Thread for basic questions

[confocaloid]

I know that cheapest known synthesis of xs12_8o6413z32 (trans-carrier tie snake) changed from 8G to 5G between 2021-03-15 and 2021-03-25. I was able to locate the 5G synthesis, and there is a 9G synthesis in Mark Niemiec's glider synthesis database. What is known about previous 8G synthesis/syntheses?

[Wyirm]

What is the bounding box of this gun? Is the entire rotor counted or just the stator? If the entire rotor counts, does this mean that edgeshooters such as hfx119h don't have any clearance at all?

[dvgrn]

What is the bounding box of this gun? Is the entire rotor counted or just the stator? If the entire rotor counts, does this mean that edgeshooters such as hfx119h don't have any clearance at all?

An edgeshooting gun has zero lanes of clearance if a glider can pass by on the lane that the gun fires on (at a time when it's not actually firing!) without doing any damage -- but a glider one lane closer to the gun will hit something. An edgeshooter has ten lanes of clearance if you can send a glider ten lanes closer to the gun without doing any damage, and so on.

An Fx119 inserter has a whopping 27hd of clearance.

The specific pattern you posted isn't really an edgeshooter or a gun -- but yes, the rotor is always counted in the bounding box, not just the stator.

[bibunsekibun]

What is the smallest synthesis for this rake at the moment?

Code: Select all

x = 6, y = 20, rule = B3/S23
o2bo$4bo$o3bo$b4o4$2b2o$bo2bo$bo2b2o$3b2o$ob2o$bo4$3b2o$b2ob2o$b4o$2b
2o!

[dvgrn]

What is the smallest synthesis for this rake at the moment?

Code: Select all

x = 6, y = 20, rule = B3/S23
o2bo$4bo$o3bo$b4o4$2b2o$bo2bo$bo2b2o$3b2o$ob2o$bo4$3b2o$b2ob2o$b4o$2b
2o!

That rake is mentioned in the LifeWiki article for Backrake 2, but no synthesis is given for the "reduced version of Backrake 2". Haven't found any attempts on Discord or the forums (?) -- which seems a little odd, since it's basically just a modified B-heptomino plus a couple of LWSSes.

13 gliders will do the trick... which means if someone has already solved this and I'm not finding it, they probably used a dozen gliders or less:

Code: Select all

x = 143, y = 69, rule = B3/S23
95bo$93b2o$94b2o4$87bo$88bo$86b3o8$bo$2bo$3o2$92bo$18bo74bo$18bobo70b
3o$18b2o4$109b2o$109b2o5$64b2o29b3o6b2o$65b2o28bo8b2o$64bo31bo5$91b3o$
93bo$92bo$15b2o$15bobo$15bo15$133b3o$133bo$78b2o54bo$77bobo61b2o$79bo
60b2o$142bo$75b2o$74bobo$76bo!

[AlbertArmStain]

What does the the pseudo-BSRD cleanup mechanism look like?

[dvgrn]

What does the the pseudo-BSRD cleanup mechanism look like?

You've already included it in your (17) & (21) seed. It's just one glider sent far southeast to knock out four Snarks-with-self-destruct-circuitry.

[AlbertArmStain]

What does the the pseudo-BSRD cleanup mechanism look like?

You've already included it in your (17) & (21) seed. It's just one glider sent far southeast to knock out four Snarks-with-self-destruct-circuitry.

Oh, yeah.
What does the nw corderabsorbers with the corderfleet look like then?

[dvgrn]

What does the nw corderabsorbers with the corderfleet look like then?

Somebody already asked that recently, and got an answer:

problem is, I can't find the NW corderfleet and corderabsorbers, somebody know where those happen to be?

The NW Corderfleet hasn't been compiled into a recipe yet, but all of the code needed to do the job can be found here.

The current NW Corderfleet and Corderabsorbers can be found here.

[AlbertArmStain]

Should there be a thread for CGoL project links?

[GUYTU6J]

A former question of mine about a synthesis gimmick:

How to convert the blinker at generation 38 to the beehive at indicated location with <4G (i.e. not by destroying and building)?

Code: Select all

x = 29, y = 35, rule = LifeHistory
14.D$13.D.DA.A$13.D.D2A$14.D2.A$A.A$.2A$.A5$15.A$15.2A$14.A.A3$7.3A9.
3A$9.A9.A7.2A$8.A11.A5.2A$28.A13$25.2A$25.A.A$25.A!

I have seen this kind of direct 2G + A → B conversion before, where A is a piece of leftover junk from previous steps and B is an object or active region at a specific location...

...27G P76 Pi hassler:

Code: Select all

x = 28, y = 23, rule = B3/S23
13b2o10b2o$12bo2bo2b4o2bo2bo$12b3o2b6o2b3o$15b10o$14bo10bo$14b2o8b2o6$
4b3o14b2o$15bo5b2o$2bo5bo7bo$2bo5bo5b3o$2bo5bo12b2o$20b2o$22bo2$2b2o$
3bo$3o$o!

...

...but I am not aware of a database for looking up these reactions. ...[trimmed for brevity]

Now I am faced with a similar case: I need to convert a block settled long ago to an R-pentomino, in a cheaper (2G or 3G) manner with direction and clearance similar to the following 4G method.

Code: Select all

x = 34, y = 16, rule = LifeHistory
12.3D$12.D$12.2D2$13.2C$13.2C3$9.3A$11.A$10.A$31.3A$6.A24.A$.A4.2A24.
A$.2A2.A.A$A.A!

This is like a spark_search.py search but without defining white "component" cells to begin with. How do I perform this magic?
EDIT: also this

Code: Select all

x = 25, y = 24, rule = B3/S23
obo$b2o$bo$18bo$18bobo$18b2o$4bobo$5b2o2bobo$5bo4b2o$10bo2$11bo$12bo7b
2ob2o$10b3o11bo$19bo2b2o$14b2o4b3o$14b2o4b3o$19bo2b2o$24bo$20b2ob2o2$
5bo2bob2obo2bo$5b4ob2ob4o$5bo2bob2obo2bo!

[AlbertArmStain]

What’s the smallest binary counter in CGoL?

[dvgrn]

What’s the smallest binary counter in CGoL?

Maybe this one, unless I'm forgetting an alternate implementation somewhere.

It's standardized universal-computer circuitry, of course, so it would be easy to pack it into a somewhat smaller space.

[AlbertArmStain]

What’s the smallest binary counter in CGoL?

Maybe this one, unless I'm forgetting an alternate implementation somewhere.

It's standardized universal-computer circuitry, of course, so it would be easy to pack it into a somewhat smaller space.

does this count?

