$28898bo
78770bobo28$107707b3o$107707bo$107708bo6$28861bo$28861b2o$28860bobo
162$28648bo79170b3o$28648b2o79169bo$28647bobo79170bo28$28609b3o$28611b
o$28610bo6$107857bo$107856b2o$107856bobo141$107655b3o$107655bo$107656b
o$28114b3o$28116bo$28115bo195$107860b3o$107860bo$107861bo$27919b3o$
27921bo$27920bo199$27939b3o$27941bo$27940bo80344b2o$108284b2o$108286bo
193$108595b3o$108595bo$108596bo$27854b3o$27856bo$27855bo198$27703b3o$
27705bo$27704bo81144b2o$108848b2o$108850bo194$109000b3o$109000bo$
109001bo$27459b3o$27461bo$27460bo199$27127b3o$27129bo$27128bo81944b2o$
109072b2o$109074bo193$109462b3o$109462bo$109463bo$27121b3o$27123bo$
27122bo198$109473b3o$109473bo$109474bo$26732b3o$26734bo$26733bo218$
26633b3o$26635bo$26634bo$109788b2o$109788bobo$109788bo15$109806b3o$
109806bo$109807bo11$26601b3o$26603bo$26602bo20$109861b3o$109861bo$
109862bo$26566b3o$26568bo$26567bo142$26446bo83570b3o$26446b2o83569bo$
26445bobo83570bo28$26407b3o$26409bo$26408bo6$110055bo$110054b2o$
110054bobo136$110194b3o$110194bo$110195bo$26253b3o$26255bo$26254bo199$
110274b3o$110274bo$110275bo$25933b3o$25935bo$25934bo196$110256b3o$
110256bo$110257bo$25515b3o$25517bo$25516bo195$110668b3o$110668bo$
110669bo$25527b3o$25529bo$25528bo210$111237b3o$111237bo$111238bo2$
25674b2o$25673bobo$25675bo31$25643b2o$25644b2o$25643bo4$111274b3o$
111274bo$111275bo149$110904b3o$110904bo$110905bo$24965b3o$24967bo$
24966bo15$110931b3o$24943b3o85985bo$24945bo85986bo$24944bo169$25126b3o
$25128bo$25127bo2$111452b2o$111452bobo$111452bo12$25108b3o$25110bo$
25109bo86360b2o$111469b2o$111471bo12$25094b3o$25096bo$25095bo27$25069b
3o$25071bo$25070bo18$25056b3o$25058bo$25057bo123$25066b3o$25068bo$
25067bo86744b2o$111811b2o$111813bo201$24528b3o$24530bo$24529bo87140b2o
$111669b2o$111671bo24$111693b3o$111693bo$111694bo4$24507b2o$24506bobo$
24508bo18$24487b2o$24486bobo$24488bo146$112218b3o$112218bo$112219bo$
24681b3o$24683bo$24682bo15$112245b3o$112245bo$24658b2o87586bo$24659b2o
$24658bo179$112427b3o$112427bo$24486b2o87940bo$24487b2o$24486bo24$
24462b3o$24464bo$24463bo4$112449b2o$112449bobo$112449bo18$112469b2o$
112469bobo$112469bo145$24267b3o$24269bo$24268bo88340b2o$112608b2o$
112610bo24$112632b3o$112632bo$112633bo4$24246b2o$24245bobo$24247bo18$
24226b2o$24225bobo$24227bo143$24037b3o$24039bo$24038bo$112776b3o$
112776bo$112777bo15$24010b3o$24012bo88785b3o$24011bo88786bo$112799bo
192$112723b3o$112723bo$112724bo$23596b3o$23598bo$23597bo3$112751b3o$
112751bo$23578b3o89171bo$23580bo$23579bo17$23558bo$23558b2o$23557bobo
2$112765b3o$112765bo$112766bo10$23536b3o89253b3o$23538bo89253bo$23537b
o89255bo135$113053b3o$113053bo$113054bo$23512b3o$23514bo$23513bo210$
113175b3o$113175bo$113176bo2$23212b2o$23211bobo$23213bo31$23181b2o$
