Puffer with unstable trail (B37/S23)

[Retrodice]

Hi. I've been looking into B37/S23 and noticed this. Would this classify as a puffer despite it's trail being constantly active?

Code: Select all

x = 5, y = 11, rule = B37/S23
2b2o$2ob2o$o2bo$o2bo$b2o2$b2o$o2bo$o2bo$2ob2o$2b2o!

[Extrementhusiast]

Yes, this would classify as a puffer, because the periodic part is stable.

[Ntsimp]

It's not hard to stabilize the end:

Code: Select all

x = 9, y = 10, rule = B37/S23
bo5bo$3o3b3o$ob2ob2obo4$4bo$3bobo$3bobo$4bo!

[Retrodice]

Thanks. Was that by trial and error or is there something here that I'm missing? If you have any links to information about how to logically go about finding a solution to problems like stabilizing a trail like this I'd love to read them.

[Ntsimp]

Yeah, that was just by trial and error. I happened to find this same puffer a few weeks ago, then just played around with adding stuff behind it until I found this.

[calcyman]

I happened to find this same puffer a few weeks ago

I discovered the twin bees puffer in DryLife (B37/S23) a year or so ago, myself.

logically go about finding a solution to problems like stabilizing a trail like this I'd love to read them.

Run the pattern until it becomes periodic, and then truncated the back (active) end of the trail to leave the clean, periodic part.


DryLife has a semi-natural 9c/28 puffer:

Code: Select all

x = 3, y = 11, rule = B37/S23
2o$b2o$bo6$bo$b2o$2o!

It can be used to construct 9c/28 spaceships in similar ways to how switch engines can be used to construct c/12 spaceships in ordinary Life.

In this case, I believe that p28 and p56 spaceships have been constructed using this method. Clean rakes are also quite easy to make.


Here is the p28 ship, the 'puddle jumper' (David Eppstein, 1998).

Code: Select all

x = 55, y = 46, rule = B37/S23
2b3o7b3o6b3o7b3o6b3o7b3o$5bo5bo12bo5bo12bo5bo$o5bo3bo5bo2bo5bo3bo5bo2b
o5bo3bo5bo$ob2o2bo3bo2b2obo2bob2o2bo3bo2b2obo2bob2o2bo3bo2b2obo$4b3o3b
3o10b3o3b3o10b3o3b3o$2bo3bo3bo3bo6bo3bo3bo3bo6bo3bo3bo3bo$2b3o7b3o6b3o
7b3o6b3o7b3o$2b3obo3bob3o6b3obo3bob3o6b3obo3bob3o2$5b3ob3o12b3ob3o12b
3ob3o$5b2o3b2o12b2o3b2o12b2o3b2o5$3b2o45b2o$2bo2bo43bo2bo$2bo2bo43bo2b
o$3b2o45b2o4$11b3o5b3o11b3o5b3o$10bo2bo5bo2bo9bo2bo5bo2bo$3b2o5bo3bo3b
o3bo9bo3bo3bo3bo5b2o$2bo2bo4bo2bo5bo2bo9bo2bo5bo2bo4bo2bo$2bo2bo5bobo
5bobo11bobo5bobo5bo2bo$3b2o45b2o4$21bo2bo5bo2bo$21bo2bo5bo2bo$21bo3bo
3bo3bo$21bob2o5b2obo$21bobo7bobo$21b3o7b3o$5bo43bo$5bo43bo2$22bobo5bob
o$22bo2bo3bo2bo$23bobo3bobo$21bo3bo3bo3bo$21bo2bo5bo2bo$21bo11bo!

The p56 ship is much larger.



DryLife is on the border between Class III and Class IV. For example, this six-cell seed (stairstep hexomino) grows indefinitely:

Code: Select all

x = 4, y = 3, rule = B37/S23
2b2o$b2o$2o!

There exist glider guns in DryLife. The elementary one is a p60, based on one by Jason Summers:

Code: Select all

x = 63, y = 65, rule = B37/S23
26b2o3b2o$25bo7bo$21b2o5bobo$20bo2bo2b2o3b2o$19bobobo$18b3obo$18b3o2$
23b2o3b3o$21bo3bobo3bo$21bo3bobo3bo5b3o$13b2o6bo3bobo3bo4b3o$14bo7b3o
3b3o$14bobo33bo$15b2o31b3o$22b2o12b3o8bo$21bob2o6bo5b3o7b2o$21bo4bo5bo
$22b3obo3b3o11b2o9bo$26bo18b2o7bob2o$44bo13bo$54bo2bobo$10b2o3b2o39bo
2bo$9bo7bo39b2o$12bobo$10b2o3b2o$59b3o$47b3o3b3o2b3o$46bo3bobo3bo$3o
43bo3bobo3bo$b3o42bo3bobo3bo$47b3o3b3o2b3o$59b3o$9b3o3b3o$b3o4bo3bobo
3bo20bobo$3o5bo3bobo3bo3b2o15b2o$8bo3bobo3bo3bobo15bo4b2o3b2o$9b3o3b3o
4bo24bobo$3b2o39bo7bo$2bo2bo39b2o3b2o$2bobobo$3bo2bo$7bo$4bobo2$13b2o
7b3o$14bo8b3o2b3o3b3o$11b3o13bo3bobo3bo8bo$11bo15bo3bobo3bo9bo$27bo3bo
bo3bo7b3o$23b3o2b3o3b3o$22b3o3$41b2o$40b3o$39bob2o$38bobo$29b2o3b2o2bo
2bo$31bobo5b2o$28bo7bo$29b2o3b2o$61bo$62bo$60b3o!

Here is a p480 gun, again by Jason Summers:

Code: Select all

x = 78, y = 79, rule = B37/S23
4$36bo5bo$36b2o3b2o$36b2o3b2o$29b2o6bo3bo$30bo$30bobo$31b2o6bo5bo5bo$
39bo5b2o2bo2bo$39b2o3b3o2bo2bo$50bo$35b3o2b2ob2o$17b2o3b2o26bo$16bo7bo
14b2o3b3o2bo2bo$19bobo17bo5b2o2bo2bo$17b2o3b2o15bo5bo5bo2$48b2o$47bo2b
o$7b3o36bobobo$8b3o34b3obo$17bo5bo13bo7b3o$16b3o3b3o10bobo$22b2ob2o9b
2o23bo$8b3o14b3o31b3o$7b3o15b3o30bo$58b2o$22b3o$10b2o4b3o3b3o41bobo$9b
o2bo4bo5bo41bo$9bobobo52bo2bo$10bo2bo52bobobo$14bo41bo5bo4bo2bo$11bobo
41b3o3b3o4b2o$55b3o$20b2o$21bo30b3o15b3o$18b3o31b3o14b3o$18bo23b2o9b2o
b2o$42bobo10b3o3b3o$32b3o7bo13bo5bo$30bob3o34b3o$29bobobo36b3o$29bo2bo
$30b2o2$28bo5bo5bo15b2o3b2o$27bo2bo2b2o5bo17bobo$27bo2bo2b3o3b2o14bo7b
o$29bo26b2o3b2o$35b2ob2o2b3o$29bo$27bo2bo2b3o3b2o$27bo2bo2b2o5bo19b2o$
28bo5bo5bo18bo3bo$49bo8bo2bo2bo$50bo7bo2bo2bo$38bo3bo5b3o7bo2b4o$37b2o
3b2o16bobo$37b2o3b2o$37bo5bo3$46b2o$42b2o4b4o$42b2o2b2ob3o$46bo4$64bo$
65bo$63b3o!

This is compatible with the p32 spinner reflector:

Code: Select all

x = 71, y = 91, rule = B37/S23
26bo$25bob2o$24b3ob3o$23b5o2b2o$25b2o3bo$28bo6$26bo$26bobo$26b2o4$36bo
$35b2o$18bo16bobo$18bobo$18b2o5$2b3o$bo2bo$4b2o5bo$ob3o7b2o$o4bo5b2o$b
o$2b3o$52bo$51b2o$51bobo$28bo$21bo5bobo$19bo7bo2bo32b2o$19b3o5bo2bo30b
o3bo$27b3o30bo6b2o$27b3o30bo4bo2bo$66b3o$57b3o$59bo$12bo45bo$11bo$11b
3o$2b3o$2bo2bo4bo30b3o$2b2o6bo30b3o$5bo3bo30bo2bo5b3o$6b2o32bo2bo7bo$
41bobo5bo$42bo$17bobo$18b2o$18bo$66b3o$69bo$58b2o5bo4bo$57b2o7b3obo$
59bo5b2o$25bobo38bo2bo$26b2o38b3o$26bo4$51b2o$50bobo$33bobo16bo$34b2o$
34bo4$43b2o$42bobo$44bo6$42bo$40bo3b2o$39b2o2b5o$40b3ob3o$42b2obo$44bo
!

DryLife doesn't support the standard spaceships, namely LWSS, MWSS and HWSS. It does, however, support the x66 bilaterally symmetric spaceship.


Can anyone make a p480 Cordergun to fire the puddle jumper?

[Paul Tooke]

Calcyman wrote:

Can anyone make a p480 Cordergun to fire the puddle jumper?

This suggestion gave me Cordership deja vu. May I suggest that anyone willing to invest their time and effort into picking up Calcymans challenge first spends a small amount of it investigating whether 10 r-pentominoes is optimal? I'm sure that I spent considerably less time and effort finding the 3-engined Cordership and then constructing a gun for it than either Dean Hickerson did when constructing the first 13-engine Cordership or Jason Summers did when constructing the first Cordership gun that fired a 7-engine Cordership. David Eppstein reduced the r-pentomino count in the B37/S23 spaceship from 16 in the p56 variant to 10 in the p28 in just 9 days and I don't think that anyone has revisited this since. If my experience with Corderships is anything to go by, there may be a much simpler 'puddle jumper' just waiting to be found.

BTW, does it really take three gliders to create a clean r-pentomino or is there a simpler way to create them in pairs?

... and in case anyone is curious, here is the p56 spaceship that Calcyman mentioned. (Dean Hickerson, 12 Oct 1998)

Code: Select all

#C p56, speed 9c/28 spaceship
x = 160, y = 41, rule = B37/S23
4b3o7b3o126b3o7b3o$4bo2bo5bo2bo126bo2bo5bo2bo$3bo3bo5bo3bo6b3o7b3o86b
3o7b3o6bo3bo5bo3bo$4bo2bo5bo2bo7bo2bo5bo2bo86bo2bo5bo2bo7bo2bo5bo2bo$
4bobo7bobo6bo3bo5bo3bo6b3o7b3o46b3o7b3o6bo3bo5bo3bo6bobo7bobo$24bo2bo
5bo2bo7bo2bo5bo2bo46bo2bo5bo2bo7bo2bo5bo2bo$24bobo7bobo6bo3bo5bo3bo6b
3o7b3o6b3o7b3o6bo3bo5bo3bo6bobo7bobo$44bo2bo5bo2bo7bo2bo5bo2bo6bo2bo5b
o2bo7bo2bo5bo2bo$44bobo7bobo6bo3bo5bo3bo4bo3bo5bo3bo6bobo7bobo$64bo2bo
5bo2bo6bo2bo5bo2bo$4b3o7b3o2b3o42bobo7bobo6bobo7bobo42b3o2b3o7b3o$6bo
7bo130bo7bo$4bobo7bobo2bobo2b3o7b3o2b3o76b3o2b3o7b3o2bobo2bobo7bobo$
20bo5bo7bo44b2o44bo7bo5bo$24bobo7bobo2bobo2b3o7b3o2b3o16bo2bo16b3o2b3o
7b3o2bobo2bobo7bobo$21bo18bo5bo7bo22b2o2b2o22bo7bo5bo18bo$21bo22bobo7b
obo2bobo2b3o7b2ob2o2b2ob2o7b3o2bobo2bobo7bobo22bo$21bo19bo18bo5bo7bo3b
4o3bo7bo5bo18bo19bo$5b2o34bo22bobo7bobo6bobo7bobo22bo34b2o$4bo2bo33bo
19bo36bo19bo33bo2bo$4bo2bo53bo36bo53bo2bo$5b2o54bo36bo54b2o$9bo140bo$
8b2o140b2o$8bobo18bo100bo18bobo$28b2o100b2o$28bobo18bo60bo18bobo$48b2o
60b2o$15bo32bobo58bobo32bo$2b3o9b2o128b2o9b3o$14bobo18bo88bo18bobo$34b
2o88b2o$8bo25bobo86bobo25bo$8bo142bo$bo3bo15bo116bo15bo3bo$3o17b2o116b
2o17b3o$7bo12bobo114bobo12bo$5b2obo142bob2o$3bo2bobo142bobo2bo$bo2bo
150bo2bo$2b3o150b3o!

Edit: I just saw what calcyman did with the topic title. I don't know how useful this is though, because the topic list and default reply subject revert to the original.

[Paul Tooke]

Here is a much simpler 9c/28 which evolves from just two clean r-pentominoes:

Code: Select all

x = 15, y = 16, rule = B37/S23
2bo$b3o$3bo2$12bo$11b3o$2o9bo$4bob2o$o2b2o$2bo4b3o$2o6b2o3b2o$2o6b2o$
10b2o2bo$12bo$13b2o$13b2o!

This certainly looks simpler to build a gun for than the puddle jumper.

[calcyman]

Here is a much simpler 9c/28 which evolves from just two clean r-pentominoes:

I am absolutely astonished!

Not to mention the fact that both R-pentominoes are in the same phase...

This certainly looks simpler to build a gun for than the puddle jumper.

p480 gun:

Code: Select all

x = 267, y = 225, rule = B37/S23
14$68b2o3b2o$67bo7bo$70bobo$61b2o5b2o3b2o$62bo111b2o3b2o$62bobo108bo7b
o$63b2o111bobo$82b3o89b2o3b2o5b2o$81b3o102bo$68bo5bo109bobo$67b3o3b3o
108b2o$49bo5bo9b2ob2o94b3o$49b2o3b2o8b3o14b3o81b3o$49b2o3b2o8b3o15b3o
89bo5bo$50bo3bo118b3o3b3o$67b3o109b2ob2o9bo5bo$52bo14b3o3b3o4b2o83b3o
14b3o8b2o3b2o$40bo10bobo14bo5bo4bo2bo81b3o15b3o8b2o3b2o$39bo2bo7bo3bo
23bobobo111bo3bo$39bo2bo8bobo24bo2bo97b3o$41bo10bo24bo89b2o4b3o3b3o14b
o$78bobo85bo2bo4bo5bo14bobo10bo$41bo10bo40bo72bobobo23bo3bo7bo2bo$39bo
2bo8bobo37b3o73bo2bo24bobo8bo2bo$39bo2bo7bo3bo35bo80bo24bo10bo$40bo10b
obo36b2o76bobo$52bo102bo40bo10bo$42b2o54b2o55b3o37bobo8bo2bo$41bo2bo
21bo31b3o57bo35bo3bo7bo2bo$41bobo21b2o9bobo19b2obo55b2o36bobo10bo$42bo
b2o19bobo9b2o21bobo93bo$43b3o31bo21bo2bo17bo28b2o54b2o$44b2o54b2o17b2o
27b3o31bo21bo2bo$91bo26b3o26bob2o19bobo9b2o21bobo$52b2o36bobo10bo13b2o
3bo23bobo21b2o9bobo19b2obo$53bo35bo3bo7bo2bo11b2ob2obo5bo17bo2bo21bo
31b3o$50b3o37bobo8bo2bo11b2obob2o5b2o17b2o54b2o$50bo40bo10bo14bo3bo6b
3o26bo$63bobo51bobo2bo3bo3b2o13bo10bobo36b2o$66bo24bo10bo12b5obo4bob2o
b2o11bo2bo7bo3bo35bo$62bo2bo24bobo8bo2bo14b2o5b2obob2o11bo2bo8bobo37b
3o$61bobobo23bo3bo7bo2bo11bobo8bo3bo14bo10bo40bo$61bo2bo4bo5bo14bobo
10bo12bobo7bo2bobo51bobo$62b2o4b3o3b3o14bo35bob5o12bo10bo24bo$74b3o51b
2o14bo2bo8bobo24bo2bo$89bo3bo36bobo11bo2bo7bo3bo23bobobo$59b3o15b3o8b
2o3b2o35bobo12bo10bobo14bo5bo4bo2bo$37bo5bo16b3o14b3o8b2o3b2o25b2o35bo
14b3o3b3o4b2o$37b2o3b2o30b2ob2o9bo5bo23bo4bo48b3o$37b2o3b2o24b3o3b3o
41bo4bo31bo3bo$30b2o6bo3bo26bo5bo42bo4bo30b2o3b2o8b3o15b3o$31bo28b3o
57b2o32b2o3b2o8b3o14b3o$31bobo25b3o92bo5bo9b2ob2o$32b2o18bo119b3o3b3o$
40bo5bo3bo2bo119bo5bo$39b3o3b3o2bo2bo132b3o$38bobobobobob2obo17b2o3b2o
17bo93b3o$37b3ob2ob2ob3o21bobo18b3o$18b2o3b2o13bobobobobob2obo16bo7bo
14bo$17bo7bo13b3o3b3o2bo2bo15b2o3b2o16b3o4b2o$20bobo17bo5bo3bo2bo42bo
58bo17b2o3b2o$18b2o3b2o27bo27bobo13bo57b3o18bobo$79bo77bo14bo7bo$49b2o
23b2o2bo4bo64b2o4b3o16b2o3b2o$48bo2bo22b2obo2bob2o68bo45bo5bo$8b3o38bo
bo26b2o9b2o61bo13bobo29b2o3b2o$9b3o25bo9b2obo38b2o78bo28b2o3b2o$18bo5b
o13bo8b3o115bo4bo2b2o24bo3bo6b2o$18bo5bo11b3o8b2o116b2obo2bob2o35bo$
17bobo3bobo36bo95b2o9b2o37bobo$9b3o3bo11b2o31b3o95b2o29bo18b2o$8b3o4bo
bo9bobo29bo128bo2bo$15bo43b2o127bo2bo6bo5b2o$17bobo3bobo164bo7bo4bobo$
11b2o5bo5bo42bo129bobo5bo$10bo2bo4bo5bo41bob2o120bo7bo18b2o3b2o$10bobo
2bo54bo117bo2bo6bo17bo7bo$11bo54bo2bobo116bo2bo14b2o11bobo$12b2obo41bo
5bo4bo2bo117bo8bo6b2o10b2o3b2o$14bo42bo5bo5b2o127bo6b2o12b3o$56bobo3bo
bo126b2o4bobo5bo13b3o$21b2o43bo123bo2bo4bo4b3o12bobobo$22bo29bobo9bobo
4b3o116bobo5bo18b3ob3o7b3o$19b3o31b2o11bo3b3o118bob2o23bobobo7b3o$19bo
36bobo3bobo127b3o24b3o$33b2o8b3o11bo5bo129b2o$32b3o8bo13bo5bo115bo39b
3o$31bob2o9bo25b3o106b3o36bobobo7b3o$30bobo38b3o108bo34b3ob3o7b3o$30bo
2bo147b2o35bobobo$31b2o186b3o$174bo45bo8b2o$29bo27b2o3b2o108b2obo30b3o
19bo2bo$28bo2bo3bo5bo17bobo109bo22bo13bo17bo2bobo$28bo2bo2b3o3b3o13bo
7bo105bobo2bo17bo13bo22bo$30bob2obobobobobo13b2o3b2o106bo2bo19b3o30bob
2o$32b3ob2ob2ob3o126b2o8bo45bo$30bob2obobobobobo136b3o$28bo2bo2b3o3b3o
136bobobo35b2o$28bo2bo3bo5bo126b3o7b3ob3o34bo$29bo31b3o105b3o7bobobo
36b3o$50bo9bo2b2o115b3o39bo$48bobo8bo5bo141b2o$39bo3bo5b2o9bob3o115b3o
24b3o$38b2o3b2o16b3o105b3o7bobobo23b2obo$38b2o3b2o123b3o7b3ob3o18bo5bo
bo$38bo5bo134bobobo12b3o4bo4bo2bo$180b3o13bo5bobo4b2o$180b3o12b2o6bo$
47b2o129b2o3b2o10b2o6bo8bo$43b2o2b2o2b2o127bobo11b2o14bo2bo$43bobo2bo
2b2o124bo7bo17bo6bo2bo$44b3o131b2o3b2o18bo7bo$45b2o149bo5bobo$196bobo
4bo7bo$196b2o5bo6bo2bo$65bo110bo33bo2bo$63bobo109bobo34bo$64b2o108bo3b
o$174bo2b2o$174b2ob2o19bo3bo$175bobo19b2o3b2o$176bo20b2o3b2o$197bo5bo
2$47b2o3b2o$46bo7bo138b2o$42b2o5bobo137b2o2b2o2b2o$41bo2bo2b2o3b2o135b
2o2bo2bobo$42bobo25bo124b3o$40b2obo26b2o123b2o$40b3o7bo18b4o$40b2o8bo
18b3obo$49bobo18bobo$53bo14bo2b2o$51bobo4b3o10bo$34b2o17bo3b3o9b3o$35b
o13bobo18bo134b2o3b2o$35bobo5bobo4bo153bo7bo$36b2o5bo6bo156bobo5b2o$
42b3o12b3o145b2o3b2o2bo2bo$40b5o13b3o104b2o47bobo$41bob3o118b2o49bob2o
$41b2ob2o8bo111bo49b3o$42b3o7bobo15b2o139bo5b2o$19bo5bo17b2o8b2o16b2o
118bo18b3o$19b2o3b2o44bo4b2o113bobo16bobobo$19b2o3b2o3b2o43bo2bo11b3o
98bo2bo4b3o7b3ob3o$20bo3bo3bo2bo42bo13b3obo97bo2bo5b3o7bobobo9b2o$28bo
bobo41bo12bo5bo96b3o17b3o10bo$29bo2bo41bob2o10b2o2bo75b3o19b3o28bobo$
33bo42b2o11b3o70bo4bo2bo39b3o8b2o$30bobo129bo6b2o28b3o7bobobo$70bo92bo
3bo30b3o7b3ob3o$13bo44bo5bo3bo2bo3b2o88b2o42bobobo$12bo2bo3bo5bo31b3o
3b3o2bo2bo3b2o133b3o$12bo2bo2b3o3b3o9bo19bobobobobob2obo141bo$14bob2ob
obobobobo8b2o8bobo6b3ob2ob2ob3o165bo5bo$16b3ob2ob2ob3o6bobo8b2o8bobobo
bobob2obo112b2o28bo20b2o3b2o$14bob2obobobobobo19bo9b3o3b3o2bo2bo110b2o
27b2o15b2o3b2o3b2o$12bo2bo2b3o3b3o31bo5bo3bo2bo139bobo13bo2bo3bo3bo$
12bo2bo3bo5bo44bo121b2o32bobobo$13bo169b2o6b2o33bo2bo6bo$51bobo127bob
2o8bo31bo10bo$50bo130bo23bobo18bobo6bobo$17b2o32bo2bo126bo6bo17b2o28bo
$18bo32bobobo125bo2bo2bo2bo15bo29bo8bo$15b3o34bo2bo3bo3bo118b2o3bo2bo
6bo45bo2bo$15bo37b2o3b2o3b2o124bo7bo38bo6bo2bo$58b2o3b2o131bobo37bo7bo
$29b2o8b2o17bo5bo124bo7bo37bobo$29bobo7b3o145bo2bo6bo38bo7bo$29bo8b2ob
2o144bo2bo45bo6bo2bo$38b3obo145bo8bo29bo15bo2bo$23b3o13b5o153bo28b2o
17bo$24b3o12b3o154bobo6bobo18bobo$33bo6bo5b2o149bo10bo$33bo4bobo5bobo
148bo6bo2bo32b2o$32bobo13bo154bobobo32bo$24b3o3bo17b2o145bo3bo3bo2bo
13bobo18b3o$23b3o4bobo161b2o3b2o3b2o15b2o20bo$30bo163b2o3b2o20bo$32bob
o159bo5bo$33bo8b2o178bo$33bo7b3o177b3o$40bob2o176bobobo$39bobo177b3ob
3o7b3o$30b2o3b2o2bo2bo177bobobo7b3o$32bobo5b2o169b2o8b3o$29bo7bo172bob
o$30b2o3b2o173bo10b3o$209b2o9bobobo7b3o$219b3ob3o7b3o$220bobobo$221b3o
$215b2o5bo$215b3o$215b2obo$217bobo$216bo2bo2b2o3b2o$217b2o5bobo$221bo
7bo$222b2o3b2o!

[calcyman]

It can be interleaved with itself to make a p240 pseudogun:

Code: Select all

x = 239, y = 406, rule = B37/S23
112bo$111b2o$110b3o$109b2o3bo$108b2ob2obo5bo$60b2o3b2o41b2obob2o5b2o$
59bo7bo41bo3bo6b3o$62bobo44bobo2bo3bo3b2o$53b2o5b2o3b2o40b5obo4bob2ob
2o$54bo56b2o5b2obob2o41b2o3b2o$54bobo51bobo8bo3bo41bo7bo$55b2o51bobo7b
o2bobo44bobo$74b3o42bob5o40b2o3b2o5b2o$73b3o44b2o56bo$122bobo51bobo$
122bobo51b2o$41bo5bo11b3o3b3o44b2o42b3o$41b2o3b2o10bo3bobo3bo4b3o34bo
4bo41b3o$41b2o3b2o5b2o3bo3bobo3bo5b3o33bo4bo$42bo3bo5bobo3bo3bobo3bo
41bo4bo$54bo4b3o3b3o44b2o51b3o3b3o11bo5bo$72b2o83b3o4bo3bobo3bo10b2o3b
2o$32bo38bo2bo81b3o5bo3bobo3bo3b2o5b2o3b2o$31bo2bo2bo5b3o24bobobo89bo
3bobo3bo3bobo5bo3bo$31bo2bo35bo2bo91b3o3b3o4bo$33bo10bo24bo89b2o$46b3o
21bobo85bo2bo38bo$33bo10bo40bo72bobobo24b3o5bo2bo2bo$31bo2bo48b3o73bo
2bo35bo2bo$31bo2bo2bo5b3o36bo80bo24bo10bo$32bo49b2o76bobo21b3o$147bo
40bo10bo$34b2o30bobo21b2o55b3o48bo2bo$33bo2bo30b2o21b3o57bo36b3o5bo2bo
2bo$33bobo31bo22b2obo55b2o49bo$34bob2o22bo31bobo$35b3o21b2o30bo2bo46b
2o21bobo30b2o$36b2o21bobo30b2o46b3o21b2o30bo2bo$139bob2o22bo31bobo$44b
2o49bo42bobo31bo22b2obo$45bo36b3o5bo2bo2bo41bo2bo30b2o21b3o$42b3o48bo
2bo42b2o30bobo21b2o$42bo40bo10bo$55bobo21b3o55bo49b2o$58bo24bo10bo41bo
2bo2bo5b3o36bo$54bo2bo35bo2bo39bo2bo48b3o$53bobobo24b3o5bo2bo2bo41bo
10bo40bo$53bo2bo38bo55b3o21bobo$54b2o82bo10bo24bo$60b3o3b3o4bo62bo2bo
35bo2bo$59bo3bobo3bo3bobo5bo3bo50bo2bo2bo5b3o24bobobo$51b3o5bo3bobo3bo
3b2o5b2o3b2o50bo38bo2bo$29bo5bo16b3o4bo3bobo3bo10b2o3b2o90b2o$29b2o3b
2o24b3o3b3o11bo5bo72bo4b3o3b3o$29b2o3b2o111bo3bo5bobo3bo3bobo3bo$22b2o
6bo3bo111b2o3b2o5b2o3bo3bobo3bo5b3o$23bo28b3o91b2o3b2o10bo3bobo3bo4b3o
$23bobo25b3o92bo5bo11b3o3b3o$24b2o18bo$42bo2bo$42bo2bo132b3o$32bo5bo4b
o17b2o3b2o17bo93b3o$31b2o5b2o23bobo18b3o$10b2o3b2o15bo5bo4bo16bo7bo14b
o$9bo7bo24bo2bo15b2o3b2o16b3o4b2o$12bobo27bo2bo42bo58bo17b2o3b2o$10b2o
3b2o27bo27bobo13bo57b3o18bobo$71bo77bo14bo7bo$41b2o23b2o2bo4bo64b2o4b
3o16b2o3b2o$26bo13bo2bo22b2obo2bob2o68bo45bo5bo$3o25bo12bobo26b2o72bo
13bobo29b2o3b2o$b3o22b3o10b2obo118bo28b2o3b2o$39b3o115bo4bo2b2o24bo3bo
6b2o$39b2o116b2obo2bob2o35bo$10bo5bo37bo106b2o37bobo$b3o5bobo3bobo34b
3o126bo18b2o$3o5bo3bobo3bo32bo128bo2bo$9bobo3bobo4b3o26b2o127bo2bo$10b
o5bo5bo159bo7bo5bo$3b2o18bo35bo51b2o77bo5bo$2bo2bo52bob2o48bobo69bo7b
2o3b2o12b2o3b2o$2bobo2bo54bo47bo2bo66bo2bo16bobo5bo7bo$3bo54bo2bobo47b
2o67bo2bo2b3o2b2ob2o2b2ob2o8bobo$4b2obo52bo2bo48bo7b2o59bo19bobo5b2o3b
2o$6bo35bo18b2o57bobo67b2o3b2o$43bo5bo5bo63bo2bo60b2o5bo5bo$13b2o26b3o
4bobo3bobo63b2o60bo2bo4bo5bo15bo$14bo32bo3bobo3bo5b3o54bo61bobo26b3o9b
3o$11b3o34bobo3bobo5b3o44bo6bo66bob2o35b3o$11bo37bo5bo52bobo3bob2o66b
3o$25b2o80b3ob6o3bo64b2o$24b3o81bo2b2o6bob2o48bo$23bob2o10b3o22b3o44b
3o6b2ob3o47b3o48b3o$22bobo12bo25b3o53bo3b2o49bo36b3o9b3o$22bo2bo13bo
79b2obo2bo47b2o37bo$23b2o95bo3bo$121b3o42bo21bo32b2o$21bo27b2o3b2o108b
2obo19bo32bo2bo$20bo2bo27bobo109bo23b3o28bo2bobo$20bo2bo24bo7bo105bobo
2bo28b3o23bo$22bo4bo5bo15b2o3b2o106bo2bo32bo19bob2o$26b2o5b2o128b2o32b
o21bo$22bo4bo5bo$20bo2bo149bo37b2o$20bo2bo16bo119b3o9b3o36bo$21bo16bob
o12b3o105b3o48b3o$39b2o11bo2b2o157bo$51bo5bo141b2o$31bo3bo16bob3o142b
3o$30b2o3b2o16b3o105b3o35b2obo$30b2o3b2o123b3o9b3o26bobo$30bo5bo136bo
15bo5bo4bo2bo$189bo5bo5b2o$189b2o3b2o$39b2o129b2o3b2o5bobo19bo$35b2o2b
2o2b2o127bobo8b2ob2o2b2ob2o2b3o2bo2bo$35bobo2bo2b2o124bo7bo5bobo16bo2b
o$36b3o131b2o3b2o12b2o3b2o7bo$37b2o150bo5bo$189bo5bo7bo$202bo2bo$168bo
33bo2bo$167bobo34bo$166bo3bo$166bo2b2o$166b2ob2o19bo3bo$167bobo19b2o3b
2o$168bo20b2o3b2o$189bo5bo2$39b2o3b2o$38bo7bo138b2o$34b2o5bobo137b2o2b
2o2b2o$33bo2bo2b2o3b2o135b2o2bo2bobo$34bobo25bo124b3o$32b2obo26b2o123b
2o$32b3o26b4o$32b2o27b3obo$36bo5bo19bobo$35bobo3bobo16bo2b2o$34bo3bobo
3bo5b3o10bo$26b2o7bobo3bobo5b3o9b3o$27bo8bo5bo19bo134b2o3b2o$27bobo
166bo7bo$28b2o39b2o128bobo5b2o$49b3o17b2o126b2o3b2o2bo2bo$34b3o7bo5b3o
153bobo$34b3obo3bobo162bob2o$38b3o2b2o163b3o$209b2o$11bo5bo165bo$11b2o
3b2o42b2o5b2o113bobo18bo$11b2o3b2o3b2o38b2o3bo2bo11b3o98bo2bo4b3o9b3o$
12bo3bo3bo2bo36bo5bo13b3obo97bo2bo5b3o21b2o$20bobobo41bo12bo5bo96b3o
30bo$21bo2bo41bob2o10b2o2bo26b3o46b3o19b3o28bobo$25bo42b2o11b3o27b3o
40bo4bo2bo9b2o39b2o$22bobo85bo3bo39bo6b2o9b2o17b3o$62bo47b3ob2o39bo3bo
30b3o9b3o$5bo54bo2bo3b2o45b2o3b3o35b2o44bo$4bo2bo32bobo17bo2bo3b2o40bo
bob2o4b3o$4bo2bo32b2o8bo5bo4bo46b2o3bo4bo3bo$6bo4bo5bo23bo7b2o5b2o50bo
2b2o4b2ob3o102bo5bo$10b2o5b2o7bo23bo5bo4bo47b3o5b2o55b2o49b2o3b2o$6bo
4bo5bo8b2o32bo2bo54b2obobo50b2o44b2o3b2o3b2o$4bo2bo17bobo32bo2bo55bo3b
2o81bo12bo2bo3bo3bo$4bo2bo54bo57b2o2bo80b2o11bobobo$5bo115b3o51b2o18bo
9bobo10bo2bo$43bobo127bob2o9b2o6bobo20bo10bo$42bo70bo59bo11b2o10bo20bo
bo7bo$9b2o32bo2bo65bobo58bo6bo6bo6bo2bo29b2o$10bo32bobobo63bo61bo2bo2b
o2bo10b2ob2o39bo$7b3o34bo2bo3bo3bo56bo61b2o3bo2bo10b2ob2o22bo2b2ob2o2b
3o2bo2bo$7bo37b2o3b2o3b2o56b2o66bo7bo3b5o37bo2bo$50b2o3b2o132bo4bobo
25b2o3b2o7bo$50bo5bo124bo7b2o3b2o25bobo4bo$179bo2bo37b5o3bo7bo$23b2o2b
3o149bo2bo2b3o2b2ob2o2bo22b2ob2o10bo2bo$23bobo3bob3o146bo39b2ob2o10bo
2bo$15b3o5bo7b3o155b2o29bo2bo13bo$16b3o170bo7bobo20bo9bo$38b2o149bo10b
o20bobo$38bobo155bo2bo10bobo9bo9b2o$25bo5bo8bo154bobobo11b2o19bo$16b3o
5bobo3bobo7b2o145bo3bo3bo2bo12bo21b3o$15b3o5bo3bobo3bo152b2o3b2o3b2o
37bo$24bobo3bobo153b2o3b2o$25bo5bo154bo5bo$34b2o$33b3o$32bob2o178bo$
31bobo179b3o9b3o$22b2o3b2o2bo2bo189b3o$24bobo5b2o169b2o$21bo7bo172bobo
$22b2o3b2o173bo$201b2o21b3o$213b3o9b3o$214bo2$207b2o$207b3o$207b2obo$
60b2o3b2o142bobo$59bo7bo140bo2bo2b2o3b2o$62bobo144b2o5bobo$53b2o5b2o3b
2o146bo7bo$54bo111b2o3b2o41b2o3b2o$54bobo108bo7bo$55b3o110bobo$57b3o6b
o7b3o89b2o3b2o5b2o$57b2o6b3o5b3o102bo$59bo4bobobo107bobo$63b3ob3o105b
3o$41bo5bo16bobobo87b3o7bo6b3o$41b2o3b2o10bo6b3o5b3o81b3o5b3o6b2o$41b
2o3b2o10bo15b3o87bobobo4bo$42bo3bo10bo7b3o95b3ob3o$60b2o2bobobo95bobob
o16bo5bo$57b2ob2ob3o6b2o83b3o5b3o6bo10b2o3b2o$32bo25bo2bo2bob2o3bo2bo
81b3o15bo10b2o3b2o$31bo2bo24b2o4b2o3bobobo90b3o7bo10bo3bo$31bo2bo31bo
3bo2bo90bobobo2b2o$33bo35bo89b2o6b3ob2ob2o$70bobo85bo2bo3b2obo2bo2bo
25bo$33bo51bo72bobobo3b2o4b2o24bo2bo$31bo2bo7bo3bo36b3o73bo2bo3bo31bo
2bo$31bo2bo5b2o5b2o33bo80bo35bo$32bo9bobobo35b2o76bobo$56bo90bo51bo$
34b2o7b3o9b2o33b2o55b3o36bo3bo7bo2bo$33bo2bo18bobo32b3o57bo33b2o5b2o5b
o2bo$33bobo54b2obo55b2o35bobobo9bo$34bob2o54bobo81bo$35b3o32bobo18bo2b
o46b2o33b2o9b3o7b2o$36b2o33b2o9b3o7b2o46b3o32bobo18bo2bo$71bo67bob2o
54bobo$44b2o35bobobo9bo42bobo54b2obo$45bo33b2o5b2o5bo2bo41bo2bo18bobo
32b3o$42b3o36bo3bo7bo2bo42b2o7b3o9b2o33b2o$42bo51bo66bo$55bobo79bo9bob
obo35b2o$58bo35bo41bo2bo5b2o5b2o33bo$54bo2bo3bo31bo2bo39bo2bo7bo3bo36b
3o$53bobobo3b2o4b2o24bo2bo41bo51bo$53bo2bo3b2obo2bo2bo25bo79bobo$54b2o
6b3ob2ob2o67bo35bo$59bobobo2b2o68bo2bo31bo3bo2bo$60b3o7bo10bo3bo50bo2b
o24b2o4b2o3bobobo$51b3o15bo10b2o3b2o50bo25bo2bo2bob2o3bo2bo$29bo5bo16b
3o5b3o6bo10b2o3b2o75b2ob2ob3o6b2o$29b2o3b2o23bobobo16bo5bo78b2o2bobobo
$29b2o3b2o22b3ob3o82bo3bo10bo7b3o$22b2o6bo3bo24bobobo4bo77b2o3b2o10bo
15b3o$23bo28b3o5b3o6b2o18bo56b2o3b2o10bo6b3o5b3o$23bobo25b3o7bo6b2o19b
o56bo5bo16bobobo$24b2o5b3o10bo123b3ob3o$31b3o8bo2bo118bo4bobobo$32bo9b
o2bo44b2o51bo18b2o6b3o5b3o$43bo17b2o3b2o75bo19b2o6bo7b3o$63bobo21bobo$
10b2o3b2o26bo16bo7bo17b2obo$9bo7bo14bo9bo2bo15b2o3b2o19bobo51b2o$12bob
o16b3o8bo2bo42bo76b2o3b2o$10b2o3b2o14b3o10bo27bobo68bobo21bobo$71bo71b
ob2o17bo7bo$41b2o23b2o2bo4bo67bobo19b2o3b2o$40bo2bo22b2obo2bob2o68bo
45bo5bo$3o14bo23bobo26b2o86bobo29b2o3b2o$b3o6bo6b2o20b2obo118bo28b2o3b
2o$9b3o4bobo20b3o115bo4bo2b2o24bo3bo6b2o$8b2ob2o18bo7b2o116b2obo2bob2o
35bo$9b3o20bo21bo106b2o37bobo$b3o6bo19b3o19b3o126bo18b2o$3o15b2o31bo
128bo2bo5b3o$10bo6b2o32b2o127bo2bo$9b3o4bobo163bo4bo5bo$3b2o3b2ob2o3b
2o41bo127b3ob3o$2bo2bo3b3o3bo2bo39bob2o120bo5bo3bo16b2o3b2o$2bobo2bo2b
o5b2o44bo117bo2bo5bobo16bo7bo$3bo44b2o5bo2bo2bobo116bo2bo11bo15bobo$4b
2obo39bo2bo3b3o3bo2bo117bo9bo5bo11b2o3b2o$6bo41b2o3b2ob2o3b2o129bo4bo$
47bobo4b3o41bo84b2o6b3obob4o$13b2o32b2o6bo43b2o81bo2bo12b2o$14bo31b2o
15b3o32b2o82bobo8bo3b2o24b3o$11b3o19b3o19bo6b3o118bob2o8b3o24b3o$11bo
21bo20b3o77bo49b3o$25b2o7bo18b2ob2o74b2o51b2o$24b3o20bobo4b3o76b2o36bo
$23bob2o20b2o6bo6b3o106b3o34b2o5b2o5b3o$22bobo23bo14b3o108bo33b3o3b3o
6b3o$22bo2bo147b2o33b2o5b2o$23b2o175b3o$166bo35bo18b2o$21bo10b3o14b2o
3b2o108b2obo33bo18bo2bo$20bo2bo8b3o16bobo109bo54bo2bobo$20bo2bo9bo14bo
7bo53b2o50bobo2bo54bo$22bo26b2o3b2o53bo2bo49bo2bo18bo33bob2o$110b2o51b
2o18bo35bo$22bo160b3o$20bo2bo9bo135b2o5b2o33b2o$20bo2bo8b3o87b2o36b3o
6b3o3b3o33bo$21bo10b3o86b2o38b3o5b2o5b2o34b3o$121bobo90bo$54bo64b3o77b
2o$31bo3bo8bo8bobo64b2o77b3o$30b2o3b2o5bobo7b2ob2o62bo41b3o24b3o8b2obo
$30b2o3b2o6b2o7bo2b2o103b3o24b2o3bo8bobo$30bo5bo15bo3bo129b2o12bo2bo$
53bobo129b4obob3o6b2o$54bo133bo4bo$39b2o129b2o3b2o11bo5bo9bo$35b2o2b2o
2b2o127bobo15bo11bo2bo$35bobo2bo2b2o124bo7bo16bobo5bo2bo$36b3o11b2o
118b2o3b2o16bo3bo5bo$37b2o11b2o140b3ob3o$192bo5bo4bo$186bo15bo2bo$186b
obo5b3o5bo2bo$170b3o13b2o16bo$169b2o2bo$168bo5bo$169b3obo16bo3bo$170b
3o16b2o3b2o$189b2o3b2o$189bo5bo2$39b2o3b2o$38bo7bo138b2o$34b2o5bobo
137b2o2b2o2b2o$33bo2bo2b2o3b2o135b2o2bo2bobo$34bobo137b2o11b3o$32b2obo
6bo15bo115b2o11b2o$32b3o6b3o13bob2o$32b2o6b2ob2o11b3ob3o$41b3o11b5o2b
2o$42bo14b2o3bo$50b3o7bo$26b2o14bo6b3o$27bo13b3o153b2o3b2o$27bobo10b2o
b2o151bo7bo$28b2o11b3o155bobo5b2o$42bo6b3o145b2o3b2o2bo2bo$31b3o16b3o
153bobo$31bo32b2o141bob2o$32bo32b2o15bo125b3o$64bo16bobo73b2o50b2o$11b
o5bo30bo31bo3bo71bo$11b2o3b2o28bobo18b2o11b2o2bo114b2o5b2o$11b2o3b2o3b
2o24b2o17bo2bo10b2ob2o70bo22b5o7b3o6b3o3b3o$12bo3bo3bo2bo42bo14bobo71b
o22b2o3bo7b3o5b2o5b2o7b2o$20bobobo41bo15bo73bobo19b2o2bo32bo$21bo2bo
41bob2o89bo20b2o31bobo$25bo42b2o87bobo53b2o$22bobo132b3o31b3o5bobo3bob
o$49b3o10bo127b3o6bo4bo2bo$5bo10b3o11bo18b3o8bo2bo3b2o130bo4b2obo$4bo
2bo8b3o11b2o18bo9bo2bo3b2o131bo2b2o$4bo2bo9bo11bobo29bo142bo$6bo194bob
o21bo5bo$61bo112b2o49b2o3b2o$6bo29bobo11bo9bo2bo110b2o6b2o36b2o3b2o3b
2o$4bo2bo9bo18b2o11b3o8bo2bo117b2o36bo2bo3bo3bo$4bo2bo8b3o18bo11b3o10b
o120bo34bobobo$5bo10b3o156b2o41bo2bo$43bobo127bob2o40bo6bobo3bobo$42bo
130bo44bobo3bo7bo$9b2o32bo2bo126bo6bo45bo3bo$10bo32bobobo125bo2bo2bo2b
o5b3o8bobo25bobo7bo$7b3o34bo2bo3bo3bo118b2o3bo2bo17b2o33bo2bo$7bo11b2o
24b2o3b2o3b2o124bo4bo5bo7bo26bobo5bo2bo$19bobo28b2o3b2o129b3ob3o33bo3b
o5bo$19bo30bo5bo124bo5bo3bo33b3ob3o$179bo2bo5bobo26bo7bo5bo4bo$35bo
143bo2bo33b2o17bo2bo$36bo143bo7bobo25bobo8b3o5bo2bo$15b3o16b3o150bo3bo
45bo$16b3o6bo159bo7bo3bobo$24b3o11b2o145bobo3bobo6bo$23b2ob2o10bobo
155bo2bo32b2o$24b3o13bo154bobobo32bo$16b3o6bo14b2o145bo3bo3bo2bo34b3o$
15b3o168b2o3b2o3b2o37bo$25bo160b2o3b2o$24b3o159bo5bo21bobo$23b2ob2o6b
2o177bo$24b3o6b3o177b2o2bo$25bo6bob2o174bob2o4bo$31bobo176bo2bo4bo6b3o
$22b2o3b2o2bo2bo175bobo3bobo5b3o$24bobo5b2o169b2o$21bo7bo172bobo$22b2o
3b2o173bo$201b2o7b2o5b2o5b3o$210b3o3b3o6b3o$210b2o5b2o2$207b2o$207b3o$
207b2obo$209bobo$208bo2bo2b2o3b2o$209b2o5bobo$213bo7bo$214b2o3b2o!

[Paul Tooke]

Calcyman wrote:

I am absolutely astonished!

I was a trifle surprised myself - and it took less than a couple of minutes to find using gencols (modified to handle other CA rules) and a puffer filter program I threw together a few years back.

Nice gun - I was working on a reaction between a single gliders and two block+blinker constellations. Using beehives makes it much simpler.

Next challenge: making a rake that fires the two-engine 9c/28, or the puffer. The latter would demonstrate quadratic growth.

[calcyman]

Next challenge: making a rake that fires the two-engine 9c/28, or the puffer. The latter would demonstrate quadratic growth.

There's an intermediate stage: create a clean 9c/28 rake. The best I can manage is this p56 8-engine abomination:

Code: Select all

x = 102, y = 45, rule = B37/S23
37b3o$40bo$35bo5bo45b3o$35bob2o2bo6bo9bo27bo$29b3o7b3o5b3o7b3o25bo5bo$
28bo8bo3bo4bo2b2o5b2o2bo7bo9bo6bo2b2obo$27bo5bo3b3o6b4o7b4o6b3o7b3o5b
3o7b3o$27bo2b2obo3b3ob3o5bobo3bobo8bo2b2o5b2o2bo4bo3bo8bo$27b3o12bo6bo
2bobo2bo8b4o7b4o6b3o3bo5bo$27bo3bo8b3o6bo2bobo2bo11bobo3bobo5b3ob3o3bo
b2o2bo$29b3o8b2o8b2o3b2o12bo2bobo2bo6bo12b3o$25b3ob3o37bo2bobo2bo6b3o
8bo3bo$26bo43b2o3b2o8b2o8b3o$26b3o19bo46b3ob3o$27b2o18bobo50bo$37b2o7b
2o9b2o4b2o13bo19b3o$36bo2bo6b2o10b2o2bo3b2o9bobo18b2o$35b6o5b3o7bo6bo
2b4o9b2o7b2o$36bo2bo6b3o7bo6bobo2b2o9b2o6bo2bo$37b2o8bo2bo9bo4b2o3bo7b
3o5b6o$48b2o7bobo2b2o2b3obo7b3o6bo2bo$64bob4o6bo2bo8b2o$68bo8b2o4$56b
3o$56bo$57bo2$42b3o$42bo$43bo2$28b3o$28bo$29bo2$14b3o$14bo$15bo2$3o$o$
bo!

It should be possible to assemble a few of these rakes to construct your breeder.



I might be able to prove the rule Turing-complete soon. With an extensible relay loop (such as the caber tosser in Life), and guns and logic gates and so forth, it is possible to emulate a cyclic Post-Tag system. You may recognise cyclic Post-Tag systems from the infamous Rule 110 proof.

[Paul Tooke]

Calcyman wrote:

There's an intermediate stage: create a clean 9c/28 rake

(for which Calcyman provided an example)
Um, thanks. Maybe. I have an observation and a question.

The observation: p56 may be a tad too quick to construct a puffer. Remember that you had 480 generations for your gun to construct that spaceship and similar time constraints apply to rakes. 56 generations may not be enough. But then, I haven't actually tried implementing a rake for the p28 spaceship rake or puffer using this yet, so perhaps I'm worrying too much.

More important to me is the question: why did you assume that the rake had to operate at 9c/28? I didn't specify that when I described the challenge and given the existence of spaceships in this rule at what I would consider to be more tractable velocities it seems to me more likely that these will yield suitably high period clean rakes.

I wish you the best of luck with the Turing-completeness proof. Whilst those kind of results interest me, I've always been more comfortable sitting back and watching while others handle the tricky details.

(BTW: have you noticed that the subject line has reverted to the OPs original? It's a bit of a chore trying to identify this as a slightly different thread)

[Sokwe]

p56 is plenty slow for a backrake:

Code: Select all

x = 173, y = 116, rule = B37/S23
54bo9bo$53b3o7b3o$34bo9bo7b2o2bo5bo2b2o6b3o$33b3o7b3o27bo2bo$23b3o6b2o
2bo5bo2b2o9b2o3b2o10bob2o$22bo2bo30b2o3b2o8b2o21bo$22b2obo10b2o3b2o13b
2o3b2o8b2o8b3o9b3o$26b2o8b2o3b2o27bo2bo6bo2bo8b2o2bo$15b3o8b2o8b2o3b2o
28b2o7b2obo9b4o$15bo2bo6bo2bo55b2o5bobo8bo$15bob2o7b2o56b2o4bo2bo7b3o$
13b2o49b2o17bo2bo3bo2bo6bo2b2o$13b2o33b3o2b3o7bo3bo16b2o5b2o7b4o$12bo
2bo17b2o12bo8bo5bo40bobo$13b2o16bo3bo7b4o9bo5bo4bo35bo2bo$36bo5bo2b2o
5b4o6bo3bo8b2o26bo2bo$31bo4bo5bo2b2ob3o12bobo11bo5bo20b2o$22b2o8bo3bo
6b2o20bo8bo2bo4bo2bo2b2o$21bo11bobo38bobo5bo3b4o$21bo2bo8bo48bo3bo8bo$
22bobo58bo3b2obo4b3o$15bo67b3ob3o2bo2bobo$13bobo38b2o29b2o3b3o3bo$13bo
bo37bobo35bo12bo$55bo46b2o2$68b2o$67bobo$69bo88bo$157b3o$24bo57b2o34b
2o7b2o27bo2b2o$23b3o55bobo7b2o24b2obo5bob2o$22bo3bo27bo9bo18bo6bo2bo
13b3o7bo2bo5bo2bo8b2o7b2o6b2o9bo$22bob2o27b3o7b3o25b2o14bo2bo6b3o7b3o
7b2obo5bob2o5b2o8b3o$16bo5bo2bo8bo9bo8bob2o5b2obo7b3o30bo3bo7b2o7b2o8b
o2bo5bo2bo5b2o7b2o2bo$15b3o4b2ob2o6b3o7b3o10bo5bo9bo2bo31bo2bo26b3o7b
3o$14bo3bo6bob2o4bob2o5b2obo10b3ob3o9bo2bo23b3o5bobo28b2o7b2o19b2o$15b
2obo5b2o2bo7bo5bo55bo2bo66b2o$15bo2bo7b2o8b3ob3o28b2o8b3o14bo3bo65b2o$
14b2ob2o52bo9bo2bo13bo2bo46bo$12b2obo65bo2bo14bobo2bo13bo9bo4bo13b2o$
12bo2b2o86b3o3b2o2b2o2b3o7b3o2b3o14bo8bobo$13b2o69b2o16bo3b2ob2obobo2b
2o9b2o2b3o3bo9bobo7b3o$33b3o13bo4b2o7bo21bo14b2ob2obo2bo3b2o22b3o8b2o
5bo3b2o$33b3o12bobo2bo2bo5bob4o30b2o4b4ob2obo24b2o9bo5b2o3b2o$22b3o18b
2o2bo3bobo2bo5bo5bobo4bo20b2o2b3o6b3o42b2o11bo$23b2o17bo2bo2bobo3b2o7b
2o11bo18b2o2bo2bo7b2o21b3o31b3o$21bob2o9b2o6bo2bo3bo14b3o8bo5bo13b2o2b
obo66b2o$22bo11b2o7b2o25bo4bo20b2o3bo$34b2o35bo3bo8b2o5b2o4b4o$70bo5bo
5bo7bo2bo3b3o$84b2o5b2o$84bo$121b3o$53b3o65bo$56bo65bo$53bo$57bo49b3o$
56bo10b3o37bo$13b2o54bo38bo$12bo2bo27bo9bo14bo$12b2o2bo25b3o7b3o38b3o$
17bo5bo9bo7bo3bo5bo3bo6b3o28bo$4b2o4b2ob2o7b3o7b3o6bob2o7b2obo6b3o15b
2o12bo63b2o$3bo2bo4bo2bo6bo3bo5bo3bo5bo2bo7bo2bo5bo3bo13bo2bo36bo9bo
27bo2bo$2bo2b2o5bo3bo4bob2o7b2obo5b2ob2o5b2ob2o5b3ob2o13b2o36b3o7b3o
25bo2b2o$bo9b2obo6bo2bo7bo2bo8bob2ob2obo12b2o3b3o35b3o6bo3bo5bo3bo7bo
9bo5bo$4b2ob2o3bo3b2o3b2ob2o5b2ob2o7b2o2bobo2b2o6bobob2o4b3o18b2o15b3o
6bob2o7b2obo6b3o7b3o7b2ob2o4b2o$4bo2bo5bo4bo5bob2ob2obo12b2o3b2o7b2o3b
o4bo3bo16bo2bo13bo3bo5bo2bo7bo2bo5bo3bo5bo3bo6bo2bo4bo2bo$2bo3bo8bo7b
2o2bobo2b2o25bo2b2o4b2ob3o17b2o13b2ob3o5b2ob2o5b2ob2o5bob2o7b2obo4bo3b
o5b2o2bo$4bob2o17b2o3b2o28b3o5b2o30b3o3b2o12bob2ob2obo8bo2bo7bo2bo6bob
2o9bo$b2o3bo62b2obobo25b3o4b2obobo6b2o2bobo2b2o7b2ob2o5b2ob2o3b2o3bo3b
2ob2o$o4bo37bo26bo3b2o23bo3bo4bo3b2o7b2o3b2o12bob2ob2obo5bo4bo5bo2bo$
3bo18bo13b3o3bobo7b2o17b2o2bo23b3ob2o4b2o2bo25b2o2bobo2b2o7bo8bo3bo$
22bo12bo3bo2bo7bo2bo18b3o28b2o5b3o28b2o3b2o17b2obo$21bo17bo3bo5bo48bob
ob2o62bo3b2o$11bo2bo16b2o2b2o12bo2bo44b2o3bo26bo37bo4bo$9b3o2b3o13b3o
3bob2o10bo13b2o31bo2b2o17b2o7bobo3b3o13bo18bo$11bo2bo20bo27bo34b3o18bo
2bo7bo2bo3bo12bo$23b2o7bo3bobo23bo60bo5bo3bo17bo$63bobo54bo2bo12b2o2b
2o16bo2bo$64bo15b2o25b2o13bo10b2obo3b3o13b3o2b3o$79bo2bo26bo27bo20bo2b
o$44b2o34b2o28bo23bobo3bo7b2o$43bobo61bobo$45bo45b2o15bo$90bo2bo$58b2o
31b2o34b2o$57bobo67bobo$59bo67bo2$72b2o39b2o$71bobo39bobo$73bo39bo2$
99b2o$99bobo$99bo3$79b2o$79b2o$81bo$79bo2b2o$84b2o6b2o$79b2o3b2o6b2o$
84b3o4bo$89b2o2bo$86b2obo$82bo9b2o$80b3o$81bo2$90bo$90b3o$91bo!

[calcyman]

p56 may be a tad too quick to construct a puffer.

Agreed. That only leaves 18 cells between adjacent puffers. However, it does have the nice side-effect of the ponds being spaced equidistantly in both directions (resembling Gaussian integers with positive real and imaginary parts).

By the way, I used p480 not because the spacing was necessary, but because I needed the p32 spinner technology to insert gliders on close lanes.


However, if you can construct a c/2 spaceship (e.g. x66), you can fire it at the exhaust of the p56 rake and rephase it by 28 generations. Then, that could be utilised as a memory bit, and thus a period-doubler. (Alternatively, you could construct and annihilate a 2-engine ship parallel to the rake.)



Another possibility for a breeder would be a gun for the 8-engine rake.

why did you assume that the rake had to operate at 9c/28?

I don't think that there are any known rakes or [clean!] puffers of different velocities. Of course, I would be pleased to be proven wrong, and considering your success in B36/S125, there should be some c/2 rakes out there.

But beware -- you no longer have *WSSes. In fact, that is the etymology of this rule: I named it 'DryLife' as it doesn't support 'fish' (*WSSes) and it rhymes with the related HighLife (B36/S23).


What you may have overlooked is the fact that the 2-engine puffer is an inside-out 2-engine spaceship, and my 6-glider synthesis doesn't work so easily. Here is a puffer that is easier to synthesise, requiring 12 gliders:

Code: Select all

x = 55, y = 53, rule = B37/S23
54bo$52b2o$53b2o15$34bo$33bobo$33bobo$34bo8$30bo$29bobo$29bobo$30bo5$
6b3o$5bob2o$4b2o2bob3o$5b3o2bo2bo$5b2obo5bo$7b2o4bo$7bo3b2o$8bo2bo2$4b
o2bo$3bo3b2o40b2o$3b2o4bo38b2o$b2obo5bo39bo$b3o2bo2bo$2o2bob3o$bob2o$
2b3o!

p56 is plenty slow for a backrake:

Thanks. The incremental synthesis reminds me of the Gosperian breeder.