Code: Select all

x = 1238, y = 230, rule = B3/S23
104b2o199b2o224b2o113b2o36b2o251b2o129b2o$104b2o162b2o34bob3obo14bo186b
o14bob3obo93bo14bob3obo34bob3obo14bo213bo15bo4bo109bo14bob3obo$119bo148b
obo33bobo3bo12b3o186b3o12bo3bobo93b3o12bo3bobo34bobo3bo12b3o213b3o11b
2obobobo109b3o12b2o4bo$104bo12b3o150bo4b2o26b2obobo2bo10bo192bo10bo2b
obob2o95bo10bo2bobob2o32b2obobo2bo10bo219bo10b2o3bob2o111bo13bobob2o$
68b2o33bobo10bo149b4ob2o2bo2bo27b2o3bo10b2o190b2o10bo3b2o97b2o10bo3b2o
38b2o3bo10b2o217b2o11bob3o113b2o10b3ob2o$67bobo33bo2bo9b2o148bo2bobob
obob2o24b3o3bo218bo3b3o108bo3b3o32b3o3bo244bo4b3o122b3o3b3o$66b3o14bo
20bo2bo161bobobobo27bo2b2obo8bo200bo8bob2o2bo99bo8bob2o2bo32bo2b2obo8b
o227bo7b3obo2bo115bo5b2o3b2o2bo$66b2o13b3o28bo157b2obobo28bo5bo2bo3bo
bo96b2o11bo6b2o80bobo3bo2bo5bo99bobo3bo2bo5bo34bo5bo2bo3bobo225bobo6b
2o3b2o115bobo4b3o3bobo$69b2o9bo23bo2bo3bobo160bo26b3o2b2obo6bo2bo13b2o
6bo11b2o61b2o10bobo4bo2bo44b2o11bo6b2o13bo2bo6bob2o2b3o61b2o11bo6b2o13b
o2bo6bob2o2b3o28b3o2b2obo6bo2bo13b2o6bo11b2o73b2o11bo6b2o60b2o11bo6b2o
13bo2bo5b3obo2b3o77b2o11bo6b2o13bo2bo3b2o3b2o2b3o46b2o6bo11b2o$68b3o9b
2o22b2o4bo2bo97b2o88bo2b2o3bo7b2o13bo2bo4bobo10b2o73bobo3bob3o44b2o10b
obo4bo2bo13b2o7bo3b2o2bo61b2o10bobo4bo2bo13b2o7bo3b2o2bo28bo2b2o3bo7b
2o13bo2bo4bobo10b2o73b2o10bobo4bo2bo59b2o10bobo4bo2bo13b2o6bo4b2o2bo77b
2o10bobo4bo2bo13b2o5b3o3b2o2bo45bo2bo4bobo10b2o$111b2o79bo14bob3obo46b
2o40bo3b2o3bo16b2o2b3obo3bobo84b2ob2obobo10b2o47bobo3bob3o2b2o16bo3b2o
3bo74bobo3bob3o2b2o16bo3b2o3bo30bo3b2o3bo16b2o2b3obo3bobo97bobo3bob3o
71bobo3bob3o2b2o17bob3o3bo31b2o57bobo3bob3o2b2o16b3ob2o3bo46b3obo3bob
o$76bo115b3o12bo3bobo47bo7b2o32b2obobo2bo16bo6bobob2ob2o87bobo3b2o7b2o
46b2ob2obobo6bo16bo2bobob2o74b2ob2obobo6bo16bo2bobob2o32b2obobo2bo16b
o6bobob2ob2o95b2ob2obobo10b2o61b2ob2obobo6bo16b2o3bob2o32b2o56b2ob2ob
obo6bo19bobob2o38b2o10bobob2ob2o$68b2o5bobo117bo10bo2bobob2o46bobo5b2o
33bobo3bo15bobo3b2o3bobo87b2obo2b4obo59bobo3b2o3bobo15bo3bobo79bobo3b
2o3bobo15bo3bobo34bobo3bo15bobo3b2o3bobo103bobo3b2o7b2o65bobo3b2o3bob
o14b2obobobo19bo75bobo3b2o3bobo15b2o4bo39b2o7b2o3bobo$68b2o4bo2bo116b
2o10bo3b2o3bo46b2o40bob3obo15b2o4bob4o2bob2o83b2obobo3bo57b2obo2b4obo
4b2o15bob3obo75b2obo2b4obo4b2o15bob3obo34bob3obo15b2o4bob4o2bob2o95b2o
bo2b4obo70b2obo2b4obo4b2o16bo4bo19b3o69b2obo2b4obo4b2o15bob3obo48bob4o
2bob2o$75b2o53b2o76bo3b2o2bo88b2o27bo3bobob2o87bobo3bo56b2obobo3bo27b
2o76b2obobo3bo27b2o36b2o27bo3bobob2o95b2obobo3bo72b2obobo3bo27b2o23bo
10b3o55b2obobo3bo27b2o4b2o45bo3bobob2o$126b2o2b2o2b2o72bob2o2b3o116bo
3bobo92bobo3bo59bobo3bo108bobo3bo71bo20bo3bobo103bobo3bo75bobo3bo50b2o
11b2o59bobo3bo32b2o44bo3bobo$126bobo2bo2b2o64b2o2bo2bo5bo118bo3bobo94b
o3b2o60bobo3bo108bobo3bo69bo20bo3bobo105bobo3bo75bobo3bo59b2o63bobo3b
o46bo29bo3bobo60bo$127b3o33b2o11bo6b2o14b3o6bob2o2bo102bo14b2o3bo162b
o3b2o14bo94bo3b2o14bo54b3o3bo14b2o3bo107bo3b2o76bo3b2o14bo39bo4b3o63b
o3b2o14bo16bo12b3o29b2o3bo62bo$128b2o33b2o10bobo4bo2bo13bo8bo3b3o101b
obo200bobo112bobo58bobo227bobo37bobo4bobo81bobo14bobo10bo98b3o$175bob
o3bob3o2b2o9b2o5bo3b2o105bo168b2o32bo114bo60bo229bo38bo2bo4b2o82bo15b
o2bo9b2o$174b2ob2obobo6bo16bo2bobob2o57b2o150b2o60b2o478b2o106bo2bo$90b
o35bo51bobo3b2o3bobo15bo3bobo58bo72b2o77b2o59bo120b2o116b2o89b2o80b2o
129b2o52bo49b2o$90b3o32bobo46b2obo2b4obo4b2o15bob3obo59b3o69b2o62b2o75b
2o118b2o61b2o53b2o89b2o80b2o37bobo89b2o44bo2bo3bobo48b2o$93bo31bo2bo45b
2obobo3bo27b2o4b2o56bo84b2o46bo2bo64b2o8b2o103b2o77bo68b2o59b2o80b2o53b
2o74b2o7b2o50b2o4bo2bo63b2o$92b2o32b2o50bobo3bo32b2o140bo2bo44bob2o42b
2o20bo2bo111bo2bo76bobo65bo2bo57bo2bo78bo2bo52bo74bo2bo5bobo57b2o13b2o
48bo2bo$179bobo3bo130b2o42b2obo43bo45b2o19bob2o42b2o67bob2o42b2o34b2o
22b2o42b2obo55bob2o42b2o34bob2o42b2o83bob2o8bo33b2o33b2o2b2o2b2ob2o42b
2obo$169b2o9bo3b2o14bo115b2o45bo42b2o66bo45b2o67bo45b2o58b2o45bo55bo45b
2o34bo45b2o83bo45b2o33bobo2bo2b2ob2o45bo$130b2o36bo3bo26bobo15b3o143b
2o108b2o113b2o152b2o53b2o80b2o129b2o81b3o54b2o$130bobo35bo31bo17b2o136b
2o35bo26b2o37b2obo89b2o121b2o311b2o104b2o$132bo36bob3o41b2o26b2o104b2o
4b2o20bo14bobo3b2o21bo31b2o4bob2o24b2o63bo22bo26b2o70bo2bo50b2o26bo27b
o26b2o53bo26b2o93bo8bo26b2o110b2o26bo$132b2o81b3o26bo9b3o59b2o31bo7bo
13b2o3bobo12bo2bo3bo21bo14b2o16b2o8b2o23bo31b2o28bobo21bobo3b2o11b2o8b
o31b2o38bobo17b2o31bo21b2o3bobo25bobo3b2o21bo31b2o19bobo3b2o21bo31b2o
58bobo7bobo3b2o21bo31b2o44b2o31bo21b2o3bobo$102b2o112bobo23bo13bo59b2o
16b2o14bo21bo3bo2bo11bobob2obo21b2o12bobo23b2o3bo21bo14b2o16b2o28b2o21b
o2bo3bo13b2o6bo14b2o16b2o39bo18b2o16b2o14bo21bo3bo2bo23bo2bo3bo21bo14b
2o16b2o18bo2bo3bo21bo14b2o16b2o58b2o7bo2bo3bo21bo14b2o16b2o33bo10b2o16b
2o14bo21bo3bo2bo$95b2o5bobo51b2o59b2o23b5o8bo5b2o71bobo12b2o21bob2obo
bo10b2obobobo36bo25bob2obo21b2o12bobo69bobob2obo12bo8b2o12bobo94bobo12b
2o21bob2obobo23bobob2obo21b2o12bobo36bobob2obo21b2o12bobo85bobob2obo21b
2o12bobo50bobo27bobo12b2o21bob2obobo$95b2o7bo50bo2bo88bo13bo74bo36bob
obob2o7bo2bob2o38b2o20bob2obobobo36bo70b2obobobo36bo98bo36bobobob2o21b
2obobobo36bo37b2obobobo36bo86b2obobobo36bo52bo2bo28bo36bobobob2o$104b
2o48bob2o42b2o42b3o12bobo74b2o38b2obo2bo5b2o16b2o47b2obob2o38b2o44b2o
22bo2bob2o38b2o98b2o38b2obo2bo17bo2bob2o38b2o35bo2bob2o38b2o74b2o8bo2b
ob2o38b2o53b2o29b2o38b2obo2bo$154bo45b2o41bo15b2o120b2o24b2o136bo2bo21b
2o100bo87b2o17b2o16b3o61b2o118bo2bo7b2o174b2o$91bo61b2o88b4o66b2o91bo
138bobo119b3ob2o2b2o122bo181bobo$90bobob2o145b2o3bo3b2o60bo2bo94b2o38b
2obob2o65b2o22bo90b2o28b4o4b2o16b2o103bo47b2o80b2o52bo76b2o35b2o3b2o$
90bobobobo43bo26b2o71bo2b3o4b2o60bobo2bob2o38b2o49bo36bobobob2obo20b2o
38b2obo2bo68b2o38b2obo2bo32b2o20bo2bob2o14bo23b2o61b2o38b2obo2bo35b2o