23182b2o$23181bo4$113212b3o$113212bo$113213bo149$23100b3o$23102bo$
23101bo90340b2o$113441b2o$113443bo24$113465b3o$113465bo$113466bo4$
23079b2o$23078bobo$23080bo18$23059b2o$23058bobo$23060bo140$113832b3o$
113832bo$23087b2o90744bo$23088b2o$23087bo212$113761b3o$113761bo$
113762bo$22634b3o$22636bo$22635bo3$113789b3o$113789bo$22616b3o91171bo$
22618bo$22617bo17$22596bo$22596b2o$22595bobo2$113803b3o$113803bo$
113804bo10$22574b3o91253b3o$22576bo91253bo$22575bo91255bo150$114005b3o
$114005bo$114006bo2$22442b2o$22441bobo$22443bo31$22411b2o$22412b2o$
22411bo4$114042b3o$114042bo$114043bo143$114417b3o$114417bo$114418bo$
22476b3o$22478bo$22477bo199$114465b3o$114465bo$22120b2o92344bo$22121b
2o$22120bo197$21903b3o$21905bo$21904bo92744b2o$114648b2o$114650bo196$
114788b3o$114788bo$114789bo$21647b3o$21649bo$21648bo202$115049b3o$
115049bo$115050bo$21512b3o$21514bo$21513bo15$115076b3o$115076bo$21489b
2o93586bo$21490b2o$21489bo170$115169b3o$115169bo$115170bo$21228b3o$
21230bo$21229bo194$21125b3o$21127bo$21126bo2$115451b2o$115451bobo$
115451bo12$21107b3o$21109bo$21108bo94360b2o$115468b2o$115470bo12$
21093b3o$21095bo$21094bo27$21068b3o$21070bo$21069bo18$21055b3o$21057bo
$21056bo123$21065b3o$21067bo$21066bo94744b2o$115810b2o$115812bo218$
20695b3o$20697bo$20696bo$115850b2o$115850bobo$115850bo15$115868b3o$
115868bo$115869bo11$20663b3o$20665bo$20664bo20$115923b3o$115923bo$
115924bo$20628b3o$20630bo$20629bo118$115938b3o$115938bo$115939bo$
20397b3o$20399bo$20398bo218$20218b3o$20220bo$20219bo$116173b2o$116173b
obo$116173bo15$116191b3o$116191bo$116192bo11$20186b3o$20188bo$20187bo
20$116246b3o$116246bo$116247bo$20151b3o$20153bo$20152bo122$20132b3o$
20134bo$20133bo$116471b3o$116471bo$116472bo15$20105b3o$20107bo96385b3o
$20106bo96386bo$116494bo198$19796bo96770b3o$19796b2o96769bo$19795bobo
96770bo28$19757b3o$19759bo$19758bo6$116605bo$116604b2o$116604bobo163$
19620b3o97170bo$19622bo97169b2o$19621bo97170bobo28$116830b3o$116830bo$
116831bo6$19584bo$19584b2o$19583bobo162$19371bo97570b3o$19371b2o97569b
o$19370bobo97570bo28$19332b3o$19334bo$19333bo6$116980bo$116979b2o$
116979bobo141$117408b3o$117408bo$117409bo$19467b3o$19469bo$19468bo192$
19288b3o$19290bo$19289bo2$117614b2o$117614bobo$117614bo12$19270b3o$
19272bo$19271bo98360b2o$117631b2o$117633bo12$19256b3o$19258bo$19257bo
27$19231b3o$19233bo$19232bo18$19218b3o$19220bo$19219bo119$117518b3o$
117518bo$117519bo$18777b3o$18779bo$18778bo198$18626b3o$18628bo$18627bo
99144b2o$117771b2o$117773bo194$117923b3o$117923bo$117924bo$18382b3o$
18384bo$18383bo196$118185b3o$118185bo$118186bo$18244b3o$18246bo$18245b
o221$17956b3o$17958bo$17957bo$118311b2o$118311bobo$118311bo15$118329b
3o$118329bo$118330bo11$17924b3o$17926bo$17925bo20$118384b3o$118384bo$