[Paul Tooke]

Calcyman wrote:

Another possibility for a breeder would be a gun for the 8-engine rake.

I did consider that, but had another project in mind...

and:

there should be some c/2 rakes out there.

Indeed (Although this needs thinning out to be useful in making a breeder.)

Code: Select all

x = 35, y = 64, rule = B37/S23
7$11bo4bo4bo$10b3ob2ob2ob3o$9b4o7b4o$8b2o2b2obobob2o2b2o$9bo13bo$8b2o
13b2o$6b2obobo9bobob2o$7bobob2o7b2obobo$5b2o2bobobo5bobobo2b2o$4bo2bob
obob2o3b2obobobo2bo$4bo4bobo3bobo3bobo4bo$5b3obobobobobobobobob3o$4b2o
bobobobobobobobobobob2o$7bobobob7obobobo$7bobobobobobobobobobo$6b2obob
ob2o3b2obobob2o$7b5obobobobob5o$7bo2b2obobobobob2o2bo$13bobobobo$13bob
obobo$15bobo$11bo3bobo3bo$11b2o2bobo2b2o$12bo2bobo2bo$13b2o3b2o7$11bo
9bo$10bo11bo$10b3o7b3o7$8bo15bo$7bo17bo$7b3o13b3o7$5bo21bo$4bo23bo$4b
3o19b3o!

[Ntsimp]

it took less than a couple of minutes to find using gencols (modified to handle other CA rules)

Have you released this source code anywhere? Would you be willing?

[Paul Tooke]

Ntsimp asked:

Have you released this [modified gencols] source code anywhere? Would you be willing?

I'm usually reluctant to unleash my code onto an unsuspecting public, but in this case my contribution is so minor I'll give it some thought. Look for something appearing in the Scripts forum over the next day or so (it's off-topic here, and guess how much documentation I produced). I'll post something, even if it's just an explanation of how I changed the code. It's really not hard and you don't need to be a C expert.

[Paul Tooke]

I wrote:

Next challenge: making a rake that fires the two-engine 9c/28, or the puffer. The latter would demonstrate quadratic growth.

I set out to do this using p2-based c/2 technology. This rule is very similar to Life and many Life patterns also work in Drylife. Having found several puffers and high period spaceships in Life, I felt it reasonable to expect to find some in Drylife.
I did. A few puffer searches at c/2, and one at 2c/4 came up with several puffers and higher period spaceships. Here are the spaceships and the cleaner puffers:

Code: Select all

x = 2058, y = 196, rule = B37/S23
372bo$223bobobobo27b3o9b3o29bobobobo21b3o2b3o2b3o29b3o36b3o37bo4bobobo
bo32bo13bo25b3o64bobobobo4bobobobo91bo14bo94bobobobo4bo5bo25b3ob3o$
257bo2bo7bo2bo56bo3bob3obo3bo26b2obob2o33bo3bo79b3o11b3o23bo3bo136b3ob
3o28b3o12b3o20bo4b2o4bo103bo2bobo2bo$223bo37bo2bo2bo33bo5bo19bo6bobo6b
o24bo2bobo2bo31b2o3b2o35bo10bo29b2obob2o7b2obob2o20b2o3b2o68bo4bo5bo
54bo2bobo2bo25b2obob2o8b2obob2o17b3ob2o2b2ob3o66bo4bo5bo23bo3bobo3bo$
256b2o3b3ob3o3b2o54bo3b2o5b2o3bo23bo3bobo3bo29b2obobob2o74bo2bobo2bo5b
o2bobo2bo18b2obobob2o132bo3bobo3bo23bo2bobo2bo6bo2bobo2bo15b4o8b4o100b
o9bo$223bo34bobobo3bobobo30bo5bo21bo11bo25bo3bobo3bo28b2ob2ob2ob2o33bo
10bo27bo3bobo3bo3bo3bobo3bo16b2ob2ob2ob2o66bo4bo5bo53bo9bo22bo3bobo3bo
4bo3bobo3bo13b2o2b2obo2bob2o2b2o64bo4bo5bo25bo5bo$257b2ob2o2bo2b2ob2o
54bobo13bobo24bo5bo31bobo3bobo73bo3bobo3bo3bo3bobo3bo17bobo3bobo134bo
5bo24bo3bobo3bo4bo3bobo3bo14bo14bo99bobo7bobo$223bobobobo27b5o5b5o29bo
bobobo17b2obob2o7b2obob2o22bobo3bobo30b3o3b3o34bo4bobobobo26b2obobobob
ob2ob2obobobobob2o16b3o3b3o61bobobobo4bo5bo52bobo7bobo23bo5bo8bo5bo15b
2o14b2o58bobobobo4bobobobo21b2obob2ob2obob2o$324bobobob2o7b2obobobo61b
o5bo73bobob2ob2obobobobob2ob2obobo17bo5bo131b2obob2ob2obob2o21bobo3bob
o6bobo3bobo12b2obobo10bobob2o94bobobo2bobo2bobobo$223bo5bo27b2ob2o5b2o
b2o29bo5bo15b2obobobobo5bobobobob2o18bobo7bobo29bo5bo35bo4bo34bob5obob
obobob5obo19bobobobo62bo10bo5bo50bobobo2bobo2bobobo57bobob2o8b2obobo
57bo16bo19b2obo4bobo4bob2o$256bobobobo3bobobobo49bo2b2obo3bo5bo3bob2o
2bo16b2obo7bob2o26bo9bo73bo7bobobobo7bo22bo132b2obo4bobo4bob2o21bo5bob
4obo5bo12b2obobo3bo6bo3bobob2o90bobobob2obobob2obobobo$223bo5bo71bo5bo
20bob2obo3bob2obo20b2obob2o5b2obob2o23b2obo5bob2o32bo4bo35bob3obo2bobo
2bob3obo21bobo65bo10bo5bo17b3o15b3o10bobobob2obobob2obobobo21b2o14b2o
13b2o3bobobo6bobobo3b2o54bo16bo17b2obo2b3obobob3o2bob2o$256bobobobo3bo
bobobo49b2o2bobobo9bobobo2b2o15bobobo7bobobo22b2obob2o3b2obob2o74bo5bo
bo5bo23b2obobo98bo2bo13bo2bo9b2obobo4bobo4bobob2o17b2obo7b2o7bob2o10b
3obo2bob2o4b2obo2bob3o88bo4bobobobobobobobo4bo$223bobobobo71bobobobo
18bobobobo5bobobobo16b2obobobob2ob2obobobob2o18bobobo3bobo3bobobo29bo
4bobobobo32bo4b2ob2o4bo23b2obob2o62bobobobo4bobobobo21bo4b3o4bo12bo2b
2obo4bobo4bob2o2bo17bobob2o10b2obobo10b2o6b3o6b3o6b2o53bobobobo10bo23b
obobobobobo$328bobo9bobo18b2obobobob2ob2obobobob2o17b2obobobobobobobob
ob2o78b3o31b2o3bo95b2o3bo3bo3bo3bo3b2o12bobo2bobobo2bobo20b2o2bobobo8b
obobo2b2o14bo3bo6bo3bo93b2o4bobob2ob2obobo4b2o$330bo9bo19bobobobobobob
obobobobobobo15bobo3bobobobobobo3bobo70b2o5b3o5b2o22b2obobo2bo94b5o3bo
5bo3b5o7b2o21b2o14bo2bobobob2o6b2obobobo2bo12b2obo10bob2o98bo11bo$360b
o3bob2o9b2obo3bo14b2obo2b2ob3ob3ob2o2bob2o71bo11bo24bo2bobo2bo93b2o2bo
2b3o5b3o2bo2b2o10bobo4bobo4bobo18bo4bobobobo4bobobobo4bo11bobobo2bo4bo
2bobobo102bobo$359bob2obo4bo5bo4bob2obo12bo2bobo2b11o2bobo2bo69b2o4bob
o4b2o22bobobob2o98bo5bob3obo5bo20bobo26b3obobob3o4b3obobob3o11b2obobob
2o4b2obobob2o96b2o9b2o$362bobobo11bobobo23b2o7b2o75b3obo2b2ob2o2bob3o
20bobobo4bo97bo5b2ob2o5bo20b2ob2o24b2obobobo2bobo2bobo2bobobob2o9bo3bo
bobobo2bobobobo3bo94bo3b7o3bo$360bobobobo11bobobobo13b2o2bo17bo2b2o66b
2o3bo2bobobo2bo3b2o23b2o2bo105bobo28bobo28bobobo2bobo2bobo2bobobo12bob
obobobobo2bobobobobobo97bo7bo$362bobo15bobo26bo3bo76bo3bo2bobo3bobo2bo
3bo19b3ob2o104b2obobob2o22b2obobob2o22b2obobobo2bobo2bobo2bobobob2o8b
2obobobobobo2bobobobobob2o93b2o11b2o$362bo19bo27bobo82bobobo3bobobo
134b2obobob2o22b2obobob2o24b2obo3b2o2b2o2b2o3bob2o11b3obobobo2b2o2bobo
bob3o99b5o$411bo78b2o5bobo3bobo5b2o24b2o105bo3bo26bo3bo26b4o2bobobo2bo
bobo2b4o11b5obobobo2bobobob5o$496b2ob2ob2ob2o30b3o168bobobobo2b2o2bobo
bobo16b2obobo2b2o2bobob2o$497b3o3b3o27b2o2b3o166bo3b3obobo2bobob3o3bo
17bobobo2bobobo$532b2o110bo3bo26bo3bo27bo2bobobobo2bobobobo2bo18bobobo
2bobobo107bo$494b3o9b3o22b2o4bo105b2o3b2o24b2o3b2o31bobo6bobo23bobo6bo
bo107bo$494bobo9bobo24bo3bo106bo3bo26bo3bo32bob2o4b2obo26bo4bo$495b3o
7b3o203bo2bo6bo2bo21b6o2b6o106bo$497b3o3b3o204b2obo8bob2o24b2o2b2o110b
o$710b2o12b2o$710b2o12b2o$709b3o12b3o$642b2o5b2o22b2o5b2o27b2o14b2o$
711b2o10b2o$711b2o10b2o25$1562b3o12b3o$obobobo33bo4b2o4bo25bo4bobobobo
35bo4bo4bo34bo4b2o4bo36bo4bobobobo21b3o2b3o2b3o23b3o18b3o15b3o2b4o2b3o
26bo4bobobobo30bo31bobobobo4bobobobo23bo17bo112bobobobo4bobobobo24b3o
2b4o2b3o36bobobobo4bo5bo20b3o9b3o22bobobobo4bobobobo27b3o2b4o2b3o21bob
obobo4bobobobo34b3o22bobobobo4bo5bo16b3o13b3o32bobobobo4bobobobo28bo
12bo48bobobobo4bobobobo21bo16bo40bobobobo4bobobobo23bo15bo88bobobobo4b
obobobo30bo3bo31bobobobo4bo5bo36bo4bo4bo41bo3bo10bo3bo59bobobobo5bobob
obo23b3ob3o20bobobobo5bobobobo29b3ob3o44bobobobo4bobobobo26bo4b2o4bo
39bo4bobobobo4bobobobo28bo4b2o4bo19bo10bo4bobobobo30bo4b2o4bo$39b3ob2o
2b2ob3o70b3ob2ob2ob3o32b3ob2o2b2ob3o67bo3bob3obo3bo22bo2bo16bo2bo14bo
3bob4obo3bo66b3o70b3o15b3o152bo3bob4obo3bo72bo3bo7bo3bo65bo3bob4obo3bo
71bo3bo54bo3bo11bo3bo76b3o10b3o85b3o14b3o79b3o13b3o134b3ob3o83b3ob2ob
2ob3o39b2o3b2o8b2o3b2o99bo2bobo2bo66bo2bobo2bo86b3ob2o2b2ob3o88b3ob2o
2b2ob3o70b3ob2o2b2ob3o$o37b4o8b4o23bo10bo33b4o7b4o30b4o8b4o34bo4bo25bo
6bobo6bo25bo14bo17bo6bo2bo6bo24bo4bo5bo27b2obob2o34bo4bo5bo22bob2o6bo
6b2obo117bo10bo22bo6bo2bo6bo40bo4bo5bo18b2o3b2o5b2o3b2o26bo4bo5bo25bo
6bo2bo6bo25bo4bo5bo32bo4b2o26bo4bo5bo14b2o3b2o9b2o3b2o36bo4bo31b2obob
2o6b2obob2o45bo16bo18b2obob2o10b2obob2o37bo10bo26b2obob2o9b2obob2o85bo
10bo5bo28b2obobob2o29bo10bo5bo34b4o7b4o37b2obobob2o6b2obobob2o63bo5bo
27bo3bobo3bo24bo5bo5bo27bo3bobo3bo42bo5bo4bo5bo24b4o8b4o37bo4bo5bo4bo
5bo26b4o8b4o17bo10bo4bo5bo28b4o8b4o$37b2o2b2obo2bob2o2b2o66b2o2b2obobo
b2o2b2o28b2o2b2obo2bob2o2b2o64bo3b2o5b2o3bo20b2o3bo14bo3b2o12bo3b2o6b
2o3bo62bo2bobo2bo66b2o2b2o4b3o4b2o2b2o150bo3b2o6b2o3bo69b2obobob2o3b2o
bobob2o62bo3b2o6b2o3bo68b2ob2obobo50b2obobob2o7b2obobob2o71bo2bobo2bo
4bo2bobo2bo79bo2bobo2bo8bo2bobo2bo73bo2bobo2bo7bo2bobo2bo129b2o7b2o79b
2o2b2obobob2o2b2o35b2ob2ob2ob2o4b2ob2ob2ob2o96bo9bo64bo9bo83b2o2b2obo
2bob2o2b2o84b2o2b2obo2bob2o2b2o66b2o2b2obo2bob2o2b2o$o37bo14bo23bo10bo
33bo13bo30bo14bo34bo4bo27bo11bo22b5o16b5o14bo12bo26bo4bo5bo25bo3bobo3b
o32bo4bo5bo21bo2bobo3b5o3bobo2bo60b3o12b3o38bo10bo24bo12bo42bo4bo5bo
16b2ob2ob2ob2ob2ob2ob2ob2o24bo4bo5bo27bo12bo27bo4bo5bo30bobo4bob2o24bo
4bo5bo12b2ob2ob2ob2o5b2ob2ob2ob2o34bo4bo29bo3bobo3bo2bo3bobo3bo43bo16b
o16bo3bobo3bo6bo3bobo3bo35bo10bo24bo3bobo3bo5bo3bobo3bo83bo10bo5bo28bo
7bo29bo10bo5bo34bo13bo37bobo3bobo6bobo3bobo63bo5bo29bo5bo26bo5bo5bo29b
o5bo44bo5bo4bo5bo24bo14bo37bo4bo5bo4bo5bo26bo14bo17bo10bo4bo5bo28bo14b
o$37b2o14b2o66b2o13b2o28b2o14b2o63bobo13bobo18b2o2bo2b2o3b4o3b2o2bo2b
2o10bobo14bobo60bo3bobo3bo68b4ob2o3b2ob4o22b3ob3o33bo3bo10bo3bo70bobo
14bobo68bobo3bobo3bobo3bobo61bobo14bobo65b2obo3bo4bo48bobo3bobo7bobo3b
obo70bo3bobo3bo2bo3bobo3bo77bo3bobo3bo6bo3bobo3bo71bo3bobo3bo5bo3bobo
3bo128b2o7b2o79b2o13b2o36b3o3b3o6b3o3b3o96bobo7bobo62bobo7bobo82b2o14b
2o84b2o14b2o66b2o14b2o$obobobo28b2obobo10bobob2o20bo4bobobobo30b2obobo
9bobob2o24b2obobo10bobob2o31bo4bobobobo17b2obob3o5b3obob2o20bo5b2ob4ob
2o5bo12b2obob2o8b2obob2o22bo4bobobobo27bo5bo28bobobobo4bo5bo20b2o3bo3b
o2bo2bo3bo3b2o17bo2bobo2bo31b2o3b2o8b2o3b2o30bobobobo4bobobobo20b2obob
2o8b2obob2o32bobobobo4bobobobo17b3o3b3o3b3o3b3o19bobobobo4bobobobo23b
2obob2o8b2obob2o17bobobobo4bo5bo28bo2bobo25bobobobo4bobobobo13b3o3b3o
7b3o3b3o29bobobobo4bobobobo25bo5bo6bo5bo45bobobobo4bobobobo18bo5bo10bo
5bo37bobobobo4bobobobo20bo5bo9bo5bo85bobobobo4bo5bo25b2obobo3bobob2o
26bobobobo4bobobobo31b2obobo9bobob2o35bo5bo8bo5bo64bo5bobobobo19b2obob
2ob2obob2o22bo5bobobobo25b2obob2ob2obob2o40bobobobo4bo5bo21b2obobo10bo
bob2o34bo4bo5bo4bo5bo23b2obobo10bobob2o14bo10bo4bo5bo25b2obobo10bobob
2o$36bobob2o8b2obobo64bobob2o7b2obobo26bobob2o8b2obobo60bobobo3bo5bo3b
obobo20bo7bo2bo7bo12bobobobo10bobobobo59bobo3bobo68b2o4bobobobo4b2o19b
o3bobo3bo29b2obobob2o6b2obobob2o66bobobobo10bobobobo67bo5bo5bo5bo60bob
obobo10bobobobo72bob2o49bo5bo9bo5bo72bobo3bobo4bobo3bobo79bobo3bobo8bo
bo3bobo73bobo3bobo7bobo3bobo128bobob2ob2obobo77bobob2o7b2obobo36bo5bob
ob2obobo5bo94b2obobob2ob2obobob2o56b2obobob2ob2obobob2o78bobob2o8b2obo
bo82bobob2o8b2obobo64bobob2o8b2obobo$o5bo26b2obob2o2bo6bo2b2obob2o18bo
4bo35b2o2bobobo5bobobo2b2o21b2obobobob2o4b2obobobob2o29bo4bo5bo15b2obo
17bob2o25bo6bo17b2obobobob2o4b2obobobob2o20bo4bo5bo24bo5bo5bo25bo10bo
5bo32bo28bo9bo28b2ob2ob2ob2o4b2ob2ob2ob2o28bo10bo25b3obobob2o4b2obobob
3o31bo16bo18bobobobo5bobobobo20bo10bo5bo22b3obobob2o4b2obobob3o22bo4bo
5bo28b2o2bo4b2o26bo10bo14b7o9b7o36bo4bo5bo96bo4bo91bo4bo5bo128bo5bo4bo
5bo23b2obobo7bobob2o24bo5bo10bo29b2obobobobo5bobobobob2o35bo7b2o7bo66b
o5bo5bo18bobobobobobobobobo21bo5bo5bo24bobobob2ob2obobobo45bo4bo5bo20b
2o2bobobo6bobobo2b2o33bo4bo5bo4bo5bo21b2obobo3bo6bo3bobob2o12bo10bo4bo
5bo23b2obobobobo6bobobobob2o$33b2obo18bob2o58bo2bobobob2o3b2obobobo2bo
20b2obobobobobo2bobobobobob2o55bo3bo5b2o3b2o5bo3bo17b2o3b2o8b2o3b2o9bo
3bobobob2o4b2obobobo3bo53b2obobobobobobob2o70bobobobo27bo5bo31bobo3bob
o6bobo3bobo66b2o2bobob2o4b2obobo2b2o70bo11bo63b2o2bobob2o4b2obobo2b2o
70b2o2bo52bobo2b2o5b2o2bobo76bobobo8bobobo83bo5bo8bo5bo77bobobo11bobob
o127b2obobo2bobo2bobob2o71b2obobobob2o3b2obobobob2o33bob2o5bo2bo5b2obo
92b2obobobobobobobobobob2o52b2obobob2o5b2obobob2o73bo2bobobob2o4b2obob
obo2bo76b2obobobobo6bobobobob2o58b2obobobob2o4b2obobobob2o$o5bo26b4obo
2b2o6b2o2bob4o18bo4bo34bo4bobo3bobo3bobo4bo20b4obobob3o2b3obobob4o29bo
4bo5bo26bobo28bo2bo16bo2bo8bo4b2obobobo2bobobob2o4bo19bo4bo5bo21bo3bob
obobobobo3bo22bo10bo5bo28b2obobob2o23bobo7bobo28b3o3b3o6b3o3b3o29bo10b
o23b2o3bo2bobobo2bobobo2bo3b2o29bo16bo19bobo11bobo21bo10bo5bo20b2o3bo
2bobobo2bobobo2bo3b2o20bo4bo5bo33b2o6bo23bo10bo17b3obob2ob2obob3o39bo
4bo5bo26bob2o10b2obo52bo4bo26b2o3bobob2obobo3b2o45bo4bo5bo21bob2o13b2o
bo86bo5bo4bo5bo24bobobo7bobobo25bo5bo10bo28bo2b2obobo3bobo3bobob2o2bo
31b2obob2o10b2obob2o63bo5bo5bo15b2obobobob5obobobob2o18bo5bo5bo21b2obo
bobob2ob2obobobob2o42bo4bo5bo24bobo3bo2bo3bobo37bo4bo5bo4bo5bo20bo2b2o
bobob2o4b2obobob2o2bo11bo10bo4bo5bo22bo2b2obobo3bo2bo3bobob2o2bo$32b2o
b2o18b2ob2o58b3obobobobobobobobob3o20b2ob2obob2obob2obob2obob2ob2o54b
2ob2o6bo3bo6b2ob2o16bobo3b2o8b2o3bobo10b2o3b2o3b4o3b2o3b2o53b2obo13bob
2o65b2obobobobob2o20b2obob2ob2obob2o28bo5bo8bo5bo66bo6bo3b4o3bo6bo66b
2obob2o5b2obob2o59bo6bo3b4o3bo6bo67bobo2b2o54bo2bo2bobo2bo2bo77b2obo
12bob2o82bo2bo5bo2bo5bo2bo76b2obo15bob2o124b2obobo3bo3bo3bobob2o69bob
4obobobobobobob4obo31bo3bobobo8bobobo3bo89bobobobobob2ob2obobobobobo
51b4obobo2bobo2bobob4o72b2o6bobobo2bobobo6b2o75bob4ob3o6b3ob4obo58bob
4obobobo2bobobob4obo$obobobo31b2obob2o2b2obob2o23bo4bobobobo28b2obobob
obobobobobobobob2o25bobo10bobo34bo4bobobobo21b3o7b3o22b2o5bo10bo5b2o
16b2obo2bob2o28bo4bobobobo19bobob2o3b2ob2o3b2obobo20bobobobo4bobobobo
25bobobobobobobobo17b2obo3b2ob2o3bob2o26bo5bobob2obobo5bo30bobobobo4bo
bobobo17bobo4bob2obo2bob2obo4bobo29bobobobo10bo17bobobobob2ob2obobobob
o19bobobobo4bobobobo20bobo4bob2obo2bob2obo4bobo14bobobobo4bobobobo30b
3obo3b3o18bobobobo10bo19bobo2bobo2bobo35bobobobo4bobobobo26bobob2o6b2o
bobo46bobobobo4bobobobo19bo3bo12bo3bo38bobobobo4bobobobo23bob2o9b2obo
88bobobobo4bobobobo21b2ob4obo2bo2bob4ob2o22bobobobo10bo34b3obobobobob
3o36bobobobob2o2b2o2b2obobobobo62bo5bobobobo14bo3bobobo7bobobo3bo17bo
5bobobobo19b2o2b2obo11bob2o2b2o34bobobobo4bobobobo20bo4b2obob4obob2o4b
o33bo4bobobobo4bobobobo26b5o6b5o17bo10bo4bobobobo28b3obobo2bobob3o$40b
2ob2o2b2ob2o68bobobob7obobobo28bobobo6bobobo66b2ob2o5b2ob2o21bobo3bobo
8bobo3bobo10bob2o3bob4obo3b2obo52b2ob3o5bobo5b3ob2o61b2obobobobobobob
2o17bobo4bobo4bobo29bo7b2o7bo77bob4obo74b3obobo2bobo2bobob3o58b3o6bob
4obo6b3o63bo3bo4bo53bo2bob4ob4obo2bo73b2obobob2o6b2obobob2o84bo3b2o2b
2o3bo80bo4b2o9b2o4bo124b3obobobobobobobobob3o70b3ob5obobob5ob3o31b2obo
bobobobob2obobobobobob2o87bob2obobobob2ob2obobobob2obo49bo8b3ob3o8bo
72bo6b3obo2bob3o6bo77b3obo14bob3o60b3ob5o2b2o2b5ob3o$41bobob2obobo69bo
bobobobobobobobobo27bob2o2b6o2b2obo65bo13bo23b2o18b2o19bobo2bobo58bo3b
obo2b2obobob2o2bobo3bo59bobobobobobobobobobo13b2o2bobo2bo3bo2bobo2b2o
24bob2o5bo2bo5b2obo73bobobo2bobobo71bobo2bo2bobobobo2bo2bobo59b2o3bobo
bo2bobobo3b2o73bo54b2obo2bobobobo2bob2o74bobo2bobo6bobo2bobo83bo16bo
80b2o2bo4bo4bo2b2o125b2o5bobobobobobo5b2o77bobobobo40b3obobob10obobob
3o92b2obobob2ob2obobob2o52bobo7bobobobo7bobo78bobob4obobo91b2o6b2o75bo
bo2bobo$41bo8bo68b2obobob2o3b2obobob2o31b8o69b2obo2bo3bo2bob2o22bob4o
10b4obo14bob2obob4obob2obo57bo4b2obobob2o4bo62b2ob7ob7ob2o12b2obo5b2ob
2o5bob2o23b2obob2o10b2obob2o74bob4obo74b2o2bo4bobo4bo2b2o61bo2bo2bob4o
bo2bo2bo65b2o6bo2bo50b2obo2bobobobobobo2bob2o70b2o2bob2ob2o4b2ob2obo2b
2o82bobo10bobo85b3ob3ob3o136bobo5bobo78b3o3bobobobo3b3o34bobobobobo8bo
bobobobo89bo5bobo7bobo5bo50b3o19b3o81bobo2bobo87b3o4bo6bo4b3o63b2obo2b
o2b2o2bo2bob2o$42bo6bo70b5obobobobob5o28bo2bo8bo2bo68b3o2bo2b3o27bobo
12bobo15bo2b2obobo2bobob2o2bo52b2o3bo2bob3ob3obo2bo3b2o57bobobobo2b2ob
2o2bobo3bo10bobobobo2bobobobo2bobobobo21bobobobobo8bobobobobo72b2obo2b
ob2o74bo2b4obobob4o2bo59b2obob2ob2obo2bob2ob2obob2o69bo2bo50b2o2bo4bob
obobo4bo2b2o68bo2bobo16bobo2bo77b3obob2o8b2obob3o85b3o141bobo3bobo84b
2obobob2o41bobobobob2o2b2obobobobo92bo2bobobo2bobo2bobobo2bo53b2o17b2o
82bo2bo2bo2bo92bobo4bobo71b3obobo2bobob3o$35bo20bo63bo2b2obobobobob2o
2bo28bo4b6o4bo68bobobobobobo26b3obo10bob3o16bobobo6bobobo58b4obo2b3o2b
ob4o60b2obobo11bobobobo10bo3bobo2bobobobo2bobo3bo21b3obob3o8b3obob3o
73bo2b2o2bo72b2obobobo2b2ob2o2bobobob2o56b2obo3bobob4obobo3bob2o69bo
53bo2bo17bo2bo68bo4bob3ob6ob3obo4bo77bo3bobobo6bobobo3bo79b3ob3ob3ob3o
137bo3bo89bobo44bob2ob2ob2o2b2ob2ob2obo97bobo7bobo56b2obo2b13o2bob2o
79b2obo4bob2o87b2o14b2o66bo4bo2b2o2bo4bo$34b3o3b2o8b2o3b3o68bobobobo
35b3obo4bob3o73b3o31bobobo8bobobo21bo6bo65bobo2bobo2bobo62bo2b2obo10bo
bo2bob2o8bob2obobo2bobobobo2bobob2obo19bobo2b2obobo6bobob2o2bobo71b2o
6b2o71b2obo8bo8bob2o56bo2bobobobobo2bobobobobo2bo71bo50b2o6bo2bo3bo2bo
6b2o68b3obo7b2o7bob3o84bob2o4b2obo84b2o13b2o136b2ob2o86b2obobob2o40bob
o18bobo90b2o3b2o3bo3bo3b2o3b2o50bo2bob2obob5obob2obo2bo178b3o12b3o69bo
bobo2bobobo$34bob2o2b2o8b2o2b2obo68bobobobo34bobo10bobo72bobo28b2ob3ob
2o6b2ob3ob2o18b2o4b2o64bo2b2obobob2o2bo66bobo12bob3o13b2ob2o3bobo3b2ob
obo22bo2bobo4bo2b2o2bo4bobo2bo152bo8bo5bo8bo55b2o2bo3bobob4obobo3bo2b
2o67bobo61bo5bo77b2obobobo12bobobob2o76b2o5bo3bo2bo3bo5b2o77bob2o3b3o
3b2obo133b3obobob3o82bo3bobo3bo46bobob2obobo96bo5bobobo2bo2bobobo5bo
48bobobobobo9bobobobobo82bo2bo90bobob2o8b2obobo70bo2b2o2bo$33b2o2b2obo
10bob2o2b2o69bobo34bobo2bo8bo2bobo69b2ob2o27b2obobobobo4bobobobob2o18b
2o4b2o67bobo3bobo64b2o16bobobobo10bo5bobo7bobobobobo23bobobo2b2ob2ob2o
2bobobo154b2o10b3o10b2o62bobobo2bobobo74b2obob2o55bo3b2ob2o3bo77bobob
2o10b2obobo78bo26bo227b3o3b3o84bobo3bobo41bobo16bobo91bo6bobobobobobo
6bo53b4o5bo5b4o87b2o91bo3bo10bo3bo69b2obo2bob2o$33bo2bobobob2o4b2obobo
bo2bo65bo3bobo3bo29b2obobob8obobob2o100bo2bobobob2o2b2obobobo2bo95bobo
bo70bobo13bobo16bobobo6bo4bobo22b2obobobobob6obobobobob2o239b2obo6bob
2o72bobobob2o60bobo79b2obobobobo8bobobobob2o78b3o2b2ob2o2b2ob2o2b3o
230b3o3b3o85bo5bo46b14o101bo2bobobobo2bo59b2o7bo7b2o179bob2obob2o4b2ob
ob2obo68b2obo2bob2o$36b5ob2o4b2ob5o68b2o2bobo2b2o28bobobobob8obobobobo
66b2o3b2o25b2o2bobobo8bobobo2b2o94bo3bo87bobo11b2o4b2obo9bobo26bobobob
o8bobobobo245bo6bo74b2ob6o59bo3bo80b2obobob2o6b2obobob2o77b2o4bo14bo4b
2o373bo14bo103bo5bo71bo191bobob2o4b2obobo72bobo2bobo$32b2o3bob2obobo2b
obob2obo3b2o65bo2bobo2bo28b2o3bob2o8b2obo3b2o97bo7bobob2obobo7bo186bob
o10bo5bo13bobo24bobobobobob2o2b2obobobobobo163bobobo72bo12bo70bo3bobo
2b2o56bobo3bobo78b4obobobo4bobobob4o84b14o380bo14bo102b3o3b3o260bobobo
bob4obobobobo$35b2o7bo2bo7b2o69b2o3b2o28bo3bobobo2b6o2bobobo3bo95bobo
5b2o8b2o5bobo92bob3obo86b3o11bo7bo10b3o27bob2obob2o2b2obob2obo165bo5bo
75bo4bo74bobobobo60bobo3bobo80b2obobob2o2b2obobob2o83b2obo12bob2o80bob
2o9b2obo133bo9bo139b10o376bobo4b2o4bobo$43bo4bo115bo4bobo6bobo4bo106b
3o6b3o100bo5bo86b3o16b2o12b3o25bo6bo8bo6bo163bo5bo70b2obobo4bobob2o68b
2obo2bobo59bobo3bobo83bobo8bobo89bo12bo83b3o11b3o132bob2o5b2obo253bo7b
o264bo4b2o4bo73bo3b2o3bo$161b2o6bo10bo6b2o103bobo6bobo24b2o4b2o68bo5bo
152bobobob2obobobo78bo8bo80bo5bo155b3obo61b2ob2ob2ob2o82bobobob2obobob
o92b8o87bo13bo133bo3bo3bo3bo250bo13bo260b3o8b3o72bob6obo$45b2o246bo8bo
24bobo4bobo68b2ob2o148b2o4bobo6bobo4b2o72bobo6bobo80bo3bo156bobobobo
60bob2ob2obo84b2o8b2o339bobobobo258bo3bo351bo2bo2bo2bo$45b2o126bo2bo
79bo71bo6bo221bo3b18o3bo71bobo6bobo243bobo63b2o3b2o86bo8bo188b2o3bo5bo
3b2o131bo4b2ob2o4bo247bo6bo3bo6bo347bo2bo$174b2o79b3o234b3o2b3o30b3o2b
3o22bo18bo75bo8bo82b3o159bob2o352bo2bo3bo3bo3bo2bo130b5obobob5o83b2ob
2o160b6o5b6o349b2o$45b2o209bo235bo44bo19b2o22b2o241bo10bo72bo3bo352b2o
3bobo3bobo3b2o129b2o3b2o3b2o3b2o82bo3bo160bo15bo$45b2o77bo9bo357b3o5bo
28bo5b3o24b16o170bo76b2o6b2o75bobo358bo5bo137b2o9b2o83bobobobo$123bo
11bo361bo2bo28bo2bo214bobo70b3obo10bob3o67bo2bobo351b3o15b3o130b2o9b2o
83b2o3b2o52b2o$45b2o76b3o7b3o35b3o2b3o113b2o8b2o192bo3b2o26b2o3bo212bo
3bo69b3o14b3o72b2o61b2o3b2o281b4ob2o9b2ob4o126b3o13b3o139b2o107b2o9b2o
$45b2o208b3o34bobo6bobo24b2o4b2o160b5o28b5o213bobo158bob3ob2o59b2o3b2o
192b4o84bo2bo2b2o9b2o2bo2bo127bo13bo248bobo11bobo$293bo8bo24bobo4bobo
66b3o3b3o84b3o32b3o214bo160bo2bo260bob2obo84b2o4b2o7b2o4b2o125bo2bo13b
o2bo132bo12bo99bobo11bobo$45b2o206bo5bo68bo6bo575bo4bo151b2ob4ob2o94bo
6bo84b2o3b3o5b3o3b2o278bobo10bobo98b2o13b2o$45b2o206bo5bo309b2o84bo8bo
245b2o156bob6obo95b2o2b2o86bo3b3o5b3o3bo128b8o3b8o132bobo2b2o2b2o2bobo
102b2o5b2o$253bo5bo394bobo6bobo244bobo2bo152bo3b2o3bo186bo3b3o7b3o3bo
131b5ob5o137bo2bo2b2o2bo2bo102bobo5bobo$45b2o124b3o2b3o475bobo6bobo78b
2o5b2o157bo2bo350bo4bo9bo4bo127b2o6bobo6b2o139b2o107b3o7b3o351b2o$45b
2o74bo15bo118bo237b2o38b2o26b4o8b4o77bo8bo79b2o5b2o158b3o354bo11bo131b
o3b5ob5o3bo136bo6bo104bo11bo351b2o$120bo17bo116bobo34b2o8b2o190b2o6b2o
22b2o6b2o26bo3bo6bo3bo689bo13bo129bobo2bo2bo3bo2bo2bobo134b2o6b2o$45b
2o73b3o13b3o116bobo34bobo6bobo24b2o4b2o166b2o22b2o39bo4bo838b2o3bob2o
3b2obo3b2o133b2o2bo2bo2b2o$45b2o209bo36bo8bo24bobo4bobo229bo6bo171bo5b
o423b2o233bobo2b5o3b5o2bobo79b2ob2o48bo2b2o2b2o2bo$253bo5bo68bo6bo67b
3o3b3o150bobo10bobo166bobo3bobo69b2o12b2o73b2o262b2o92bob2o3b2obo131b
4obo9bob4o134b3o4b3o$45b2o124b3o2b3o74bo5bo484bobo3bobo69b2o12b2o72bo
4b2o152bo6bo192b3o5b3o134b2o11b2o77bo2bo3bobo3bo2bo45b2o2b2o$45b2o206b
o5bo485bo5bo165bo146bo5b2o2b2o5bo178bo9bo7bo9bo125b4o7b4o78b2o11b2o45b
o6bo$910bo2b4o146b2o5b2o2b2o5b2o176bobo3b3o13b3o3bobo126b2o7b2o81bo3b
2ob2o3bo$256bo398bo8bo82b3o160bo3b2o147bo3bo2b2o2b2o2bo3bo176bobo25bob
o122bobo2bo7bo2bobo130b2o3bo2bo2bo2bo3b2o457bo10bo$118bo21bo114bobo34b
2o8b2o258bo14bo76bobo6bobo243b2o3bo152bo10bo181bo8bo9bo8bo124bo15bo
129b2obo4b2o4b2o4bob2o454bobo8bobo$117bo23bo113bobo34bobo6bobo24b2o4b
2o158b2o38b2o26bo14bo76bobo6bobo241b2o2b2o62b2o3b2o83bobo2b2o2b2o2bobo
188bo9bo133bo15bo129b2o6bo6bo6b2o455bo10bo$117b3o19b3o29b3o2b3o77bo36b
o8bo24bobo4bobo157b2o6b2o22b2o6b2o26bo3b2o4b2o3bo77bo8bo79b2o5b2o156bo
65b2o3b2o88b2o2b2o95b2o6b2o88bo9bo232b2ob2o42b2obo7b2o7bob2o$253bo5bo
68bo6bo166b2o22b2o38b2o4b2o170b2o5b2o418b2o6b2o331b2ob2o43b2ob2o4bo2bo
4b2ob2o$253bo5bo143b3o3b3o502bo154bo6bo94b2o6b2o381b2obo4b2o4bob2o$
253bo5bo650b2o2bo3b2o149bo2b2o2bo91bobo10bobo378bo3bo8bo3bo$745bo5bo
159bo6b2o152b2o94bo2b2o6b2o2bo378bo3bo8bo3bo$256bo487bobo3bobo157b2o7b
2o145bo2bo2b2o2bo2bo88bobo10bobo229b2o13b2o133b2o12b2o459bo10bo$171b3o
2b3o76bobo486bobo3bobo160b2o4b2o144b3o10b3o90b2o6b2o232b2o13b2o607bobo
8bobo$255bobo487bo5bo70b2o12b2o81bo144b2o2bo8bo2b2o89b2o6b2o83b2o17b2o
753bo10bo$256bo305bo14bo244b2o12b2o76bo150bo4b2o2b2o4bo90b2o6b2o83b2o
17b2o275b2o18b2o$494b2o38b2o26bo14bo169b3o316bo12bo481b3o14b3o$494b2o
6b2o22b2o6b2o26bo3b2o4b2o3bo489bo10bo483bo2bo10bo2bo103bo3bo$502b2o22b
2o38b2o4b2o697bo5bo283b6o8b6o101bobobobo$744b2o5b2o517bobo3bobo282b2ob
2o10b2ob2o101bobobobo$744b2o5b2o310b2o16b2o187bobo3bobo139b2o3b2o136b
2o2bo4b2o4bo2b2o102bo3bo$1062bo2bo14bo2bo187bo5bo139b3o3b3o136bo2bo4b
2o4bo2bo98bo13bo$1063b2o16b2o329bob5o5b5obo134bo10bo101bo13bo$745bo5bo
659b5ob2o5b2ob5o79b2o3b2o44bo2bo10bo2bo98bo13bo$744bobo3bobo658bob2o
13b2obo79bobobobo45bobo10bobo95b2o19b2o$744bobo3bobo422b2o237bo4bo3bo
4bo84bobo48bo12bo96b2o19b2o$745bo5bo423b2o91b2o9b2o132bobo3bo3bo3bobo
83bobo$1268b2o9b2o132b3o11b3o81bobobobo$747b3o72b2o12b2o574b2o2b3o5b3o
2b2o80b2o3b2o$822b2o12b2o425b2o19b2o394b2o7b2o$1262bo2bo2b2o9b2o2bo2bo
221bo11bo157bob2o7b2obo$1263b2o3b2o9b2o3b2o222bo11bo157bo3bo5bo3bo350b
2o$1062b2o18b2o424bo11bo47b2o2b2o105b2obo5bob2o351b2o$1062b2o18b2o484b
2o2b2o97b2o3bo4b2o5b2o4bo3b2o$1504b3o3b3o3b3o3b3o145bobo2bobo15bobo2bo
bo$1569b4o98bo3bobo15bobo3bo$907b3o254bo22bo320bo11bo47b6o102bo17bo$
1164bo22bo320bo11bo45bo3b2o3bo$1063b2o16b2o81bo22bo320bo11bo44bo2bo4bo
2bo$1062bo2bo14bo2bo428b2ob2o49b3o4b3o456b2o20b2o$1063b2o16b2o429b2ob
2o515b2o20b2o2$912bo500b2o13b2o$912bo500b2o13b2o140b2o$912bo657b2o3$
1407b3o23b3o$1407bo27bo$1408bo25bo$2043b2o$1175b2o866b2o$1175b2o383b2o
18b2o$1560b2o18b2o2$1567bo6bo108bo3bo$1566bobo4bobo106bobobobo$1566bob
o4bobo106bobobobo$1567bo6bo108bo3bo$1416bo9bo251bo13bo345bo10bo$1415bo
bo7bobo250bo13bo344bobo8bobo$1415b2o9b2o250bo13bo345bo10bo$1164bo22bo
204b3o53b3o223b2o19b2o$1164bo22bo204bo57bo223b2o19b2o$1164bo22bo205bo
55bo117bo6bo$1566bobo4bobo$907b3o657bo6bo$2038bo10bo$2037bobo8bobo$
2038bo10bo2$1671b2o9bo5bo9b2o$912bo500b2o13b2o240bobo9bo5bo9bobo$912bo
500b2o13b2o241bo10bo5bo10bo$912bo1120b3o16b3o3$1377b3o83b3o$1377bo87bo
$1378bo85bo5$1560b2o18b2o$1560b2o18b2o2$1567bo6bo$1566bobo4bobo$1566bo
bo4bobo$1567bo6bo!