38b2obo2bo21b2o61b2o38b2obo2bo35bobo2bo2bob2o38b2o6bo$87b2obobobobo2b
o39bobo3b2o21bo21bo9b2o38b2obo69b2ob2obobobo36bo47bobo12b2o21bob2obo25b
o36bobobob2o70bo36bobobob2o58b2obobobo12b2o22bo61bo36bobobob2o37bo36b
obobob2o22bo2bo4b2o54bo36bobobob2o39bo4b2obobobo36bo5b2o$87bo2bo2b2ob
4o38bo2bo3bo21bo14b2o4b2o10b2o41bo72bo2bob2obo21b2o12bobo27b2o16b2o14b
o21bo3b2o23bobo12b2o21bob2obobo69bobo12b2o21bob2obobo60bobob2obo10b2o
9b2o12bobo57bobo12b2o21bob2obobo36bobo12b2o21bob2obobo23bobo5b2o23bob
o26bobo12b2o21bob2obobo26b2o12b2o4bobob2obo21b2o12bobo3bobo$89b2o4bo42b
obob2obo21b2o12bobo5b2o52b2o71bobobo3bo21bo14b2o16b2o9b2o31bo23b2o8b2o
16b2o14bo21bo3bo2bo29b2o20b2o16b2o14bo21bo3bo2bo60bo2bo3bo21bo14b2o16b
2o21b2o16b2o14bo21bo3bo2bo18b2o16b2o14bo21bo3bo2bo24bo34bo7b2o16b2o14b
o21bo3bo2bo25bo2bo4b2o11bo2bo3bo21bo14b2o16b2o$73b2o20bobo39b2obobobo
36bo132bobobobo3b2o21bo31b2o42b2o24b2obo4b2o31bo21b2o3bobo26b4o4b2o16b
2o31bo21b2o3bobo62bobo3b2o21bo31b2o21b2o31bo21b2o3bobo19b2o31bo21b2o3b
obo32bo23bo4bo2b2o2b2o31bo21b2o3bobo26bobo4bo2bo11bobo3b2o21bo31b2o$74b
o21b2o37bo2bob2o38b2o132b2o3bo26b2o101bob2o37b2o26bo27b3ob2o2b2o49b2o
26bo64bo26b2o87b2o26bo53b2o26bo21b2o9bobo22b2obo2bob2o35b2o26bo28bo5b
o15bo26b2o$72bo7b2o3b2o6bo41b2o95b2o7b2o8b2o184b2o112bo349bo45bo9bo2b
o25b2o102bo$70b4o6b2o3b2o5bobo137b2o7b2o9bo18bo60b2o56b2o45bo66b2o113b
2o90b2o115b2o70bo9b2o32b3o11bo2bo79b2o36b2o9bob2o25b2o$45bo23bo23bo108b
2o45b3o19b3o18b2o16b2o21bo45b2o9b2o42b2obo19b2o45bo67b2o45bo92bo45b2o
21b2o45bo34b2o35b3o7bo33bo49b2o45bo38bo11b2o26bo45b2o$43b2o23bo2b3o83b
2o38b2obo2bo45bo24bo18bo15bo2bo20bob2o42b2o52bo2bo20b2o42b2obo67b2o42b
2obo66b2o24bob2o42b2o21b2o42b2obo34b2o42b2obo47bo2bo32b2o42b2obo2b2o31b
3o40bob2o42b2o$44b2o23b2o2bo83bo36bobobob2o71b2o18bobo13bobo22bo2bo96b
2o64bo2bo111bo2bo67bo26bo2bo107bo2bo78bo2bo48b2o77bo2bo4bo31bo43bo2bo
$71b2o75b2o5bobo12b2o21bob2obobo93b2o14bo24b2o82b2o80b2o113b2o66bobo27b
2o109b2o80b2o129b2o5bobo43b2o29b2o$71bo65b2o10b2o4b2o14bo21bo3bo2bo149b
2o67b2o65b2o113b2o81b2o43b2o79b2o80b2o129b2o21b2o43b2o44b2o$72bo12bo51b
2o9bo21bo21b2o3bobo7b2o21b3o9b3o105b2o134b2o113b2o126b2o79b2o80b2o129b
2o112b2o$69b3o12b3o83b2o26bo9bo24bo7bo56b2o91bo$69bo14bo2bo120bobo19b
o3bo5bo3bo52bo2bo13b2o63bo10bobo65bo114bo106b2o76bo23bo81bo130bo56bo113b
o$82b2o2b3o9b2o84b2o23b2o19bo13bo53bobo9b4o4b2o58bobo10bo14b2o3bo45bo
bo112bobo76b2o26bo2bo74bobo21bobo79bobo128bobo53b2obo111bobo$82b3o2bo
10bo38b2o45bo44b2o4bo3bo4b2o37b2o14bo10b3ob2o2b2o39bo3b2o14bo26bo3bob
o45bo14b2o3bo94bo14b2o3bo57b2o26bobo56bo3b2o14bo23bo14b2o3bo61bo14b2o
3bo110bo14b2o3bo37bo92bo3b2o14bo$81b2o2b2o12b3o35b2o42b2obo15b2o27b2o
4bo3bo4b2o30b2o5bobo29bo19b2o21bobo3bo42bo3bobo59bo3bobo108bo3bobo71b
o13bo56bobo3bo53bo3bobo75bo3bobo124bo3bobo33b3o92bobo3bo$81b3o17bo78b
o2bo16bo2bo9b2o15bo13bo31b2o7bo49b2o20bobo3bo44bo3bobob2o56bo3bobo108b
o3bobo68b3o69bobo3bo55bo3bobo75bo3bobo124bo3bobo126bobo3bo$81bob4o94b
2o3bo25bo2bo14bo3bo5bo3bo40b2o34bo31b2obobo3bo37b2o4bob4o2bob2o57bo3b
obob2o105bo3bobob2o50b3o10bo68b2obobo3bo57bo3bobob2o72bo3bobob2o121bo
3bobob2o118b2obobo3bo$81b2o2b2o99b3o11bo2bo9bobo17bo7bo52b2o25b3o12bo
16b2obo2b4obo4b2o29bobo2bobo3bobo53b2o4bob4o2bob2o97b2o4bob4o2bob2o50b
2o11b2o67b2obo2b4obo4b2o41b2o4bob4o2bob2o64b2o4bob4o2bob2o113b2o4bob4o
2bob2o118b2obo2b4obo4b2o$66bo15b2o10b2o2b2ob2o86bo9bo2bo11bo15b3o9b3o
27bo17b2obo2bob2o24bo10bobo19bobo3b2o3bobo31b4o2bo2bob2ob2o49bobo3b2o
3bobo101bobo3b2o3bobo57b2o29b2o50bobo3b2o3bobo41bobo3b2o3bobo68bobo3b
2o3bobo117bobo3b2o3bobo28b2o96bobo3b2o3bobo$64b3o27bobo2bobobo61b3obo
18b2o9bobo69bobob2o13bo4bo2b2o23b2o9bo2bo15b2ob2obobo6bo33bo2bo3bobo2b
obo52bo6bobob2ob2o99bo6bobob2ob2o52b3o4bo20b4o4b2o42b2ob2obobo6bo45bo
6bobob2ob2o66bo6bobob2ob2o115bo6bobob2ob2o20b2o4b4o88b2ob2obobo6bo$63b
o15b2o16b2o2bobo34bo31bo29bo70bobobobo16bo38bo2bo17bobo3bob3o2b2o34b2o
5bo2bo2bo10b2o40b2o2b3obo3bobo100b2o2b3obo3bobo52bobo4bobo19b3ob2o2b2o
43bobo3bob3o2b2o45b2o2b3obo3bobo67b2o2b3obo3bobo116b2o2b3obo3bobo21b2o
2b2ob3o89bobo3bob3o2b2o10bo$62bobo15bo9bo7bobobo34bobo26bo3bo22bo74b2o
bobobobo2bo10bobo34bo13b2o10bobo4bo2bo49b2o11b2o44bo2bo4bobo10b2o92bo
2bo4bobo10b2o40b2o4bo2bo24bo35b2o10bobo4bo2bo53bo2bo4bobo10b2o59bo2bo
4bobo10b2o108bo2bo4bobo10b2o13bo82b2o10bobo4bo2bo15b2o$62bobo12b3o11b
o3bo2bo2bo36bo14b2o3bo9b2o22bobo5b2o7b2o57bo2bo2b2ob4o46bobo3bo2bo5b2o
11bo6b2o110b2o6bo11b2o93b2o6bo11b2o47b2o61b2o11bo6b2o55b2o6bo11b2o60b
2o6bo11b2o109b2o6bo11b2o96b2o11bo6b2o15b2o$63bo13bo11b3o2bobob3o52bo3b
obo32bo2bo4b2o3b2o2b2o2b2o55b2o4bo50bo2bo4b2o49bobo25b2o$95bobo56bo3b
obo32b2o10bobo2bo2b2o17b2o7b2o33bobo49b2o56b2o26b2o361bo$96bo2b2o54bo
3bobob2o41b3o23b2o7b2o34b2o108bo389bobo$97b2ob3o44b2o4bob4o2bob2o42b2o
421b4o143b2o99b4o$103bo43bobo3b2o3bobo468bo3bo243bo3bo$7b2o5b2o31b2o48b
2ob3o35bobo8bo6bobob2ob2o79b2o35b2o350bo247bo$8bo5b2o31b2o48b2obo37b2o
9b2o2b3obo3bobo80bo36bobo63bo215bobo63bo2bo244bo2bo$8bobo128bo13bo2bo
4bobo10b2o42b2o22bobo38bo4b2o55b3o215b2o327b2o$9b2o78b2o63b2o6bo11b2o
41bo2bo21b2o35b4ob2o2bo2bo52bo44bobo172bo324b3ob2o$13b2o53bob2o17b2o101b
2o22b2o61bo2bobobobob2o52b2o44b2o14b2o26bo34b2o17b2o95b2o302b5o$12bob
o53b2obo82b2o36b2o21b3o5bo58bobobobo33b2o66bo15bo27b3o32b2o18bo95bobo
61bo240b3o$13bo141bo59bo2bo3bobo12b2o44b2obobo32bo2bo4b2o73bobo30bo46b
o4bobo95bo4b2o53b2o$9bo69bob2o70bo7b2o3b2o6bo17bo23b3o3b2o12bobo48bo33b
obo5b2o21b2o7b2o5b2o34b2o30b2o44b3o5b2o91b4ob2o2bo2bo52b2o4bo324bo$60b
2o17b2obo68b4o6b2o3b2o5bobo15bobo42bo55bo29bo30bo8bo5b2o98b3o10bo101b
o2bobobobob2o56b2o324bo$7b3obo48b2o88bo23bo16bo2bo21b3o3b2o13b2o34b2o
17b3o58bob2o5bobo44b2o57b2o11b2o103bobobobo60b2o323b3o$6bob2o139bo2b3o
