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Just Friends (B2-a/S12)

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Just Friends (B2-a/S12)

Postby Hdjensofjfnen » October 27th, 2016, 9:03 pm

I would like to dedicate a thread to this rule. It seems mostly unexplored and is not explosive.

Two oscillators (p26 and p14):
x = 15, y = 8, rule = B2-a/S12
5o$14bo$2bo11bo$2bo11bo$12b2o$o3bo2$2bo!
Life is hard. Deal with it.
My favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
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Re: Just Friends (B2-a/S12)

Postby Hdjensofjfnen » October 27th, 2016, 10:23 pm

Weird 7-cell synthesis of a 15-bitter:

x = 21, y = 7, rule = B2-a/S12
15bo2bo$2o13bob2o$4bo10bo4bo$2o2bo7b2obo3bo$3bo12bo2bo$15bo$15bo!
Life is hard. Deal with it.
My favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
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Re: Just Friends (B2-a/S12)

Postby FlameandFury » October 27th, 2016, 10:33 pm

It has been searched pretty thoroughly, but feel free to do more searches, and thanks for making this thread! Attached below is a pattern collection by David Bell.
Attachments
JustFriends.zip
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Re: Just Friends (B2-a/S12)

Postby Hdjensofjfnen » November 7th, 2016, 9:59 pm

Here is a weird reaction:

x = 7, y = 4, rule = B2-a/S12
5b2o$3o$o$3o!
Life is hard. Deal with it.
My favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
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Re: Just Friends (B2-a/S12)

Postby Hdjensofjfnen » November 7th, 2016, 10:06 pm

COOL!!!

x = 5, y = 4, rule = B2-a/S12
o3bo$o3bo$bobo$bobo!


EDIT: COOLER!

x = 7, y = 7, rule = B2-a/S12
2o3b2o$2bobo$bo3bo$bobobo2$2bobo$2b3o!
Life is hard. Deal with it.
My favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
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Re: Just Friends (B2-a/S12)

Postby A for awesome » December 17th, 2016, 1:54 pm

A number of spaceships:
x = 11, y = 37, rule = B2-a/S12
2b2o3b2o2$o2bobobo2bo$o2bobobo2bo$o9bo$o9bo$o9bo$o9bo$o4bo4bo$o
b3ob3obo$o4bo4bo$bo7bo$bo7bo$2bob3obo$2bobobobo$o3b3o3bo$bo7bo$b
o7bo$bo3bo3bo$bob5obo$bo3bo3bo$2bo5bo$2bo5bo$3bobobo$3b5o$3b5o$2b
2o3b2o$4bobo$4bobo2$5ob5o$2bo5bo$5bo$2b2obob2o$5bo$4bobo$4bobo!

x = 11, y = 74, rule = B2-a/S12
2b2o3b2o$3bo3bo$3bo3bo$4bobo3$5bo$2bo2bo2bo$2o3bo3b2o$5bo$bo3bo
3bo$bo3bo3bo$obo2bo2bobo$2o3bo3b2o$obo2bo2bobo$o2bobobo2bo$o2bo3b
o2bo$o9bo$obo5bobo$o9bo$o2bobobo2bo$o2bo3bo2bo$o2bo3bo2bo$o3bobo
3bo$o3bobo3bo$o3bobo3bo$o9bo$ob2o3b2obo$o9bo$ob2o3b2obo$o2bo3bo2b
o$bobo3bobo$bo3bo3bo$3b5o$2bo2bo2bo$3bo3bo$obo2bo2bobo$o2bo3bo2b
o$o9bo$obo5bobo$o3bobo3bo$bob2ob2obo$bob2ob2obo$bobobobobo$bo2bo
bo2bo3$2b7o$2bo5bo$2b2obob2o$3obobob3o$2bobobobo$2bobobobo$3bobo
bo2$b2o5b2o3$bobo3bobo2$5bo$3b5o$3b5o$2b2o3b2o$4bobo$4bobo2$5ob5o
$2bo5bo$5bo$2b2obob2o$5bo$4bobo$4bobo!

x = 11, y = 90, rule = B2-a/S12
2b2o3b2o$2bo5bo$obo5bobo$o4bo4bo$bob5obo$bo7bo$bo2bobo2bo$bo7bo
$bobo3bobo$bo7bo$2bo5bo$2bobobobo3$2bo5bo2$3bo3bo$3bobobo4$bo3bo
3bo$5bo$2o3bo3b2o$5bo$5bo$obo2bo2bobo$5bo$bo3bo3bo$o9bo$o2bobobo
2bo$o2b2ob2o2bo$o4bo4bo$ob3ob3obo$o3bobo3bo$o2bo3bo2bo$o2bo3bo2b
o$o2bo3bo2bo$o4bo4bo$o9bo$o3bobo3bo$o3b3o3bo$ob2o3b2obo$o9bo$obo
5bobo$3bo3bo$bobo3bobo$bobo3bobo$3b2ob2o2$3bo3bo$o3b3o3bo$o2bo3b
o2bo$o3bobo3bo$ob2obob2obo$o3bobo3bo$bo7bo$bo2bobo2bo$bobobobobo
$bo7bo3$3b5o$2bo5bo2$2o2bobo2b2o$2bobobobo$2bobobobo3$b2o5b2o$2b
o5bo$2bo5bo$b3o3b3o3$4bobo$3bo3bo2$3bobobo3$2o2b3o2b2o$2bo2bo2bo
$2bo2bo2bo$2b2obob2o$5bo$3bo3bo2$5bo!

x = 11, y = 103, rule = B2-a/S12
2b2o3b2o2$o2bobobo2bo$o2bobobo2bo$o9bo$o9bo$o9bo$o9bo$o3bobo3bo
$o2b5o2bo$o9bo$o4bo4bo$obobobobobo$o9bo$bobobobobo$bobobobobo$bo
bo3bobo$bob5obo$bo3bo3bo$bob5obo$bo7bo$bo3bo3bo$bob2ob2obo$bo7bo
$2bo2bo2bo$2bo5bo$4bobo$4b3o$2b2o3b2o2$3bo3bo$3bo3bo2$4b3o$5bo$2b
o2bo2bo$o4bo4bo$5bo$b2o2bo2b2o$b2o2bo2b2o$2b2obob2o$bo3bo3bo$bo3b
o3bo$o4bo4bo$o9bo$ob2o3b2obo$o4bo4bo$obob3obobo$o4bo4bo$o2bo3bo2b
o$o2bobobo2bo$o9bo$o3bobo3bo$o9bo$o9bo$obo5bobo$o3b3o3bo$ob7obo$
o3bobo3bo$bo7bo$bob2ob2obo$bobo3bobo$bo7bo$3b2ob2o$o9bo$o3b3o3bo
$o9bo$o4bo4bo$ob3ob3obo$bo3bo3bo$bo7bo$bo3bo3bo$bob2ob2obo$2bo2b
o2bo$3bo3bo$3b5o$3bo3bo2$4bobo$bobobobobo$2bo5bo$5bo2$b2o2bo2b2o
$3bo3bo$2bo5bo$2bo2bo2bo$2bo2bo2bo$3bobobo3$3bobobo$4bobo$4bobo$
3bo3bo$4b3o$2o7b2o$bo3bo3bo$b3obob3o2$4bobo$4bobo$4b3o!

x = 11, y = 26, rule = B2-a/S12
3bo3bo$b3o3b3o$3bo3bo$2b2o3b2o3$3b2ob2o$b3o3b3o$3bobobo$2bo2bo2b
o$2bobobobo$2bobobobo$o9bo$bobo3bobo$bo3bo3bo$bo7bo$bo7bo$bo7bo$
2bo2bo2bo$2bobobobo$4bobo$4b3o$4b3o$4b3o2$4bobo!

x = 19, y = 20, rule = B2-a/S12
3b2o9b2o$4bobo5bobo$3bo11bo$ob2obo7bob2obo$obobobo5bobobobo$o5b
o5bo5bo$o2bo11bo2bo2$b2o6bo6b2o$bo5b5o5bo$bo5bo3bo5bo$2bo4b5o4bo
$3bo5bo5bo$b2o4bobobo4b2o$8bobo$b2o4bobobo4b2o$3bobob2ob2obobo$3b
ob3obob3obo$7bobobo$9bo!