Several puffers like the p56 in the collection above consisted of two copies of the same puffing engine arranged symmetrically. Different spacing between the engines leads to different periods. Here are some with the engines isolated. These are very messy and their exact period is debatable because for some, their trail appears to never settle down:

Code: Select all

x = 246, y = 30, rule = B37/S23
148b3o2b3o2b3o$obobobo23bo39bo13bo28bo4bobobobo22bo3bob3obo3bo22bobobo
bo4bo5bo20b3o15b3o$29b3o37b3o11b3o60bo6bobo6bo59bo2bo13bo2bo$o5bo20b2o
bob2o33b2ob3o9b3ob2o25bo4bo27bo3b2o5b2o3bo21bo10bo5bo24bo4b3o4bo$26bo
2bobo2bo33bo2bob2o5b2obo2bo61bo11bo60b2o3bo3bo3bo3bo3b2o$o5bo18bo3bobo
3bo29b2obo4bobo3bobo4bob2o23bo4bo26bobo13bobo20bo10bo5bo19b5o3bo5bo3b
5o$25bo3bobo3bo29b2obobo2bob2ob2obo2bobob2o54b2obob2o7b2obob2o55b2o2bo
2b3o5b3o2bo2b2o$obobobo20bo5bo31bo8bobobobo8bo23bo4bobobobo18bobobob2o
7b2obobobo18bobobobo4bobobobo23bo3bob3obo3bo$26bobo3bobo29b2o7b2obobob
2o7b2o51b2ob6o6bobobobob2o57bo2bobobobobobo2bo$o5bo69bobo34bo4bo5bo16b
o3bobo2b2o5bo3bob2o2bo16bo5bo10bo24b2obobobobob2o$26bo7bo36b3obo3bob3o
61bo10bob2obo63bobobobobobobobo$o5bo17b2o9b2o33b2o11b2o28bo4bo5bo16b2o
3bo12bobobo2b2o16bo5bo10bo21bobobobo5bobobobo$25bob2o3b2obo34bo10b2obo
72bobobo60b2obobo9bobob2o$obobobo15b2obob2o3b2obob2o30b2o42bo4bobobobo
34bobo22bobobobo10bo19bobobob2o2b3o2b2obobobo$22b2obobobobobobobo120b
2ob2o57b2obob3o3bobo3b3obob2o$23bobobobobobobobob2o118b3o57bo2b2ob7ob
7ob2o2bo$20b2obob5ob5obob2o190bobo$20b2ob3o2b2ob2ob2obobobo39b2obo134b
2o2bob4ob5ob4obo2b2o$20b5o12bo3bo40b3o141bobobobobobobo$18b2o17bob2obo
40bo142bobobobobobobo$18bo2b2ob3o9b2obo188bobobobobo$21b2o3bo12bobo
186bobo3bobo$17b2o4bobobo8b2obo190b2ob2o$37b3o189b3ob3o$228b9o$228bo3b
o3bo$227b3o5b3o3$229b2o3b2o!

The asymmetic p12 spaceship, which is the only thing I found at 2c/4, is highly versatile. It has a spark that extends out beyond the width of the front part of the spaceship. This enables it to safely interact with still lifes as well as gliders. One p12 spaceship on its own can delete still lifes, convert boats and beehives into gliders (and back again), duplicate backward gliders and reflect forward gliders.
This spaceship, combined with the almost clean p60 rake/puffer makes it fairly easy to complete the first part of my challenge. Here is a p60 rake that fires 9c/28 spaceships sideways:

Code: Select all

x = 871, y = 211, rule = B37/S23
858bo$857b3o$856b2obo$856bo$588bo9b2obo252b3o9bo$587b4o6bo4bo262b3o$
554bo9b2obo18b2o2b3o3bo3bo3b3ob2o255bob2o$553b4o6bo4bo16b2ob3o4b2ob3o
5b3o259bo$149bo9b2obo389b2o2b3o3bo3bo3b3ob2o8bo2b2o3bo11b5o259b3o$148b
4o6bo4bo3b2o382b2ob3o4b2ob3o5b3o9bo8b9ob3o2bo$147b2o2b3o3bo3bo4b3o381b
o2b2o3bo11b5o9bo2b2o3bo4bo4b4o2b2o245bo2bo$146b2ob3o4b2ob3o2bob3ob2o
378bo8b9ob3o2bo10b2ob3o3b3obobo3b2ob2o251bo$145bo2b2o3bo9b2o385bo2b2o
3bo4bo4b4o2b2o10b2o2b3o2b2ob2obo6bobobo240bo5bo$145bo8b10o387b2ob3o3b
3obobo3b2ob2o12b4o9bo8b2obo244bo3bo$145bo2b2o3bo4bo5bo3bo383b2o2b3o2b
2ob2obo6bobo11bo21b2o244bo2b2o3b3o$146b2ob3o3b3obob2obo3b2obo381b4o9bo
8b2o276bobo4b9obo$147b2o2b3o2b2ob2o3bo4b2o383bo306b2o5bo$148b4o9b2o7bo
439b2o252bo3b2o$149bo22b2o404b5o27b2o$172bo16bo29bo29bo29bo29bo29bo29b
o29bo29bo29bo29bo29bo29bo314bo2bo$188bobo27bobo27bobo27bobo27bobo27bob
o27bobo27bobo27bobo27bobo27bobo27bobo27bobo26b2o248b2o37bo$188bobo27bo
bo27bobo27bobo27bobo27bobo27bobo27bobo27bobo27bobo27bobo27bobo27bobo
26b2o2bo244bob2o$189bo29bo29bo29bo29bo29bo29bo29bo29bo29bo29bo29bo29bo
29b2o245bo2bo$827b3o$827b2o7b2o$835b2obo$165b3o667bo2bo$165bo669b3o$
166bo669b2o$825bo5b3o$823bo2b3obo2bo$823bo6bob2o2b2o$823bo6b2o2b2o3bo$
471bo9b2obo340b4o5b2obo2bo$470b4o6bo4bo340bo13bo$469b2o2b3o3bo3bo3b3ob
2o102bo239b3o3bo$468b2ob3o4b2ob3o5b3o102bo240b2o3bo$467bo2b2o3bo11b5o
102b3o240b3o$467bo8b9ob3o2bo305bo40bo$467bo2b2o3bo4bo4b4o2b2o303bobo$
468b2ob3o3b3obobo3b2ob2o304bob2o$150b3o316b2o2b3o2b2ob2obo6bobo303bo$
150bo319b4o9bo8b2o313bo$151bo319bo25bo308bobo$496bobo306b2obo$495bo2bo
300bo7bo$447b2o9bo37bo300b2o2bo$446bo3bo6b5o3bo329bo5bo$445bo3bo5b2obo
b2o3b2ob2o327bo2b2o$445bo4bobo2b3ob2o4bo328b2ob2o4b2o$444bob3o4bo7bobo
5bo140bo184b2o9bo$443b3o6b10o147bo194b3o2bo$444bob3o13bo6bo139b3o195bo
$445bo4bob3o3bob3o2b3o338b2ob2o$372bo9b2obo59bo3bo4bobobo2bo5b2obo337b
2o$371b4o6bo4bo59bo3bo8b2o11bo$135b3o86b2o9bo102bo9b2obo18b2o2b3o3bo3b
o3b3ob2o53b2o20b3o$135bo87bo3bo6b5o3bo24b2o9bo58b4o6bo4bo16b2ob3o4b2ob
3o5b3o$136bo85bo3bo5b2obob2o3b2ob2o19bo3bo6b5o3bobo48b2o2b3o3bo3bo3b3o
b2o8bo2b2o3bo11b5o374bo$222bo4bobo2b3ob2o4bo22bo3bo5b2obob2o2bo50b2ob
3o4b2ob3o5b3o9bo8b9ob3o2bo373b3obo$221bob3o4bo7bobo5bo18bo4bobo2b3ob5o
bob2o45bo2b2o3bo11b5o9bo2b2o3bo4bo4b4o2b2o69b2o300b2o4bo$220b3o6b10o
25bob3o4bo9b2obo47bo8b9ob3o2bo10b2ob3o3b3obobo3b2ob2o69bobo34bo265b6o$
221bob3o13bo6bo16b3o6b10o52bo2b2o3bo4bo4b4o2b2o10b2o2b3o2b2ob2obo6bo2b
o68bo35bo265b2ob2o6bo$222bo4bob3o3bob3o2b3o19bob3o14bo3b2o46b2ob3o3b3o
bobo3b2ob2o12b4o9bo8bo104b3o265b3ob2ob2ob3o$222bo3bo4bobobo2bo5b3o18bo
4bob3o3bobo2b2o2bo2bo45b2o2b3o2b2ob2obo6bobobo9bo24bo370bob2o6b2o$223b
o3bo8b2o27bo3bo4bobobo8bo3bo45b4o9bo8b2obo32bobo227bo138b2o4bo2b7o$
224b2o23bo16bo3bo8b2o7b2obo46bo21b2o262bo141b3o5b2ob2o$249bo17b2o21bo
99b2o232b3o137b3o7bob3o$390b2o382bobo$299bo29bo29bo414bo4b2o$268b2o28b
obo27bobo27bobo415b3o$120b3o144bobo28bobo27bobo27bobo417b3o$120bo147bo
30bo29bo29bo$121bo2$241b3o174b2o346bo4bo$241bo175bobo124bo192b2o26bo6b
o$242bo176bo125bo190bo2bo26bo4bo$543b3o189bo2b2o$734bo$640bo96b2ob2o4b
2o$639bo97bo2bo4bo2bo$639b3o93bo3bo5b2o2bo$377bo359bob2o9bo$376bo357b
2o3bo3b2ob2o$376b3o354bo4bo5bo2bo$105b3o628bo8bo3bo$105bo638b2obo$106b
o638bo3b2o$746bo4bo$226b3o128bo390bo$226bo129b4o9b2o7bo210bo$227bo39bo
9b2obo74b2o2b3o2b2ob2o3bo4b2o211bo$106bo9b2obo146b4o6bo4bo72b2ob3o3b3o
bob2obo3b2obo208b3o146bo2bo$105b4o6bo4bo3b2o107bo9b2obo18b2o2b3o3bo3bo
3b3ob2o64bo2b2o3bo4bo5bo3bo358b3o2b3o$104b2o2b3o3bo3bo4b3o17b2o9bo77b
4o6bo4bo16b2ob3o4b2ob3o5b3o65bo8b10o283bo52bo28bo2bo$103b2ob3o4b2ob3o
2bob3ob2o13bo3bo6b5o3bo69b2o2b3o3bo3bo3b3ob2o8bo2b2o3bo11b5o65bo2b2o3b
o9b2o281bo52bobo$102bo2b2o3bo9b2o19bo3bo5b2obob2o3b2ob2o64b2ob3o4b2ob
3o5b3o9bo8b9ob3o2bo66b2ob3o4b2ob3o2bob3ob2o274b3o49bo3bo$102bo8b10o20b
o4bobo2b3ob2o4bo67bo2b2o3bo11b5o9bo2b2o3bo4bo4b4o2b2o66b2o2b3o3bo3bo4b
3o329bo3b2o$102bo2b2o3bo4bo5bo3bo14bob3o4bo7bobo5bo63bo8b9ob3o2bo10b2o
b3o3b3obobo3b2ob2o68b4o6bo4bo3b2o329b2o8bo$103b2ob3o3b3obob2obo3b2obo
10b3o6b10o71bo2b2o3bo4bo4b4o2b2o10b2o2b3o2b2ob2obo6bo2bo66bo9b2obo344b
obo$90b3o11b2o2b3o2b2ob2o3bo4b2obo10bob3o13bo6bo64b2ob3o3b3obobo3b2ob
2o12b4o9bo8bo415b3ob2obo2bo3bo$14bo75bo14b4o9b2o7b3o11bo4bob3o3bob3o2b
3o67b2o2b3o2b2ob2obo6bobobo9bo24bo411b2obob2o2b2o3bo$11b4o28bob2o20b2o
22bo14bo34bo3bo4bobobo2bo5b2obo65b4o9bo8b2obo32bobo411bo2b2o8b2o$11b3o
27b6o19b5o71bo3bo8b2o11bo64bo21b2o448b4o$8b2o3bo16b2o8b2o5b2o17bo3bo
72b2o20b3o43b3o71b2o419bo6bob2ob3o$8b5o17b7ob2ob4ob3o6b2o9bo2b2o14b2o
28b2o94bo73b2o347bo79b2obob2o$6bo5b2o15bo6bobo3bo12b2o10b2o16b2o28b2o
77bo17bo11bo29bo380bo80b2o2bo$6b7o2bo8bo3b4ob2o4bo2bobob2o17b2ob2o33b
2o28b2o28b2o28bobo27bobo27bobo377b3o80b4o$3bobo6b7o4bob2obobo6bo3b2obo
22bo2bo31bobo27bobo27bobo28bobo27bobo27bobo254bo9b2obo194bo$2b9o5b2obo
3bo3bo9b3o2bob3o19b3o2bo31bo29bo29bo30bo29bo29bo254b4o6bo4bo145bo38bo$
b2o9b4obo2bo5b2o11bobob3o17bo6bo437b2o2b3o3bo3bo3b3ob2o137bo38b2o$2o4b
2o3bo4b2obo5bo2bo8bobo2b2o19b2o4bo437b2ob3o4b2ob3o5b3o138b3o35b3o$b2o
4bobo3b2o2b2o7b3o8b2o467bo2b2o3bo11b5o177b2o$12bo493bo8b9ob3o2bo178bo$
b2o4bobo3b2o2b2o7b3o8b2o467bo2b2o3bo4bo4b4o2b2o146bo$2o4b2o3bo4b2obo5b
o2bo8bobo2b2o19b2o4bo437b2ob3o3b3obobo3b2ob2o146b3o$b2o9b4obo2bo5b2o
11bobob3o17bo6bo437b2o2b3o2b2ob2obo6bobobo141b2o2bo$2b9o5b2obo3bo3bo9b
3o2bob3o19b3o2bo31bo29bo29bo30bo314b4o9bo8b2obo142b4o$3bobo6b7o4bob2ob
obo6bo3b2obo22bo2bo31bobo27bobo27bobo28bobo314bo21b2o141bobo8bo$6b7o2b
o8bo3b4ob2o4bo2bobob2o17b2ob2o33b2o28b2o28b2o28bobo478bo2bo7b3o$6bo5b
2o15bo6bobo3bo12b2o10b2o16b2o28b2o77bo77bo283b2o28b2o28b2o28b2o26bo2bo
6bo2b2o$8b5o17b7ob2ob4ob3o6b2o9bo2b2o14b2o28b2o108b2o44bo283bo2bo26bo
2bo26bo2bo26bo2bo26b2o7b4o$8b2o3bo16b2o8b2o5b2o17bo3bo72b2o20b3o57b2o
44b3o282b2o28b2o28b2o28b2o39bobo$11b3o27b6o19b5o71bo3bo8b2o11bo4bo21b
2o490bo2bo$11b4o28bob2o20b2o22bo14bo34bo3bo4bobobo2bo5b2obo5b4o9bo8b2o
bo32bobo64b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o12b3o13b2o28b2o28b2o
28b2o28b2o28bo2bo$14bo75bo14b4o9b2o7b3o11bo4bob3o3bob3o2b3o7b2o2b3o2b
2ob2obo6bobobo9bo24bo63bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo2bo
26bo2bo13bo12bo2bo26bo2bo26bo2bo26bo2bo26bo2bo28b2o$90b3o11b2o2b3o2b2o
b2o3bo4b2obo10bob3o13bo6bo4b2ob3o3b3obobo3b2ob2o12b4o9bo8bo68b2o28b2o
28b2o28b2o28b2o28b2o28b2o28b2o13bo14b2o28b2o28b2o28b2o28b2o$103b2ob3o
3b3obob2obo3b2obo10b3o6b10o11bo2b2o3bo4bo4b4o2b2o10b2o2b3o2b2ob2obo6bo
2bo43bo$102bo2b2o3bo4bo5bo3bo14bob3o4bo7bobo5bo3bo8b9ob3o2bo10b2ob3o3b
3obobo3b2ob2o23bo22b2o$102bo8b10o20bo4bobo2b3ob2o4bo7bo2b2o3bo11b5o9bo
2b2o3bo4bo4b4o2b2o21b4o9b2o7bo$102bo2b2o3bo9b2o19bo3bo5b2obob2o3b2ob2o
4b2ob3o4b2ob3o5b3o9bo8b9ob3o2bo21b2o2b3o2b2ob2o3bo4b2o$103b2ob3o4b2ob
3o2bob3ob2o13bo3bo6b5o3bo9b2o2b3o3bo3bo3b3ob2o8bo2b2o3bo11b5o20b2ob3o
3b3obob2obo3b2obo$104b2o2b3o3bo3bo4b3o17b2o9bo17b4o6bo4bo16b2ob3o4b2ob
3o5b3o19bo2b2o3bo4bo5bo3bo$105b4o6bo4bo3b2o47bo9b2obo18b2o2b3o3bo3bo3b
3ob2o18bo8b10o$106bo9b2obo86b4o6bo4bo25bo2b2o3bo9b2o$207bo9b2obo27b2ob
3o4b2ob3o2bob3ob2o$249b2o2b3o3bo3bo4b3o$250b4o6bo4bo3b2o$251bo9b2obo$
106bo369b3o$105bo372bo$105b3o369bo11$245bo9b2obo$244b4o6bo4bo3b2o$121b
o121b2o2b3o3bo3bo4b3o166b3o$120bo121b2ob3o4b2ob3o2bob3ob2o165bo$120b3o
118bo2b2o3bo9b2o171bo$241bo8b10o$241bo2b2o3bo4bo5bo3bo$242b2ob3o3b3obo
b2obo3b2obo$243b2o2b3o2b2ob2o3bo4b2o$244b4o9b2o7bo$245bo5$264b3o$264bo
$136bo128bo120b3o$135bo252bo$135b3o249bo4$307bo$305bobo$306b2o3$156bo
29bo30bo29bo$155bobo27bobo28bobo27bobo$156b2o28b2o28bobo27bobo$217bo
29bo$278b2o61b3o$149bo17b2o21bo87b2o50bo12bo$124b2o23bo16bo3bo8b2o7b2o
bo34bo21b2o55b2o23bo11bo$123bo3bo8b2o27bo3bo4bobobo8bo3bo33b4o9bo8b2ob
o32bobo18bo3bo8b2o$122bo3bo4bobobo2bo5b3o18bo4bob3o3bobo2b2o2bo2bo33b
2o2b3o2b2ob2obo6bobobo9bo24bo17bo3bo4bobobo2bo5b3o$122bo4bob3o3bob3o2b
3o19bob3o14bo3b2o34b2ob3o3b3obobo3b2ob2o12b4o9bo8bo21bo4bob3o3bob3o2b
3o$121bob3o13bo6bo16b3o6b10o40bo2b2o3bo4bo4b4o2b2o10b2o2b3o2b2ob2obo6b
o2bo18bob3o13bo6bo12bo$120b3o6b10o25bob3o4bo9b2obo35bo8b9ob3o2bo10b2ob
3o3b3obobo3b2ob2o20b3o6b10o18bobo$121bob3o4bo7bobo5bo18bo4bobo2b3ob5ob
ob2o33bo2b2o3bo11b5o9bo2b2o3bo4bo4b4o2b2o20bob3o4bo7bobo5bo11b2o$122bo
4bobo2b3ob2o4bo22bo3bo5b2obob2o2bo38b2ob3o4b2ob3o5b3o9bo8b9ob3o2bo22bo
4bobo2b3ob2o4bo$122bo3bo5b2obob2o3b2ob2o19bo3bo6b5o3bobo36b2o2b3o3bo3b
o3b3ob2o8bo2b2o3bo11b5o22bo3bo5b2obob2o3b2ob2o$123bo3bo6b5o3bo24b2o9bo
46b4o6bo4bo16b2ob3o4b2ob3o5b3o23bo3bo6b5o3bo$124b2o9bo90bo9b2obo18b2o
2b3o3bo3bo3b3ob2o23b2o9bo$259b4o6bo4bo$260bo9b2obo$329bo21b2o$328b4o9b
o8b2obo$327b2o2b3o2b2ob2obo6bobobo$326b2ob3o3b3obobo3b2ob2o$325bo2b2o
3bo4bo4b4o2b2o$325bo8b9ob3o2bo$325bo2b2o3bo11b5o$326b2ob3o4b2ob3o5b3o$
327b2o2b3o3bo3bo3b3ob2o$328b4o6bo4bo$329bo9b2obo!