37bo2bo19bo2bo3bobo13bo14b2o19bo7b2o11bo21b2o9b2obo13b2o4b3o2bo6b2o35b
2o8bo60b2o21b2o91b2obobo$6b2obo40bob2o48b2o46b2o2bo5b3o8bo43b3o5bo29b
2o19bobo5b2o10bobo21bo10bobo13b2o3bo3b2o11b2o30bo2bo4b3o27b3o30b3o4bo
15bo2bo94bo$4bob3o39b3ob2o48b2o48b2o4bo3b2o2bo3bo4bo16bo2bo20b2o50bo6b
2o17bobo18b3o12bo19b4o12bobo30bobo5bo31bo29bobo4bobo15bobo$47bo104bo5b
o5bo2b2o6b2o15b2o23bo2bo18b4o23b3o26bo19bo13b2o5b2o15bo9bo3bo32bo36bo
bo29b2o4bo2bo16bo81b2o301b6o$6bo41b3ob2o62bo36bo4bo3b2o2b5obo3b2o40b2o
18bo7b2o4b2obo9bo63b2o4bobo12b3o10b2o73b2o6b2o28b2o100bo7b2o291bo5bo$
50b2o2bo59b3o33b3o6bo7b2obo2b4o21bo5bo33bo3b2o2b2o5bobo9b2o62b2o4bo13b
o12b2obo73b2o5bobo129bobo5b2o297bo$53bobo57bo36bo9b2o3bo2bobo2b2o22b3o
3b3o33bo2b2o10bo79b2o14b5o6bo2b3o58b2o12b2o7bo55bo74b2o298bo4bo$50b3o
bobo16bo13bo24bobo49bo4bo9b2o15bobobobobobo46b2o6bo92bo5bobobo36b4o20b
obo20b2o40b2o10bobo376b2o$49bo2bo2bo15b3o12bobo23bobo64bo15b2obobobob
ob2o45b2o5bobo47b2o40bo6bobobo36bo7b2o17bo58b2obo2bob2o7b2o15b2o116b3o
$48bobobo17bo15bobo24bo66b3o12bob4ob4obo45b2o4bo2bo22b2o23b2o40b2o3b3o
2bo37bo3b2o2b2o9bo7b2o6bo50bo4bo2b2o24bo119bo$47bobo2b2o16b2o15bo94bo
12b5o3b5o52b2o23bo37bo34bob2o39bo2b2o12b3o13bobob2o50bo27bobo10b2o5b2o
99bo350b2o24b2o38b2o104b2o45b2o$47bobobo2bobo27b3o199b3o34b3o33b2o56b
2o2bo12bobobobo46bobo28b2o12bo5b2o450b2o24bobo36bob3obo14bo85b2o45bo$
48b2ob2o2b2o27bo202bo2bo35bo33bo55bob4o9b2obobobobo2bo88bobo441bo25bo
14b3o35bobo3bo12b3o100bo29bobo$147bo27b2o2b2ob2o15b2ob2o39b2o40bo3b2o
34b2o89bobo12bo2bo2b2ob4o89b2o54b2o385b3o23b3o13b2o34b2obobo2bo10bo34b
2o29b2o21bo12b3o29b2o$97b2o11bo34b3o27bobo2bobobo13bobobobo39bo40b2o46b
o82b3o14b2o4bo74b2o21b2o50bo357b2o30bo9bob2o12bo9b2o40b2o3bo10b2o33bo
29bo2bo19bobo10bo$49bo47b2o10bobo32bo15b2o16b2o2bobo14bo3bo40bobo85bo
106bobo71bo2bo19bobo51b3o355bo29b2o9bobo12b2o9b3o36b3o3bo45bobo29bo15b
o6bo2bo9b2o$49b3o56bo3bo30bobo15bo17bobobo61b2o50b2o18b2o13b3o79b2ob2o
21b2o71bobo21bo54bo145bo209bobo39bo63bo2b2obo8bo36b2o30bo13b3o7bo2bo37b
2o$52bo55bo3bo30bobo12b3o15bo2bo2bo114b2o18bo96b5o10bo84bo222bobo209b
2o32bo6b2o17bo45bo5bo2bo3bobo67bob2o9bo18bo31bo2bo$51b2o55b2ob2o5bob2o
22bo13bo16bobob3o132b2obo95bo2b3ob3o4b3o102b3o203bo243bobo5b2o16bobo5b
2o34b3o2b2obo6bo2bo69b2o9b2o9bo2bo3bobo30bobo$81bo36b2obo54bobo70b2o54b
2obo5bo2b3o4b2o82b2ob4o11bo11bo93b3o447bo2bo4b2o16bo2bo4b2o34bo2b2o3b
o7b2o32b2o58b2o4bo2bo31bo$79b3o95bo2b2o66bo2bo53b2ob3o4b2o3bo3b2o82bo
b2o2b2o10b2o8b3o93b3o418b2o28b2o24b2o42bo3b2o3bo38bo2bo42bo21b2o$78bo
99b2ob3o9b2o7b2o45bobo59bo5b4o114bo15b2o65b2o9b3o86bo333bo2bo98b2obob
o2bo38bobo35b2o5bobo$79bo104bo8b2o7b2o46bo54b2ob3o6bo15b2o100b2o15bo61b
2o2b2o2b2o5b3o84b3o118b2o214bobo99bobo3bo40bo36b2o4bo2bo$78b2o48b2o10b
3o35b2ob3o120bo2b2o9b3o12bobo115bo62b2o2bo2bobo5b3o83bo121b2o215bo100b
ob3obo84b2o59b2o$77bo2b2o46b2o9bo3bo34b2obo121bobo15bo13bo115b2o67b3o
40bo51b2o439b2o145b2obo2bob2o$77b3o2bo17bob2o34bo5bo140bo16bobob2obo6b
5o14b2o76b2o105b2o39b3o178b2o4b2o453b2o2bo4bo$57bo23bo16b3ob2o34bo5bo
97bo2b2o38b3o15bo2bob2o6bo96b2o50b2o93bo181b2o4b2o356b2o100bo$56bobo5b
2o3b2o6b4o16bo40b3ob3o4bob2o40bo9bo37bo3b2o2b2o37bo17bo11bo146bo94b2o
388bo151b2obo2bob2o97bobo$57bo6b2o3b2o7bo19b3ob2o45b2obo39bobo7bobo36b
o7b2o36b2o16b2o10b2o143b2obo414b2o63b3ob2o2b2o147b2o2bo4bo$76bo23b2o2b
o87bo2bo5bo2bo37b4o14b2o40bobo2b2o152bo2bo33b2o242b2o3b3o130b2o22bo40b
4o4b2o152bo$76b2o25bobo54bob2o29b2o7b2o55bo2bo4b2o33b2o2bo2bo101bob2o
47b2o27b2o4bo2bo215bo2b2o21b2o3b2o146bo8bobo42b2o157bobo$99bob2obobo53b
2obo4b3ob3o17bo11bo47b2o5bobo5b2o38b2o100b3ob2o32b2o42bo2bo3bobo104b2o
108bo3b2o2b2o25b2o141b3o8b2o$99b2obo2bo16b2o44bo5bo77bo7bo147bo13b2o23b
2o50bo104bobo5b2o101bo7b2o24b3o127b2o11bo178b2o40b2o$102bo19bo45bo5bo
75bobo156b3ob2o8bo67bo2bo109bo7b2o102b4o28bobo128b2obo9b2o176bo4bo37b
2o$102b2o16bobo8bob2o34bo3bo9b2o7bo11bo45b2o3b2o9b3o142bobo6b3o67bo2b
o9b2o45b2o51b2o143b2o132bo187bobobob2o50bo$100b2o2bobo13b2o7b3ob2o35b
3o10b2o8b2o7b2o52bo9b2o143bobo6bo69bobo10bo45bobo5b2o323bo5bo180b2obo
3b2o48b3o$99bo2bo2b2o21bo63bo2bo5bo2bo48b3o13b2o141bo21b2o3bo51bo12b3o
42bo7b2o58bo261bo2bo4bobo80b2o24b2o70bo3b3obo35b2o11bo30b2o24b2o$100b
2o27b3ob2o57bobo7bobo41b2o5bo14b3o14bo148bo3bobo65bo41b2o63b2obobo96b
o164b2o4bo2bo79bo2bo4b2o16bo2bo4b2o62bo2b2o4bo6b2o27b2obo9b2o22b2o4bo
2bo16b2o4bo2bo$131b2o2bo57bo9bo41bo2bo18bobo13b2ob2o147bo3bobo49b2o119b
obobobo95bobo170b2o80bobo5b2o16bobo3bo2bo62b3o2bob3o5bo2bo29bo33b2o5b
obo16b2o5bobo$134bobo108bobo19b2o10b3ob2o4b4o7b2o134bo3bobob2o45b2o69b
o46bo2bobobobob2o92bo2bo252bo25bo73b2o3b2o6bobo29bo5bo35bo17b2o6bo$26b
o104b3obobo16bo13bo77bo32b4o6bo10b2o132bob4o2bob2o112b2obobo45b4ob2o2b
o2bo93b2o284bo2bo64bo2bob3o7bo27bo2bo4bobo53bo$24b3o83b2o18bo2bo2bo15b
3o12bobo113bo6bo142bobo3bobo115bobobobo49bo4b2o345b2o9b2o13b2o9bo2bo63b
3o4bo36b2o4bo2bo26b3o9b2o12bobo9b2o$23bo87b2o17b2obo17bo15bobo113bo6b
o142bobo2bo2b2ob2o108bo2bobobobob2o44bobo352bo9b2obo12bo10bobo66b3obo
11b2o30b2o28b2o9bo12b2obo9bo$22bobo56b2o24b2o4bo19b2o16b2o15bo24b2o7b
2o84bo2bo9b2o131bo3b2o2bobo109b4ob2o2bo2bo44b2o106b2o242b3o13bo9b3o12b
o64b2obo3b2o10bo58b2o13b3o23b3o$22bobo56bo24bo6b2o15b3o2bobo27b3o25b2o
7b2o46bo37b2o11bo140bobo10b2o101bo4b2o154bobo241bo15bo9bo80bobobob2o11b
3o55b3o14bo25bo$23bo55bobo24b3ob2obo4bobo8bo3bo2b2o27bo54b2o24b2o2b2o
b3o34bo11b3o138bo11b2o99bobo162bo254bo2bo23b2o65bo4bo15bo56bobo24b2o$
79b2o26bo9bo2bo8b4o88bo24b2o4b4o48bo251b2o163b2o254b2o24b2o66b2o76b2o
24b2o$109bo7bo3bo99bobo26b2o864bo$103b2o4b2o6bo2bo6b4o91b2o673b2o217b
obo$75b2o27bo13b3o5bo3b3o391bo2bo244bo2bo120b2o122bo2bo92b2o3bo$7b2o65b
o2bo23b3o22b2o5bo394bo3bo2bo240bo3bo2bo114bo125bo3bo2bo22b2o65bobo$7b