x = 19, y = 22, rule = B2-a/S12
2o3b2o5b2o3b2o2$b5o7b5o$2bobo9bobo$2b3o9b3o4$bobo11bobo2$b2o6bo
6b2o$bo5b5o5bo$bo5bo3bo5bo$2bo4b5o4bo$3bo5bo5bo$b2o4bobobo4b2o$8b
obo$b2o4bobobo4b2o$3bobob2ob2obobo$3bob3obob3obo$7bobobo$9bo!

x = 19, y = 22, rule = B2-a/S12
b2o13b2o$2bo3b2o3b2o3bo$2bo3bo5bo3bo$o5bo5bo5bo$bo3bo7bo3bo$bob
o11bobo$2bo13bo$2bo13bo$2bo13bo$o2bo11bo2bo$b2o13b2o$7bo3bo$bo15b
o$b3o3bo3bo3b3o$3bo2bo5bo2bo$b3o3bo3bo3b3o$o2bo2bo5bo2bo2bo$b4o9b
4o$3bobo7bobo$3bobo7bobo$4bo2bobobo2bo$9bo!

x = 19, y = 22, rule = B2-a/S12
6b2o3b2o$b2o3bo5bo3b2o$2bo3bo5bo3bo$2bo3bo5bo3bo$3bo2bo5bo2bo2$
2b2o11b2o$2bo13bo$2bo13bo$b3o11b3o2$2bo13bo$bo6bobo6bo$bo5bo3bo5b
o$8bobo$3bo11bo$2b2o11b2o$o3b3obobob3o3bo$2bo2bobobobobo2bo$3bob
o7bobo$3bo2bo5bo2bo$8bobo!

I haven't really sorted them or anything, so they may or may not be new.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

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Re: Just Friends (B2-a/S12)