For the second challenge, a breeder, I followed Calcymans suggestion. This requires two rakes and p60 is too fast because it leaves insufficient space to insert the second 9c/28. The p24 spaceship is useful here because it can thin a p60 forward glider stream down to p120. Inserting them at strategic places within the p60 rake converts it to p120. Here is a p120 breeder that emits Calcymans 9c/28 puffer:

Code: Select all

x = 1091, y = 407, rule = B37/S23
875b2o9bo$874bo3bo6b5o3bobo$841b2o9bo20bo3bo5b2obob2o2bo$840bo3bo6b5o
3bobo11bo4bobo2b3ob5obob2o$436b2o9bo391bo3bo5b2obob2o2bo13bob3o4bo9b2o
bo$435bo3bo6b5o3bo384bo4bobo2b3ob5obob2o8b3o6b10o$434bo3bo5b2obob2o3b
2ob2o379bob3o4bo9b2obo11bob3o14bo3b2o$434bo4bobo2b3ob2o4bo382b3o6b10o
17bo4bob3o3bobo2b2o2bo2bo$433bob3o4bo7bobo5bo379bob3o14bo3b2o10bo3bo4b
obobo8bo3bo$432b3o6b10o388bo4bob3o3bobo2b2o2bo12bo3bo8b2o7b2obo$433bob
3o13bo6bo380bo3bo4bobobo8bo2bo10b2o21bo$434bo4bob3o3bob3o2b3o383bo3bo
8b2o7b2o$434bo3bo4bobobo2bo5b2obo381b2o$435bo3bo8b2o11bo$436b2o20b3o$
500bo59bo59bo59bo59bo59bo59bo$499bobo57bobo57bobo57bobo57bobo57bobo57b
obo$499bobo57bobo57bobo57bobo57bobo57bobo57bobo$500bo59bo59bo59bo59bo
59bo59bo7$450b2o$449b2o$451bo2$758b2o9bo$757bo3bo6b5o3bobo$756bo3bo5b
2obob2o2bo$756bo4bobo2b3ob5obob2o$755bob3o4bo9b2obo$754b3o6b10o$755bob
3o14bo3b2o$756bo4bob3o3bobo2b2o2bo$756bo3bo4bobobo8bo2bo$757bo3bo8b2o
7b2o$758b2o3$735bo9b2obo$734b4o6bo4bo145bo$733b2o2b3o3bo3bo3b3ob2o136b
2o$732b2ob3o4b2ob3o5b3o138b2o$731bo2b2o3bo11b5o$394bobo334bo8b9ob3o2bo
$393bo2bo334bo2b2o3bo4bo4b4o2b2o$392b2o338b2ob3o3b3obobo3b2ob2o$391bo
267b2o9bo62b2o2b3o2b2ob2obo6bobobo$390b4o264bo3bo6b5o3bobo54b4o9bo8b2o
bo$389bo4bo5bobo109bo9b2obo99b2o9bo20bo3bo5b2obob2o2bo58bo21b2o$388b5o
3b2obo2bo108b4o6bo4bo28bo9b2obo55bo3bo6b5o3bobo11bo4bobo2b3ob5obob2o$
385b2o6b3o3bo110b2o2b3o3bo3bo3b3ob2o20b4o6bo4bo3b2o48bo3bo5b2obob2o2bo
13bob3o4bo9b2obo$384bo3b3ob2o2bo4bo18b2o87b2ob3o4b2ob3o5b3o20b2o2b3o3b
o3bo4b3o48bo4bobo2b3ob5obob2o8b3o6b10o$383bo3bo4b4o4bo18b2o87bo2b2o3bo
11b5o19b2ob3o4b2ob3o2bob3ob2o44bob3o4bo9b2obo11bob3o14bo3b2o$383bo5bo
6bo3bo3bo16bo86bo8b9ob3o2bo18bo2b2o3bo9b2o50b3o6b10o17bo4bob3o3bobo2b
2o2bo$383b3o3b8obobo4bo102bo2b2o3bo4bo4b4o2b2o17bo8b10o52bob3o14bo3b2o
10bo3bo4bobobo8bo2bo365b3o$400bo5bo102b2ob3o3b3obobo3b2ob2o18bo2b2o3bo
4bo5bo3bo48bo4bob3o3bobo2b2o2bo2bo9bo3bo8b2o7b3o58bo306bo2bo$383b3o3b
8obobo4bo104b2o2b3o2b2ob2obo6bo2bo16b2ob3o3b3obob2obo3b2obo45bo3bo4bob
obo8bo3bo9b2o21b3o56b2o305bob2o17bo$383bo5bo6bo3bo3bo106b4o9bo8bo19b2o
2b3o2b2ob2o3bo4b2obo45bo3bo8b2o7b2obo33b2o55bobo303b2o20b3o$383bo3bo4b
4o4bo111bo24bo16b4o9b2o7b3o46b2o21bo397b2o8b3o8bo2b2o$384bo3b3ob2o2bo
4bo133bobo17bo115b2o372bo2bo6bo2bo$385b2o6b3o3bo271b2o373b2o7b2obo7b2o
9bo$388b5o3b2obo2bo207bo448b2o5b2o8b3o$389bo4bo5bobo146b2o58bobo447b2o
5b2o7b2o2bo$390b4o154bobo58bobo446bo2bo$391bo157bo60bo448b2o18b2o$392b
2o427bo257b2o$393bo2bo8b2o415b2o255b2o$394bobo7b2o415b2o226bobo$406bo
642bo2bo$925bo126bo11b2o3bobo$923b2o125b2o10b3o2b5o$491bobo430b2o132bo
2bo5b2ob2o$490bo2bo168bo398bo2bo2bo2b2o$489b2o169b2o396bobo4b2o11bo$
488bo172b2o415b3o$487b4o588b2o$486bo4bo5bobo$485b5o3b2obo2bo$482b2o6b
3o3bo574b2o$481bo3b3ob2o2bo4bo571bo2bo$480bo3bo4b4o4bo573b2o$390b2o88b
o5bo6bo3bo3bo167bo$389b2o89b3o3b8obobo4bo141b2o23bo394b2o$391bo105bo5b
o139bo3bo8b2o406b2o$480b3o3b8obobo4bo51b2o9bo76bo3bo4bobobo2bo5b3o$
393b2o9bo75bo5bo6bo3bo3bo9b2o40bo3bo6b5o3bobo67bo4bob3o3bob3o2b3o$392b
o3bo6b5o3bo68bo3bo4b4o4bo12b2o8b2o9bo20bo3bo5b2obob2o2bo69bob3o13bo6bo
$391bo3bo5b2obob2o3b2ob2o15bo9b2obo36bo3b3ob2o2bo4bo13bo6bo3bo6b5o3bob
o11bo4bobo2b3ob5obob2o64b3o6b10o412b2o$391bo4bobo2b3ob2o4bo18b4o6bo4bo
36b2o6b3o3bo21bo3bo5b2obob2o2bo13bob3o4bo9b2obo67bob3o4bo7bobo5bo403bo
2bo$390bob3o4bo7bobo5bo13b2o2b3o3bo3bo3b3ob2o32b5o3b2obo2bo18bo4bobo2b
3ob5obob2o8b3o6b10o73bo4bobo2b3ob2o4bo408b2o$389b3o6b10o20b2ob3o4b2ob
3o5b3o34bo4bo5bobo17bob3o4bo9b2obo11bob3o14bo3b2o66bo3bo5b2obob2o3b2ob
2o$390bob3o13bo6bo11bo2b2o3bo11b5o35b4o25b3o6b10o17bo4bob3o3bobo2b2o2b
o68bo3bo6b5o3bo401b2o$391bo4bob3o3bob3o2b3o13bo8b9ob3o2bo36bo28bob3o
14bo3b2o10bo3bo4bobobo8bo2bo66b2o9bo408b2o$391bo3bo4bobobo2bo5b2obo10b
o2b2o3bo4bo4b4o2b2o36b2o27bo4bob3o3bobo2b2o2bo2bo9bo3bo8b2o7b3o410b2o$
300bobo44b3o42bo3bo8b2o8b2o11b2ob3o3b3obobo3b2ob2o38bo2bo24bo3bo4bobob
o8bo3bo9b2o21b3o407bobo$299bo2bo44b3o43b2o34b2o2b3o2b2ob2obo6bobobo35b
obo25bo3bo8b2o7b2obo33b2o331bo75bo2bo17b2o$298b2o42bo7bo24b2o53b4o9bo
8b2obo64b2o21bo368b2o74b2o17bo2bo60b2o$296bo4bo40bo6bo24b2o55bo21b2o
111b2o343b2o76bo7b2o8bo62bo2bo$295b2ob2o24b3o9b2o3bo6bo17b2o8bo19b2o
168b2o429bobo8b3o60b2o$294bo4bobo6b2o8bo7bo9b2o28b2o28b2o77bo29bo29bo
419bo40bo2bo17b2o$293b6o6bobo10bo2b2o2bo16bo4b2o35b2o28b2o28b2o28bobo
19b2o6bobo27bobo416b2o42b2o17bo2bo44b2o$290b2o8b4o13bo25b3o37bobo27bob
o27bobo28bobo18b2o7bobo27bobo260b2o9bo145b2o41bo21bo44b2o$289bo3b5obo
4bo6b2o5b3obob2o17b2o4b2o33bo29bo29bo30bo21bo7bo29bo260bo3bo6b5o3bobo
168bo6bo16bo5b3o$288bo3bo4b7o6bobo6bo6bo17bo5bo444bo3bo5b2obob2o2bo
170bobo3bob2o14bo2bo$288bo5b3o12bo2bo8bo3bo19b5o445bo4bobo2b3ob5obob2o
165b3ob6o3bo8b2o5bo$288b3o3b3o3b2o3bo3b3o10b3o469bob3o4bo9b2obo168bo2b
2o6bob2o5bo5bobo57b2o$300bo492b3o6b10o174b3o6b2ob3o3bo2bo2bob2o56bo2bo
$288b3o3b3o3b2o3bo3b3o10b3o469bob3o14bo3b2o177bo3b2o3bo2b2o6b3o52b2o$
288bo5b3o12bo2bo8bo3bo19b5o445bo4bob3o3bobo2b2o2bo2bo175b2obo2bo3b2o8b
ob2o$288bo3bo4b7o6bobo6bo6bo17bo5bo444bo3bo4bobobo8bo3bo175bo3bo14bo3b
2o42b2o$289bo3b5obo4bo6b2o5b3obob2o17b2o4b2o33bo29bo29bo30bo81bo238bo
3bo8b2o7b2obo176b3o16bobo2bo41b2o$290b2o8b4o13bo25b3o37bobo27bobo27bob
o28bobo78b2o240b2o21bo196b2o2bo$293b6o6bobo10bo2b2o2bo16bo4b2o35b2o28b
2o28b2o28bobo79b2o461b2o$294bo4bobo6b2o8bo7bo9b2o28b2o28b2o77bo391b2o
58b2o$295b2ob2o24b3o9b2o3bo6bo17b2o8bo19b2o108b2o358bo2bo56bo2bo81b2o
58b2o$296bo4bo40bo6bo24b2o55bo21b2o51b2o359b2o58b2o81bo2bo56bo2bo$298b
2o42bo7bo24b2o53b4o9bo8b2obo4b2o21bo527b2o58b2o$299bo2bo44b3o43b2o34b
2o2b3o2b2ob2obo6bobobo3bo3bo8b2o7b2obo33b2o58b2o28b2o28b2o28b2o28b2o
28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o58b2o58b2o$300bobo44b3o
42bo3bo8b2o8b2o11b2ob3o3b3obobo3b2ob2o6bo3bo4bobobo8bo3bo9b2o21b3o57bo
2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo
2bo26bo2bo26bo2bo26bo2bo33b2o21bo2bo33b2o21bo2bo$391bo3bo4bobobo2bo5b
2obo10bo2b2o3bo4bo4b4o2b2o5bo4bob3o3bobo2b2o2bo2bo9bo3bo8b2o7b3o60b2o
28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o34b2o
22b2o34b2o22b2o$391bo4bob3o3bob3o2b3o13bo8b9ob3o2bo5bob3o14bo3b2o10bo
3bo4bobobo8bo2bo281b2o$390bob3o13bo6bo11bo2b2o3bo11b5o4b3o6b10o17bo4bo
b3o3bobo2b2o2bo23b2o20b3o237b2o$389b3o6b10o20b2ob3o4b2ob3o5b3o5bob3o4b
o9b2obo11bob3o14bo3b2o21bo3bo8b2o11bo235bo$390bob3o4bo7bobo5bo13b2o2b
3o3bo3bo3b3ob2o5bo4bobo2b3ob5obob2o8b3o6b10o27bo3bo4bobobo2bo5b2obo$
391bo4bobo2b3ob2o4bo18b4o6bo4bo12bo3bo5b2obob2o2bo13bob3o4bo9b2obo22bo
4bob3o3bob3o2b3o$391bo3bo5b2obob2o3b2ob2o15bo9b2obo14bo3bo6b5o3bobo11b
o4bobo2b3ob5obob2o19bob3o13bo6bo$392bo3bo6b5o3bo48b2o9bo20bo3bo5b2obob
2o2bo22b3o6b10o$393b2o9bo88bo3bo6b5o3bobo20bob3o4bo7bobo5bo$494b2o9bo
30bo4bobo2b3ob2o4bo$391bo144bo3bo5b2obob2o3b2ob2o$389b2o146bo3bo6b5o3b
o$390b2o146b2o9bo2$948b2o$947bo2bo$947b5o$947b2o3bo$957b2o$947bo4bo3bo
2bo$949b2obo2b5o$945bobobo4bo3b2o$944bo2bo2b2o$945b2o7bo4bo$954bob2o$
406bo550bobobo$394bobo7b2o126b2o9bo411b2o2bo2bo$393bo2bo8b2o124bo3bo6b
5o3bo409b2o$392b2o136bo3bo5b2obob2o3b2ob2o$391bo138bo4bobo2b3ob2o4bo$
390b4o135bob3o4bo7bobo5bo$389bo4bo5bobo125b3o6b10o162b2o237bo2bo$388b
5o3b2obo2bo126bob3o13bo6bo155b2o235b2o2b2o$385b2o6b3o3bo130bo4bob3o3bo
b3o2b3o156bo238bo2bo$384bo3b3ob2o2bo4bo128bo3bo4bobobo2bo5b3o$383bo3bo
4b4o4bo130bo3bo8b2o$383bo5bo6bo3bo3bo5bo121b2o23bo$383b3o3b8obobo4bo2b
obo146bo$400bo6bo$383b3o3b8obobo4bo2bobo$383bo5bo6bo3bo3bo5bo$383bo3bo
4b4o4bo$384bo3b3ob2o2bo4bo$385b2o6b3o3bo$388b5o3b2obo2bo146b2o$389bo4b
o5bobo145b2o$390b4o156bo$391bo$392b2o$393bo2bo$394bobo2$889bo$888b3o$
498bo388bo3bo$436bo60bobo388b2obo$434b2o61bobo388bo2bo5bo$435b2o61bo
122b4o262b2ob2o4b3o$435bobo121b2o59bo3bo260b2obo6bo3bo$435bobo17bo103b
2o55b2ob3ob2o260bo2b2o5bob2o$412bo24bo16b4o9b2o7b3o34b2o21bo56bo22bo2b
o3b2o261b2o7bo2bo$411b4o9bo8bo19b2o2b3o2b2ob2o3bo4b2obo33bo3bo8b2o7b2o
bo33b2o19b4o9bo10bo2b5o271b2ob2o$410b2o2b3o2b2ob2obo6bo2bo16b2ob3o3b3o
bob2obo3b2obo33bo3bo4bobobo8bo3bo9b2o21b3o18b2o2b3o2b2ob2obo6b2o2b2o2b
2o275bob2o$409b2ob3o3b3obobo3b2ob2o18bo2b2o3bo4bo5bo3bo36bo4bob3o3bobo
2b2o2bo2bo9bo3bo8b2o7b3o19b2ob3o3b3obobo3b2ob2o283b2o2bo$408bo2b2o3bo
4bo4b4o2b2o17bo8b10o40bob3o14bo3b2o10bo3bo4bobobo8bo2bo18bo2b2o3bo4bo
4b4o2b2o284b2o$408bo8b9ob3o2bo18bo2b2o3bo9b2o38b3o6b10o17bo4bob3o3bobo
2b2o2bo21bo8b9ob3o2bo$408bo2b2o3bo11b5o19b2ob3o4b2ob3o2bob3ob2o32bob3o
4bo9b2obo11bob3o14bo3b2o20bo2b2o3bo11b5o$409b2ob3o4b2ob3o5b3o20b2o2b3o
3bo3bo4b3o36bo4bobo2b3ob5obob2o8b3o6b10o28b2ob3o4b2ob3o5b3o275b3o$410b
2o2b3o3bo3bo3b3ob2o20b4o6bo4bo3b2o36bo3bo5b2obob2o2bo13bob3o4bo9b2obo
24b2o2b3o3bo3bo3b3ob2o274b2o$411b4o6bo4bo28bo9b2obo43bo3bo6b5o3bobo11b
o4bobo2b3ob5obob2o23b4o6bo4bo281b2obo$412bo9b2obo87b2o9bo20bo3bo5b2obo
b2o2bo28bo9b2obo284bo$546bo3bo6b5o3bobo$547b2o9bo$616b2o21bo$615bo3bo
8b2o7b2obo$614bo3bo4bobobo8bo3bo$614bo4bob3o3bobo2b2o2bo2bo$588bo9b2ob
o11bob3o14bo3b2o$587b4o6bo4bo3b2o4b3o6b10o$554bo9b2obo18b2o2b3o3bo3bo
4b3o5bob3o4bo9b2obo$553b4o6bo4bo3b2o11b2ob3o4b2ob3o2bob3ob2o3bo4bobo2b
3ob5obob2o$149bo9b2obo389b2o2b3o3bo3bo4b3o10bo2b2o3bo9b2o10bo3bo5b2obo
b2o2bo$148b4o6bo4bo387b2ob3o4b2ob3o2bob3ob2o7bo8b10o12bo3bo6b5o3bobo$
147b2o2b3o3bo3bo3b3ob2o379bo2b2o3bo9b2o14bo2b2o3bo4bo5bo3bo8b2o9bo$
146b2ob3o4b2ob3o5b3o380bo8b10o16b2ob3o3b3obob2obo3b2obo$145bo2b2o3bo
11b5o380bo2b2o3bo4bo5bo3bo12b2o2b3o2b2ob2o3bo4b2o$145bo8b9ob3o2bo381b
2ob3o3b3obob2obo3b2obo10b4o9b2o7bo$145bo2b2o3bo4bo4b4o2b2o381b2o2b3o2b
2ob2o3bo4b2obo10bo22b2o$146b2ob3o3b3obobo3b2ob2o383b4o9b2o7b3o33bo$
147b2o2b3o2b2ob2obo6bo2bo381bo26bo$148b4o9bo8bo409bobo$149bo24bo404bo
3bo$172bobo45bo59bo59bo59bo59bo59bo57bo3bo246bo$219bobo57bobo57bobo57b
obo57bobo57bobo55b6o245b3o$219bobo57bobo57bobo57bobo57bobo57bobo56bo2b
o245bo2b2o$220bo59bo59bo59bo59bo59bo58b3o244b3ob2o$580bo246b5o5bo$829b
o6b3o$166b2o667b2o2bo$166bobo666b2ob3o$166bo668b5o$832b4obo$826b4ob5o$
825bo4b2o3b2o$825bo7b6o$825bo4b2obo4b3o$471bo9b2obo340bo3bob2ob4o2b3o$
470b4o6bo4bo3b2o335bobo6bo2b2o$469b2o2b3o3bo3bo4b3o344b2o2bo$468b2ob3o
4b2ob3o2bob3ob2o342bo5bo$467bo2b2o3bo9b2o350bo$467bo8b10o351bo2bo$467b
o2b2o3bo4bo5bo3bo348bo$468b2ob3o3b3obob2obo3b2obo$469b2o2b3o2b2ob2o3bo
4b2obo$470b4o9b2o7b3o$471bo3$447b2o9bo$446bo3bo6b5o3bobo$445bo3bo5b2ob
ob2o2bo$445bo4bobo2b3ob5obob2o$444bob3o4bo9b2obo$108bo334b3o6b10o148bo
$105b4o335bob3o14bo3b2o141bobo$105b2o338bo4bob3o3bobo2b2o2bo142b2o$
103bo268bo9b2obo59bo3bo4bobobo8bo2bo$103b4o29b2o233b4o6bo4bo3b2o54bo3b
o8b2o7b3o$101bo12bo21bobo85b2o9bo102bo9b2obo18b2o2b3o3bo3bo4b3o55b2o
21b3o$101b5o3bob4o21bo86bo3bo6b5o3bobo22b2o9bo58b4o6bo4bo3b2o11b2ob3o
4b2ob3o2bob3ob2o76b2o295bo$98bobo6b2ob2obo108bo3bo5b2obob2o2bo24bo3bo
6b5o3bo50b2o2b3o3bo3bo4b3o10bo2b2o3bo9b2o379b3o$97b6obo2bobo3bo108bo4b
obo2b3ob5obob2o19bo3bo5b2obob2o3b2ob2o45b2ob3o4b2ob3o2bob3ob2o7bo8b10o
382bo$96b2o5b3ob3o3b2o106bob3o4bo9b2obo21bo4bobo2b3ob2o4bo48bo2b2o3bo
9b2o14bo2b2o3bo4bo5bo3bo72b3o$95b2o4b2o6b2o2b2o105b3o6b10o25bob3o4bo7b
obo5bo44bo8b10o16b2ob3o3b3obob2obo3b2obo71bo311bo$96b2o4b9o2b5o3bobo
97bob3o14bo3b2o17b3o6b10o52bo2b2o3bo4bo5bo3bo12b2o2b3o2b2ob2o3bo4b2o
71bo311b3o$113b5o2b2ob2o97bo4bob3o3bobo2b2o2bo19bob3o13bo6bo45b2ob3o3b
3obob2obo3b2obo10b4o9b2o7bo372b2o9bo$96b2o4b9o2b5o3bobo98bo3bo4bobobo
8bo2bo17bo4bob3o3bob3o2b3o48b2o2b3o2b2ob2o3bo4b2o12bo397bob2o$95b2o4b
2o6b2o2b2o108bo3bo8b2o7b2o18bo3bo4bobobo2bo5b2obo46b4o9b2o7bo406bo2b2o
$96b2o5b3ob3o3b2o109b2o40bo3bo8b2o11bo45bo22b2o405bo4b3o$97b6obo2bobo
3bo153b2o20b3o69bo29b2o373b2o6b2o3b2o$98bobo6b2ob2obo277b2o373b2o6b2o$
101b5o3bob4o215bo445b2o2bo$101bo12bo6b2o146b2o58bobo446bo$103b4o14bobo
144bobo58bobo447b2o$103bo17bo147bo60bo448b2o$105b2o$105b4o$108bo2$546b
o$544bobo$205bo339b2o$202b4o$202b2o436bo$200bo439bobo$200b4o436b2o$
198bo12bo165bo$106b2o90b5o3bob4o165bobo$106bobo86bobo6b2ob2obo166b2o$
106bo87b6obo2bobo3bo$193b2o5b3ob3o3b2o$192b2o4b2o6b2o2b2o15b2o$193b2o
4b9o2b5o3bobo6bobo127bo$210b5o2b2ob2o5bo128b4o9bo8b2o$193b2o4b9o2b5o3b
obo46bo9b2obo74b2o2b3o2b2ob2obo6bobo$106bo9b2obo72b2o4b2o6b2o2b2o54b4o
6bo4bo3b2o67b2ob3o3b3obobo3b2ob2o$105b4o6bo4bo72b2o5b3ob3o3b2o21bo9b2o
bo18b2o2b3o3bo3bo4b3o66bo2b2o3bo4bo4b4o2b2o$104b2o2b3o3bo3bo3b3ob2o15b
2o9bo39b6obo2bobo3bo21b4o6bo4bo3b2o11b2ob3o4b2ob3o2bob3ob2o63bo8b9ob3o
2bo330b3o$103b2ob3o4b2ob3o5b3o15bo3bo6b5o3bobo31bobo6b2ob2obo20b2o2b3o
3bo3bo4b3o10bo2b2o3bo9b2o70bo2b2o3bo11b5o329bo$102bo2b2o3bo11b5o14bo3b
o5b2obob2o2bo37b5o3bob4o18b2ob3o4b2ob3o2bob3ob2o7bo8b10o72b2ob3o4b2ob
3o5b3o328bo5bo$102bo8b9ob3o2bo14bo4bobo2b3ob5obob2o33bo12bo17bo2b2o3bo
9b2o14bo2b2o3bo4bo5bo3bo68b2o2b3o3bo3bo3b3ob2o327bo2b2obo$102bo2b2o3bo
4bo4b4o2b2o12bob3o4bo9b2obo37b4o25bo8b10o16b2ob3o3b3obob2obo3b2obo66b
4o6bo4bo334b3o7b3o$91b2o10b2ob3o3b3obobo3b2ob2o12b3o6b10o42bo28bo2b2o
3bo4bo5bo3bo12b2o2b3o2b2ob2o3bo4b2o68bo9b2obo335bo3bo8bo$91bobo10b2o2b
3o2b2ob2obo6bobobo9bob3o14bo3b2o37b2o26b2ob3o3b3obob2obo3b2obo10b4o9b
2o7bo419b3o3bo5bo$14bo76bo13b4o9bo8b2obo10bo4bob3o3bobo2b2o2bo38b4o25b
2o2b3o2b2ob2o3bo4b2o12bo436b3ob3o3bob2o2bo$11b4o28bo62bo21b2o11bo3bo4b
obobo8bo2bo38bo26b4o9b2o7bo450bo12b3o$11b3o21bo5b2obo22b2o73bo3bo8b2o
7b3o45b2o19bo22b2o447b3o8bo3bo$8b2o3bo19bo3bob2ob3o3bo17b2o4bo70b2o21b
3o43bobo41bo29b2o418b2o8b3o$8b5o17bo2bo3bobobo2bo4b2o5b2o9b2ob3o13b2o
28b2o49b2o43bo73b2o428b3ob3o$6bo5b2o14b3o2b3obo6b3obo7b2o8b4obo14b2o
28b2o77bo29bo29bo380bo84bo$6b7o12b2o2bob2o4bo5bob2o19b2o2b2o32b2o28b2o
28b2o28bobo27bobo27bobo377bobo82b3o$3bobo6b4o3bo4bo4bob2o4b2ob5ob2o18b
o5bo30bobo27bobo27bobo28bobo27bobo27bobo253bo9b2obo111b2o82b2o$2b9o5bo
2b3o3bo3bo7b2obo2bo2b3o16b3o4bo31bo29bo29bo30bo29bo29bo253b4o6bo4bo3b
2o179b2o$b2o9b4o3b3o3bobob2o6b2obob2o20b4o4bo435b2o2b3o3bo3bo4b3o140bo
37bo2bo$2o4b2o3bo4b3ob2o4bobobo6b2ob4o20b2o3b2o436b2ob3o4b2ob3o2bob3ob
2o137bobo34b6o$b2o4bobo3b2o3b2o7b3o8b3o465bo2b2o3bo9b2o144b2o36bo2bo$
12bo493bo8b10o184b2o$b2o4bobo3b2o3b2o7b3o8b3o465bo2b2o3bo4bo5bo3bo$2o
4b2o3bo4b3ob2o4bobobo6b2ob4o20b2o3b2o436b2ob3o3b3obob2obo3b2obo$b2o9b
4o3b3o3bobob2o6b2obob2o20b4o4bo435b2o2b3o2b2ob2o3bo4b2o$2b9o5bo2b3o3bo
3bo7b2obo2bo2b3o16b3o4bo31bo29bo29bo30bo313b4o9b2o7bo$3bobo6b4o3bo4bo
4bob2o4b2ob5ob2o18bo5bo30bobo27bobo27bobo28bobo313bo22b2o$6b7o12b2o2bo
b2o4bo5bob2o19b2o2b2o32b2o28b2o28b2o28bobo336bo$6bo5b2o14b3o2b3obo6b3o
bo7b2o8b4obo14b2o28b2o77bo391b2o58b2o$8b5o17bo2bo3bobobo2bo4b2o5b2o9b
2ob3o13b2o28b2o49b2o57b2o44bo313bo2bo56bo2bo$8b2o3bo19bo3bob2ob3o3bo
17b2o4bo70b2o21b3o27bo29b2o44bobo312b2o58b2o$11b3o21bo5b2obo22b2o73bo
3bo8b2o7b3o6bo22b2o74b2o249b2o$11b4o28bo62bo21b2o11bo3bo4bobobo8bo2bo
5b4o9b2o7bo103b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o12bobo13b2o28b2o
28b2o28b2o28b2o28b2o$14bo76bo13b4o9bo8b2obo10bo4bob3o3bobo2b2o2bo7b2o
2b3o2b2ob2o3bo4b2o12bo89bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo2b
o26bo2bo13bo12bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo2bo$91bobo10b2o2b3o
2b2ob2obo6bobobo9bob3o14bo3b2o5b2ob3o3b3obob2obo3b2obo10b4o9b2o7bo69b
2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o$
91b2o10b2ob3o3b3obobo3b2ob2o12b3o6b10o11bo2b2o3bo4bo5bo3bo12b2o2b3o2b
2ob2o3bo4b2o45bobo$102bo2b2o3bo4bo4b4o2b2o12bob3o4bo9b2obo6bo8b10o16b
2ob3o3b3obob2obo3b2obo21bo24bo409bo$102bo8b9ob3o2bo14bo4bobo2b3ob5obob
2o4bo2b2o3bo9b2o14bo2b2o3bo4bo5bo3bo23b4o9bo8bo390bo22b2o$102bo2b2o3bo
11b5o14bo3bo5b2obob2o2bo9b2ob3o4b2ob3o2bob3ob2o7bo8b10o27b2o2b3o2b2ob
2obo6bo2bo387b4o9b2o7bo$103b2ob3o4b2ob3o5b3o15bo3bo6b5o3bobo7b2o2b3o3b
o3bo4b3o10bo2b2o3bo9b2o25b2ob3o3b3obobo3b2ob2o389b2o2b3o2b2ob2o3bo4b2o
$104b2o2b3o3bo3bo3b3ob2o15b2o9bo17b4o6bo4bo3b2o11b2ob3o4b2ob3o2bob3ob
2o17bo2b2o3bo4bo4b4o2b2o387b2ob3o3b3obob2obo3b2obo$105b4o6bo4bo52bo9b
2obo18b2o2b3o3bo3bo4b3o20bo8b9ob3o2bo387bo2b2o3bo4bo5bo3bo$106bo9b2obo
86b4o6bo4bo3b2o20bo2b2o3bo11b5o387bo8b10o$207bo9b2obo27b2ob3o4b2ob3o5b
3o387bo2b2o3bo9b2o$249b2o2b3o3bo3bo3b3ob2o387b2ob3o4b2ob3o2bob3ob2o$
250b4o6bo4bo395b2o2b3o3bo3bo4b3o$251bo9b2obo397b4o6bo4bo3b2o$663bo9b2o
bo$106bo$106bobo$106b2o10$108bo136bo9b2obo$105b4o135b4o6bo4bo173b2o$
105b2o136b2o2b3o3bo3bo3b3ob2o165bobo$103bo17bo120b2ob3o4b2ob3o5b3o168b
o$103b4o14bobo117bo2b2o3bo11b5o$101bo12bo6b2o118bo8b9ob3o2bo$101b5o3bo
b4o126bo2b2o3bo4bo4b4o2b2o$98bobo6b2ob2obo128b2ob3o3b3obobo3b2ob2o$97b
6obo2bobo3bo129b2o2b3o2b2ob2obo6bobo$96b2o5b3ob3o3b2o129b4o9bo8b2o$95b
2o4b2o6b2o2b2o130bo$96b2o4b9o2b4obobo$113b4obo2bo$96b2o4b9o2b4obobo$
95b2o4b2o6b2o2b2o150b2o$96b2o5b3ob3o3b2o150bobo$97b6obo2bobo3bo151bo$
98bobo6b2ob2obo$101b5o3bob4o$101bo12bo$103b4o$103bo$105b2o$105b4o$108b
o4$157bo60bo$156bobo58bobo$157b2o58bobo$218bo124b2o$279b2o61bobo$167b
2o20b3o57bo29b2o63bo$124b2o40bo3bo8b2o11bo33bo22b2o54b2o$123bo3bo8b2o
7b2o18bo3bo4bobobo2bo5b2obo34b4o9b2o7bo56bo3bo8b2o7b2o$122bo3bo4bobobo
8bo2bo17bo4bob3o3bob3o2b3o36b2o2b3o2b2ob2o3bo4b2o12bo42bo3bo4bobobo8bo
2bo$122bo4bob3o3bobo2b2o2bo19bob3o13bo6bo33b2ob3o3b3obob2obo3b2obo10b
4o9b2o7bo21bo4bob3o3bobo2b2o2bo$121bob3o14bo3b2o17b3o6b10o40bo2b2o3bo
4bo5bo3bo12b2o2b3o2b2ob2o3bo4b2o20bob3o14bo3b2o14bo$120b3o6b10o25bob3o
4bo7bobo5bo32bo8b10o16b2ob3o3b3obob2obo3b2obo18b3o6b10o22bo$121bob3o4b
o9b2obo21bo4bobo2b3ob2o4bo36bo2b2o3bo9b2o14bo2b2o3bo4bo5bo3bo22bob3o4b
o9b2obo15b3o$122bo4bobo2b3ob5obob2o19bo3bo5b2obob2o3b2ob2o33b2ob3o4b2o
b3o2bob3ob2o7bo8b10o28bo4bobo2b3ob5obob2o$122bo3bo5b2obob2o2bo24bo3bo
6b5o3bo38b2o2b3o3bo3bo4b3o10bo2b2o3bo9b2o27bo3bo5b2obob2o2bo$123bo3bo
6b5o3bobo22b2o9bo46b4o6bo4bo3b2o11b2ob3o4b2ob3o2bob3ob2o21bo3bo6b5o3bo
bo$124b2o9bo90bo9b2obo18b2o2b3o3bo3bo4b3o25b2o9bo$259b4o6bo4bo3b2o$
260bo9b2obo78bo$329bo22b2o$328b4o9b2o7bo$327b2o2b3o2b2ob2o3bo4b2o$326b
2ob3o3b3obob2obo3b2obo$325bo2b2o3bo4bo5bo3bo$325bo8b10o$325bo2b2o3bo9b
2o$326b2ob3o4b2ob3o2bob3ob2o$327b2o2b3o3bo3bo4b3o$328b4o6bo4bo3b2o$
329bo9b2obo!

