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4-Life (LtL R2,S4,B4)

Posted: December 13th, 2020, 11:50 pm

by volcanrb

I am very surprised how little exploration into this rule I could find online, based on how simple it is to describe and how interesting the dynamics are that it produces. I could only find two other mentions of it online, one of which was by Kellie Evans in her thesis where she named it the LtL rule with the most interesting dynamics. I creatively named it 4-life since a cell will live next step if it currently has 4 neighbors.

It has a number of 3c/2 orthogonal ships. All the ones I've found are shown below:

Code: Select all

x = 89, y = 264, rule = R2,C0,M0,S4..4,B4..4,NM
13b2o26b2o21b2o$b4o8b2o11b2o13b2o21b2o$13b2o11b2o13b2o21b2o$o4bo6bo3b
o9b2o12bo2bo18bo4bo$o4bo10b2o7bo3bo10bo2bo2$62bo4bo4$62bo4bo$63bo2bo$
64b2o9$63b4o$62bo4bo5$58bo4bo2bo4bo$57bo14bo$57bo3bo6bo3bo$60b2o6b2o3$
55bo2bo12bo2bo$55b3o14b3o$55bo18bo2$60bo8bo$60bo8bo2$55bo18bo$55b3o14b
3o$55bo2bo12bo2bo2$58bo12bo$58bo12bo$58bo12bo$58bo12bo16$64b2o$62bo4b
o$64b2o$63bo2bo$64b2o13$46b4o30b4o$46bo2bo30bo2bo$50bo28bo$45bo38bo$52b
o24bo$46bo6b2o20b2o6bo$46bo7bo20bo7bo$47bo6bo20bo6bo$48b2o3b2o20b2o3b
2o$51bo26bo24$49b2o28b2o$48bobo28bobo$46b2o2bo28bo2b2o$46b2o2bo28bo2b
2o$48bo32bo3$54b4o14b4o$57bo14bo$53bo2bo16bo2bo$54b2o18b2o$54b2o18b2o
19$41b4o40b4o$41bo2bo3bobobo24bobobo3bo2bo$41bo3bobo2bo28bo2bobo3bo$41b
o10bo24bo10bo$43bo42bo$44bo5bo28bo5bo$50bo13b2o13bo$63bo2bo$44bo7bo8b
o6bo8bo7bo$46bo13bo8bo13bo2$60bo3b2o3bo$47bo4bo24bo4bo$49b2o28b2o$62b
o4bo3$60bo3b2o3bo2$60bo8bo$61bo6bo$63bo2bo$64b2o5$43b2o40b2o2$46bo36b
o$46bo36bo$41bo46bo$44bo40bo$42b2o42b2o3$44bobo36bobo$42bo4bo34bo4bo$
43bo42bo$43bo19bo2bo19bo$42bo4bo34bo4bo$42bo44bo2$62bo4bo$56b2o14b2o$
56b2o14b2o$62bo4bo$62bo4bo$62bo4bo$62bo4bo$62bo4bo10$52bo2bo18bo2bo3$
52bo24bo$53b2o20b2o$64b2o$64b2o$53b2ob2o14b2ob2o$52bo4bo6b2o6bo4bo$52b
o11b2o11bo$55bo18bo$54b2o18b2o15$64b2o$63bo2bo$62b2o2b2o$63bo2bo$62bo
4bo$60bo8bo$59bob3o2b3obo$58bo2b2o4b2o2bo$59bob3o2b3obo$60bo8bo$62bo4b
o$63bo2bo$62b2o2b2o$63bo2bo$64b2o6$64b2o$63bo2bo$62b2o2b2o$63bo2bo$62b
o4bo$60bo8bo$59bob3o2b3obo$58bo2b2o4b2o2bo$59bob3o2b3obo$60bo8bo$62bo
4bo$63bo2bo$62b2o2b2o$63bo2bo$64b2o!

Below are all the oscillators found by myself and others (credited at the bottom):