Postby A for awesome » September 2nd, 2017, 8:05 pm

A bunch of c/7 and c/8 spaceships:
x = 504, y = 246, rule = B2-a/S12
421b2o5b2o$422bo2bo2bo$422bobobobo$422bobobobo2$423b5o$405b3o14b2o3b2o
$401b2o7b2o8b2ob5ob2o2$402bobo3bobo10bob2ob2obo$402bo7bo10bo7bo$403bo
5bo12bo5bo$403bobobobo12bobobobo$422bobobobo$423bo3bo2$424bobo$386bo3b
o13bo3bo14bo3bo$384b2o5b2o10b2obob2o10b3o2bo2b3o$362b2o5b2o12bo9bo7b2o
bobobob2o9bobobobobo$363bo5bo13b3o5b3o10bobobo12bo3bo3bo$363bo2bo2bo
13bobo5bobo10bobobo12bobobobobo$363b2obob2o13bobo5bobo9b2obob2o11b2o2b
o2b2o$366bo16bobo5bobo12bo14bobobobobo$363b2obob2o13bobo5bobo9b2obob2o
10b3o2bo2b3o$364bobobo14bo2bobobo2bo10bobobo11bo2bo3bo2bo$361bo2bobobo
2bo11bo2b2ob2o2bo7bo2bobobo2bo8bo2bobobo2bo$361b2obobobob2o11bo9bo7b2o
bobobob2o9bobobobobo$363bobobobo13bo3bobo3bo9bobobobo13bobobo$383bo3bo
bo3bo29b2ob2o$383bobob3obobo29bobobo$361bo9bo14bo3bo10bo9bo8bo3bobo3bo
$361bobo2bo2bobo12bo3bo3bo8bobo2bo2bobo8bo4bo4bo$364b2ob2o15bob2ob2obo
11b2ob2o14b2ob2o$366bo17bo7bo13bo$385bobobobo$343bo3bo15bo5bo15bo5bo
11bo5bo12bo2bo2bo$341b2o5b2o35bo5bo30bo5bo$362b2o5b2o14bo5bo10b2o5b2o
10bo7bo$341bo2bobo2bo16bo18bo2bo2bo14bo$340bo2bo3bo2bo35bo3bo33bobo$
340bo3b3o3bo10bob2o3b2obo14bo3bo10bob2o3b2obo8bo9bo$343bobobo13b3o5b3o
29b3o5b3o8b2o2bobo2b2o$345bo19bobo18bo3bo14bobo17bo2$345bo$344bobo39bo
3bo$344bobo18bobo18b5o14bobo15bo3bo$341bo3bo3bo14b2ob2o15b2o5b2o11b2ob
2o14b5o$343bo3bo14b2o5b2o31b2o5b2o10b2o5b2o$364bo3bo16b2o3b2o12bo3bo$
386b5o31b2o3b2o$386b5o32b5o$388bo34b5o$343b5o77bo$343bo3bo17b3o20bo16b
3o$318b2o5b2o17bobo17bo3bo16b7o12bo3bo16bo$319bo2bo2bo16b2o3b2o37bobob
o31b7o$319bobobobo37b2o3b2o16bo3bo12b2o3b2o13bobobo$341b2o5b2o13bo5bo
14bo7bo10bo5bo13bo3bo$340b2o3bo3b2o11bo7bo13bo7bo9bo7bo10bo7bo$343bo3b
o37bo5bo29bo7bo$272bo7bo36b2o2bobo2b2o15bo3bo14bob2ob2obo31bob2ob2obo
11bo5bo$272bobo3bobo16bo3bo16bob2ob2obo18bo18bobobo18bobo14bobobo$273b
o5bo15b2o5b2o14bo3bo3bo18bo20bo39bo17bobo$275b3o40bobo3bobo17b3o19bo
39bo$275bobo17bo2bobo2bo17bobo21bo$275bobo16bo2bo3bo2bo38bo3bo18bo39bo
$275bobo16bo3b3o3bo16bobo21bo18b2ob2o17bobobo13b2ob2o$273bobobobo17bob
obo19bobo19bo3bo16bobobo18bobo14bobobo14bobobo$273bo5bo19bo19bobobobo
18bobo17bo3bo18bobo14bo3bo15bobo$252bo3bo16b2obob2o64bobo18bobo17bobob
obo13bobo16bobo$250b2o5b2o16bobo21bo19bo2bo2bo15b2o5b2o15bobo17bo5bo
13bobo14bobobobo$249bo9bo38bobo20bobo38b2obobob2o14b2obob2o10b2obobob
2o11bo5bo$249b3o5b3o14bo3bo41b5o17bo5bo15b5o18bobo14b5o13b2obob2o$249b
obo5bobo12bobo3bobo39bo3bo38bo5bo33bo5bo14bobo$249bobo5bobo35b2o5b2o
16bo3bo61bo3bo$249bobo5bobo37bo3bo17bo5bo17bo3bo36bobo3bobo30bo3bo$
249bobo2bo2bobo36bo5bo39b2o3b2o15bo3bo35bo3bo12bobo3bobo$249bob2o3b2ob
o11bo9bo12bo9bo58b2o3b2o33b2o3b2o$249bo4bo4bo11b2o3bo3b2o12bo9bo12bo9b
o$249bobo5bobo13bo5bo14bo9bo12bobo5bobo12bo9bo32bo9bo$249bo3b3o3bo15bo
bo16bobob3obobo14b3ob3o14bobob3obobo10bo9bo11b2o3bo3b2o7bo9bo8bo9bo$
249bo3b3o3bo15bobo16bo2bo3bo2bo16bobo18bobobobo12bobo2bo2bobo13bo5bo9b
obo2bo2bobo8b2o3bo3b2o$249bob2o3b2obo34bo9bo16bobo20bobo16bobobobo17bo
bo13bobobobo12bo5bo$249bo3bobo3bo11bo9bo12bo4bo4bo17bo21bobo40bobo34bo
bo$232b3o14bob2o3b2obo34bob7obo39bobo18bobo37bobo16bobo$228b2o7b2o10bo
9bo13bo5bo14bo4bo4bo13bo7bo38b3o15bo9bo11b3o$250bobo3bobo15bo3bo15bob
2o3b2obo14b2o3b2o14b3o5b3o69bo9bo$229bobo3bobo12bobo3bobo12bo2bo3bo2bo
16bobo17bobo3bobo16bo3bo14bo7bo14bo5bo10bo7bo$229bo7bo15b3o15bo2b5o2bo
13bobo3bobo13bo9bo15bo3bo13bo2bo3bo2bo14bo3bo10bo2bo3bo2bo10bo5bo$230b
o5bo14b2obob2o13bo9bo13bobo3bobo13bo2bobobo2bo17bo15b2obo3bob2o11bo2bo
3bo2bo7b2obo3bob2o11bo3bo$230bobobobo12bobo5bobo11bo2bo3bo2bo13bo3bo3b
o13bobo5bobo12bo9bo10bo2bo3bo2bo11bo2b5o2bo7bo2bo3bo2bo8bo2bo3bo2bo$
209bo3bo57bo9bo12bo9bo12bo9bo12bo9bo10bob3ob3obo11bo9bo7bob3ob3obo8bo
2b5o2bo$207b2o5b2o38bo16bob3ob3obo13bo7bo13bo4bo4bo12bo4bo4bo10bob3ob
3obo11bo2bo3bo2bo7bob3ob3obo8bo9bo$253bobo15bo9bo35bob7obo12bo9bo10bo
9bo11bo9bo7bo9bo8bo2bo3bo2bo$207bo2bobo2bo56bo7bo36bo4bo4bo12bob2o3b2o
bo10bo9bo11bob3ob3obo7bo9bo8bo9bo$206bo2bo3bo2bo14bo3bo36bo7bo16bo3bo
16bo7bo13bo9bo10bob2o3b2obo11bo9bo7bob2o3b2obo8bob3ob3obo$156b2o5b2o
41bo3b3o3bo13b2obob2o35bo2bobo2bo18bo18bo3bo3bo14bo2bobo2bo11bo9bo12bo
7bo8bo9bo8bo9bo$157bo5bo45bobobo14b2obobobob2o11bo7bo13bobobobobo15bo
2bo2bo15bob2ob2obo14bobo3bobo12bo2b3o2bo13bo7bo9bo2b3o2bo10bo7bo$157bo
2bo2bo17b2o5b2o21bo19bobobo14bo3bo3bo13bobobobobo14bobo3bobo14bobo3bob
o14bo2bobo2bo12bo3bo3bo13bo2bobo2bo9bo3bo3bo10bo7bo$157b2obob2o18bo2bo
2bo42bobobo14bobo3bobo36bo7bo14bobobobobo14bob2ob2obo12bobo3bobo13bobo
bobobo9bobo3bobo10bo2bobo2bo$160bo21bobobobo22bo18b2obob2o14bo2bo2bo
16bo3bo16bobo3bobo16bo3bo16bobo3bobo12bo7bo13bobobobobo9bo7bo10bobobob
obo$157b2obob2o18bo2bo2bo21bobo20bo17bobobobo39bo3bo41bo3bo14bobo3bobo
31bobo3bobo10bobobobobo$130b2o3bo3b2o17bobobo20bo3bo18b3o5b3o13b2obob
2o36bo2bo2bo19bo19b3ob3o16bo2bo2bo15bo3bo17bo3bo13bo3bo$134bobo18bo2bo
bobo2bo17bo3bo43bobobo15b2obob2o15b2o3b2o16bobobobo16bobobobo16bobobob
o17bo39bo16bo3bo$155b2obobobob2o17bo3bo40bo2bobobo2bo15bo19b2ob2o17bob
obobo39bo5bo14bobobobo15bo2bo2bo11bobobobo$135bo21bobobobo20bobo24bo
16b2obobobob2o15bo19bobobo18bobobo40b2obob2o14bobobobo15b2o3b2o11bobob
obo12bo2bo2bo$130bo3b3o3bo65bo9bo13bobobobo37bo3bo43bo22bo18bobobo17b
2ob2o13bobobo13b2o3b2o$110b2o5b2o11bobo5bobo65bob2o3b2obo36bobo20bo22b
o20bobobo20bo40bobobo32b2ob2o$111bo2bo2bo12bo3b3o3bo14bo9bo15b2o5b2o
16bo9bo34bo5bo15b7o19bo45bo20bo19bo3bo15bo16bobobo$111bo5bo12bo4bo4bo
14bobo2bo2bobo16bo2bo2bo17bo2bo3bo2bo11bo9bo37bo42b2o3b2o18bobo19bo21b
o17bo16bo3bo$112bo3bo13bo9bo17b2ob2o19bo5bo17bo9bo11bobo2bo2bobo13bo3b
o39b2o3b2o39b2o3b2o36b7o33bo$88bo3bo3bo33bo9bo19bo22bo3bo18bo9bo14b2ob
2o40bo44b3o20b3o16b2o3b2o18bo14b2o3b2o12b7o$66bo3bo18bo2bo2bo18bo15bo
3b3o3bo65bo9bo16bo42bo21bobo21bo22bo79bo$43bo3bo16b2o5b2o16bo2bo2bo17b
obo14bo3bobo3bo44bo20bo3bobo3bo59bo45bo21bobo18bobo20bo16bobo$41b2o5b
2o13bo9bo13bo9bo15bobo18bobo19b2o5b2o19bobo23b3o40bobo19bobo21bo44b3o
41bo36bo$63b3o5b3o13bo3b3o3bo35bobobo19bo5bo20bobo42b2o5b2o15b3o20bo
21bobo20bobo20bobo19bo21bo17bo18bo$41bo2bobo2bo13bobo5bobo13bo9bo32bob
o5bobo16bo5bo42b2o7b2o13bo5bo61bobo20b3o20bobo18bobo19bobo15bobo17bo$
40bo2bo3bo2bo12bobo5bobo17b3o15b2o7b2o35bo2bo3bo2bo42bo5bo15bo5bo12b2o
7b2o11bo4bo4bo39b3o21bo19bobo20bo16bobo16bobo$40bo3b3o3bo12bobo5bobo
57bobo3bobo15bo3bobo3bo14b2o7b2o16bo3bo3bo12bo2bo3bo2bo12bo5bo14bo2bob
o2bo36b2o2b3o2b2o97bo$43bobobo15bobo5bobo16bo3bo15bobo3bobo12bo7bo15bo
9bo41bob5obo12bo3bobo3bo11bo3bo3bo13bo7bo13b2o7b2o13bo2bobo2bo13b2o7b
2o32bo4bo4bo$45bo17bo2bobobo2bo13bo9bo12bo7bo12bob2ob2obo15bobo5bobo
15bobo3bobo17bo7bo12bo9bo11bob5obo13bobo3bobo37bob5obo34b2o7b2o12bo2bo
bo2bo8b2o7b2o8bo4bo4bo$63bo2b2ob2o2bo13bo9bo12bobo3bobo13bo5bo16bo9bo
15bo7bo19bobobo14bobo5bobo11bo7bo13bo7bo14bobo3bobo14bo7bo14bo7bo34bo