[calcyman]

Very impressive!

[Sokwe]

Here's a 5-engine 9c/28 backrake:

Code: Select all

x = 48, y = 36, rule = B37/S23
7b2o$6b2o$8bo3$44bobo$26bo17bobo$26b2o16bo$36b2o$16b2o9b2o9bo$14b5o16b
o2bo$13bo4bo16bobo$13bo2b3o$17bo$13bo2bo28b2o$16bo27bo2bo$13b3o29b2o$
45b2o$32b2o7b2obo$23b3o5bo2bo6bo2bo$2o20b2o2bo5b2o8b3o$2o19bo3b2o5b2o$
2bo17b2obobo8bob2o$o2b2o14b2o13bo2bo$5b2o6b2o4b2ob3o9b3o$2o3b2o6b2o5bo
3bo$5b3o4bo8b3o$10b2o2bo6b3o$7b2obo$3bo9b2o$b3o$2bo2$11bo$11b3o$12bo!

Unlike Calcyman's period-56 rake, this one can be synthesized relatively easily and should allow the construction of a rake puffer or rake gun:

Code: Select all

x = 65, y = 98, rule = B37/S23
49b2o$49b2o$48bo$46b2o2bo$36b2o6b2o$36b2o6b2o3b2o$38bo4b3o$36bo2b2o$
40bob2o$36b2o9bo$47b3o$48bo2$39bo$37b3o$38bo8$5b2o$4bo2bo$5b2o2$16b2o$
15bo2bo$bo14b2o$b2o$obo2$21bo$20b2o$20bobo23$27b2o$26bo2bo$27b2o35$62b
2o$62bobo$62bo!

Also, this 3-engine puffer is quite easy to synthesize:

Code: Select all

x = 35, y = 34, rule = B37/S23
2o$2o$2bo$o2b2o$5b2o6b2o$2o3b2o6b2o$5b3o4bo$10b2o2bo$7b2obo$3bo9b2o$b
3o$2bo2$11bo$11b3o$12bo4$22b2o$21bo2bo$22b2o10$33bo$32b2o$32bobo!

[Paul Tooke]

Sokwe wrote:

Here's a 5-engine 9c/28 backrake:
...
Unlike Calcyman's period-56 rake, this one can be synthesized relatively easily and should allow the construction of a rake puffer or rake gun:

It's certainly possible to make a rake puffer (although I had to completely re-engineer my c/2 rake to produce the 'flipped' 9c/28). Here is a p120 c/2 MMM breeder based on two different rakes and an R-pentomino inserter. It could probably be made a good deal smaller by using fewer p60 engines and more glider duplications, but I felt more comfortable with a modular design.