Code: Select all

x = 207, y = 88, rule = R2,C0,M0,S4..4,B4..4,NM
16bo2bo$13bo8bo$12bo10bo75bo$99bo$99b4o$11bo4bo2bo4bo72b4o$67bo32bo79b
2o$100bo77bo4bo$11bo4bo2bo4bo41bobo108bo6bo$69b2o$65bo69bo2b2o36bo8bo
$5bo2bo14bo42bo68bo3bo36bo8bo$2bo19bo46b2o14b2o48b2o2bo$bo14bo2bo47bo
bo14bo2bo36b3o24bo25bo6bo$83b2o2b2o10bo7bo3bo5bo6bobo23bob3o23bo4bo$82b
o6bo8bobo6bo3bo4bo35b2o26b2o$o4bo2bo4bo68bo6bo8bobo16bobo28b2o$83b2o2b
2o10bo9bo8bo7bob2o6bobo8b3obo$28bo55bo2bo21bo14b2o4bo4bo3bo10bo$o4bo2b
o4bo10bo60b2o37bo4bo6bobo$23bo$24bo$bo10bo16bo$2bo8bo8bo12bo$5bo2bo10b
obo3b3o$24bo2bo$24bo2bo120bo$24b3o3bobo10bo2bo38b2o62bobo$18bo12bo8bo
8bo33bob2obo58bo$22bo16bo10bo94bo7bo$27bo53b2o6b2o55bo$28bo53bo6bo25b
o8b3o7bobo16bo$27bo10bo4bo2bo4bo29b2o6b2o5bo9b3o5b2o7bo7bo3bo3bo6bo7b
o$23bo74bo6bo3bo2bo3bo14bo7bo12bo$83bob2obo6b2o9b2o5b3o10bo7bobo11bob
o$38bo4bo2bo4bo33b2o10bo8bo16b3o25bo3$32bo2bo14bo$29bo19bo$28bo14bo2b
o$195b2o2$27bo4bo2bo4bo152b2o2b2o$64b4o124bo6bo$64bo2bo124bo6bo$27bo4b
o2bo4bo22bob2obo126b2o$63b6o126b2o$64bo2bo14b2o22b2o$28bo10bo21bo8bo9b
o4bo5bobo2bobo5b2o3bo$29bo8bo22bo2bo2bo2bo9bo4bo7bo2bo7bo6b2o$32bo2bo
26b3o2b3o14bo8bo2bo$79bo11bobo2bobo14bo$113bo$78bo25bo5bo$78bo25bo6b2o
$79bo115b2o$62b3o2b3o9b2o3b2o109b2o$61bo2bo2bo2bo121bo6bo$61bo8bo121b
o6bo$64bo2bo125b2o2b2o$63b6o40bo2bo$63bob2obo126b2o$64bo2bo11bo2bo26b
4o$64b4o$79b4o$109b4o2$79b4o26bo2bo2$79bo2bo$201b2o$199bo4bo$198bo6bo
$106b2o3b2o66bo2bo$112bo63bo8bo11bo8bo$79b2o6bo25bo61bo10bo10bo8bo$81b
o5bo25bo$78bo119bo6bo$78bo14bobo2bobo11bo61bo4bo2bo4bo11bo4bo$95bo2bo
8bo93b2o$79b2o6bo7bo2bo7bo4bo$82bo3b2o5bobo2bobo5bo4bo62bo4bo2bo4bo$84b
2o22b2o2$175bo10bo$176bo8bo$179bo2bo!

and I've found a number of still lives, only a few of which occur commonly:

Code: Select all

x = 43, y = 22, rule = R2,C0,M0,S4..4,B4..4,NM
19bobo4bobo4bobo4b3o$26bo7bo5bobo$bo5bo6bo4b3o5b2o4bobo$obo5b2o2b2o$o
bo5b2o2b2o3$obo5b2o2b2o6b2o2b2o$obo5b2o2b2o7bo2bo7b2o2b2o$bo5bo6bo4b2o
4b2o4b3o2b3o5$9bo2bo$8b2o2b2o$7b2o4b2o3$7b2o4b2o$8b2o2b2o$9bo2bo!

I've also found two exploding patterns, the first of which is somewhat common, and is responsible for making large enough soups rarely stabilize:

Code: Select all

x = 4, y = 4, rule = R2,C0,M0,S4..4,B4..4,NM
b2o$b2o$b2o$o2bo!

Code: Select all

x = 14, y = 2, rule = R2,C0,M0,S4..4,B4..4,NM
2o10b2o$2o10b2o!

EDIT: I found a 4c/61 diagonal spaceship!

Code: Select all

x = 15, y = 15, rule = R2,C0,M0,S4..4,B4..4,NM
14bo$12b2o$13b2o$12bo9$bobo$b2o$obo!

My next goals for this rule:
1. Find more non-orthogonal ships
2. Find an orthogonal ship with a speed other than 3c/2o
3. Extend the following list of known oscillator periods:
2,3,4,6,8,9,11,24,28,120

Any contributions would be greatly appreciated! I'll edit this to add anyone's discoveries.
Contributions:
Thanks to Hunting for period 3,4, 6, and 28 oscillators
Thanks to bubblegum for a rake
Thanks for yujh for period 11 and 120 oscillators
(See all below)

Re: 4-Life (LtL R2,S4,B4)

Posted: December 14th, 2020, 12:02 am

by bubblegum

Okay, I'll start with three notes:
1) c is always 1 cell per tick. These ships are 3c/2o.
2) 5c/6 what
3) 4-Life is okay, but there is the concern of the other rule 4life.

In other words, a predecessor for a rake:

Code: Select all

x = 92, y = 178, rule = R2,C0,M0,S4..4,B4..4,NM
45b2o$45b2o$45b2o$44bo2bo172$b4o82b4o2$o4bo80bo4bo!

Re: 4-Life (LtL R2,S4,B4)

Posted: December 14th, 2020, 12:53 am

by Hunting

volcanrb wrote: December 13th, 2020, 11:50 pm 3c/2 (c = 2 cells per step)

c is 1 cell per generation.

volcanrb wrote: December 13th, 2020, 11:50 pm 3. Find more oscillators (especially one with odd cycle length)
Any contributions would be greatly appreciated! I'll edit this to add anyone's discoveries.