7bo28bo2bobo2bo$20bo7bo16bo17bo9bo13bo3bobo3bo14bobobo15b3ob3o16bobo5b
obo15bobo3bobo19bo3bo14bo9bo13bobobo17bobobo16bo7bo14bobo3bobo14bob2ob
2obo12bobo3bobo13bobo3bobo9bobo3bobo10bo7bo$20bobo3bobo16bo17bo3bobo3b
o13bo9bo14bobobo17bobo18bobobobobobo17bobobo21b2ob2o14bobo5bobo13bo3bo
17bobobo16bobo3bobo16bobobo16bobo3bobo12bo7bo13bo7bo9bo7bo10bobo3bobo$
21bo5bo35bo3bobo3bo13bobo5bobo37bo19bo9bo17bobobo23bo16bobobobobobo13b
2ob2o40bobobo18bobobo18bobobo14bobo3bobo15bobobo11bobo3bobo10bo7bo$23b
3o37bobob3obobo13bo2bo3bo2bo37bo19bo4bo4bo62bo9bo15bo20bobo19bobobo18b
o3bo18bobobo16bobobo17bobobo13bobobo14bobobo$23bobo17bo3bo18bo3bo17bo
3bo3bo36bo3bo17bo9bo43bobobo14bo4bo4bo35bo3bo41b5o19bobo17bobobo35bobo
bo14bobobo$23bobo19bo18bo3bo3bo15bob2ob2obo36bo3bo17bobo5bobo43b5o14bo
9bo13bobobo17bo3bo41bobobo62bobo$23bobo16b2o3b2o15bob2ob2obo15bo7bo14b
ob3obo15bo3bo18bobo3bobo46bo16bobo5bobo13b5o19bo43bo3bo61bo3bo33bobo$
21bobobobo15bo3bo16bo7bo16bo2bo2bo18bo16b2o5b2o16bobobobobo17bob3obo
18b9o13bobo3bobo16bo17bo7bo38bobobobo17bo3bo38bo3bo32bo3bo$b2o5b2o11bo
5bo16bobo18bobobobo17bo2bo2bo14b2o5b2o16bo20bo7bo20bo24bobo16bobobobob
o12b9o37bob3obo40b2ob2o40bo34bo3bo$2bo2bo2bo12b2obob2o16bobo18bo5bo17b
o5bo17b3o16bobobobo18bobobobo17b2o5b2o18bobobobo14bo7bo15bobo17bo5bo
19bo18b2o5b2o36bob3obo14bo7bo10bob3obo15bo$2bobobobo14bobo15b3obob3o
15bo5bo17bo5bo15bobobobo14bobobobo18bobobobo20b3o21bo5bo15bobobobo14bo
bobobo15bobobobo15b2o5b2o15bo2bo2bo15b3o3b3o16bo39bo14bo7bo$2bo2bo2bo
34bo3bo17bo5bo17bobobobo15bo5bo14bo5bo18bo2bo2bo18bobobobo19bobobobo
15bobobobo14bo5bo15bobobobo18b3o18bobobobo18bobo15b2o5b2o14bo5bo10b2o
5b2o$3bo3bo14bo3bo38bo2bo2bo18bo3bo16bobobobo14bo2bo2bo43bo5bo19bo5bo
15bo2bo2bo14bobobobo15bo2bo2bo16bobobobo16bobobobo16bobobobo16b3o17bob
obobo13b3o14bo5bo$3bo3bo14bo3bo39bo3bo19bo3bo17bo3bo17b3o45bobobobo62b
o5bo38bo5bo16bob3obo16bobobobo14bobobobo15bobobobo11bobobobo12bobobobo
$3bo3bo14bobobo39bo3bo18b3ob3o17b3o18bobo22bobo21bo3bo23bo84bobobobo
39bob3obo14bo5bo15bo2bo2bo11bo5bo12bobobobo$4bobo15b5o16bo3bo65bobo19b
o21b3ob3o20b3o22b2ob2o18bobo19bo20bobo19bo3bo20bo19bo5bo14bobobobo33bo
bobobo12bo2bo2bo$24bo18bo3bo18bo3bo42bobo16b2o3b2o45bobo20b2o2bo2b2o
14b3ob3o15b2ob2o16b3ob3o18b3o20bobo40bo3bo35bo3bo$24bo18bo3bo63bo2bo2b
o15bo3bo20bo3bo21bobo19b2obo3bob2o33b2o2bo2b2o39bobo18bobobobo39b3o19b
obo15b3o$4bobo16bobo86bo3bo16bo3bo17bo2bo3bo2bo16bo2bo2bo17bo2bo3bo2bo
14bo3bo13b2obo3bob2o14bo3bo19bobo21bo21bobo18bobo17b3ob3o13bobo16bobo$
2b2obob2o12b2obob2o17bo43b2obob2o13bo2bo3bo2bo10bo3bobo3bo14bo9bo17bo
3bo18bo2bo3bo2bo11bo2bo3bo2bo10bo2bo3bo2bo11bo2bo3bo2bo14bo2bo2bo17bo
3bo17bo2bo2bo16bobo37bobo14b3ob3o$20bo2bobo2bo15bobo17b2o5b2o18bobo15b
o2bo3bo2bo10bo9bo14bo3b3o3bo14bo2bo3bo2bo15bob2o3b2obo11bo9bo10bo2bo3b
o2bo11bo9bo15bo3bo15bo2bo3bo2bo13bobo3bobo13bo2bo2bo16bo3bo12bo2bo2bo$
o9bo8bo9bo12bo5bo14b2o2bobo2b2o35bobo2bo2bobo10bo9bo14bo9bo14bo2bo3bo
2bo15bob3ob3obo11bo3b3o3bo10bob2o3b2obo11bo3b3o3bo12bo2bo3bo2bo12bo2bo
3bo2bo12bo2bo3bo2bo13bo3bo14bo2bo3bo2bo10bo3bo14bo3bo$o3b3o3bo8bo3bobo
3bo33bo2b2ob2o2bo13bo9bo11bo2bo3bo2bo10bo4bo4bo14bo3b3o3bo14bobo2bo2bo
bo15bo3bobo3bo11bo9bo10bob3ob3obo11bo9bo12bo2bo3bo2bo12bo3b3o3bo12bo2b
o3bo2bo10bo2bo3bo2bo11bo9bo7bo2bo3bo2bo8bo2bo3bo2bo$obobobobobo8bobo5b
obo14b3o16bo2bobobo2bo13bobo5bobo11bo2b5o2bo10bo2b2ob2o2bo14bo9bo14bo
2bo3bo2bo15bo3bobo3bo11bo3b3o3bo10bo3bobo3bo11bo3b3o3bo12bobo2bo2bobo
12bo2bo3bo2bo12bobo5bobo10bo2bo3bo2bo11bo3b3o3bo7bo2bo3bo2bo8bo9bo$obo
bobobobo8bobobobobobo10bo9bo12bobobobobobo13bobo5bobo11bo9bo10bob2o3b
2obo14bo9bo14bo2b5o2bo15bo9bo11bo9bo10bo3bobo3bo11bo9bo12bo2bo3bo2bo
12bo3b3o3bo12bo9bo10bobo2bo2bobo11bo9bo7bobo2bo2bobo8bo3b3o3bo$obo5bob
o8bobo2bo2bobo10bobo5bobo12bobobobobobo13bobobobobobo11bo9bo10bobo5bob
o14bobo5bobo14bo9bo15bobo5bobo11bo9bo10bo9bo11bo9bo12bo2b5o2bo12bo9bo
12bo2bobobo2bo10bo2bo3bo2bo11bo3b3o3bo7bo2bo3bo2bo8bo9bo$o9bo8bo9bo10b
obo2bo2bobo12bobob3obobo13bo9bo11bobo2bo2bobo10bobobobobobo14bobobobob
obo14bo9bo15bobobobobobo11bobo5bobo10bobo5bobo11bobo5bobo12bo9bo12bo9b
o12bo9bo10bo2b5o2bo11bo9bo7bo2b5o2bo8bo3b3o3bo$o9bo8bo9bo10bobo2bo2bob
o12bo9bo13bo2b2ob2o2bo11bobo2bo2bobo10bobo2bo2bobo14bo9bo14bobo2bo2bob
o15bo2bobobo2bo11bobobobobobo10bobobobobobo11bobobobobobo12bo9bo12bobo
2bo2bobo12bo9bo10bo9bo11bo9bo7bo9bo8bo9bo$obo5bobo8bo2bobobo2bo10bobob
obobobo12bo3bobo3bo13bo2bobobo2bo11bobobobobobo10bo9bo14bo2b2ob2o2bo
14bobo2bo2bobo15bo3bobo3bo11bo9bo10bo2bobobo2bo11bo9bo12bobo2bo2bobo
12bobo2bo2bobo12bobo2bo2bobo10bo9bo11bobo5bobo7bo9bo8bo9bo$o3bobo3bo8b
o2b2ob2o2bo10bob2o3b2obo12bo2bobobo2bo13bo3bobo3bo11bob2o3b2obo10bo9bo
14bo2bobobo2bo14bobobobobobo15bo3bobo3bo11bo2b2ob2o2bo10bo3bobo3bo11bo
2b2ob2o2bo12bobo2bo2bobo12bobo5bobo12bobo5bobo10bobo2bo2bobo11bobobobo
bobo7bobo2bo2bobo8bobo5bobo$o4bo4bo8bo3b3o3bo10bobo2bo2bobo12bo9bo13bo
9bo11bobo2bo2bobo10bo2bobobo2bo14bo3bobo3bo14bob2o3b2obo15bob2obob2obo
11bo2bobobo2bo10bo3bobo3bo11bo2bobobo2bo12bobobobobobo12bo2bo3bo2bo12b
o3bobo3bo10bobo2bo2bobo11bo9bo7bobo2bo2bobo8bobobobobobo29b2o5b2o$o9bo
8bo3bobo3bo10bo2b2ob2o2bo12bo9bo13bo9bo11bo2b2ob2o2bo10bo2b2ob2o2bo14b
o9bo14bobo2bo2bobo15bo3bobo3bo11bo3bobo3bo10bob2obob2obo11bo3bobo3bo
12bob2o3b2obo12bo9bo12bo9bo10bobobobobobo11bo2b2ob2o2bo7bobobobobobo8b
o9bo30bo2bo2bo$ob2o3b2obo8bob7obo10bo4bo4bo12bo9bo13bo9bo11bo4bo4bo10b
o3b3o3bo14bo9bo14bo2b2ob2o2bo15bo9bo11bo9bo10bo3bobo3bo11bo9bo12bobo2b
o2bobo12bo2b2ob2o2bo12bo4bo4bo10bob2o3b2obo11bo2bobobo2bo7bob2o3b2obo
8bo2b2ob2o2bo12b2o5b2o9bobobobo$o3bobo3bo8bo3bobo3bo10bo9bo12bobo5bobo
13bob2o3b2obo11bo9bo10bo3bobo3bo14bo9bo14bo4bo4bo15bo9bo11bo9bo10bo9bo
11bo9bo12bo2b2ob2o2bo12bo4bo4bo12bob2o3b2obo10bobo2bo2bobo11bo3bobo3bo
7bobo2bo2bobo8bo2bobobo2bo13bo2bo2bo10bo2bo2bo$obo2bo2bobo8bobo5bobo
10bo9bo12bo9bo13bobo5bobo11bo9bo10bob7obo14bob2o3b2obo14bo9bo15bob2o3b
2obo11bo9bo10bo9bo11bo9bo12bo4bo4bo12bo9bo12bo4bo4bo10bo2b2ob2o2bo11bo
9bo7bo2b2ob2o2bo8bo3bobo3bo13bo5bo11bo3bo13bo3bo$obo2bo2bobo8bobo5bobo
10bob2o3b2obo12bobo2bo2bobo13bobob3obobo11bob2o3b2obo10bo3bobo3bo14bob
o5bobo14bo9bo15bo9bo11bob2o3b2obo10bob2o3b2obo11bob2o3b2obo12bo9bo12bo
9bo12bo9bo10bo4bo4bo11bo9bo7bo4bo4bo8bo9bo14bo3bo12bo3bo13bo3bo$obobob
obobo8bobo5bobo10bo3b3o3bo12bobo5bobo13bobo2bo2bobo11bo3b3o3bo10bobo5b
obo14bobob3obobo14bob2o3b2obo15bobo2bo2bobo11bobo5bobo10bo9bo11bobo5bo
bo12bo9bo12bob2o3b2obo12bo9bo10bo9bo11bo9bo7bo9bo8bo9bo27b2o9b2o5b2o9b
2o$o2b2ob2o2bo8bobobobobobo10bobo2bo2bobo12bobo2bo2bobo13bobo2bo2bobo
11bobo2bo2bobo10bobo5bobo14bobo2bo2bobo14bo3b3o3bo15bobo2bo2bobo11bobo
b3obobo10bobo2bo2bobo11bobob3obobo12bob2o3b2obo12bo9bo12bob2o3b2obo10b
o9bo11bob2o3b2obo7bo9bo8bo9bo16bo45bo9bo$o9bo8bo9bo10bobobobobobo12bob