Code: Select all

x = 1405, y = 566, rule = B37/S23
1369bo$1368bobo$1367b2obo$1369bo$1359bo$1358bobo$1358bob2o$1359bo7bo$
1365bo2b2o9bo$1365bo5bo6b3o$1365b2o2bo6b3ob2o$1362b2o4b2ob2o3b2o3b2o8b
3o$1360bo9b2o8b2o8bo2bo$1357bo2b3o16bo10bobobo$1359bo18b4obo9b2o$1356b
2ob2o16bo6bo6bobo5b3o$1357b2o24bo4b2ob2o6bo2bo$1379bo2bo5bo2bo6bobobo$
1381b2o6b2o7b2o$1371b2o26bobo$1370b3o27b2ob2o$1371bob2o26bo2bo$1373b2o
27b2o$1373bobo$1375b2o$1371b4obo16bo$1371bo2b3o15b2obo$1393bobo$1383bo
10bo$1382bo2bo15bo$1383b2o16bo5$1363bobo$1363b2o$1364bo$1308b2o$1307bo
2bo$1307b2o2bo$1312bo$1299b2o4b2ob2o$1298bo2bo4bo2bo$1297bo2b2o5bo3bo$
1296bo9b2obo$1299b2ob2o3bo3b2o$1299bo2bo5bo4bo$1297bo3bo8bo7b3o$1299bo
b2o15bo2bo$1296b2o3bo16bo2bo$1295bo4bo30b3o22bobo$1298bo22b2o7bo2bo22b
2o$1322bo7bo3bo22bo$1330bo2bo$1306bo2bo21bobo5b3o$1304b3o2b3o6b2o19bo
2bo$1306bo2bo10bo17bo3bo$1314b2o4b4o15bo2bo$1313bo3bo2bo15bo2bobo$
1313bo16b2o3b3o$1313b3o9b2o3b2ob2o3bo$1325b2o4bo2bob2ob2o$1321b3o6b2ob
4o4b2o$1321b3o5b3o6b3o2b2o$1329b2o7bo2bo2b2o$1339bobo2b2o$1339bo3b2o4b
obo$1340b4o5b2o$1305bobo33b3o6bo$1305b2o$1017b2o9bo277bo$1016bo3bo6b5o
3bo$870bo9b2obo99b2o9bo20bo3bo5b2obob2o3b2ob2o$869b4o6bo4bo3b2o23bo9b
2obo55bo3bo6b5o3bo13bo4bobo2b3ob2o4bo$868b2o2b3o3bo3bo4b3o22b4o6bo4bo
53bo3bo5b2obob2o3b2ob2o8bob3o4bo7bobo5bo$867b2ob3o4b2ob3o2bob3ob2o18b
2o2b3o3bo3bo3b3ob2o46bo4bobo2b3ob2o4bo11b3o6b10o$866bo2b2o3bo9b2o24b2o
b3o4b2ob3o5b3o46bob3o4bo7bobo5bo8bob3o13bo6bo208bo$866bo8b10o24bo2b2o
3bo11b5o45b3o6b10o17bo4bob3o3bob3o2b3o209b3o$866bo2b2o3bo4bo5bo3bo19bo
8b9ob3o2bo46bob3o13bo6bo9bo3bo4bobobo2bo5b2obo205bo2b2o$867b2ob3o3b3ob
ob2obo3b2obo16bo2b2o3bo4bo4b4o2b2o46bo4bob3o3bob3o2b3o12bo3bo8b2o11bo
203b4o$868b2o2b3o2b2ob2o3bo4b2o18b2ob3o3b3obobo3b2ob2o47bo3bo4bobobo2b
o5b2obo10b2o20b3o198bo8bobo$869b4o9b2o7bo19b2o2b3o2b2ob2obo6bobo46bo3b
o8b2o8b2o232b3o7bo2bo$870bo22b2o17b4o9bo8b2o47b2o253b2o2bo6bo2bo89bobo
$893bo19bo325b4o7b2o90b2o$1237bobo58bobo42bo$997bo238bo2bo20bo37b2o$
937b2o57bobo237bo2bo18b2obo37bo$937bo58bobo238b2o19b2obo$937bo59bo261b
2o9b3o$1269bo2bo$1247bo23bo3bo$1245b3o27bo$1245bobo24bo7b3o$1246bo9bo
13bo5bo3bo2bo$884bo353bo17bo12b2obo8bo$883b2o354b2o15b3o2b3o5b2obob2ob
o$883bobo374bob2o7bo8bo$1261b3o5b2o6b2o3bo$1269bo7b2obob2o51bobo$1280b
ob2o51b2o$1281bo9bobo42bo$1282b2o7b2o$1247bobo33bo8bo$1247b2o5b5o$
1248bo4b3ob2o$1253b3o2b2o$1254bo2bo11b2o4b2o$1255bo4$833bobo197bobo$
832bo2bo197b2o$831b2o201bo$830bo497bobo$829b4o495b2o$828bo4bo5bobo346b
2o94bobo42bo$827b5o3b2obo2bo345b2obo93b2o$824b2o6b3o3bo348bo2bo49bobo
42bo$823bo3b3ob2o2bo4bo346b3o50b2o$822bo3bo4b4o4bo339b2o7b2o51bo$822bo
5bo6bo3bo2bo335bob2o$822b3o3b8obobo2bo2b2o331bo2bo$839bo2bob3o332b3o
17b2o$822b3o3b8obobo2bo2b2o7bo324b2o17bo2bo$822bo5bo6bo3bo2bo10b2o328b
3o5bo6b2o2bo9bo$822bo3bo4b4o4bo13bobo327bo2bob3o2bo3bo2bo10b3o$823bo3b
3ob2o2bo4bo338b2o2b2obo6bo2b5o9b2ob3o$824b2o6b3o3bo338bo3b2o2b2o6bo2b
2o2b2o7b2o3b2o$827b5o3b2obo2bo14b2o9bo308bo2bob2o5b4o6bo2bo8b2o8bo$
828bo4bo5bobo13bo3bo6b5o3bobo299bo13bo6b2o2b3o8bo6b3o99bobo$829b4o21bo
3bo5b2obob2o2bo19bo9b2obo268bo3b3o15b2o4bo4bob4o3b3ob2o98b2o$830bo23bo
4bobo2b3ob5obob2o14b4o6bo4bo16bo9b2obo238bo3b2o20b2o3bo6bo2b2o3b2o53bo
bo42bo$831b2o20bob3o4bo9b2obo15b2o2b3o3bo3bo3b3ob2o8b4o6bo4bo238b3o28b
o12b2o54b2o$832bo2bo16b3o6b10o19b2ob3o4b2ob3o5b3o8b2o2b3o3bo3bo3b3ob2o
232bo30bo2bo7bo12bobo42bo$833bobo17bob3o14bo3b2o11bo2b2o3bo11b5o7b2ob
3o4b2ob3o5b3o264b2o8b4obo8b2o$854bo4bob3o3bobo2b2o2bo2bo9bo8b9ob3o2bo
6bo2b2o3bo11b5o244bobo26bo6bo8bo$812bo41bo3bo4bobobo8bo3bo8bo2b2o3bo4b
o4b4o2b2o5bo8b9ob3o2bo244b2o33bo$763bobo45bobo41bo3bo8b2o7b2obo9b2ob3o
3b3obobo3b2ob2o6bo2b2o3bo4bo4b4o2b2o244bo4bo24bo2bo$762bo2bo46b3o24bo
16b2o21bo11b2o2b3o2b2ob2obo6bobo5b2ob3o3b3obobo3b2ob2o250b3o24b2o$761b
2o50b2o23b2o52b4o9bo8b2o6b2o2b3o2b2ob2obo6bobo250b2o13b2o$759bo4bo24b
2o47bobo52bo29b4o9bo8b2o116bobo131bo13bo2bo$758b2ob2o25bobo9b2o10bo17b
2o28b2o62bo138b2o129bobo14bo2bo$757bo4bobo25bo9b2o28b2o28b2o202bo130bo
15bo2bo$756b6o4b2o13b2o24b2o2bobo34b2o28b2o28b2o28bo273b2o$753b2o8b6o
12bo2b2ob3o17b2o3b3o32bobo27bobo27bobo28bo$752bo3b5obo5bo6b3o3bo4bo3bo
16b5o2bo33bo29bo29bo29bo375bobo$751bo3bo4b8o6bo2bo4bo2b2o3bo17bo5bo
499b2o$751bo5b3o13bo2b2o7bo22bo4bo456bobo42bo$751b3o3b3o3b2o8b3o10bo2b
o19bo3bo456b2o$763bo462bobo42bo$751b3o3b3o3b2o8b3o10bo2bo19bo3bo412b2o
$751bo5b3o13bo2b2o7bo22bo4bo368bobo42bo$751bo3bo4b8o6bo2bo4bo2b2o3bo
17bo5bo367b2o$752bo3b5obo5bo6b3o3bo4bo3bo16b5o2bo33bo29bo29bo29bo190bo
53bo$753b2o8b6o12bo2b2ob3o17b2o3b3o32bobo27bobo27bobo28bo187bob3o$756b
6o4b2o13b2o24b2o2bobo34b2o28b2o28b2o28bo186bo4b2o$757bo4bobo25bo9b2o
28b2o28b2o264b6o$758b2ob2o25bobo9b2o10bo17b2o28b2o62bo194bo6b2ob2o$
759bo4bo24b2o47bobo52bo29b4o9bo8b2o171b3ob2ob2ob3o$761b2o50b2o23b2o52b
4o9bo8b2o6b2o2b3o2b2ob2obo6bobo170b2o6b2obo$762bo2bo46b3o24bo16b2o21bo
11b2o2b3o2b2ob2obo6bobo5b2ob3o3b3obobo3b2ob2o172b7o2bo4b2o$763bobo45bo
bo41bo3bo8b2o7b2obo9b2ob3o3b3obobo3b2ob2o6bo2b2o3bo4bo4b4o2b2o172b2ob
2o5b3o7b3o166bobo$731bo9b2obo67bo41bo3bo4bobobo8bo3bo8bo2b2o3bo4bo4b4o
2b2o5bo8b9ob3o2bo173b3obo7b3o5bo2bo165b2o$730b4o6bo4bo108bo4bob3o3bobo
2b2o2bo2bo9bo8b9ob3o2bo6bo2b2o3bo11b5o175bobo14bobobo121bobo42bo$697bo
9b2obo18b2o2b3o3bo3bo3b3ob2o80bobo17bob3o14bo3b2o11bo2b2o3bo11b5o7b2ob
3o4b2ob3o5b3o171b2o4bo14b2o12b3o109b2o$390b2o9bo294b4o6bo4bo16b2ob3o4b
2ob3o5b3o80bo2bo16b3o6b10o19b2ob3o4b2ob3o5b3o8b2o2b3o3bo3bo3b3ob2o172b
3o17bobo9bo2bo65bobo42bo$389bo3bo6b5o3bobo284b2o2b3o3bo3bo3b3ob2o8bo2b
2o3bo11b5o79b2o20bob3o4bo9b2obo15b2o2b3o3bo3bo3b3ob2o8b4o6bo4bo177b3o
20b2ob2o6bo2bo65b2o$388bo3bo5b2obob2o2bo286b2ob3o4b2ob3o5b3o9bo8b9ob3o
2bo78bo23bo4bobo2b3ob5obob2o14b4o6bo4bo16bo9b2obo202bo2bo31bobo42bo$
388bo4bobo2b3ob5obob2o281bo2b2o3bo11b5o9bo2b2o3bo4bo4b4o2b2o76b4o21bo
3bo5b2obob2o2bo19bo9b2obo234b2o6b2o8b3o13b2o$387bob3o4bo9b2obo283bo8b
9ob3o2bo10b2ob3o3b3obobo3b2ob2o76bo4bo5bobo13bo3bo6b5o3bobo272bo9bo2bo
13bo$386b3o6b10o288bo2b2o3bo4bo4b4o2b2o10b2o2b3o2b2ob2obo6bobo73b5o3b
2obo2bo14b2o9bo225bobo29bo4bo28bo2bo$387bob3o14bo3b2o282b2ob3o3b3obobo
3b2ob2o12b4o9bo8b2o70b2o6b3o3bo254b2o29bo6bo8bo$388bo4bob3o3bobo2b2o2b
o2bo281b2o2b3o2b2ob2obo6bo2bo10bo91bo3b3ob2o2bo4bo253bo30bo4bo9bo21b2o
$388bo3bo4bobobo8bo3bo281b4o9bo8bo103bo3bo4b4o4bo13bobo276b2o29bo$389b
o3bo8b2o7b2obo282bo24bo99bo5bo6bo3bo2bo10b2o276bo2bo5bo10bo$390b2o21bo
306bobo10b2o87b3o3b8obobo2bo2b2o7bo276bo2bo5bo9bo2bo$733b2o104bo2bob3o
284b2ob2o18bo$431bo60bo59bo59bo59bo149b3o3b8obobo2bo2b2o286b2o9bo7b2o
5bo140bobo$430bobo58bobo57bobo57bobo57bobo148bo5bo6bo3bo2bo301bo8bo
146b2o$431b2o58bobo57bobo57bobo57bobo148bo3bo4b4o4bo301bob2o8bo8b2o92b
obo42bo$492bo59bo59bo59bo150bo3b3ob2o2bo4bo301b2o10bo5bo95b2o$251b2o9b
o195b2o364b2o6b3o3bo323b2o48bobo42bo$250bo3bo6b5o3bo164b2o21b3o367b5o
3b2obo2bo320bo49b2o$249bo3bo5b2obob2o3b2ob2o159bo3bo8b2o7b3o270bo99bo
4bo5bobo326bobo42bo$249bo4bobo2b3ob2o4bo162bo3bo4bobobo8bo2bo269bo101b
4o335b2o$248bob3o4bo7bobo5bo158bo4bob3o3bobo2b2o2bo272b3o100bo69b2o58b
2o58b2o58b2o42bobo42bo$247b3o6b10o165bob3o14bo3b2o375b2o66bo2bo56bo2bo
56bo2bo56bo2bo41b2o$248bob3o13bo6bo156b3o6b10o383bo2bo64b2o58b2o58b2o
58b2o43bo$249bo4bob3o3bob3o2b3o159bob3o4bo9b2obo379bobo29b2o$249bo3bo
4bobobo2bo5b2obo157bo4bobo2b3ob5obob2o385b2o21b3o$250bo3bo8b2o8b2o157b
o3bo5b2obob2o2bo388bo3bo8b2o7b3o203bo$251b2o180bo3bo6b5o3bobo384bo3bo
4bobobo8bo2bo202bobo$434b2o9bo393bo4bob3o3bobo2b2o2bo204bo3bo$838bob3o
14bo3b2o202b2o3bo222bobo$837b3o6b10o204bo8b2o222b2o$272b2o564bob3o4bo
9b2obo198bobo187bobo42bo$271b2o566bo4bobo2b3ob5obob2o195bo3bo2bob2ob3o
176b2o$273bo565bo3bo5b2obob2o2bo199bo3b2o2b2obob2o132bobo42bo$840bo3bo
6b5o3bobo196b2o8b2o2bo132b2o$841b2o9bo215b4o89bobo42bo$350b2o704b3ob2o
bo6bo90b2o$351b2o703b2obob2o99bo$350bo705bo2b2o30bo$1057b4o29bob2o$
1058bo31bob2o$1067bo23b2o$1067b2o32bo$1067b3o29b2obo$1067b2o30b2obo$
294bo772bo24bo7b2o184bobo$293b4o9bo8b2o775bobo191b2o$292b2o2b3o2b2ob2o
bo6bobo773b3o2b2o145bobo42bo$291b2ob3o3b3obobo3b2ob2o773b2ob2ob3o145b
2o$290bo2b2o3bo4bo4b4o2b2o442bo329b2ob2o105bobo42bo$290bo8b9ob3o2bo
442bo330b4o5bo2bo97b2o$290bo2b2o3bo11b5o442b3o339b3o52bobo42bo$291b2ob
3o4b2ob3o5b3o786bob2o49b2o$292b2o2b3o3bo3bo3b3ob2o784b2ob2o50bo$293b4o
6bo4bo792b4o$294bo9b2obo$347bobo$348b2o$348bo3$242b2o316bo9b2obo705bob
o$241b2o316b4o6bo4bo704b2o$206bobo34bo314b2o2b3o3bo3bo3b3ob2o653bobo
42bo$205bo2bo348b2ob3o4b2ob3o5b3o654b2o$204b2o350bo2b2o3bo11b5o610bobo
42bo$203bo352bo8b9ob3o2bo427bo182b2o$202b4o350bo2b2o3bo4bo4b4o2b2o425b
3o182bo$201bo4bo5bobo342b2ob3o3b3obobo3b2ob2o426bob2o$200b5o3b2obo2bo
343b2o2b3o2b2ob2obo6bo2bo426bo$197b2o6b3o3bo347b4o9bo8bo418bo9b3o$196b
o3b3ob2o2bo4bo346bo24bo413b3o$195bo3bo4b4o4bo370bobo412b2obo$195bo5bo
6bo3bo3bo781bo$195b3o3b8obobo4bo2b2ob2o771b3o$212bo5bob2ob2o$195b3o3b
8obobo4bo2b2ob2o2b2o779bo2bo19b2o$195bo5bo6bo3bo3bo9b2o238b2o9bo528bo
23bo2bo238bobo$195bo3bo4b4o4bo15bo236bo3bo6b5o3bo522bo5bo15bo2b2o238b
2o$196bo3b3ob2o2bo4bo250bo3bo5b2obob2o3b2ob2o299bo216bo3bo21bo2bo193bo
bo42bo$197b2o6b3o3bo252bo4bobo2b3ob2o4bo302bo212b3o3b2o2bo20b5o4b2o
186b2o$200b5o3b2obo2bo14b2o9bo222bob3o4bo7bobo5bo298b3o206bob9o4bobo
16b2o2b2o3bo2bo141bobo42bo$201bo4bo5bobo13bo3bo6b5o3bo214b3o6b10o517bo
5b2o24bo2bo5b2o2bo140b2o$202b4o21bo3bo5b2obob2o3b2ob2o14bo9b2obo183bob
3o13bo6bo131bo376b2o3bo25b3o2b2o3bo2bo143bo$203bo23bo4bobo2b3ob2o4bo
17b4o6bo4bo3b2o11bo9b2obo153bo4bob3o3bob3o2b3o134bo406bo4b2o2b5o$204b
2o20bob3o4bo7bobo5bo12b2o2b3o3bo3bo4b3o10b4o6bo4bo3b2o147bo3bo4bobobo
2bo5b3o130b3o377bo2bo25b2o7b2o2b2o$205bo2bo16b3o6b10o19b2ob3o4b2ob3o2b
ob3ob2o6b2o2b3o3bo3bo4b3o120bobo25bo3bo8b2o520bo38bo2bo$206bobo17bob3o
13bo6bo10bo2b2o3bo9b2o12b2ob3o4b2ob3o2bob3ob2o118b2o26b2o23bo546b2o2b
3o$227bo4bob3o3bob3o2b3o12bo8b10o12bo2b2o3bo9b2o125bo52bo546b2o4bo$
227bo3bo4bobobo2bo5b2obo9bo2b2o3bo4bo5bo3bo7bo8b10o189bo59bo481b2o$
136bobo89bo3bo8b2o11bo8b2ob3o3b3obob2obo3b2obo4bo2b2o3bo4bo5bo3bo183bo
bo57bobo$135bo2bo48bo24b2o15b2o20b3o10b2o2b3o2b2ob2o3bo4b2obo4b2ob3o3b
3obob2obo3b2obo180bobo57bobo$134b2o51bo23b2o52b4o9b2o7b3o5b2o2b3o2b2ob
2o3bo4b2obo180bo59bo$132bo4bo25b3o21bo25bo52bo29b4o9b2o7b3o710bo2bo
230bobo$131b2ob2o29bo8b2o28b2o28b2o61bo124b2o20b3o584b4o230b2o$130bo4b
obo24b2o10b2o11bo16b2o28b2o185bo3bo8b2o11bo93bo489bo2bo186bobo42bo$
129b6o19b3o3bo3bo16bo5b2o33b2o28b2o28b2o28bo107bo3bo4bobobo2bo5b2obo
94b4o9b2o7b3o33bo622b2o$126b2o8b3o2b3o5b3o2bo2bob2o3bo16bo3b2o34bobo
27bobo27bobo28bo107bo4bob3o3bob3o2b3o96b2o2b3o2b2ob2o3bo4b2obo10bo22b
2o622bo$125bo3b5obo6bo6b3o2b3obo3bo21b3o2bo32bo29bo29bo29bo106bob3o13b
o6bo93b2ob3o3b3obob2obo3b2obo10b4o9b2o7bo$124bo3bo4b9o6bo3bo5b3o23bo
233b3o6b10o100bo2b2o3bo4bo5bo3bo12b2o2b3o2b2ob2o3bo4b2o$124bo5b3o7b2o
5bo2b2o7b2o22bo3b2o230bob3o4bo7bobo5bo92bo8b10o16b2ob3o3b3obob2obo3b2o
bo$124b3o3b3o3b2o9b5o268bo4bobo2b3ob2o4bo96bo2b2o3bo9b2o14bo2b2o3bo4bo
5bo3bo$136bo283bo3bo5b2obob2o3b2ob2o93b2ob3o4b2ob3o2bob3ob2o7bo8b10o$
124b3o3b3o3b2o9b5o235b2o9bo22bo3bo6b5o3bo98b2o2b3o3bo3bo4b3o10bo2b2o3b
o9b2o$124bo5b3o7b2o5bo2b2o7b2o22bo3b2o197bo3bo6b5o3bobo14b2o9bo106b4o
6bo4bo3b2o11b2ob3o4b2ob3o2bob3ob2o351bo$124bo3bo4b9o6bo3bo5b3o23bo200b
o3bo5b2obob2o2bo136bo9b2obo18b2o2b3o3bo3bo4b3o353bobo$125bo3b5obo6bo6b
3o2b3obo3bo21b3o2bo32bo29bo29bo29bo72bo4bobo2b3ob5obob2o165b4o6bo4bo3b
2o352b2obo$126b2o8b3o2b3o5b3o2bo2bob2o3bo16bo3b2o34bobo27bobo27bobo28b
o71bob3o4bo9b2obo168bo9b2obo360bo$129b6o19b3o3bo3bo16bo5b2o33b2o28b2o
28b2o28bo70b3o6b10o537bo$130bo4bobo24b2o10b2o11bo16b2o28b2o148bob3o14b
o3b2o409bo119bobo317bobo$131b2ob2o29bo8b2o28b2o28b2o61bo87bo4bob3o3bob
o2b2o2bo409bo120bob2o316b2o$132bo4bo25b3o21bo25bo52bo29b4o9b2o7b3o64bo
3bo4bobobo8bo2bo406b3o119bo7bo266bobo42bo$134b2o51bo23b2o52b4o9b2o7b3o
5b2o2b3o2b2ob2o3bo4b2obo65bo3bo8b2o7b3o534bo2b2o264b2o$135bo2bo48bo24b
2o15b2o20b3o10b2o2b3o2b2ob2o3bo4b2obo4b2ob3o3b3obob2obo3b2obo67b2o21b
3o297bo234bo5bo263bo$136bobo89bo3bo8b2o11bo8b2ob3o3b3obob2obo3b2obo4bo
2b2o3bo4bo5bo3bo94b2o298bo233b2o2bo$227bo3bo4bobobo2bo5b2obo9bo2b2o3bo
4bo5bo3bo7bo8b10o397b3o230b2o4b2ob2o18b3o$227bo4bob3o3bob3o2b3o12bo8b
10o12bo2b2o3bo9b2o51bo9b2obo562bo9b2o18bo2bo$206bobo17bob3o13bo6bo10bo
2b2o3bo9b2o12b2ob3o4b2ob3o2bob3ob2o43b4o6bo4bo558bo2b3o27bobobo$205bo
2bo16b3o6b10o19b2ob3o4b2ob3o2bob3ob2o6b2o2b3o3bo3bo4b3o45b2o2b3o3bo3bo
3b3ob2o553bo33b2o$204b2o20bob3o4bo7bobo5bo12b2o2b3o3bo3bo4b3o10b4o6bo
4bo3b2o44b2ob3o4b2ob3o5b3o551b2ob2o30bobo5b3o$203bo23bo4bobo2b3ob2o4bo
17b4o6bo4bo3b2o11bo9b2obo49bo2b2o3bo11b5o552b2o29b2ob2o6bo2bo$202b4o
21bo3bo5b2obob2o3b2ob2o14bo9b2obo80bo8b9ob3o2bo583bo2bo6bobobo$201bo4b
o5bobo13bo3bo6b5o3bo112bo2b2o3bo4bo4b4o2b2o583b2o7b2o$200b5o3b2obo2bo
14b2o9bo120b2ob3o3b3obobo3b2ob2o594bobo$197b2o6b3o3bo150b2o2b3o2b2ob2o
bo6bobo593b2ob2o$196bo3b3ob2o2bo4bo149b4o9bo8b2o594bo2bo266bobo$195bo
3bo4b4o4bo15bo135bo617b2o267b2o$195bo5bo6bo3bo3bo9b2o1024bo$195b3o3b8o
bobo4bo2b2ob2o2b2o$212bo5bob2ob2o748bo$195b3o3b8obobo4bo2b2ob2o747b2ob
o$195bo5bo6bo3bo3bo756bobo$195bo3bo4b4o4bo761bo$196bo3b3ob2o2bo4bo767b
o$197b2o6b3o3bo100b2o9bo657bo$200b5o3b2obo2bo96bo3bo6b5o3bobo$201bo4bo
5bobo95bo3bo5b2obob2o2bo99bo$202b4o104bo4bobo2b3ob5obob2o96b2o$203bo
105bob3o4bo9b2obo97b2o$204b2o102b3o6b10o521bo$205bo2bo100bob3o14bo3b2o
15bo497bo$206bobo34bo66bo4bob3o3bobo2b2o2bo2bo13b2o496b3o394bobo$241b
2o67bo3bo4bobobo8bo3bo11bobo537b2o354b2o$242b2o67bo3bo8b2o7b2obo463bo
86bo2bo354bo$312b2o21bo465bo85b2o2bo$349bo449b3o90bo$348b4o527b2o4b2ob
2o$292bo9b2obo42bo3bo525bo2bo4bo2bo$291b4o6bo4bo41bo3bo524bo2b2o5bo3bo
$290b2o2b3o3bo3bo3b3ob2o34bo2bo524bo9b2obo$289b2ob3o4b2ob3o5b3o35bo
530b2ob2o3bo3b2o$288bo2b2o3bo11b5o32b5o529bo2bo5bo4bo$288bo8b9ob3o2bo
33bobo528bo3bo8bo$288bo2b2o3bo4bo4b4o2b2o33bo531bob2o$289b2ob3o3b3obob
o3b2ob2o563b2o3bo$290b2o2b3o2b2ob2obo6bo2bo559bo4bo30b3o$291b4o9bo8bo
564bo31bo2bo$292bo24bo592bo3bo$315bobo592bo2bo$886bo2bo21bobo5b3o$349b
2o58b2o58b2o58b2o58b2o58b2o58b2o58b2o58b2o53b3o2b3o27bo2bo$348bo2bo56b
o2bo56bo2bo56bo2bo56bo2bo56bo2bo56bo2bo56bo2bo56bo2bo54bo2bo28bo3bo$
349b2o58b2o58b2o58b2o58b2o58b2o58b2o58b2o58b2o88bo2bo$337b2o577bo2bobo
$313b2o21b3o179b2o58b2o58b2o58b2o58b2o58b2o90b2o3b3o$312bo3bo8b2o7b3o
180bo2bo56bo2bo56bo2bo56bo2bo56bo2bo56bo2bo87bob2ob2o3bo$311bo3bo4bobo
bo8bo2bo181b2o58b2o58b2o58b2o58b2o58b2o86b3o2bo2bob2ob2o$311bo4bob3o3b
obo2b2o2bo574bob2ob4o4b2o$310bob3o14bo3b2o155b2o21bo395b3o6b3o2b2o$
309b3o6b10o161bo3bo8b2o7b2obo394b2o7bo2bo2b2o$310bob3o4bo9b2obo155bo3b
o4bobobo8bo3bo404bobo2b2o$273bo37bo4bobo2b3ob5obob2o153bo4bob3o3bobo2b
2o2bo2bo405bo3b2o$274b2o35bo3bo5b2obob2o2bo156bob3o14bo3b2o408b4o$273b
3o36bo3bo6b5o3bobo152b3o6b10o416b3o$274b2o37b2o9bo162bob3o4bo9b2obo$
249b2o237bo4bobo2b3ob5obob2o$248bo3bo8b2o225bo3bo5b2obob2o2bo$247bo3bo
4bobobo2bo5b3o217bo3bo6b5o3bobo$247bo4bob3o3bob3o2b3o220b2o9bo$246bob
3o13bo6bo$245b3o6b10o$246bob3o4bo7bobo5bo$247bo4bobo2b3ob2o4bo$247bo3b
o5b2obob2o3b2ob2o$248bo3bo6b5o3bo$249b2o9bo8$587b2o9bo251b3o$586bo3bo
6b5o3bo243bo2bo$553b2o9bo20bo3bo5b2obob2o3b2ob2o241bo3bo$552bo3bo6b5o
3bo13bo4bobo2b3ob2o4bo249bo$148b2o9bo391bo3bo5b2obob2o3b2ob2o8bob3o4bo
7bobo5bo242bo7b3o$147bo3bo6b5o3bobo382bo4bobo2b3ob2o4bo11b3o6b10o248bo
5bo3bo2bo$146bo3bo5b2obob2o2bo384bob3o4bo7bobo5bo8bob3o13bo6bo239b2obo
8bo$146bo4bobo2b3ob5obob2o379b3o6b10o17bo4bob3o3bob3o2b3o241b2obob2obo
$145bob3o4bo9b2obo382bob3o13bo6bo9bo3bo4bobobo2bo5b2obo240bo8bo$144b3o
6b10o388bo4bob3o3bob3o2b3o12bo3bo8b2o11bo236b2o6b2o3bo$145bob3o14bo3b
2o381bo3bo4bobobo2bo5b2obo10b2o20b3o237bo7b2obob2o$146bo4bob3o3bobo2b
2o2bo383bo3bo8b2o8b2o283bob2o$146bo3bo4bobobo8bo2bo381b2o306bo$147bo3b
o8b2o7b3o432b2o256b2o$148b2o21b3o430b2o257bo$172b2o9bo59bo59bo59bo59bo
59bo59bo$182bobo57bobo57bobo57bobo57bobo57bobo57bobo$182bobo57bobo57bo
bo57bobo57bobo57bobo57bobo$183bo59bo59bo59bo59bo59bo59bo305b2o4b2o11$
470b2o9bo109bobo$469bo3bo6b5o3bo102b2o$468bo3bo5b2obob2o3b2ob2o99bo$
468bo4bobo2b3ob2o4bo$467bob3o4bo7bobo5bo$466b3o6b10o$467bob3o13bo6bo$
468bo4bob3o3bob3o2b3o$468bo3bo4bobobo2bo5b2obo298bo$469bo3bo8b2o8b2o
297b3o$148bo321b2o318b2ob3o$147b2o640b2o3b2o$147bobo640b2o8bo$447bo9b
2obo331bo6b3o$446b4o6bo4bo3b2o321bob4o3b3ob2o$445b2o2b3o3bo3bo4b3o20b
2o298bo6bo2b2o3b2o$444b2ob3o4b2ob3o2bob3ob2o18b2o298bo12b2o$443bo2b2o
3bo9b2o24bo301bo2bo7bo$106bobo334bo8b10o327b2o8b4obo$105bo2bo334bo2b2o
3bo4bo5bo3bo331bo6bo$104b2o338b2ob3o3b3obob2obo3b2obo334bo$103bo267b2o
9bo62b2o2b3o2b2ob2o3bo4b2o331bo2bo$102b4o264bo3bo6b5o3bo56b4o9b2o7bo
333b2o$101bo4bo5bobo109bo9b2obo99b2o9bo20bo3bo5b2obob2o3b2ob2o53bo22b
2o320b2o$100b5o3b2obo2bo108b4o6bo4bo3b2o23bo9b2obo55bo3bo6b5o3bo13bo4b
obo2b3ob2o4bo80bo320bo2bo$97b2o6b3o3bo110b2o2b3o3bo3bo4b3o22b4o6bo4bo
53bo3bo5b2obob2o3b2ob2o8bob3o4bo7bobo5bo397bo2bo$96bo3b3ob2o2bo4bo107b
2ob3o4b2ob3o2bob3ob2o18b2o2b3o3bo3bo3b3ob2o46bo4bobo2b3ob2o4bo11b3o6b
10o103bobo299bo2bo$95bo3bo4b4o4bo107bo2b2o3bo9b2o24b2ob3o4b2ob3o5b3o
46bob3o4bo7bobo5bo8bob3o13bo6bo96b2o300b2o$95bo5bo6bo3bo2bo104bo8b10o
24bo2b2o3bo11b5o45b3o6b10o17bo4bob3o3bob3o2b3o98bo$95b3o3b8obobo2bo4bo
bo97bo2b2o3bo4bo5bo3bo19bo8b9ob3o2bo46bob3o13bo6bo9bo3bo4bobobo2bo5b3o
$112bo2bo4b3o98b2ob3o3b3obob2obo3b2obo16bo2b2o3bo4bo4b4o2b2o46bo4bob3o
3bob3o2b3o12bo3bo8b2o236bobo$95b3o3b8obobo2bo4bobo99b2o2b3o2b2ob2o3bo
4b2o18b2ob3o3b3obobo3b2ob2o47bo3bo4bobobo2bo5b2obo10b2o23bo224b2o$95bo
5bo6bo3bo2bo107b4o9b2o7bo19b2o2b3o2b2ob2obo6bobobo44bo3bo8b2o11bo33bo
225bo$95bo3bo4b4o4bo111bo41b4o9bo8b2obo45b2o20b3o$96bo3b3ob2o2bo4bo
153bo21b2o$97b2o6b3o3bo$100b5o3b2obo2bo178bo59bo$101bo4bo5bobo177bobo
57bobo$102b4o186bobo57bobo$103bo189bo59bo$104b2o12bo$105bo2bo8b2o$106b
obo8bobo2$239bo$238b2o169b2o$203bobo32bobo169b2o$202bo2bo203bo$201b2o
528b3o$200bo529bo2bo$199b4o527bo2bo$198bo4bo5bobo$197b5o3b2obo2bo517b
2o8b3o$194b2o6b3o3bo520bo9bo2bo$193bo3b3ob2o2bo4bo528bo2bo$103bo88bo3b
o4b4o4bo$102b2o88bo5bo6bo3bo2bo366bobo160b2o$102bobo87b3o3b8obobo2bo4b
obo136b2o222b2o161bo$209bo2bo4b3o135bo3bo8b2o7b2o201bo$192b3o3b8obobo
2bo4bobo4bo41b2o9bo76bo3bo4bobobo8bo2bo353bo$105b2o9bo75bo5bo6bo3bo2bo
10b2o40bo3bo6b5o3bo69bo4bob3o3bobo2b2o2bo274bobo80bo$104bo3bo6b5o3bobo
66bo3bo4b4o4bo13bobo6b2o9bo20bo3bo5b2obob2o3b2ob2o64bob3o14bo3b2o273b
2o79b2o5bo$103bo3bo5b2obob2o2bo20bo9b2obo36bo3b3ob2o2bo4bo20bo3bo6b5o
3bo13bo4bobo2b3ob2o4bo67b3o6b10o281bo77bo2bo$103bo4bobo2b3ob5obob2o15b
4o6bo4bo3b2o31b2o6b3o3bo21bo3bo5b2obob2o3b2ob2o8bob3o4bo7bobo5bo64bob
3o4bo9b2obo357bo8b2o$102bob3o4bo9b2obo16b2o2b3o3bo3bo4b3o34b5o3b2obo2b
o18bo4bobo2b3ob2o4bo11b3o6b10o73bo4bobo2b3ob5obob2o356bo5bo$101b3o6b
10o20b2ob3o4b2ob3o2bob3ob2o32bo4bo5bobo17bob3o4bo7bobo5bo8bob3o13bo6bo
65bo3bo5b2obob2o2bo368b2o$102bob3o14bo3b2o12bo2b2o3bo9b2o40b4o25b3o6b
10o17bo4bob3o3bob3o2b3o68bo3bo6b5o3bobo365bo$103bo4bob3o3bobo2b2o2bo2b
o10bo8b10o42bo28bob3o13bo6bo9bo3bo4bobobo2bo5b3o67b2o9bo$61bo41bo3bo4b
obobo8bo3bo9bo2b2o3bo4bo5bo3bo38b2o27bo4bob3o3bob3o2b3o12bo3bo8b2o$12b
obo45bobo41bo3bo8b2o7b2obo10b2ob3o3b3obob2obo3b2obo36bo2bo24bo3bo4bobo
bo2bo5b2obo10b2o23bo$11bo2bo46b3o24bo16b2o21bo12b2o2b3o2b2ob2o3bo4b2o
38bobo25bo3bo8b2o11bo33bo$10b2o50b2o23b2o53b4o9b2o7bo67b2o20b3o$8bo4bo
24b2o47bobo53bo22b2o111b2o$7b2ob2o25bobo9b2o10bo17b2o28b2o55bo112b2o$
6bo4bobo25bo9b2o28b2o28b2o77bo20bo8bo29bo$5b6o4b2o13b2o24b2o2bobo34b2o
28b2o28b2o28bobo18b2o7bobo27bobo$2b2o8b6o12bo2b2ob3o17b2o3b3o32bobo27b
obo27bobo28bobo18bobo6bobo27bobo259b2o9bo$bo3b5obo5bo6b3o3bo4bo3bo16b
5o2bo33bo29bo29bo30bo29bo29bo259bo3bo6b5o3bo$o3bo4b8o6bo2bo4bo2b2o3bo
17bo5bo443bo3bo5b2obob2o3b2ob2o$o5b3o13bo2b2o7bo22bo4bo444bo4bobo2b3ob
2o4bo$3o3b3o3b2o8b3o10bo2bo19bo3bo443bob3o4bo7bobo5bo$12bo492b3o6b10o$
3o3b3o3b2o8b3o10bo2bo19bo3bo443bob3o13bo6bo$o5b3o13bo2b2o7bo22bo4bo
444bo4bob3o3bob3o2b3o$o3bo4b8o6bo2bo4bo2b2o3bo17bo5bo443bo3bo4bobobo2b
o5b2obo$bo3b5obo5bo6b3o3bo4bo3bo16b5o2bo33bo29bo29bo30bo319bo3bo8b2o
11bo$2b2o8b6o12bo2b2ob3o17b2o3b3o32bobo27bobo27bobo28bobo78bobo238b2o
20b3o137bo$5b6o4b2o13b2o24b2o2bobo34b2o28b2o28b2o28bobo78b2o400bob2o$
6bo4bobo25bo9b2o28b2o28b2o77bo80bo280b2o58b2o58bob2o$7b2ob2o25bobo9b2o
10bo17b2o28b2o55bo52b2o328bo2bo56bo2bo58b2o$8bo4bo24b2o47bobo53bo22b2o
51b2o329b2o58b2o69bo$10b2o50b2o23b2o53b4o9b2o7bo7b2o20b3o482b2obo$11bo
2bo46b3o24bo16b2o21bo12b2o2b3o2b2ob2o3bo4b2o6bo3bo8b2o11bo33bo59b2o28b
2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o26b2obo$12bob
o45bobo41bo3bo8b2o7b2obo10b2ob3o3b3obob2obo3b2obo4bo3bo4bobobo2bo5b2ob
o10b2o23bo58bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo2bo26bo
2bo26bo2bo26bo2bo26bo2bo26bo2bo26b2o$61bo41bo3bo4bobobo8bo3bo9bo2b2o3b
o4bo5bo3bo7bo4bob3o3bob3o2b3o12bo3bo8b2o71b2o28b2o28b2o28b2o28b2o28b2o
28b2o28b2o28b2o28b2o28b2o28b2o28b2o$103bo4bob3o3bobo2b2o2bo2bo10bo8b
10o11bob3o13bo6bo9bo3bo4bobobo2bo5b3o45b2o$102bob3o14bo3b2o12bo2b2o3bo
9b2o9b3o6b10o17bo4bob3o3bob3o2b3o23b2o21b3o$101b3o6b10o20b2ob3o4b2ob3o
2bob3ob2o3bob3o4bo7bobo5bo8bob3o13bo6bo20bo3bo8b2o7b3o388b2o20b3o$102b
ob3o4bo9b2obo16b2o2b3o3bo3bo4b3o7bo4bobo2b3ob2o4bo11b3o6b10o27bo3bo4bo
bobo8bo2bo387bo3bo8b2o11bo$103bo4bobo2b3ob5obob2o15b4o6bo4bo3b2o7bo3bo
5b2obob2o3b2ob2o8bob3o4bo7bobo5bo19bo4bob3o3bobo2b2o2bo389bo3bo4bobobo
2bo5b2obo$103bo3bo5b2obob2o2bo20bo9b2obo14bo3bo6b5o3bo13bo4bobo2b3ob2o
4bo22bob3o14bo3b2o388bo4bob3o3bob3o2b3o$104bo3bo6b5o3bobo46b2o9bo20bo
3bo5b2obob2o3b2ob2o17b3o6b10o394bob3o13bo6bo$105b2o9bo88bo3bo6b5o3bo
22bob3o4bo9b2obo388b3o6b10o$206b2o9bo30bo4bobo2b3ob5obob2o387bob3o4bo
7bobo5bo$248bo3bo5b2obob2o2bo392bo4bobo2b3ob2o4bo$102bobo144bo3bo6b5o
3bobo389bo3bo5b2obob2o3b2ob2o$102b2o146b2o9bo399bo3bo6b5o3bo$103bo558b
2o9bo2$468bo$468b2o$467bobo9$106bobo8bobo124b2o9bo$105bo2bo8b2o124bo3b
o6b5o3bobo$104b2o12bo123bo3bo5b2obob2o2bo$103bo138bo4bobo2b3ob5obob2o$
102b4o135bob3o4bo9b2obo$101bo4bo5bobo125b3o6b10o$100b5o3b2obo2bo126bob
3o14bo3b2o$97b2o6b3o3bo130bo4bob3o3bobo2b2o2bo$96bo3b3ob2o2bo4bo128bo
3bo4bobobo8bo2bo$95bo3bo4b4o4bo130bo3bo8b2o7b2o$95bo5bo6bo3bo2bo128b2o
$95b3o3b8obobo2bo2b2o$112bo2bob3o$95b3o3b8obobo2bo2b2o$95bo5bo6bo3bo2b
o$95bo3bo4b4o4bo19bobo$96bo3b3ob2o2bo4bo18b2o$97b2o6b3o3bo21bo$100b5o
3b2obo2bo$101bo4bo5bobo263bo$102b4o191bo80b2o$103bo194b2o77bobo$104b2o
191b2o$105bo2bo$106bobo4$180bo60bo$179bobo58bobo$180b2o58bobo$241bo2$
167bo21b2o$124bo41b4o9bo8b2obo33b2o20b3o55bo$123b4o9b2o7bo19b2o2b3o2b
2ob2obo6bobobo32bo3bo8b2o11bo33bo19b4o9b2o7bo$122b2o2b3o2b2ob2o3bo4b2o
18b2ob3o3b3obobo3b2ob2o35bo3bo4bobobo2bo5b2obo10b2o23bo18b2o2b3o2b2ob
2o3bo4b2o$121b2ob3o3b3obob2obo3b2obo16bo2b2o3bo4bo4b4o2b2o34bo4bob3o3b
ob3o2b3o12bo3bo8b2o29b2ob3o3b3obob2obo3b2obo$120bo2b2o3bo4bo5bo3bo19bo
8b9ob3o2bo34bob3o13bo6bo9bo3bo4bobobo2bo5b3o19bo2b2o3bo4bo5bo3bo$120bo
8b10o24bo2b2o3bo11b5o33b3o6b10o17bo4bob3o3bob3o2b3o21bo8b10o$120bo2b2o
3bo9b2o24b2ob3o4b2ob3o5b3o34bob3o4bo7bobo5bo8bob3o13bo6bo19bo2b2o3bo9b
2o$121b2ob3o4b2ob3o2bob3ob2o18b2o2b3o3bo3bo3b3ob2o34bo4bobo2b3ob2o4bo
11b3o6b10o28b2ob3o4b2ob3o2bob3ob2o$122b2o2b3o3bo3bo4b3o22b4o6bo4bo41bo
3bo5b2obob2o3b2ob2o8bob3o4bo7bobo5bo21b2o2b3o3bo3bo4b3o$123b4o6bo4bo3b
2o23bo9b2obo43bo3bo6b5o3bo13bo4bobo2b3ob2o4bo26b4o6bo4bo3b2o$124bo9b2o
bo87b2o9bo20bo3bo5b2obob2o3b2ob2o23bo9b2obo$258bo3bo6b5o3bo$259b2o9bo$
328b2o20b3o$327bo3bo8b2o11bo$326bo3bo4bobobo2bo5b2obo$326bo4bob3o3bob
3o2b3o$325bob3o13bo6bo$324b3o6b10o$325bob3o4bo7bobo5bo$326bo4bobo2b3ob
2o4bo$326bo3bo5b2obob2o3b2ob2o$327bo3bo6b5o3bo$328b2o9bo!

A gun should also be possible, although my initial attempts suggest that a different gun arrangement is need to add the final R-pentomino. If done naively the newly created rake promptly hoses the gun with its gliders! [EDIT: Ah! One eater fixes that problem.]