2o65bobo24bo30b2o9bo4bo77b2o289b2o5bo3bo7bo228b2o5bo3bo7bo228b2o5bo3b
o7bo19b2ob2o64b2o$75bo62b2o2bobo2bo3b2o9bo62bo2bo49b4o231b4ob2o5b4o3b
o3bo224b4ob2o5b4o3bo3bo224b4ob2o5b4o3bo3bo19b4o$136b4o2bob2o7bo6b3o63b
obo48bo4bob2o227b6o14b4o224b6o14b4o224b6o14b4o20b2o$28bob2o103b2o3bob
5o2b2o3bo4bo12bo3bo11bo3bo34bo49bo4bo3bo227b4o244b4o244b4o$28b2obo45b
2o57b2o6b2o2bo5bo5bo10bobobobo9bobobobo86b2o4bo$76b3o28bo29bo4bo3bo2b
2o3bo4b2o9bo2bobo2bo9b2ob2o84b2o4bo2bo504b2o246b2o$75bobo2bo2b2o22b3o
31bo8b3o5bo2b2o6b2ob2ob2ob2o44bobo15bo33bo2bo3bo2bo3b2o496b3ob2o43b3o
196b3ob2o$20b2o53b2o2b2o2b2o25bo47b3o2bo4bo3bo3bo3bo42bo16bobo33bo2bo
4b2o3bobo496b5o44bo198b5o$20bo58b2o28b2o27bo23bo4bo2bob2ob2obo2bo2b2o
9b2o21b2o2bo4bo13b2o33bo4b2o7bo498b3o46bo198b3o$21bo115bobo5b2o3b2o6b
4o8bo7bo5bob4ob4obo21b2obo2bob2o48bo3bo4bo$10bob2o124bo6b2o3b2o7bo12b
2ob2o8bo3bobo3bo26b2o53b2obo4bo$8b3ob2o5bo137bo9bo5bobo5bo3bo3bobo3bo
85b4o$7bo14bo134b2o9b2ob2o3b2ob2o5b3o3b3o$8b3ob2o5bo2bo$10bobo8b3o17b
2o46bo4b2o$10bobo8b3o18bo45bobo3b2o48bo123bo247bo247bo247bo$11bo8bo2b
o18bobo25b2o17bo52bo3bo119bo3bo243bo3bo243bo3bo243bo3bo23b2o$20bobo20b
2o25b2o75bo123bo10b5o232bo10b5o232bo10b5o232bo10b5o3b4ob2o$20b3o62bo56b
o4bo118bo4bo9bo4bo227bo4bo9bo4bo227bo4bo9bo4bo227bo4bo9bo4bo3b6o$83b3o
11b2o2b2o40b5o119b5o14bo228b5o14bo228b5o14bo228b5o14bo4b4o$47b2o20b2o
bo9bo14b2o2b2o178bo3bo243bo3bo243bo3bo243bo3bo$46bo2bo20bobo9b2o30b2o
167bo247bo247bo247bo$20b2o25bobo21bo42b2o$20b2o26bo21b2o6bo$70b2o5bob
o21b2o$70b2o4bo2bo17b4o4b2o$77b2o18b3ob2o2b2o$44b4o54bo$39b2o7bo$39b2o
2b2o3bo$43b2o2bo190b2o246b2o246b2o246b2o$236bo4bo242bo4bo242bo4bo242b
o4bo$242bo247bo247bo247bo$236bo5bo241bo5bo241bo5bo241bo5bo$65bo171b6o
242b6o242b6o242b6o$66bo165b2o78b2o166b2o246b2o246b2o102b2o$64b3o162b3o
b2o78b2o162b3ob2o242b3ob2o242b3ob2o102b2o$229b5o78bo164b5o243b5o243b5o
102bo$9b2o219b3o245b3o245b3o245b3o$9bobo373b2o$10bo373b2o$288b2o96bo$
28b2o11bo6b2o60b2o6bo11b2o54b2o11bo6b2o79b3o47b2o11bo6b2o46b2o6bo11b2o
45b2o6bo11b2o126b2o11bo6b2o15bo52b2o11bo6b2o67b2o11bo6b2o70b2o6bo11b2o
46b2o6bo11b2o55b2o11bo6b2o37b2o6bo11b2o71b2o6bo11b2o$28b2o10bobo4bo2b
o58bo2bo4bobo10b2o54b2o10bobo4bo2bo77bobo2bo2b2o41b2o10bobo4bo2bo44bo
2bo4bobo10b2o44bo2bo4bobo10b2o126b2o10bobo4bo2bo14b2o51b2o10bobo4bo2b
o66b2o10bobo4bo2bo68bo2bo4bobo10b2o45bo2bo4bobo10b2o55b2o10bobo4bo2bo
35bo2bo4bobo10b2o70bo2bo4bobo10b2o$40bobo3bob3o2b2o50b2o2b3obo3bobo78b
obo3bob3o2b2o73b2o2b2o2b2o53bobo3bob3o2b2o36b2o2b3obo3bobo52b2o2b3obo
3bobo150bobo3bob3o2b2o9bobo63bobo3bob3o2b2o74bobo3bob3o2b2o60b2o2b3ob
o3bobo53b2o2b3obo3bobo79bobo3bob3o2b2o27b2o2b3obo3bobo78b2o2b3obo3bob
o$11bo3b2o22b2ob2obobo6bo21bobo2bobo21bo6bobob2ob2o76b2ob2obobo6bo77b
2o56b2ob2obobo6bo36bo6bobob2ob2o51bo6bobob2ob2o148b2ob2obobo6bo74b2ob
2obobo6bo73b2ob2obobo6bo60bo6bobob2ob2o52bo6bobob2ob2o77b2ob2obobo6bo
27bo6bobob2ob2o77bo6bobob2ob2o$9b2obo30bobo3b2o3bobo17b2o2b4o2b2o17bo
bo3b2o3bobo84bobo3b2o3bobo137bobo3b2o3bobo32bobo3b2o3bobo53bobo3b2o3b
obo156bobo3b2o3bobo76bobo3b2o3bobo75bobo3b2o3bobo56bobo3b2o3bobo54bob
o3b2o3bobo85bobo3b2o3bobo23bobo3b2o3bobo79bobo3b2o3bobo$9b3o27b2obo2b
4obo4b2o11b2o5b2o6b2o5b2o11b2o4bob4o2bob2o76b2obo2b4obo4b2o133b2obo2b
4obo4b2o32b2o4bob4o2bob2o49b2o4bob4o2bob2o148b2obo2b4obo4b2o72b2obo2b
4obo4b2o71b2obo2b4obo4b2o56b2o4bob4o2bob2o50b2o4bob4o2bob2o77b2obo2b4o
bo4b2o23b2o4bob4o2bob2o75b2o4bob4o2bob2o$8bo6bo23b2obobo3bo19b2o6bo6b
o6b2o19bo3bobob2o76b2obobo3bo141b2obobo3bo48bo3bobob2o57bo3bobob2o148b
2obobo3bo80b2obobo3bo79b2obobo3bo72bo3bobob2o58bo3bobob2o77b2obobo3bo
39bo3bobob2o83bo3bobob2o$7bo2bobobobo26bobo3bo60bo3bobo84bobo3bo82b2o
2b2o56bobo3bo46bo3bobo60bo3bobo156bobo3bo83bobo3bo82bobo3bo70bo3bobo61b
o3bobo85bobo3bo37bo3bobo86bo3bobo$8b3obob2o28bobo3bo58bo3bobo86bobo3b
o81b2o2b2o57bobo3bo44bo3bobo60bo3bobo158bobo3bo83bobo3bo82bobo3bo68bo
3bobo61bo3bobo87bobo3bo35bo3bobo86bo3bobo$34bo10bo3b2o14bo28bo14b2o3b
o88bo3b2o14bo130bo3b2o14bo14bo14b2o3bo46bo14b2o3bo160bo3b2o14bo69bo3b
2o14bo68bo3b2o8bo5bo38bo14b2o3bo47bo14b2o3bo89bo3b2o14bo5bo14b2o3bo72b
o14b2o3bo$8b3obob2o17bo30bobo26bobo126bobo148bobo12bobo64bobo198bobo87b
obo80b3o3bobo36bobo65bobo127bobo3bobo90bobo$7bo2bobobobo16b2obobo26bo
28bo128bo79bo70bo14bo66bo200bo89bo80bo2b2o3bo38bo67bo129bo5bo92bo$8bo
6bo21bo71bo2bo184b2o3bobo47bobo126b2o4bo340bo3bo$9b3o25bo70bo3bo9b2o70b
2o101b2o4bo41b2o9bobo58b2o61bobo145b2o88b2o87b2o21bobo70b2o66b2o71b2o
61b2o91b2o$9b2obo55b2o6bo6bo6b2o16bo4bo8b2o70b2o149b2o11bo58b2o60b2ob
o145b2o88b2o87b2o94b2o66b2o71b2o61b2o91b2o$11bo3b2o4b2o45b2o5b2o6b2o5b
2o16bo4bo23b2o40b2o149b2o20bo3bobo73b2o46b2o17b2o112b2o88b2o87b2o33b2o
b2o86b2o66b2o41b2o91b2o91b2o$20bo2bo50b2o2b4o2b2o23bo3bo22bo2bo38bo2b
o126bo20bo2bo19bob2o75bo2bo46bo16bo2bo110bo2bo86bo2bo85bo2bo34b3o85bo
2bo64bo2bo39bo2bo89bo2bo89bo2bo$19bob2o42b2o9bobo2bobo9b2o15bobo24b2o
bo36bob2o42b2o78b3ob2o2b2o15bob2o42b2o12b2o42b2obo19b2o42b2obo108bob2o
42b2o42bob2o42b2o41bob2o37b2o3b2o36b2o42b2obo20b2o42b2obo37bob2o42b2o
3b2o42b2obo45b2o42b2obo$19bo45b2o26b2o45bo36bo45b2o78b4o4b2o15bo45b2o
12b2o45bo19b2o45bo108bo45b2o42bo45b2o41bo40bo4b2o36b2o45bo20b2o45bo37b
o45b2o3b2o45bo45b2o45bo$18b2o120b2o34b2o129b2o18b2o106b2o65b2o106b2o88b
2o87b2o130b2o66b2o35b2o97b2o91b2o$152bob2o160bo512bo103bob2o64bob2o7b
2obo$5bo26b2o92b2o24b2obo7bo26b2o122b3o24b2o78b2o26bo38b2o26bo80bo26b
2o61bo26b2o60bo26b2o23b3o76b2o24b2obo38b2o24b2obo7bob2o24b2o69b2o26bo
64b2o26bo$4bobo3b2o21bo31b2o26b2o31bo23b2o10bobo3b2o21bo31b2o86bobo3b
2o23bo31b2o12b2o31bo21b2o3bobo4b2o31bo21b2o3bobo78bobo3b2o21bo31b2o27b
obo3b2o21bo31b2o26bobo3b2o21bo23bo7b2o36b2o31bo23b2o9b2o31bo23b2o15b2o