o2bo2bobo13bobo2bo2bobo11bobobobobobo10bobo5bobo14bobo2bo2bobo14bobo2b
o2bobo15bo9bo11bobo2bo2bobo10bobo2bo2bobo11bobo2bo2bobo12bo3b3o3bo12bo
bobobobobo12bo9bo10bob2o3b2obo11bobo5bobo7bob2o3b2obo8bob2o3b2obo15bob
o10bobo5bobo7bobo5bobo5bobo5bobo$o3bobo3bo8bo2b5o2bo10bobo5bobo12bobo
5bobo13bob3ob3obo11bobo5bobo10bobobobobobo14bobo2bo2bobo14bobobobobobo
15bobobobobobo11bobo2bo2bobo10bo9bo11bobo2bo2bobo12bobo2bo2bobo12bobo
5bobo12bobo5bobo10bo3b3o3bo11bobob3obobo7bo3b3o3bo8bobo5bobo15bobo10bo
9bo7bo9bo5bo9bo$o2bo3bo2bo8bo2bo3bo2bo10bo2b2ob2o2bo12bo2bobobo2bo13bo
bo5bobo11bo2b2ob2o2bo10bo9bo14bob3ob3obo14bobo5bobo15bo4bo4bo11bobo2bo
2bobo10bobobobobobo11bobo2bo2bobo12bobobobobobo12bobo2bo2bobo12bobobob
obobo10bobo2bo2bobo11bobo2bo2bobo7bobo2bo2bobo8bobob3obobo28bobo2bo2bo
bo7bobo2bo2bobo5bobo2bo2bobo$4bobo16bobo14bo4bo4bo12bo9bo16bobobo14bo
4bo4bo10bo2b5o2bo14bobo5bobo14bo2b2ob2o2bo15bo3bobo3bo11bob3ob3obo10bo
4bo4bo11bob3ob3obo12bobo5bobo12bo9bo12bobo5bobo10bobobobobobo11bobo2bo
2bobo7bobobobobobo8bobo2bo2bobo28bobo5bobo7bobo5bobo5bobo5bobo$4bobo
33bo9bo15b5o38bo9bo10bo2bo3bo2bo17bobobo17bo4bo4bo15bo4bo4bo11bobo5bob
o10bo3bobo3bo11bobo5bobo12bo2b2ob2o2bo12bo3bobo3bo12bob3ob3obo10bobo5b
obo11bobo2bo2bobo7bobo5bobo8bobo2bo2bobo11b2o7b2o6bobo2bo2bobo7bobo2bo
2bobo5bobo2bo2bobo$3bobobo14bobobo13bo3b3o3bo15bo3bo19bo3bo14bo3b3o3bo
14bobo43bo9bo19bobo18bobobo13bo4bo4bo14bobobo15bo4bo4bo12bo9bo12bo4bo
4bo10bo2b2ob2o2bo11bob3ob3obo7bo2b2ob2o2bo8bobo2bo2bobo28bobo2bo2bobo
7bobo2bo2bobo5bobo2bo2bobo$3bo3bo14bo3bo18bo20bo3bo19bo3bo19bo43bo3bo
17bo3b3o3bo19bobo40bobo38bo9bo13b4ob4o13bo9bo10bo4bo4bo11bobo5bobo7bo
4bo4bo8bob3ob3obo12bobo3bobo7bobo5bobo7bobo5bobo5bobo5bobo$3bo3bo14bo
3bo39bo3bo62bobobo20bo3bo22bo23bo3bo17bo3bo17bobo18bo3bo15bo3b3o3bo14b
2o3b2o14bo3bobo3bo10bo9bo14bobobo10bo9bo8bobo5bobo12bo7bo7bo2bobobo2bo
7bo2bobobo2bo5bo2bobobo2bo$2bo2bo2bo12bo5bo15bobobo18bo3bo21bo19bobobo
16bo3bo71bo3bo17bo3bo16bo3bo17bo3bo20bo20bo3bo36bo3b3o3bo29bo3b3o3bo
11bobobo15bobo3bobo7bo9bo7bo9bo5bo9bo$3bo3bo35b5o17b2o3b2o40b5o16bo3bo
22bo22bobobo21bo3bo38bo3bo63bo3bo20bo20bo19bo3bo15bo36b3o3b3o10b5o13b
5o11b5o$3b5o14bobobo18bo19b3ob3o42bo17bo5bo44b5o22b3o20bo18bo3bo19bo
20bobobo19bobo19bo3bo38bo3bo32bo3bo15bo7bo10bo3bo13bo3bo11bo3bo$67bobo
21bobo91bo23bo3bo39b3o41b5o41bo3bo16bobobo35bobobo14bo3bo14bo9bo9bo3bo
13bo3bo11bo3bo$45bo21bobo20bobobo19bo18bobobo21bobo48b3o39bo3bo42bo64b
5o19bo15b5o33bobo5bobo9bo3bo13bo3bo11bo3bo$2bo2bo2bo12bo2bo2bo61bo2bo
2bo62bobobo22bo46bobo18b3o19bobo44bo21b3o19bo39bo18bo16b3o5b3o9bo3bo
13bo3bo11bo3bo$2bo2bo2bo12bo5bo17bo19bo5bo17bobobobo18bo42bo2bo2bo67bo
bobo38bobobo20bo20b2ob2o136b2o3b2o11b2o3b2o9b2o3b2o$2bobobobo14bobo18b
3o18bobobobo17bo5bo17b3o16bo2bo2bo18bobobobo21bo22bo2bo2bo15bo2bo2bo
36bo2bo2bo39b2o3b2o18b3o19bo20bobo16bo39bobo12b3ob3o11b3ob3o9b3ob3o$2b
2o3b2o33bobobobo17bobobo40bobobobo14bo5bo18bo5bo20b3o21bo2bo2bo15bobob
obo14bo2bo2bo15bobobobo19bo19bo5bo60bobobo33bobo17b2o3b2o12bobo15bobo
13bobo$2bo2bo2bo15bo17bob3obo18bobo41bob3obo16bobo45bobobobo19bo5bo15b
o5bo14bo2bo2bo15bo5bo18b3o18bobobobo40bo18bo2bo2bo14bo16bobobo16bobobo
bo12bobo15bobo13bobo$3b2ob2o13b2o3b2o39bobo19bo5bo86bob3obo20bo3bo37bo
5bo38bobobobo16bo2bo2bo16bo5bo16b3o17bobobobo13b3o14bo2bo2bo15bo5bo$5b
o18bo19bobo18b2obob2o19bobo19bobo19bo21bo5bo88bo3bo39bob3obo39bobobobo
14bobobobo15bo5bo11bobobobo12bobobobo14bo2bobo2bo9bo5bo11bo5bo9bo5bo$
43bobobo19bobo22bo19bobobo15b2o3b2o20bobo22bobo22b2ob2o16bo5bo36bo5bo
83bob3obo33bob3obo12bo5bo14bobo3bobo9bobobobo11bobobobo9bobobobo$135bo
24bo22bobobo23bo20bobo17b2ob2o18bobo20bobo19bobobo18b2ob2o97bo3bo12bob
obo13bobobo11bobobo$233bo20bo21bo20bobobo18b2ob2o18bobobo17bobo17bo5bo
13bobo35bo7bo11bobo15bobo13bobo$321b3o20bobo17bobobo18bobo14bobobo13bo
5bo16bo3bo13bobo15bobo13bobo$388bo35bobo19bobo12b2obob2o11b2obob2o9b2o
bob2o$425bo18b2o3b2o12bobo15bobo13bobo7$57bo7bo$57b3o3b3o$56b2o7b2o$
56bo9bo$56bo4bo4bo$56bob2o3b2obo$56bo9bo$57bo3bo3bo$40b3o14bo3bo3bo
105bo2b2o15bo$57bo7bo102bo5bo14b3o$36b2o7b2o10bobo3bobo104b2o16bo2b2o$
37bo7bo11bo7bo123bo2bo$18b2o7b2o8bo7bo11bo2bobo2bo109bo16bo$19bo3bo3bo
9bo3bo3bo11bo2b3o2bo105b3obo11bo2bobo$19bob2ob2obo9bob2ob2obo12bobobob
o106bobobo10bo3bobo$19bo7bo9bo7bo12bobobobo106bobobo9bo2bobobo$20bo5bo
11bo5bo13bo5bo63bo23bo15bo2bo3bo9bob2obobo$20bo5bo11bo5bo13b2o3b2o61b
3o23b3o13bobo2bobo9bo2bo3bo$20bo5bo11bo5bo13bo5bo63bo23bo15bo2bo3bo9bo
2b3obo$20bob3obo11bob3obo13bo2bo2bo62b2o2b2o15b2o2b2o14bo4bobo9bo2bo3b
o$20bobobobo11bobobobo13bo2bo2bo103bo6bo9bo3bo2bo$21bo3bo13bo3bo13b2o
2bo2b2o102bo3b2obo9bo3bo2bo$18b4o3b4o7b4o3b4o14bo65bo2bob2o13b2obo2bo
14bo2bo3bo9bo6bo$21bo3bo13bo3bo12b2o3bo3b2o60bo5bo13bo5bo14bo6bo9bo3bo
2bo$20bo5bo11bo5bo14bo3bo63bo4b2o13b2o4bo14bobo4bo9bobo4bo$57bo2bobo2b
o44b2o3b2o10bobo2b2o13b2o2bobo14bobo4bo9bobobo2bo$5bo3bo8bobobobobobo
7bobobobobobo10bobo3bobo14bo2b2o13bo12bo3bo12bo3bo15bo3bo15bo3bobo12bo
bobo$3b3o3b3o7b4ob4o9b4ob4o14bobo14bo5bo12b3o12bo3bo12bo3bo15bo3bo18b
2obo12b3obo$5bo3bo11bo3bo13bo3bo15bo3bo15b2o14bo2b2o12bobo14bobo17bobo
20bobo16bo$4b2o3b2o12bo17bo18b3o33bo2bo13bo16bo19bo19bobobo12b3obo$23b
o17bo16bob3obo19bo14bo13bo16bo19bo23bo12bo3bo$61bo18b3obo9bo2bobo69bo
4bo$5b2ob2o12bobo15bobo17b3o17bobobo8bo3bobo69bo16b2o$3b3o3b3o8b2obob
2o11b2obob2o12b2o5b2o14bobobo7bo2bobobo13bobo14bobo17bobo37bo$5bobobo
12bobo15bobo18bo15bo2bobobo7bo2bo3bo15bo16bo19bo17bo3bo13bobo$4bo2bo2b
o7bo2bobobo2bo7bo2bobobo2bo11bo2bo2bo12bobo4bo7bo3b2obo9b3o3bo10b3o3bo
13b3o3bo36bo$4bobobobo7bo9bo7bo9bo11bo5bo15b3obo7b2o5bo9bob3obo10bob3o
bo13bob3obo19bo$4bobobobo7bob2o3b2obo7bob2o3b2obo11bobobobo19bo8bo3bob
o16bo16bo19bo17bo$2bo9bo5bo3bobo3bo7bo3bobo3bo9bo2bobobo2bo15bobo8bo3b
obo15b2o15b2o18b2o16bo17b3o$3bobo3bobo7bo3bo3bo9bo3bo3bo11bob2ob2obo
11b3o2bobo7bo2b2o2bo10bob2o2bo10bob2o2bo13bob2o2bo16bob3o12bobo$3bo3bo
3bo7bo3bo3bo9bo3bo3bo11bo3bo3bo13bo4bo7b4o3bo10bobo2b2o10bobo2b2o13bob
o2b2o20b2o12b2o$3bo7bo7bo3bo3bo9bo3bo3bo11bo7bo12b2o4bo14bo11b2o3bo11b
2o3bo14b2o3bo16b2o3bo16bo$3bo7bo7bo7bo9bo7bo11bo7bo18bo14bo10b4o2bo10b
4o2bo13b4o2bo15bo5bo16bo$3bo7bo7bo7bo9bo7bo11bo7bo18bo8bob3obo10bob2o
2bo10bob2o2bo13bob2o2bo14bo4bobo9bo6bo$4bo2bo2bo9bo2bo2bo11bo2bo2bo13b
o5bo13bo3bobo8bobobobo10bobobobo10bobobobo13bobobobo14bobobobo10bobo3b
o$4bobobobo9bobobobo11bobobobo13bobobobo13bobobobo8bobobobo10bobobobo
10bobobobo13bobobobo14bo5bo10bobobobo$6bobo13bobo15bobo17bobo15bob3obo
8bo2bo2bo10bo5bo10bo5bo13bo5bo14bobobobo10bob3obo$6b3o13b3o15b3o18bo
106bob3obo$6b3o13b3o15b3o38bo14bo73b3o15bo$6b3o13b3o15b3o18bo18bobo12b
obo13bo3bo12bo3bo15bo3bo17b3o14bobo$60bobo32b3o15bo16bo19bo$6bobo13bob
o15bobo17b3o18bo31bo16bo19bo19bobo15bo!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce
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Re: Just Friends (B2-a/S12)