[Paul Tooke]

Here is a gun for Sokwes nice 5-engine rake. It's composed of 2.5 copies of Calcymans p480 gun with some of the parts rearranged and a strategically placed eater to prevent the glider backwash fron destoying the gun. As with the rake puffer, it may be possible to reduces its size. I just kept adding components until I got something that worked.

Code: Select all

x = 592, y = 354, rule = B37/S23
258bo$257bobo$256bo3bo$256b2o2bo$256b2ob2o$257bobo$258bo19$282b2o$278b
2o2b2o2b2o$278bobo2bo2b2o$279b3o$280b2o2$264b3o19bo5bo$264bobo19b2o3b
2o$266bo12b2o5b2o3b2o$263bobo13bobo5bo3bo$262bo16bo$262bo$301bo$263bo
24b3o5bo2bo2bo$264b2o33bo2bo$210bo78bo10bo$208b3o74b3o$207bo59b2o3b2o
15bo10bo$207b2o57bo7bo24bo2bo$269bobo16b3o5bo2bo2bo$267b2o3b2o27bo2$
298b2o$297bo2bo$257b3o38bobo$258b3o6bo5bo22b2obo$266bobo4b2o12bo8b3o$
272bobo13bo7b2o$266b3o17b3o22bo$258b3o15bo32b3o$257b3o15bo32bo$273bo2b
o31b2o$266b3o5bo$260b2o10bobo41bo$259bo2bo3bobo4bo41bob2o$259bobo2bo2b
o5bo45bo$260bo45bo5bo2bo2bobo$261b2obo41bo4bobo3bo2bo$263bo41bobo10b2o
$305bo5b3o$270b2o31bo2bo$271bo32bo15b3o$268b3o32bo15b3o$268bo22b3o17b
3o$282b2o7bo13bobo$281b3o8bo12b2o4bobo$280bob2o22bo5bo6b3o$279bobo38b
3o$279bo2bo$280b2o2$278bo27b2o3b2o$277bo2bo2bo5b3o16bobo41bo5bo$277bo
2bo24bo7bo38b2o3b2o$279bo10bo15b2o3b2o39b2o3b2o$292b3o58bo3bo6b2o$279b
o10bo73bo$277bo2bo81bobo$277bo2bo2bo5b3o51bo10b3o5b2o$278bo18b2o43bo2b
o8b3o$297bobo42bo2bo9bo$299bo44bo$288bo3bo6b2o$287b2o3b2o50bo26b2o3b2o
$287b2o3b2o48bo2bo9bo14bo7bo$267b2o3b2o13bo5bo48bo2bo8b3o16bobo$266bo
7bo68bo10b3o14b2o3b2o$174bo94bobo5b2o$172b2o93b2o3b2o2bo2bo65b2o$173b
2o101bobobo63bo2bo$277bob3o62bobo23bo14b3o$279b3o63bob2o20b2o6bo6b3o$
346b3o20bobo4b3o$273bo73b2o7bo18b2ob2o$272b3o58bo21bo20b3o$260b3o8b2ob
2o57b3o19b3o19bo6b3o$261b3o8b3o10b2o49bo31b2o15b3o$273bo11bo49b2o32b2o
6bo$283bobo83bobo4b3o$273bo9b2o43bo41b2o3b2ob2o3b2o$261b3o8b3o51b2obo
39bo2bo3b3o3bo2bo$260b3o8b2ob2o49bo44b2o5bo2bo2bobo$272b3o49bobo2bo2bo
5b2o44bo$273bo50bo2bo3b3o3bo2bo39bob2o$325b2o3b2ob2o3b2o41bo$295bo5bo
29b3o4bobo$295b2o3b2o30bo6b2o32b2o$252bo21b2o14b2o3b2o3b2o20b3o15b2o
31bo$252b3o18b2o14bo2bo3bo3bo22b3o6bo19b3o19b3o$207bo5bo41bo19bo11bo2b
obo38b3o20bo21bo$207b2o3b2o40b2o35bo38b2ob2o18bo7b2o91bo5bo$207b2o3b2o
3b2o48bo19bob2o6b3o31b3o4bobo20b3o90b2o3b2o$208bo3bo3bo2bo48b2o18bo8b
3o23b3o6bo6b2o20b2obo89b2o3b2o3b2o$216bobo2bo28bo16b2o29bo23b3o14bo23b
obo89bo3bo3bo2bo$217bo31bo2bo54bo54bo2bo97bobo2bo75b2o3b2o$218b2obo27b
o2bo52bo2bo54b2o99bo78bo7bo$220bo30bo6b3o44bo2bo156b2obo77bobo$213bo
44b3o37bo7bo25b2o3b2o14b3o10bo89b3o8bo76b2o3b2o5b2o$201bo11bo37bo7bo
37b3o34bobo16b3o8bo2bo188bo$200bo2bo8bobo34bo2bo44b3o6bo24bo7bo14bo9bo
2bo80bo8bo96bobo$200bo2bo9bo11b2o22bo2bo52bo2bo3b2o18b2o3b2o26bo81bo2b
o2b3o4bo93b2o$202bo10bo11bo24bo54bo2bo3b2o133bo2bo6bo5bo8b2o60b3o$223b
obo33bo29b2o16bo57bo83bo13bo8bo62b3o$202bo10bo9b2o33b3o8bo18b2o23bo15b
2o23bo9bo2bo88b3o3b3o5bobo$200bo2bo9bo44b3o6b2obo19bo10bobo8bobo13bo
24b3o8bo2bo81bo14bo5b2o$200bo2bo8bobo51bo35b2o7bo2bo38b3o10bo80bo2bo
92b3o3b3o11bo5bo$201bo11bo51bobo2bo11bo19bo7bo2bo13bo119bo2bo10bob2ob
2o67b3o4bo3bobo3bo10b2o3b2o$213bo43bo3bo3bo2bo14b2o42bo120bo13b2o2bo
67b3o5bo3bobo3bo3b2o5b2o3b2o$256b2o3b2o3b2o14b2o26bo2bo14bobo12bo8bo3b
o96bobo10bo75bo3bobo3bo3bobo5bo3bo$235b2o3b2o14b2o3b2o49b2o17bo11bobo
5b2o3b2o95b2o7bo2bo77b3o3b3o4bo$234bo7bo13bo5bo66bobo11b2o6b2o3b2o96bo
8b2o17b2o3b2o48b2o$192bo37b2o5bobo89b3o19bo5bo123bo7bo46bo2bo38bo$192b
3o19b3o12bo2bo2b2o3b2o42bo154bo37b2o5bobo49bobobo24b3o5bo2bo2bo$195bo
18bo15bobo50b3o59b2o92b3o34bo2bo2b2o3b2o48bo2bo35bo2bo$194b2o9b2o8bo
12b2obo50b2ob2o8b3o46b3o95bo34bobo61bo24bo10bo$205b3o20b3o7bo44b3o8b3o
46bobo2bo2b2o88b2o32b2obo59bobo21b3o$204b2ob2o19b2o8bo34b2o9bo58b2o2b
2o2b2o122b3o47bo40bo10bo$204b3obo28bobo32bobo32bo39b2o126b2o48b3o48bo
2bo$189b3o13b5o31bo30bo11bo21bobo219bo36b3o5bo2bo2bo$190b3o12b3o31bobo
4b3o22b2o10b3o8b3o8b2obo127b3o88b2o49bo$199bo6bo34bo3b3o34b2ob2o8b3o8b
obo128b3o2b3o3b3o42b3o$199bo4bobo30bobo43b3o121b2o3b2o27bo3bobo3bo8bo
20b3o3b3o2b3o24b2o21bobo30b2o$198bobo30bobo4bo45bo24b2o95bo7bo26bo3bob
o3bo9bo8b3o7bo3bobo3bo27b3o21b2o30bo2bo$190b3o3bo34bo6bo170bobo5b2o22b
o3bobo3bo7b3o8bo9bo3bobo3bo26bob2o22bo31bobo$189b3o4bobo31b3o12b3o4b2o
22b3o128b2o3b2o2bo2bo17b3o2b3o3b3o20bo8bo3bobo3bo25bobo31bo22b2obo$
196bo31b5o13b3o3b2o22b3obo27bo107bobo17b3o42b3o3b3o2b3o4b2o15bo2bo30b
2o21b3o$198bobo28bob3o43bobobo26bo24bo83bob2o72b3o3b2o16b2o30bobo21b2o
$199bo8b2o19b2ob2o8bo35bo2bo2b2o3b2o41b3o83b3o78b2o$199bo7b3o20b3o7bob
o8bob2o24b2o5bobo42b3obo83b2o34b2o43bo14bo49b2o$206bob2o12bo8b2o8b2o8b
obo29bo7bo38b2obo2bo117b3o42bobo12bo2bo2bo5b3o36bo$205bobo15bo28bo31b
2o3b2o40b2o79b3o38bob2o41b2obo12bo2bo48b3o$196b2o3b2o2bo2bo12b3o28b2o
77b2ob2o64b3o9bobo37bobo61bo10bo40bo$198bobo5b2o44b2o79bo67b3o8b3o10b
2o16b2o3b2o2bo2bo73b3o21bobo$195bo7bo48b2o171bo19bobo5b2o44b2o15bo10bo
24bo$196b2o3b2o220bobo16bo7bo44b2o2b2o13bo2bo35bo2bo$323bo99b2o18b2o3b
2o17b2o8bo15bobo18bo2bo2bo5b3o24bobobo$224bo98bobo75b3o8b3o51bo2bo7b2o
15b2o19bo38bo2bo$224bo11bo86b2o75b3o9bobo50bo10bobo76b2o$223bobo8bo2bo
174b3o50bo2b2o13bo53bo4b3o3b3o$224bo9bo2bo16b2o208b2ob2obo10bo2bo40bo
3bo5bobo3bo3bobo3bo$213b2o9bo10bo7b3o8b2o225bo2bo39b2o3b2o5b2o3bo3bobo
3bo5b3o$212bobo27bo192bo5bo18b2o5bo14bo41b2o3b2o10bo3bobo3bo4b3o$212bo
11bo10bo5bo4bo188b2o3b2o17bobo5b3o3b3o48bo5bo11b3o3b3o$211b2o11bo9bo2b
o3bob3o146bo22bo14b2o3b2o3b2o17bo8bo13bo$223bobo8bo2bo7b2o145b3o19b2o
13bo2bo3bo3bo17b2o8bo5bo6bo2bo$224bo11bo5bo2bo149bo18bobo11bobobo38bo
4b3o2bo2bo4bo66b3o$224bo18b3o148b2o9bobo20bo2bo42bo8bo8b2o63b3o$217bo
190bo18bo61b2ob2o$216bob2o186bobo19bobo6b3o24bo8b3o14bob2o$220bo169bo
16bo30bo24bob2o24bo33bo$216bo2bobo167bo2bo16bo28bo8bo19bo55b2ob2o15b2o
3b2o$218bo2bo3bo3bo159bo2bo48b2o2bo2bo14bo2bobo57b2o17bobo$219b2o3b2o
3b2o160bo46bo6bo2bo16bo2bo3bo3bo45bo2bob2o13bo7bo$224b2o3b2o167b3o4bo
32bo7bo19b2o3b2o3b2o45bob3o15b2o3b2o$224bo5bo160bo7bo32bo4b3o31b2o3b2o
46b3o$389bo2bo6bo46bo24bo5bo47bo5bo$389bo2bo2b2o48bo2bo3b2o75b2o8b2o$
390bo8bo28bo16bo2bo3b2o76b2o3b2obo2bob2o$399bo30bo16bo87b2o2bo4bo$398b
3o6bobo19bobo9bo98bo$410bo18bo12b2o9b2o86bobo$406bo2bo20bobo8b2o8bob2o
$405bobobo11bobo27bo$397bo3bo3bo2bo13b2o27bo$396b2o3b2o3b2o14bo28bo2bo
$229bo166b2o3b2o49b2o$67bo6bo152b2obo165bo5bo$67bo8bo149bo4bo306bo$65b
3o6b3o142b2o10b2o303b2obo$64b2o8bo3bo139bo2b2o2bobobobo191b3o110b2ob2o
$63b2o8b2o4bo138b2ob2o2bo3b2o192bobo9b3o98b2o$64b2o7b2o144b3o4b2ob2o
192b3o8b3o103bo$73b2obobo147b2o185b2o33bo$74bo148b3o186bobo31b2obo$74b
2o147bobo186bo31b3ob3o$72bob2o147bo2bo184b2o10b3o8b3o6b2o2b5o$70bo2b2o
149b3o196bobo9b3o6bo3b2o$60b2o9bobo141b3o205b3o20bo$59b2o8bo144b2ob2o
5bo2bo$60b2o10bo141bo2b2o5bo2bo189b2o$61b3o9bo141b2o7bo2b2o188b3o101bo
$63bo5bo4bo148bo3bo189b2obo98b2o$63bo355bobo98b2o$71bo2bo149b3o191bo2b
o2b2o3b2o$419b2o5bobo$423bo7bo69bo$424b2o3b2o68b2o$54bo445b2o$52b2o$
53b2o4$56b2o$55b2o$57bo2$230bo$76b3o150bobo151b2o$71bo4bobo147bo5b2o
149bobo$70bo3b3o148b3obo3bo145b2o4bo$69bo2b3o11b3o135b2obobo9b3o136bo
3b3o$69bobobo13bo135b2o3b2o2bo5bo3bo135bobo2bo9bo$70b2obob3o9bo136b2o
3bo8bo3bo135b2ob2o9b3o$72b3ob2o8b3o136b2o3bo8b3o138b2o13bo$33b2o38b2o
150b2o166b2o$34b2o$33bo43b2o150b2o$76b3ob2o147b2o3bo149b2o$74b2obob3o
146b2o3bo148b2ob2o$73bobobo149b2o3b2o2bo145bobo2bo$73bo2b3o149b2obobo
148bo3b3o7b2o$74bo3b3o148b3obo3bo145b2o4bo$75bo4bobo147bo5b2o149bobo
107b2o$80b3o150bobo151b2o107b2o$234bo263bo3$196bo5bo144bo$196b2o3b2o
143b3o$191b2o3b2o3b2o142bob3o$190bo2bo3bo3bo142bo2bob2o$188bo2bobo154b
2o$192bo4bo3bo124b2o17b2ob2o$188bob2o4bo5bo123bobo18bo$189bo6bo5bo123b
o$196bo5bo12b3o210b2o3b2o$2bobo193b3o7bo5bo2bo209bo7bo$b2o203bo2bo7b2o
204b2o5bobo$o182b2o13b3o5bo2bo3bob3o113bo90bo2bo2b2o3b2o$b3o180bo11bo
5bo4bo5bo4bo112b2o90bobo$b3o44bo5bo129bobo9bo5bo11bo115bobo88b2obo$48b
2o3b2o130b3o8bo5bo4bo7b3o203b3o$48b2o3b2o3b2o127b3o16bo2bo211b2o$49bo
3bo3bo2bo126b2o9b3o5bo2bo138b2o$57bobo2bo126bo18bo135b2o2b2o2b2o73b3o
20bo$58bo285bobo2bo2b2o73bobo9b3o6bo3b2o$59b2obo282b3o67b2o10b3o8b3o6b
2o2b5o$51bo9bo106b2o3b2o105b2o3b2o43b2o14b2o68bo31b3ob3o$33b3o14b3o3bo
110bo7bo28bobo17b2o53bo7bo40bo3bo83bobo31b2obo$33bo2bo5bo6bobobobo2bo
111bobo5b2o25b2o17b2o49b2o5bobo42bo6b2o16bo5bo58b2o33bo64b2o$32b2o7bo
2bo3b3ob2ob2ob3o107b2o3b2o2bo2bo24bo18b2o48bo2bo2b2o3b2o40bo4bo2bo16b
2o3b2o68b3o8b3o75b2o$33b3obo3bo2bo4bobobobobobo6b2o109bobo44bo48bobobo
55b3o16b2o3b2o68bobo9b3o76bo$32bo4bo5bo6b3o3b3o7bo111bob2o41bobo46b3ob
o76bo3bo69b3o$36bo14bo5bo6bobo54bobo55b3o41bob2o45b3o$33b3o7bo20b2o54b
o59b2o$41bo2bo11b3o56b2o2bo4bo81b3o91bo66bo32bo5bo$41bo2bo11b2obo55b2o
bo2bob2o48b3o11b3o16bobo9b3o3b2o51bo5bo14b2ob2o62bo2bo31b2o3b2o49b2o$
42bo5bobo8bo59b2o40b3o9bobo13bo16b3o8b3o4b2o49b2ob2ob2ob2o5b3o4b2o65bo
2bo31b2o3b2o3b2o14bo28bo2bo$48b2o3b2o2b2o46bo56b3o8b3o12bo78b2o8bo5bo
6b3o4b2obo2bo62bo34bo3bo3bo2bo13b2o27bo83bobo$49bo5bobo46b3o161bo29b3o
bo106bobobo11bobo27bo32bo5bo42b4o2bo$31b2o43b2o3b2o20bob3o15b2o3b2o
138bobo28b3o31b2o3b2o26bo43bo2bo20bobo8b2o8bob2o29b2o3b2o42bo2bo2bo$
25b2o4bobo41bo7bo18bo2bob2o13bo7bo62bo12b3o8b3o49b2o29bo31bo7bo12bo3bo
7bo2bo45bo18bo12b2o9b2o24b2o3b2o3b2o42bo2bo2bo$25b2o4bo39b2o5bobo25b2o
8b2o7bobo34b3o8b3o16bo13bobo9b3o55bo7bo5b3o42bobo13b2o5b2o5bo2bo33b3o
6bobo19bobo9bo36bo2bo3bo3bo44bo3bo$25b2o43bo2bo2b2o3b2o20b2ob2o7b2o6b
2o3b2o31b3o9bobo16b3o11b3o67bo8bo5b3o39b2o3b2o13bobobo9bo35bo30bo16bo
28bo2bobo54b2o$26bo44bobo31bo11bo55b3o100b4o3b3o57bo50bo8bo28bo16bo2bo
3b2o26bo$25bobo41b2obo127b2o76b3o62b2o9b3o7b2o27bo2bo2b2o48bo2bo3b2o
22bob2o25bobo$24b2obo41b3o54bo73b3o77bo61bobo18bo2bo26bo2bo6bo46bo30bo
29b2o$69b2o55bo10b3o26b2o32b2obo48bo5bo64b3o38bobo28bo7bo32bo4b3o43b3o
23bo$125bobo8b3o28bo34bobo47b2o3b2o42bo6b2o14b3o35b2obo36b3o4bo32bo7bo
35bo3bo9bo9b3o$25b2o3b3o90bo40b3o9bo24bo2bo2b2o3b2o38b2o3b2o3b2o37b2o
5b2o20bo5bo25b3o30bo46bo6bo2bo33bo3bo7bo2bo8b3o$25b2o4b3o19bo33b3o33bo
bo38bo10b2o25b2o5bobo41bo3bo3bo2bo35bobo25b2ob2ob2ob2o23b2o29bo2bo48b
2o2bo2bo22b2o9bo3bo7bo2bo$37bo5bo10bo31b3o15bo5bo12bo51bobo28bo7bo46bo
bo2bo41bo21bo5bo40bo15bo2bo16bo28bo8bo24bo10b3o9bo$35b2ob2ob2ob2o6b3o
21bo5bo21b2o3b2o14bobo8b3o68b2o3b2o48bo44bobo14b3o48b3o16bo16bo30bo33b
obo72b2o$37bo5bo21b3o6b2ob2ob2ob2o19b2o3b2o15bo10b3o123b2obo40bo2bo12b
3o31bo16bo35bobo19bobo6b3o33b2o8b3o9bo47b2obo2bob2o$31b3o31bo10bo5bo
22bo3bo16bo138bo42bo2bo46bo15b2o36bo18bo54bo3bo7bo2bo45bo4bo2b2o$30b3o
33bo19b3o84bo18bo110bo52b3o39b2o9bobo20bo2bo50bo3bo7bo2bo49bo$87b3o45b
2o35bo2bo5b3o9b2o51bo36bo9b3o5bo2bo3bo2bo14b2o54bo16bo18bobo11bobobo
49bo3bo9bo47bobo$95bo38bo2bo34bo2bo16b3o50bo2bo32b2o18bo2bo3b2o15bo2bo
41b2o9bob2o11b3o19b2o13bo2bo3bo3bo42b3o$49b2o43bo2bo35bobobo36bo4bo5bo
8b3o48bo2bo33b2o8bobobo5bo22bobo2bo10bo29b2o12bo10bo22bo14b2o3b2o3b2o
109b2o3b2o$48b3o43bo2bo6bo5b2o21bo2bo42bo5bo9bobo49bo5bo3bo32b2o5b2o
27bo12b2o29bo10bo2bobo52b2o3b2o14b2o3b2o80b2o5bo7bo$47bob2o32b2o11bo7b
o4bobo20bo41bo4bo5bo11bo53b2o5b2o32bo3bo5bo24b2obo9b2o41bo2bo52bo5bo
13bo7bo48b2o16bo11b2o9bobo$46bobo34bo19bobo5bo11bobo7bobo36bo2bo5b3o
13b2o48bo5bobobo8b2o33bo2bo24bo54b2o76bobo5b2o14b3o27b2o15b3o12bo6b2o
3b2o$37b2o3b2o2bo2bo34b3o9bo7bo19b2o22bo23bo2bo69bo2bo18b2o32bo2bo48b
3o104b2o3b2o2bo2bo15bo43bo$39bobo5b2o37bo7bo2bo6bo19bo21b3o24bo7b3o61b
o2bo5b3o9bo36bo32b2o15bo62b3o50bobo15bo18b2o25b3o4b2o16bo$36bo7bo49bo
2bo14b2o31bo33bo5bo60bo90bo16bo31b3o15b3o9bobo44bo6bob2o31bobo7b2obo
18bo19bobo$37b2o3b2o51bo8bo6b2o32b2o32bo5bo6bo91bo49b3o48b3o17b3o8b3o
43bobo6b3o19bo13bo8bobo18bo31b3o$62bobo5bo33bo6b2o66bo5bo4b2obo89bob2o
47bo40bo5bo45b2o43b2o18bo24bo39b3o8b3o$61b2o2b2o3b2o25b2o4bobo5bo41b2o
25bo3bo4bo60b2o35bo60b2o23b2ob2ob2ob2o43bobo32b3o27b3o21b2o$60bo8bobo
5bo18bo2bo4bo4b3o41b3o32bobo2bo57bo31bo2bobo58b3o25bo5bo47bo80b3o3b2o$
60bob2o11bo2bo17bobo5bo48b2obo23bo3bo3bo2bo56b3o34bo2bo3bo3bo49bob2o
35b3o17b3o8b3o10b2o22b3o46bo6b3o4b2o18bo5bo$61b3o11bo2bo18bob2o48bo5bo
bo21b2o3b2o3b2o57bo37b2o3b2o3b2o47bobo38b3o15b3o9bobo35b3o44bobo32b2o
3b2o14b3o8b3o$54b2o20bo21b3o41b3o4bo4bo2bo21b2o3b2o105b2o3b2o47bo2bo
18bobo46b3o43b3o71b2o3b2o26b3o$53bobo6bo5bo30b2o41bo5bobo4b2o22bo5bo
105bo5bo48b2o7b3o9b2o132b3o33bo3bo15bobo$53bo7b3o3b3o6bo64b2o6bo119bo
98bo54b2o37bobo44b3o46bo$52b2o6bobobobobobo4bo2bo28b2o32b2o6bo8bo110b
3o72bo9bobobo13b2o3b2o43b3o29b3o6bo46b3o54b2o$59b3ob2ob2ob3o3bo2bo29bo
31b2o14bo2bo104b3o3b4o69bo2bo5b2o5b2o13bobo44bob2o28b3o71bo38bo2bo$61b
o2bobobobo6bo27b3o21bo19bo6bo2bo96b3o5bo8bo69bo2bo7bo3bo12bo7bo40bobo
48b3o27b3o22bo2bo13b2o20bobobo$63bo3b3o35bo22b2o19bo7bo99b3o5bo7bo71bo
26b2o3b2o32b2o3b2o2bo2bo49bo18b2o32bo2bo5b3o4bobo20bo2bo$58bo9bo49bobo
7bobo11bo5bobo128b2o132bobo5b2o49bo19b3o6bobo24bo5bo3bo5bo19bo$57bob2o
60bo20bobo4bo7bo121bobo63bo64bo7bo39b2o32b2obo6bo31bo3bo26bobo$61bo55b
o2bo21b2o5bo6bo2bo121bo61bo2bo64b2o3b2o41bo18bo15bobo31bo5bo3bo17bobo
21bo$57bo2bobo53bobobo35bo2bo97b3o6bo5bo8b2o60bo2bo109b3o18bo15bo2bo2b
2o3b2o20bo2bo5b3o19b2o19b3o$59bo2bo3bo3bo45bo2bo38bo97b3o5b2ob2ob2ob2o
69bo18b2o91bo20b3o14b2o5bobo22bo2bo13b3o11bo19bo$60b2o3b2o3b2o45b2o
147bo5bo90bobo132bo7bo20bo7b3o39b2o$65b2o3b2o293bo133b2o3b2o28bo3bo3bo
bo$65bo5bo55bo16bo3bo205bo3bo6b2o162b2o3bo3bo2b2obo40b2o$114b3o10bo15b
2o3b2o125b3o75b2o3b2o116b3o49bo2bo6bo2bo2bo40b3o$115b3o8bobo14b2o3b2o
123bob3o75b2o3b2o105bo9bo3bo48bobo4b3o4b2o41b2obo$130bo12bo5bo122bobob
o76bo5bo104bo2bo7bo3bo49bob2o41b2o4b3o4bobo$128bobo132b2o3b2o2bo2bo
188bo2bo7bo3bo50b3o40bo2bo2bo6bo2bo$130bo134bobo5b2o191bo9b3o8b2o42b2o
40bob2o2bo3bo3b2o$115b3o8bobo133bo7bo216bobo83bobo3bo3bo$114b3o10bo
135b2o3b2o196bo9b3o10bo49b2o39b3o7bo$127bo6b2o328bo2bo7bo3bo9b2o49bo
19bo11b3o13bo2bo$134bobo327bo2bo7bo3bo57b3o19b2o19b3o5bo2bo$136bo328bo
9bo3bo57bo21bobo17bo3bo5bo$124b2o3b2o5b2o338b3o71bobo26bo3bo$126bobo
355bo68bo19bo5bo3bo5bo$123bo7bo350b2obo63bo2bo20bobo4b3o5bo2bo$124b2o
3b2o350bo66bobobo20b2o13bo2bo$480bobo2bo62bo2bo38bo$472bo3bo3bo2bo65b
2o$471b2o3b2o3b2o76bo$471b2o3b2o80bobo15bo3bo$471bo5bo68b3o26b2o3b2o$
547b3o8b3o14b2o3b2o$575bo5bo3$547b3o8b3o$546b3o$558bobo5b2o$559bo6bobo
$568bo$556b2o3b2o5b2o$558bobo$555bo7bo$556b2o3b2o!

[calcyman]

Sokwe and Paul, thanks for the rake and gun, respectively. DryLife seems to be 'very rich in nice things'!

... composed of 2.5 copies of Calcymans p480 gun ...

Do I not deserve a genitive apostrophe?


Anyway, that is an impressive construction. One could theoretically create a p32n gun based on this, where gliders from the rakes (and you have plenty -- infinitely many -- at your disposal) are recycled, via spinners, to construct the rakes themselves. Then you are no longer constrained to p60n.

[Paul Tooke]

Calcyman wrote:

DryLife seems to be 'very rich in nice things'!

DryLife appears to be very similar to Life and although it lacks some things: the XWSSs, switch engine[*] and Herschel for example, I believe that this simply makes engineered patterns more challenging. It doesn't rule them out completely.
(* It could be argued that the R-pentomino is DryLife's switch engine. I wonder whether it's possible to stabilise a single r-pentomino in a similar way.)

My punctuation usage in the parenthetical remark takes us slightly(!) OT:

Do I not deserve a genitive apostrophe?

Oops! Sorry. Unlike "feasable" and "reduces" this wasn't an accidental typo. I tend to err in the side of caution with the use of apostrophes, to the point where I rarely use them for the possessive. After all "Calcymans" can't be a plural can it? Surely that would be "Calcymen"! But, you're right, you were deserving of an apostrophe and I see that I've failed to supply you with at least one other in the past. To redress this, here is a collection of apostrophes that you can use to correct my past and future mistakes. Keep a careful eye on them because these are slippery little critters that like to sneak into places where they don't belong.

Code: Select all

''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

Getting back OT:

One could theoretically create a p32n gun based on this, where gliders from the rakes [...] are recycled,

Yes, although I for one will not be leaping to this challenged immediately - I've got enough on my plate as it is. A possible fly in the ointment here is the phasing/colour square issue. Successive gliders from the same rake are emitted on alternating colour squares, but with a one phase offset between each. Furthermore the gun's period is necessarily a multiple of four, so successive rakes emit gliders of the same colour square and phasing flavour. Unless the p32 spinner can reflect a glider in more than one way (I haven't checked) it might be tricky finding the right flavours of gliders to create the beehives.