118385bo$17889b3o$17891bo$17890bo142$17769bo100770b3o$17769b2o100769bo
$17768bobo100770bo28$17730b3o$17732bo$17731bo6$118578bo$118577b2o$
118577bobo136$118717b3o$118717bo$118718bo$17576b3o$17578bo$17577bo210$
119234b3o$119234bo$119235bo2$17671b2o$17670bobo$17672bo31$17640b2o$
17641b2o$17640bo4$119271b3o$119271bo$119272bo145$118758b3o$118758bo$
118759bo$16817b3o$16819bo$16818bo198$17299b3o$17301bo$17300bo102344b2o
$119644b2o$119646bo212$17097b3o$17099bo$17098bo$119824b3o$119824bo$
119825bo3$17069b3o$17071bo$17070bo102771b3o$119842bo$119843bo17$
119864bo$119863b2o$119863bobo2$17055b3o$17057bo$17056bo10$17028b3o
102853b3o$17030bo102853bo$17029bo102855bo135$16649b3o$16651bo$16650bo
2$119775b2o$119775bobo$119775bo12$16631b3o$16633bo$16632bo103160b2o$
119792b2o$119794bo12$16617b3o$16619bo$16618bo27$16592b3o$16594bo$
16593bo18$16579b3o$16581bo$16580bo133$120174b3o$120174bo$120175bo2$
16611b2o$16610bobo$16612bo31$16580b2o$16581b2o$16580bo4$120211b3o$
120211bo$120212bo143$120462b3o$120462bo$120463bo$16521b3o$16523bo$
16522bo196$119968b3o$119968bo$119969bo$15627b3o$15629bo$15628bo196$
120163b3o$120163bo$120164bo$15422b3o$15424bo$15423bo199$15803b3o$
15805bo$15804bo105144b2o$120948b2o$120950bo193$121224b3o$121224bo$
121225bo$15683b3o$15685bo$15684bo196$121405b3o$121405bo$121406bo$
15464b3o$15466bo$15465bo204$121555b3o$121555bo$121556bo$15218b3o$
15220bo$15219bo15$121582b3o$121582bo$15195b2o106386bo$15196b2o$15195bo
196$15049b3o106770bo$15051bo106769b2o$15050bo106770bobo28$121859b3o$
121859bo$121860bo6$15013bo$15013b2o$15012bobo136$121776b3o$121776bo$
121777bo$14635b3o$14637bo$14636bo202$122164b3o$122164bo$14623b2o
107540bo$14624b2o$14623bo24$14599b3o$14601bo$14600bo4$122186b2o$
122186bobo$122186bo18$122206b2o$122206bobo$122206bo145$14404b3o$14406b
o$14405bo107940b2o$122345b2o$122347bo24$122369b3o$122369bo$122370bo4$
14383b2o$14382bobo$14384bo18$14363b2o$14362bobo$14364bo162$14262bo
108370b3o$14262b2o108369bo$14261bobo108370bo28$14223b3o$14225bo$14224b
o6$122671bo$122670b2o$122670bobo143$13823b3o$13825bo$13824bo108740b2o$
122564b2o$122566bo24$122588b3o$122588bo$122589bo4$13802b2o$13801bobo$
13803bo18$13782b2o$13781bobo$13783bo160$13880b3o$13882bo$13881bo$
123035b2o$123035bobo$123035bo15$123053b3o$123053bo$123054bo11$13848b3o
$13850bo$13849bo20$123108b3o$123108bo$123109bo$13813b3o$13815bo$13814b
o124$123169b3o$123169bo$13624b2o109544bo$13625b2o$13624bo193$123452b3o
$123452bo$123453bo$13511b3o$13513bo$13512bo199$123388b3o$123388bo$
13043b2o110344bo$13044b2o$13043bo197$12826b3o$12828bo$12827bo110744b2o
$123571b2o$123573bo195$123954b3o$123954bo$123955bo$12813b3o$12815bo$
12814bo203$123972b3o$123972bo$123973bo$12435b3o$12437bo$12436bo15$