Postby A for awesome » September 3rd, 2017, 11:53 am

Two c/9 ships:
x = 36, y = 54, rule = B2-a/S12
24bo9bo$24b3o5b3o$23b2o9b2o$23bobo7bobo$23bob4ob4obo$23bobobobobobobo$
23bobobobobobobo$23bobobo3bobobo$23bobob2ob2obobo$23bo5bo5bo$23bo5bo5b
o$23bo4b3o4bo$23bo2b7o2bo$bo9bo11bo4b3o4bo$b3o5b3o11bo3bobobo3bo$2o2bo
bobo2b2o10bob3obob3obo$o4bobo4bo10bobo7bobo$o11bo10bobo7bobo$o11bo10bo
bobo3bobobo$ob2o5b2obo10bobobobobobobo$o11bo10bobobobobobobo$o2bo5bo2b
o10bo3bobobo3bo$o2bobobobo2bo10bo2bobobobo2bo$o2bobobobo2bo10bo11bo$o
2bob3obo2bo10bo11bo$o2bob3obo2bo10bo11bo$o2bo2bo2bo2bo10bo2bo5bo2bo$o
2bo2bo2bo2bo10bo2bo5bo2bo$o2bo2bo2bo2bo10bo2bo5bo2bo$o3b2ob2o3bo10bo2b
obobobo2bo$o4bobo4bo10bo4bobo4bo$o11bo10bo5bo5bo$o5bo5bo10bo3bobobo3bo
$obo7bobo10bob2obobob2obo$obo2bobo2bobo10bo11bo$ob3obob3obo10bo11bo$o
11bo10bobo2b3o2bobo$o2bo5bo2bo10bob4ob4obo$obobo3bobobo10bobob5obobo$o
bobo3bobobo10bobobobobobobo$obobo3bobobo10bobobo3bobobo$o2bo5bo2bo10bo
11bo$o2bo5bo2bo10bobobo3bobobo$o11bo10bo11bo$obo7bobo10bo11bo$obobo3bo
bobo10bobo2bobo2bobo$obo7bobo10bobo2bobo2bobo$o3bo3bo3bo10bo2bo5bo2bo$
3b3ob3o13bo11bo$5bobo21bo$28bobo$6bo21bobo$6bo$6bo22bo!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

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Re: Just Friends (B2-a/S12)

Postby Hdjensofjfnen » September 3rd, 2017, 2:17 pm

Nice that this thread is alive again!