23bo31b2o3b2o31bo21b2o3bobo30b2o31bo21b2o3bobo$3bo2bo3bo21bo14b2o16b2o
26b2o16b2o14bo21bo3b2o6bo2bo3bo21bo14b2o16b2o78b2o2b2o2b2ob2o3bo21bo14b
2o16b2o12b2o16b2o14bo21bo3bo2bo3b2o16b2o14bo21bo3bo2bo76bo2bo3bo21bo14b
2o5bo10b2o26bo2bo3bo21bo14b2o16b2o25bo2bo3bo21bo14b2o9b2ob2o2b2o36b2o
16b2o14bo21bo3b2o6b2o16b2o14bo21bo3b2o9b2o3bo21bo14b2o16b2o3b2o16b2o14b
o21bo3bo2bo29b2o16b2o14bo21bo3bo2bo$3bobob2obo21b2o12bobo62bobo12b2o21b
ob2obo6bobob2obo21b2o12bobo96b2o2b2o5bob2obo21b2o12bobo48bobo12b2o21b
ob2obobo21bobo12b2o21bob2obobo76bobob2obo21b2o12bobo3b2o39bobob2obo21b
2o12bobo43bobob2obo21b2o12bobo10bobo59bobo12b2o21bob2obo24bobo12b2o21b
ob2obo9bob2obo21b2o12bobo39bobo12b2o21bob2obobo47bobo12b2o21bob2obobo
$2b2obobobo36bo66bo36bobobob2o2b2obobobo36bo106b2obobobo36bo52bo36bob
obob2o22bo36bobobob2o74b2obobobo36bo6b2o37b2obobobo36bo44b2obobobo36b
o13bo62bo36bobobob2obo21bo36bobobob2o3b2obobobo36bo43bo36bobobob2o48b
o36bobobob2o$o2bob2o38b2o66b2o38b2obobo2bob2o38b2o105bobob2o38b2o52b2o
38b2obo2bo20b2o38b2obo2bo70bo2bob2o38b2o43bo2bob2o38b2o42bo2bob2o38b2o
76b2o38b2obob2o21b2o38b2obobobobob2o38b2o43b2o38b2obo2bo46b2o38b2obo2b
o$2o156b2o135bo14bo92bobo47b2o65b2o70b2o88b2o87b2o234bobo66bo66b2o91b
2o$158bo135bobo3b2o7b2o93b2o601bobo65bobo$67b2o22b2o66bo65b2o68bo4b2o
74b2o8b2o16bo48b2o204b2o88b2o87b2o32b2o66b2o66bo66bobo91b2o$22b2o38b2o
bo2bo22bo2bob2o38b2o20b2o20b2o38b2obo2bo104b2o38b2obo2bo8bo2bob2o38b2o
20bo2bob2o38b2o114b2o38b2obo2bo43b2o38b2obo2bo42b2o38b2obo2bo32bo2bob
2o38b2o21bo2bob2o38b2o43b2o38b2obobobobob2o38b2o46bo2bob2o38b2o$22bo36b
obobob2o26b2obobobo36bo42bo36bobobob2o106bo36bobobob2o12b2obobobo36bo
22b2obobobo36bo114bo36bobobob2o45bo36bobobob2o44bo36bobobob2o36b2obob
obo36bo23b2obobobo36bo43bo22bobo11bobobob2o3b2obobobo36bo48b2obobobo36b
o$20bobo12b2o21bob2obobo28bobob2obo21b2o12bobo38bobo12b2o21bob2obobo105b
obo12b2o21bob2obobo14bobob2obo21b2o12bobo21bobob2obo21b2o12bobo110bob
o12b2o21bob2obobo44bobo12b2o21bob2obobo43bobo12b2o21bob2obobo38bobob2o
bo21b2o12bobo22bobob2obo21b2o12bobo39bobo12b2o8b2o11bob2obo9bob2obo21b
2o12bobo47bobob2obo21b2o12bobo$2b2o16b2o14bo21bo3bo2bo28bo2bo3bo21bo14b
2o16b2o2b2o16b2o14bo21bo3bo2bo87b2o16b2o14bo21bo3bo2bo14bo2bo3bo21bo14b
2o16b2o3bo2bo3bo21bo14b2o16b2o74b2o16b2o14bo21bo3bo2bo26b2o16b2o14bo21b
o3bo2bo25b2o16b2o14bo21bo3bo2bo38bo2bo3bo21bo14b2o16b2o4bo2bo3bo21bo14b
2o16b2o3b2o16b2o14bo9bo11bo3b2o9b2o3bo21bo14b2o11bo4b2o29bo2bo3bo21bo
14b2o10bo5b2o$2b2o31bo21b2o3bobo30bobo3b2o21bo31b2o2b2o31bo21b2o3bobo
88b2o31bo21b2o3bobo16bobo3b2o21bo31b2o4bobo3b2o21bo31b2o74b2o31bo21b2o
3bobo27b2o31bo21b2o3bobo26b2o31bo21b2o3bobo40bobo3b2o21bo31b2o5bobo3b
2o21bo31b2o3b2o31bo23b2o15b2o23bo24b2ob2o2b2o30bobo3b2o21bo24bo6b2o$35b
2o26bo32bo26b2o68b2o26bo122b2o26bo18bo26b2o38bo26b2o140b2o26bo61b2o26b
o60b2o26bo42bo26b2o39bo26b2o18b3o48b2o24b2obo7bob2o24b2o20bo3b2o38bo26b
2o24b2o$990b2o77bob2o7b2obo46bo96b2o$49b2o58b2o96b2o149b2o44b2o65b2o168b
2o88b2o87b2o68b2o66b2o30b2obob2o60b2o35b2o40b3o48b2o38bo$2b2o45bo60bo
45b2o2b2o13bo3bo27bo103b2o45bo46bo45b2o19bo45b2o74b2o45bo42b2o45bo41b
2o45bo70bo45b2o20bo30b4o2bo8b2o3b2o45bo37bo40bo4b2o45bo36bo3bo4b2o$2b
2o42b2obo60bob2o42b2o2b2o12b3obo2bo22b2obo103b2o42b2obo46bob2o42b2o19b
ob2o42b2o74b2o42b2obo42b2o20bo21b2obo41b2o42b2obo70bob2o42b2o20bob2o28b
o4bo8b2o3b2o42b2obo37bob2o37b2o3b2o45bob2o32b2o8b2o$45bo2bo62bo2bo59b
obobo24bo2bo147bo2bo48bo2bo63bo2bo160bo2bo63b2o21bo2bo85bo2bo72bo2bo15b
2o3b2o42bo2bo28b4o57bo2bo39bo2bo89bo2bo31b2o3bo$46b2o64b2o66bo23b2o149b
2o50b2o65b2o162b2o63b2o23b2o87b2o74b2o14b4o3bobo42b2o23bobo3b2o60b2o41b
2o91b2o34b2o$31b2o94b2o51b2o7b2o149b2o80b2o65b2o132b2o77bo11bo87b2o104b
o2bo2bo3bo57b2o8b2o51b2o71b2o19b3o69b2o$31b2o94b2o45bo3bobo8b2o149b2o
80b2o65b2o132b2o78b5o5b2o87b2o104bo4bo3b2o57b2o9bo51b2o71b2o19bo2b2o67b
2o$178bobo523bo204bo3bo220b3o$914bo220bo2$18b2o3bo112bo3b2o34b2o3bo145b
2o3bo98bo3b2o61bo3b2o106b2o3bo84b2o3bo83b2o3bo122bo3b2o62bo3b2o35b2o3b
o89bo3b2o87bo3b2o$18bo3bobo110bobo3bo34bo3bobo144bo3bobo96bobo3bo60bo
bo3bo106bo3bobo83bo3bobo82bo3bobo120bobo3bo61bobo3bo35bo3bobo87bobo3b
o86bobo3bo$19bo3bobo108bobo3bo36bo3bobo144bo3bobo94bobo3bo60bobo3bo108b
o3bobo83bo3bobo82bo3bobo118bobo3bo61bobo3bo37bo3bobo85bobo3bo86bobo3b
o$20bo3bobob2o100b2obobo3bo38bo3bobob2o141bo3bobob2o86b2obobo3bo57b2o
bobo3bo110bo3bobob2o80bo3bobob2o79bo3bobob2o110b2obobo3bo58b2obobo3bo
39bo3bobob2o77b2obobo3bo83b2obobo3bo$18bob4o2bob2o100b2obo2b4obo34bob
4o2bob2o139bob4o2bob2o86b2obo2b4obo55b2obo2b4obo106bob4o2bob2o78bob4o
2bob2o77bob4o2bob2o110b2obo2b4obo56b2obo2b4obo35bob4o2bob2o77b2obo2b4o
bo81b2obo2b4obo$9b2o7b2o3bobo108bobo3b2o7b2o16b2o7b2o3bobo134b2o7b2o3b
obo94bobo3b2o7b2o50bobo3b2o7b2o88b2o7b2o3bobo73b2o7b2o3bobo72b2o7b2o3b
obo118bobo3b2o7b2o51bobo3b2o7b2o17b2o7b2o3bobo85bobo3b2o7b2o76bobo3b2o
7b2o$9b2o10bobob2ob2o100b2ob2obobo10b2o16b2o10bobob2ob2o130b2o10bobob
2ob2o86b2ob2obobo10b2o46b2ob2obobo10b2o88b2o10bobob2ob2o69b2o10bobob2o
b2o68b2o10bobob2ob2o110b2ob2obobo10b2o47b2ob2obobo10b2o17b2o10bobob2o
b2o77b2ob2obobo10b2o72b2ob2obobo10b2o$18b3obo3bobo102bobo3bob3o34b3ob
o3bobo140b3obo3bobo88bobo3bob3o56bobo3bob3o106b3obo3bobo79b3obo3bobo78b
3obo3bobo112bobo3bob3o57bobo3bob3o35b3obo3bobo79bobo3bob3o82bobo3bob3o
$18bo2bo4bobo10b2o78b2o10bobo4bo2bo34bo2bo4bobo10b2o128bo2bo4bobo10b2o
64b2o10bobo4bo2bo44b2o10bobo4bo2bo106bo2bo4bobo10b2o67bo2bo4bobo10b2o
66bo2bo4bobo10b2o88b2o10bobo4bo2bo45b2o10bobo4bo2bo35bo2bo4bobo10b2o55b
2o10bobo4bo2bo70b2o10bobo4bo2bo$19b2o6bo11b2o78b2o11bo6b2o36b2o6bo11b
2o129b2o6bo11b2o64b2o11bo6b2o45b2o11bo6b2o108b2o6bo11b2o68b2o6bo11b2o
67b2o6bo11b2o88b2o11bo6b2o46b2o11bo6b2o37b2o6bo11b2o55b2o11bo6b2o71b2o
11bo6b2o!