123999b3o$123999bo$12412b2o111586bo$12413b2o$12412bo169$12248b3o$
12250bo$12249bo2$124174b2o$124174bobo$124174bo12$12230b3o$12232bo$
12231bo111960b2o$124191b2o$124193bo12$12216b3o$12218bo$12217bo27$
12191b3o$12193bo$12192bo18$12178b3o$12180bo$12179bo120$12112b3o$12114b
o$12113bo$124443b3o$124443bo$124444bo36$12064b3o112418b3o$12066bo
112418bo$12065bo112420bo182$11818b3o$11820bo$11819bo$124573b2o$124573b
obo$124573bo15$124591b3o$124591bo$124592bo11$11786b3o$11788bo$11787bo
20$124646b3o$124646bo$124647bo$11751b3o$11753bo$11752bo122$11802b3o$
11804bo$11803bo113144b2o$124947b2o$124949bo209$124797b3o$124797bo$
124798bo$11245b3o$11247bo$11246bo194$125345b3o$125345bo$125346bo$
11404b3o$11406bo$11405bo192$11225b3o$11227bo$11226bo2$125551b2o$
125551bobo$125551bo12$11207b3o$11209bo$11208bo114360b2o$125568b2o$
125570bo12$11193b3o$11195bo$11194bo27$11168b3o$11170bo$11169bo18$
11155b3o$11157bo$11156bo119$125389b3o$125389bo$125390bo$10648b3o$
10650bo$10649bo197$125581b3o$125581bo$125582bo$10440b3o$10442bo$10441b
o198$125798b3o$125798bo$125799bo$10257b3o$10259bo$10258bo211$126371b3o
$126371bo$126372bo2$10408b2o$10407bobo$10409bo31$10377b2o$10378b2o$
10377bo4$126408b3o$126408bo$126409bo148$10236b3o$10238bo$10237bo
116344b2o$126581b2o$126583bo200$126394b3o$126394bo$126395bo$9642b3o$
9644bo$9643bo207$9834b3o$9836bo$9835bo$126961b3o$126961bo$126962bo3$
9806b3o$9808bo$9807bo117171b3o$126979bo$126980bo17$127001bo$127000b2o$
127000bobo2$9792b3o$9794bo$9793bo10$9765b3o117253b3o$9767bo117253bo$
9766bo117255bo149$127097b3o$127097bo$127098bo2$9534b2o$9533bobo$9535bo
31$9503b2o$9504b2o$9503bo4$127134b3o$127134bo$127135bo149$126816b3o$
126816bo$126817bo$8877b3o$8879bo$8878bo15$126843b3o$8855b3o117985bo$
8857bo117986bo$8856bo177$9126b3o$9128bo$9127bo118344b2o$127471b2o$
127473bo194$127799b3o$127799bo$127800bo$9058b3o$9060bo$9059bo204$
127878b3o$127878bo$127879bo$8741b3o$8743bo$8742bo15$127905b3o$127905bo
$8718b2o119186bo$8719b2o$8718bo170$128161b3o$128161bo$128162bo$8620b3o
$8622bo$8621bo196$128342b3o$128342bo$128343bo$8401b3o$8403bo$8402bo
203$128487b3o$128487bo$8146b2o120340bo$8147b2o$8146bo24$8122b3o$8124bo
$8123bo4$128509b2o$128509bobo$128509bo18$128529b2o$128529bobo$128529bo
145$7927b3o$7929bo$7928bo120740b2o$128668b2o$128670bo24$128692b3o$
128692bo$128693bo4$7906b2o$7905bobo$7907bo18$7886b2o$7885bobo$7887bo
164$7786b3o121170bo$7788bo121169b2o$7787bo121170bobo28$128996b3o$
128996bo$128997bo6$7750bo$7750b2o$7749bobo162$7599bo121570b3o$7599b2o
121569bo$7598bobo121570bo28$7560b3o$7562bo$7561bo6$129208bo$129207b2o$
129207bobo139$129292b3o$129292bo$7347b2o121944bo$7348b2o$7347bo216$
7217b3o$7219bo$7218bo$129572b2o$129572bobo$129572bo15$129590b3o$