Component:
x = 9, y = 15, rule = B2-a/S12
3bo$3bo$bo$bob4o2$obobo$4bo$2bobo$2bobo$4bo3$8bo$7bo$7bo!


EDIT: How come I never noticed this oscillator before? Weird:

x = 3, y = 3, rule = B2-a/S12
obo2$obo!


EDIT: 2G in 2G:

x = 10, y = 10, rule = B2-a/S12
2bo$2o6$8b2o$8bo$8bo!
Life is hard. Deal with it.
My favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
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Re: Just Friends (B2-a/S12)

Postby toroidalet » September 3rd, 2017, 9:17 pm

Is this 17-cell p708 glider shuttle known?
x = 65, y = 74, rule = B2-a/S12
63bo$63bo4$61bo$64bo$59bobo2bo46$18bo$19b2o12$4bo$4bo4$2bo$5bo$obo2bo!

EDIT: fixed period
Last edited by toroidalet on September 3rd, 2017, 10:34 pm, edited 1 time in total.
x = 11, y = 5, rule = B2ck3-ij5n78/S01e2ei3-k5ai
8b2o$2o3b2o$bo4bo3bo$2bo2b2o$o7bo!

(Check Gen 2)
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Re: Just Friends (B2-a/S12)

Postby Hdjensofjfnen » September 3rd, 2017, 9:22 pm

toroidalet wrote:Is this 17-cell p704 glider shuttle known?
x = 65, y = 74, rule = B2-a/S12
63bo$63bo4$61bo$64bo$59bobo2bo46$18bo$19b2o12$4bo$4bo4$2bo$5bo$obo2bo!


Probably not, knowing that I haven't ever seen the reflectors...
Life is hard. Deal with it.
My favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
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Re: Just Friends (B2-a/S12)

Postby AforAmpere » January 18th, 2018, 6:47 pm

C/10 wickstretcher:
x = 15, y = 62, rule = B2-a/S12
4bo5bo$4bo5bo$2b2ob2ob2ob2o$5bo3bo$5bobobo2$6bobo$5bo3bo$7bo$o2bo7bo2b
o$o2b2o5b2o2bo$obo9bobo$obo9bobo$obo2bobobo2bobo$obobo5bobobo$obo2b5o
2bobo$o13bo4$3o4bo4b3o$2bobo2bo2bobo$4b2o3b2o$5b5o$b2o9b2o$7bo$7bo$4bo
bobobo3$7bo$5b2ob2o$5bobobo$6bobo4$4b2o3b2o$2bo2bo3bo2bo2$2bo9bo$obob
2o3b2obobo$2bo4bo4bo2$3bo7bo$o13bo$obo2bo3bo2bobo$obo9bobo$ob2o2b3o2b
2obo$o13bo$o5bobo5bo$o4b5o4bo$o13bo$o13bo$o3bo5bo3bo$o2bo2bobo2bo2bo$o
2bo7bo2bo$obo9bobo$ob3o5b3obo$obo9bobo$o2bo7bo2bo$o2bo7bo2bo!
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
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Re: Just Friends (B2-a/S12)

Postby Hdjensofjfnen » February 11th, 2019, 5:07 pm

Hmm. The front moves at c/3 and the back at c/5:
x = 7, y = 7, rule = B2-a/S12
6bo$3b4o$2o$o2bo$2o$3b4o$6bo!

EDIT: Oops, I found this two years ago :oops:
Life is hard. Deal with it.
My favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
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Re: Just Friends (B2-a/S12)

Postby Freywa » May 16th, 2019, 9:44 pm

I randomly apgsearched Just Friends in D4_+1 and found this p83 in three different stator variants that's not in David Bell's oscillators file:
x = 25, y = 19, rule = B2-a/S12
9bo5bo$9bo5bo6$o23bo$o9b2ob2o9bo$o23bo$o9b2ob2o9bo$o23bo6$9bo5bo$9bo5b
o!

And this true p60:
x = 11, y = 9, rule = B2-a/S12
5bo$5bo2$11o$o9bo$3b5o$2bo5bo$2bo2bo2bo$2bo2bo2bo!

And… this thing? (The inner part grows at 2c/28.)
x = 31, y = 31, rule = B2-a/S12
5o2bobo2b2obob2o2bobo2b5o$obob2obobobo2bobo2bobobob2obobo$bobo2b3o4b2o
b2o4b3o2bobo$2o4b4obo3bo3bob4o4b2o$ob2o2b4obo2bobo2bob4o2b2obo$2b2obo
3b2o3bobo3b2o3bob2o$4ob3ob2o3b3o3b2ob3ob4o$4b3o2b2ob2obob2ob2o2b3o$3b
3o2b2obo7bob2o2b3o$3bob2ob4o2b3o2b4ob2obo$2b4o4bob2obob2obo4b4o$3b2o
21b2o$b2o3bobobobo2bo2bobobobo3b2o$3obob2ob3obo3bob3ob2obob3o$6b2o4b3o
b3o4b2o$3b2ob3o3bo5bo3b3ob2o$6b2o4b3ob3o4b2o$3obob2ob3obo3bob3ob2obob
3o$b2o3bobobobo2bo2bobobobo3b2o$3b2o21b2o$2b4o4bob2obob2obo4b4o$3bob2o
b4o2b3o2b4ob2obo$3b3o2b2obo7bob2o2b3o$4b3o2b2ob2obob2ob2o2b3o$4ob3ob2o
3b3o3b2ob3ob4o$2b2obo3b2o3bobo3b2o3bob2o$ob2o2b4obo2bobo2bob4o2b2obo$
2o4b4obo3bo3bob4o4b2o$bobo2b3o4b2ob2o4b3o2bobo$obob2obobobo2bobo2bobob
ob2obobo$5o2bobo2b2obob2o2bobo2b5o!

And this growing ship with a c/8 back end:
x = 25, y = 9, rule = B2-a/S12
o$ob2o$4b19o$b2o20b2o$bobo$b2o20b2o$4b19o$ob2o$o!

Since Just Friends is proven omniperiodic, here's the smallest non-trivial oscillator for each period up to p20. Please tell me if I've missed any smaller oscillators or stator reductions.
x = 46, y = 103, rule = B2-a/S12
25bo$25bo2b4o$5b2o21bo$28b3o$25bo$25bo3$6bo$3b2obo$5bo18b3o$5bo$3b2obo
21b3o$6bo5$5bo14bo11bo$5bo$3b2ob2o9b2obo4bobo4bob2o$5bo18bo3bo$5bo19b
3o2$24bo3bo4$5bo$3b3o20b2o$4b3o16bo$4bo20bo4$25bo$23bobo$2b2o3b2o14bob
o4bo$5bo24bo$b9o11b3obo2bobo$5bo22bo$2b2o3b2o15b3obo$28bo4$26bo$5bo20b
o$5bo18bo2b3o$6b2o14b3o2bo$25bo$25bo6$5bo$5bo17bo3bo$5bo17bobobo$23bo
4bo$b3o3b3o11bo16bo$21bo16bo$5bo25bo4bo$5bo26bobobo$5bo26bo3bo4$22bo3b
o$22bo3bo$19b2o7b2o$5bo15b7o$5bobo$5bobob2o13bo$22b2ob2o$5b2obo15bo$b
2o5bo$21b7o$19b2o7b2o$22bo3bo$22bo3bo4$o11bo20bobo$ob2o5b2obo$o3bo3bo
3bo20b5o$ob2o5b2obo$o11bo20b3o$30bo$30bo6$8bo$bo2bo3bo16b3o4b3ob3o4b3o
$bo2b3obo$3bo6bo15b3o3bo5bo3b3o$3bo2bo3bo21bob3obo$3bo28bo5bo!
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Re: Just Friends (B2-a/S12)

Postby Hdjensofjfnen » May 28th, 2019, 7:51 pm

Freywa wrote:And… this thing? (The inner part grows at 2c/28.)