[dani]

What are some things in Life that seem "miraculous"? I have the following incomplete list:

• The fact that these simple "birth on 3, survival on 2 and 3" rules give us so much complexity, that has enabled this game to be playing for over 5 decades, and will probably continue for a very long time.
• The R-pentomino sequence lasts significantly longer than most other small patterns, and its existence and commonness probably boosts Life's soup activity by quite a bit.
• The GGG's glider stream just narrowly escapes its grasp, and is the only combination of 2 queen bees that successfully grows infinitely. The outgoing gliders destroy the gun if rewinded by just 2 generations. Also, the fact that this arrangement and 2 others produce any gliders at all in the center is kind of miraculous given how small the active region is.
• The inline inverter reaction is really delicate and hits the trailing edge of one of the queen bees while somehow still surviving. I noticed this one while trying to construct one without a reference, and I was unable to.
• The stable orbits of switch engines are easy to take for granted, but they enable small linear growth to exist at all in life. Note that in B3/S236e, the only INT rule where the main mechanism works, no single-engine orbits are known despite searches being done.
• Speaking of switch engines, RCT's binary slow salvo mechanism only works because switch engines are exactly 3x as slow as gliders. This enables the glider to always reach the ends twice as fast as last time, and always in one of two phases. Considering the front of switch engines have a period of 96, we got really lucky there. It could've just as easily been something like 97 instead.