129590bo$129591bo11$7185b3o$7187bo$7186bo20$129645b3o$129645bo$129646b
o$7150b3o$7152bo$7151bo121$129677b3o$129677bo$129678bo$6936b3o$6938bo$
6937bo195$129989b3o$129989bo$129990bo$6848b3o$6850bo$6849bo208$6525b3o
$6527bo$6526bo123544b2o$130070b2o$130072bo208$130268b3o$130268bo$
130269bo$6327b3o$6329bo$6328bo192$6148b3o$6150bo$6149bo2$130474b2o$
130474bobo$130474bo12$6130b3o$6132bo$6131bo124360b2o$130491b2o$130493b
o12$6116b3o$6118bo$6117bo27$6091b3o$6093bo$6092bo18$6078b3o$6080bo$
6079bo140$130694b3o$130694bo$130695bo2$5931b2o$5930bobo$5932bo31$5900b
2o$5901b2o$5900bo4$130731b3o$130731bo$130732bo148$5759b3o$5761bo$5760b
o125144b2o$130904b2o$130906bo212$5557b3o$5559bo$5558bo$131084b3o$
131084bo$131085bo3$5529b3o$5531bo$5530bo125571b3o$131102bo$131103bo17$
131124bo$131123b2o$131123bobo2$5515b3o$5517bo$5516bo10$5488b3o125653b
3o$5490bo125653bo$5489bo125655bo141$131322b3o$131322bo$131323bo$5381b
3o$5383bo$5382bo198$131484b3o$131484bo$131485bo$5143b3o$5145bo$5144bo
196$131665b3o$131665bo$131666bo$4924b3o$4926bo$4925bo224$4709b3o
127170bo$4711bo127169b2o$4710bo127170bobo28$131919b3o$131919bo$131920b
o6$4673bo$4673b2o$4672bobo162$4522bo127570b3o$4522b2o127569bo$4521bobo
127570bo28$4483b3o$4485bo$4484bo6$132131bo$132130b2o$132130bobo159$
4340b3o$4342bo$4341bo$132295b2o$132295bobo$132295bo15$132313b3o$
132313bo$132314bo11$4308b3o$4310bo$4309bo20$132368b3o$132368bo$132369b
o$4273b3o$4275bo$4274bo121$132512b3o$132512bo$132513bo$4171b3o$4173bo$
4172bo213$132511b3o$132511bo$132512bo$3772b3o$3774bo$3773bo15$132538b
3o$3750b3o128785bo$3752bo128786bo$3751bo187$132773b3o$132773bo$132774b
o$3621b3o$3623bo$3622bo195$132965b3o$132965bo$132966bo$3424b3o$3426bo$
3425bo203$133155b3o$133155bo$133156bo$3218b3o$3220bo$3219bo15$133182b
3o$133182bo$3195b2o129986bo$3196b2o$3195bo179$133373b3o$133373bo$
133374bo$3036b3o$3038bo$3037bo15$133400b3o$133400bo$3013b2o130386bo$
3014b2o$3013bo177$133564b3o$133564bo$133565bo$2823b3o$2825bo$2824bo
202$133744b3o$133744bo$133745bo$2603b3o$2605bo$2604bo199$133945b3o$
133945bo$133946bo$2404b3o$2406bo$2405bo198$134141b3o$134141bo$134142bo
$2200b3o$2202bo$2201bo196$134346b3o$134346bo$134347bo$2005b3o$2007bo$
2006bo246$134389b3o$134389bo$134390bo$1650b3o$1652bo$1651bo15$134416b
3o$1628b3o132785bo$1630bo132786bo$1629bo222$134650b3o$134650bo$134651b
o$1509b3o$1511bo$1510bo200$134849b3o$134849bo$134850bo$1308b3o$1310bo$
1309bo200$135058b3o$135058bo$135059bo$1117b3o$1119bo$1118bo213$135521b
3o$135521bo$135522bo$1190b3o$1192bo$1191bo36$1148b3o134418b3o$1150bo
134418bo$1149bo134420bo169$135700b3o$135700bo$135701bo$959b3o$961bo$
960bo204$135903b3o$135903bo$135904bo$762b3o$764bo$763bo157$3o$2bo$bo
36$136109b3o$136109bo$136110bo$568b3o$570bo$569bo!