Nice find! Looks like a wickstretcher trapped within a wickstretcher.
Life is hard. Deal with it.
My favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
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Re: Just Friends (B2-a/S12)

Postby bidibangboom » May 30th, 2019, 6:03 pm

so i found a signal that moves a line of cells, but deletes 5 cells from it.
x = 51, y = 31, rule = B2-a/S12
50bo$48bobo$49bo$49bo$49bo$49bo$49bo$49bo$49bo$49bo$bo47bo$2b36o11bo$
2o47bo$49bo$49bo$49bo$49bo$49bo$49bo$49bo$49bo$49bo$49bo$49bo$49bo$49b
o$49bo$49bo$49bo$49bo$49bo!

2 signal wave that does not move the line and makes an oscillator.
x = 4, y = 34, rule = B2-a/S12
bo$bobo$2bo$2bo$obo$bo$bo$bo$bo$bo$bo$bo$bo$bo$bo$bo$bo$bo$bo$bo$bo$bo
$bo$bo$bo$bo$bo$bo$bo$bo$bo$bo$bo$bo!

(sorry if known)
EDIT: so i added a cell to a c/9 spaceship to get this multiple wick stretcher!
x = 13, y = 44, rule = B2-a/S12
o11bo$o11bo$obo7bobo$obo7bobo$obobo3bobobo$obobo3bobobo$obobobobobobo$
obobobobobobo$obobobobobobo$obobobobobobo$obobobobobobo$ob2o2bo2b2obo$
o11bo$o11bo$o11bo$o11bo$o2bo5bo2bo$o2bo5bo2bo$o2bo5bo2bo$o2bo2bo2bo2bo
$o4bobo4bo$o4bobo4bo$o3b2ob2o3bo$o4bobo4bo$obo7bobo$o2b2o3b2o2bo$o11bo
$obo3bo3bobo$o11bo$obobo3bobobo$obobo3bobobo$obobo3bobobo$o2bo5bo2bo$o
11bo$o11bo$obo3bo3bobo$obob2ob2obobo$obo3bo3bobo$b5ob5o$5bobo$5bobo2$
6bo$6bo!

(again, sorry if known)
EDIT 2: a p8 ocillator
x = 15, y = 8, rule = B2-a/S12
2bo9bo$2bo9bo$3bobo3bobo$2obobo3bobob2o$3bobobobobo$3bobobobobo2$2b11o
!

(sorry if known)
#C A period 8 oscillator that was found in 1972.
#C http://www.conwaylife.com/wiki/index.php?title=Roteightor
x = 14, y = 14, rule = 23/3
bo12b$b3o8b2o$4bo7bob$3b2o5bobob$10b2o2b2$6b2o6b$5b2obo5b$6b3o5b$2b2o
3b3o4b$bobo5b2o3b$bo7bo4b$2o8b3ob$12bo!
fun
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Re: Just Friends (B2-a/S12)

Postby Hdjensofjfnen » Yesterday, 2:30 pm

Is anyone up to find a rake in this rule?
Life is hard. Deal with it.
My favorite oscillator of all time:
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
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Re: Just Friends (B2-a/S12)

Postby Moosey » Yesterday, 2:58 pm

Hdjensofjfnen wrote:Is anyone up to find a rake in this rule?

Well, there has been a dirtyrake;
If someone wants to add some bits with cleanup, I have it from the golly pattern collection along with a few reactions.
x = 1513, y = 211, rule = B2-a/S12
12b3o1032bo$11bo2b2o$12bo2bo23bo$12b2obo23bo1007bo$32bo$2b3o5b21obo$bo
2b2ob3o22bo5bo1008bo$2bo2bo4b20obo6bo$2b2obo25bo5bo$11b2obo1032bo$2obo
7bo2bo$o2bo9bo$2bo8b2o1034bo$2o2$1047bo3$459b2o586bo$459bo$459bo2bo$
460b3o584bo2$461b2obo$461bo2bo582bo$463bo$461b2o$1047bo3$1047bo3$1047b
o3$1047bo3$1047bo3$1047bo3$1047bo3$1047bo3$1047bo3$1047bo3$1047bo2$
1352b3o$1047bo303bo2b2o$1352bo2bo$647b2o703b2obo$647bo399bo296b2o$647b
o2bo693bo9b2obo$333b3o312b3o693bo2bo$332bo2b2o710bo297b3o5bo$333bo2bo
312b2obo700b2o$333b2obo312bo2bo693b2obo$325b2o324bo395bo298bo2bo$325bo
9b2obo310b2o697bo$325bo2bo1017b2o$326b3o5bo712bo$334b2o$327b2obo$327bo
2bo716bo311b2o$329bo1029bo$327b2o325b2o204b2o642bo$654bo205bo186bo268b
2o42b2obo$860bo2bo452bo186b2o$655b2obo202b3o452bo2bo38b2obo$340b2o705b
o269b3o38bo2bo$340bo312b2obo205b2obo491bo2b2o$653bo2bo205bo2bo452b2obo
36b3o$297b2o42b2obo307bo2b2o207bo182bo270bo2bo$297bo213b3o139b3o206b2o
456bo188b2o$297bo2bo38b2obo167bo2b2o803b2o191bo$298b3o38bo2bo168bo2bo
162b2o368bo461bo2bo$338bo2b2o168b2obo70b3o91bo829b2obo$299b2obo36b3o
161b2o79bo2b2o88bo2bo$299bo2bo200bo9b2obo68bo2bo88b2obo366bo460b3o$
301bo201bo2bo78b2obo732b2o184bo2bo$299b2o203b3o5bo163b3o828bo$512b2o
73b2obo84bo2bo368bo273bo185b2o$505b2obo166bo$505bo2bo77bo88b2o$507bo
78b2o459bo$505b2o2$1047bo2$518b2o$518bo528bo2$475b2o42b2obo$475bo571bo
$475bo2bo38b2obo$476b3o38bo2bo$516bo2b2o526bo$477b2obo36b3o$477bo2bo$
479bo567bo$288b2o187b2o$288bo$1047bo$289b2obo2$287b2obo756bo$287bo2bo$
286bo2b2o$287b3o757bo2$882b2o$561b2o319bo164bo$561bo$393b2o488b2obo$
395bo166b2obo481bo$393bo2bo172b2o310b2obo$393b2obo36b3o124b2obo7bo309b
o2bo10b2o$432bo2b2o123bo2bo5bo2bo307bo2b2o12bo149bo$392b3o38bo2bo122bo
2b2o5b2obo308b3o11bo2bo$391bo2bo38b2obo123b3o332b2obo$391bo176b3o476bo
$391b2o42b2obo128bo2bo323b3o$567bo325bo2bo$434bo132b2o324bo153bo$434b
2o457b2o2$1047bo2$421b2o$423bo623bo$421bo2bo$421b2obo$428b2o617bo$420b
3o5bo$419bo2bo$419bo9b2obo614bo$419b2o$427b2obo$427bo2bo616bo$426bo2b
2o$427b3o$1047bo2$1362b2o$1047bo316bo$1362bo2bo$1362b2obo$1047bo306b2o
$1354bo9b2obo$1364bo2bo$1047bo307b2obo4bo2b2o$1364b3o$1357b3o$1047bo
308bo2bo$1356bo$1356b2o$1047bo3$1047bo322b3o$1369bo2b2o$1370bo2bo$526b
2o519bo278b2o42b2obo$526bo799bo$1368b2obo$527b2obo516bo279b2obo37bo2bo
$1370bo$525b2obo800b3o36b2o$525bo2bo518bo280bo2bo$524bo2b2o799bo$525b
3o800b2o$1047bo2$593b3o$592bo2b2o450bo$593bo2bo$593b2obo$1047bo$595b2o
bo2$594bo452bo$594b2o2$1047bo3$1047bo274bo$1320bobo$589b2o$591bo455bo$
589bo2bo725b3o$589b2obo724bo2b2o$1047bo270bo2bo$588b3o727b2obo$587bo2b
o$587bo459bo268b2obo$587b2o727bo2bo$1318bo$1047bo268b2o!

My rules:
They can be found here

Also, the tree game
Bill Watterson once wrote: "How do soldiers killing each other solve the world's problems?"
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