[mniemiec]

What are some things in Life that seem "miraculous"? I have the following incomplete list: ...

One other feature that has been extremely vital in Life is that even though linear and quadratic growth are possible, they are rare. This permits things like apgsearch (and the resulting Catagolue) to exist at all. Many rules like B34/S34 that have small explosive growth patterns are effectively unsearchable using such methods.

[dvgrn]

I think it's moderately miraculous that an R-pentomino turns into a B-heptomino which turns into a Herschel, and all of these things travel. Life-like rules where this traveling trio doesn't work out for one reason or another (which is the very large majority of them, I believe) don't make it nearly so easy to complete the kind of stable signal circuitry that enabled the first stable reflectors, the first edition of the complete p14-p1000 glider gun collection, the pi and phi calculators, the Gemini spaceship, etc.

Active reactions like LOMs, even if they expand quite nicely, are much much harder to deal with in stable circuitry (which is why even now we don't have a lot of LOM-to-X conduits.) You really have to have common active stuff that moves a good distance without blowing up uncontrollably in the process, and without leaving too much uncommon stuff behind -- and by sheer luck, B3/S23 got a whole little team of ominoes that fit the bill.

EDIT: Oh, and the fact that the smallest asymmetric still life is (a) constructible from just two gliders, and (b) such an incredibly useful catalyst and eater ... total amazing luck. Conway didn't even know about any of that when his team was deciding on B3/S23 out of the range of available choices to study. It doesn't show up in the evolutionary sequences of any small ominoes, and apparently it was over a year before anybody noticed it -- at least, its discovery date (and the discovery of its eating ability) are listed as being 1971, not 1970.

[dani]

I think it's moderately miraculous that an R-pentomino turns into a B-heptomino which turns into a Herschel, and all of these things travel.

In the draft of my post I had included something like "there are many sprawling and linearly traveling signals that are easy to make conduits out of" but cut it because the wording wasn't coming together. But yeah, your post puts it much better.

I'm not well versed in signal splitters, but the fact that the herschel sequence splits off into two seems like a convenient property for that. Here's a fun fact: it's actually one cell off of becoming two more B-heptominoes, and would have replicated messily, infinitely, if not for that:

Code: Select all

x = 89, y = 15, rule = LifeSuper
14.4B56.4B$13.7B4.B48.2A5B4.A$13.9B.3B47.2A7B.3A$14.13B47.3B3A3BAB2A$
13.15BD44.5B2A6B2AC$11.17B43.13B3AB$4.2B2.19B37.2B2.15BA2BA$3.C23B36.
D22BA$.3BC13B.7B35.3BD13B.3BA3B$4BC13B2.B.4B34.2A2BD13B2.B.A2BA$2B3C
13B4.3B35.2A3D13B4.3A$.16B44.16B$2.3B.4B52.3B.A3B$6.3B57.ABA$6.2B58.
2A!

... which kind of ties into mniemiec's point about ease of searching. How convenient!

[GUYTU6J]

...
I'm not well versed in signal splitters, but the fact that the herschel sequence splits off into two seems like a convenient property for that. Here's a fun fact: it's actually one cell off of becoming two more B-heptominoes, and would have replicated messily, infinitely, if not for that...

Note that the R64_Lx65 Herschel splitter/duplicator has been completed at p5 or p6.
---
Suppose a p8 180-degree glider reflector and/or a p8 HRx74B is used to construct a period-p' oscillator A', and their hypothetical stable equivalent/counterpart is used to construct a period-p oscillator A without changing anything else. If 8∤p, can I say the oscillator A' is an LCM oscillator due to its period being p' = lcm(8,p)? Examples include this p728 [=lcm(8,182)] and this p1064 [=lcm(8,133)] (by EV2).

[PHPBB12345]

does this count?

Code: Select all

Sierpinski triangle generator

no.

[Bullet51]

What are some things in Life that seem "miraculous"? I have the following incomplete list:

• Sparkers, stationary and moving. They perturb reactions while keeping itself intact.
• All of (L/M/H)WSS are natural and can be synthesized in 3 gliders, giving birth to orthogonal technology.
• That transparent catalysis exists at all (i.e. life does not die out completely too often). This gives the snark and the syringe.
• Slow gliders can destruct virtually anything. Thus, as long as we can make something, we can cleanly make something.
• The slow glider+block slow salvo is universal. This is why glider-loop replicators exist.

Among Life-like rules, Dotlife does not support point 1, 2, Highlife does not support point 3. It's hard to come up with an example that defies 4 or 5 (though B368/S235 may be a contrived example that defies both) but the point is about balance: if birth is too common then destruction may require too many stages - it may even involve generation of synchronized gliders to reduce the waste that otherwise explodes, and if birth is too scarce then universal salvos would be too complicated or just not exist. The last three points demonstrate the perfect balance of birth and death in B3/S23.

[squareroot12621]

Which spaceships don't have guns yet?

[dvgrn]

Which spaceships don't have guns yet?

There are two places you can look for answers on this, neither of which are guaranteed to be complete, but at least it's a start.

One is the on-wiki Game of Life Status page, the "Velocities of general moving objects" section. There's a column that says whether a gun exists for at least one object of the given velocity -- but doesn't go into specifics.

In general if a glider synthesis for an object exists, a gun is going to be "trivial" to build, but possibly not "reasonable". For example, we have syntheses for pretty much all of the universal-constructor-based macro-spaceships (because they have to contain an encoded version for a synthesis of themselves anyway). But we only have guns for a few of them, like the original Gemini and the 0hd Demonoid. The 0hd Demonoid is the only spaceship so far where the first copy that existed was fired out of a gun.

Most of the macro-spaceships aren't listed in the above table, except generally under "Other", and it's probably best to leave things that way.

The second place to look is the Stable signal converters thread. That first post has links to a pretty good list of the spaceships and other signals that it would be vaguely reasonable to build a {signal X}-to-glider converter and a glider-to-{signal X} converter for, with links to where such things can be found.

Not doubt that list needs to be expanded at this point, with all the new spaceships for which syntheses have been found recently. As that first "Stable signal converters" post says, "Donations gratefully accepted" -- if someone posts a list of things that ought to be added to that initial checklist, I'll be happy to edit things in.

[Book]

Is there a reference and/or rle for the pattern in fig 4.46 in CGOL-M&C?

[dvgrn]

Is there a reference and/or rle for the pattern in fig 4.46 in CGOL-M&C?

The figure is clickable in the PDF version, if you're using Adobe Acrobat, to get the RLE. (Very nearly all of the illustrations work that way.)

The pattern is lightspeed.rle in Golly's Patterns/Life/Miscellaneous folder. It comes from Jason Summers' "jslife" pattern collection.