This should make it possible to produce a Geminoid MSS breeder with the two constructors producing interleaved lines of SS guns. An SSS gun is also possible but it looks a bit trickier to construct an infinite line of these guns using a Geminoid two arm constructor. It seems to me that eventually one of the construction arms is going to need to fire through a gun or its line of fire. The only way I can see this working is if the constructor builds them sufficiently far apart that the average speed of the construction elbows away from the constructor exceeds the speed at which the lines of blocks are grown, 3c/1086 in this case. It may be necessary to widen the glider guns or completely redesign the SS gun to increase its period to something that the construction arms can keep up with.
(Alternatively one could take advantage of the fact that the constructor does not need to be constructible )

[Keiji]

It seems to me that eventually one of the construction arms is going to need to fire through a gun or its line of fire.

I don't see why - if the SSes are to be constructed in the orientation in your post, the SSS could extend its reflectors down to the right, and construct a line of those SSes at intervals.

[Paul Tooke]

Keiji wrote:

if the SSes are to be constructed in the orientation in your post, the SSS could extend its reflectors down to the right, and construct a line of those SSes at intervals

I'm not quite sure what you're getting at here. What do you mean by "could extend its reflectors down to the right"? Do you mean the construction elbows? Both X and Y elbows moving SE? They can't both do that.

I regret producing this pattern in this orientation now. I only did so because it matched that of my original 're-imagining' of Calcyman's SS gun. I always anticipated it firing SW or SE if constructed by a Gemini constructor as oriented as in its original posting.

To explain what I was getting at, let's rotate our co-ordinate system so that the X constructor arm of our Gemini is firing directly E, and the Y arm is firing N. This aligns it with the way that we usually draw axes. The X elbow is then always on the X-axis, constrained to move only E or W and must always be East of the construction arm. Similarly, the Y elbow is always on the Y-axis, moving only N or S and constrained to remain North of its construction arm.

Construction gliders are fired Northwards from the X elbow and Eastwards from the Y elbow, meeting somewhere in a quarter plane NE of the constructor. To build an infinite line of any object, that line must extend roughly NE in this plane. Both elbows have to be gradually moving away from the construction arms otherwise they are eventually going to be firing through previously constructed objects.

Now consider how this would look after we have built a few SS guns. We would have a line of glider salvos running E from the X constructor arm to the X elbow and then a (probably ragged looking) line of construction gliders extending N from here to the construction site. Likewise we would have a line of glider salvos running N from the Y constructor arm and a line of construction gliders extending E from there to the construction site. This means that all of the gliders form a box with the constructor at the SW corner and the construction site at the NE corner, the two elbows being at the SE and NW corners. This box completely encloses the previously constructed SS guns.

Now which direction should those SS guns be firing in? In our rotated co-ordinate system we have a choice of N,E,S or W. If we choose S or W then eventually they are going to extend their lines of blocks across one of the axes used by the construction salvos, preventing any further construction. If they fire N or E then they are going to intersect a line of construction gliders, *unless* we can build fast enough that the box of gliders is always growing faster than the output from the SS guns.

This was my point. The SS gun that I posted grows at 3c/1086 and the fastest that an unmodified Gemini can move its construction elbows is c/580 and only then if it's doing nothing else. We therefore need to either slow down the SS guns (making them larger) or speed up the constructor. Neither of these is a trivial task. The activation sequence on the SS gun is period-dependent and was a nightmare to set up.

A moving Gemini wouldn't have this problem because it could always build its SS gun in a position and orientation that isn't going to interfere with any of its decendents. A single armed "slow salvo" constructor also avoids this problem. I wonder whether Calcyman has a "slow salvo" version of his script?

[calcyman]

A moving Gemini wouldn't have this problem because it could always build its SS gun in a position and orientation that isn't going to interfere with any of its decendents.

Yes, the SS linear-growth patterns (henceforth 'slide puffers') could be produced collinear to the Gemini, with the line of blocks extending infinitely northwest.

I wonder whether Calcyman has a "slow salvo" version of his script?

I could do that, but it wouldn't be pretty. At all. It would construct temporary constellations of blocks, analogous to those in your slide puffer.

As I mentioned to Dave Greene, I require five basic constellations of blocks:

• A component to split a glider;
• A component to turn a glider;
• A component to delay a glider by p generations;
• A component to delay a glider by q generations;
• A component to change the parity (colour) of a glider.

Additionally, p and q must be relatively prime. Then it is a simple exercise to attain any position, timing and orientation.

Finally, I need slow-salvo constructions for each of these five basic constellations.

[Keiji]

Keiji wrote:

if the SSes are to be constructed in the orientation in your post, the SSS could extend its reflectors down to the right, and construct a line of those SSes at intervals

I'm not quite sure what you're getting at here. What do you mean by "could extend its reflectors down to the right"? Do you mean the construction elbows? Both X and Y elbows moving SE? They can't both do that.

Sure, they can.

If you'll excuse my rough MSpaint sketch:



Making the movable reflectors would be the hard part (a glider in one line would have to be reflected while a glider in another line would have to cause the reflector to translate itself).
The rightmost one would be even more complicated, as it'd need to be able to move in three directions (NE, SW and SE) rather than just one (SE).