Four known oscillators... three p2s... I'm pretty sure a PlutoniumSearch would do.

EDIT: Hold on, I realized nbsearch2 (which uses random soups instead of brute-force patterns) supports more symmetry, so here:

Code: Select all

x = 6, y = 6, rule = R2,C0,M0,S4..4,B4..4,NM
3b2o$o$o$5bo$5bo$b2o!

I call this "James' p6 but in 4-Life".

EDIT: Adjusting nbsearch2's parameters slightly makes it much faster and avoids handling explosions (which is pointless, they won't stabilize into oscillators.)

Also unfortunately, nbsearch2, unlike Plutonium, does not support spaceship searching. I believe a slight tweak would allow spaceships, but I don't have time rn.

EDIT:

p3 at 14 cells:

Code: Select all

x = 10, y = 10, rule = R2,C0,M0,S4..4,B4..4,NM
6bo$3bobo$7bo$bo7bo$8bo$bo$o7bo$2bo$4bobo$3bo!

p6 at 10 cells:

Code: Select all

x = 4, y = 8, rule = R2,C0,M0,S4..4,B4..4,NM
3bo$2b2o$2b2o3$2o$2o$o!

EDIT: p28 at 9 cells:

Code: Select all

x = 8, y = 6, rule = R2,C2,M0,S4..4,B4..4,NM
4bo2$o5b2o$o5bo$7bo$4b2o!

I'm done for now

Re: 4-Life (LtL R2,S4,B4)

Posted: December 14th, 2020, 5:33 pm

by volcanrb

Hunting wrote: December 14th, 2020, 12:53 am Hold on, I realized nbsearch2 (which uses random soups instead of brute-force patterns) supports more symmetry, so here:

Thanks for the oscillators!

Where can I get nbsearch2? I couldn't find it searching the forums or online.

Re: 4-Life (LtL R2,S4,B4)

Posted: December 15th, 2020, 2:45 am

by wildmyron

volcanrb wrote: December 14th, 2020, 5:33 pm
Hunting wrote: December 14th, 2020, 12:53 am Hold on, I realized nbsearch2 (which uses random soups instead of brute-force patterns) supports more symmetry, so here:
Thanks for the oscillators!

Where can I get nbsearch2? I couldn't find it searching the forums or online.

It's buried in the Scripts request thread, here: https://conwaylife.com/forums/viewtopic ... 750#p52750

It's not a polished script and there's practically no documentation. Like Hunting said, you'll want to adjust the parameters slightly to reduce the time spent exploring soups that are exploding. In particular, I suggest reducing max_period (perhaps to 50 or 100) and experimenting with stab_step and x. stab_step controls how long soup is run to stabilise before checking periodicity and x is the soup size (smaller probably is better for explosive rules).

Re: 4-Life (LtL R2,S4,B4)

Posted: December 15th, 2020, 6:46 am

by Hunting

wildmyron wrote: December 15th, 2020, 2:45 am
volcanrb wrote: December 14th, 2020, 5:33 pm
Hunting wrote: December 14th, 2020, 12:53 am Hold on, I realized nbsearch2 (which uses random soups instead of brute-force patterns) supports more symmetry, so here:
Thanks for the oscillators!

Where can I get nbsearch2? I couldn't find it searching the forums or online.
It's buried in the Scripts request thread, here: https://conwaylife.com/forums/viewtopic ... 750#p52750

It's not a polished script and there's practically no documentation. Like Hunting said, you'll want to adjust the parameters slightly to reduce the time spent exploring soups that are exploding. In particular, I suggest reducing max_period (perhaps to 50 or 100) and experimenting with stab_step and x. stab_step controls how long soup is run to stabilise before checking periodicity and x is the soup size (smaller probably is better for explosive rules).

I believe x is fine as-is. I also trivially modified it to have a "known oscillators" file like dr, so I could get other oscillators with known periods.

Also experiment with soup density - for this rule, it is probably better to have sparse soups, both reduces explosiveness and gives more "natural" soups - this rule tends to evolve into sparse stuff.

Re: 4-Life (LtL R2,S4,B4)

Posted: December 15th, 2020, 7:44 am

by yujh

Code: Select all

x = 29, y = 76, rule = R2,C0,M0,S4..4,B4..4,NM
3bo2bo$3bo2bo$2b2o2b2o$3o4b3o3$3o4b3o$2b2o2b2o$3bo2bo$3bo2bo15$25bo2$
21b2obo2b2o$20bo3b2obo$22bobo$20bo3bob2o$24bo27$13b2o10b2o$13b2o10b2o
16$4b2o$4b2o!

P120, mod 60
Edit:P11:

Code: Select all

x = 40, y = 40, rule = R2,C0,M0,S4..4,B4..4,NM
28bo2bo$32bo$28bo2$17b4o$17b4o2$bo$o3$obo6$34b2o$34b2o$4b2o28b2o$4b2o
28b2o$4b2o$4b2o6$37bobo3$39bo$38bo2$19b4o$19b4o2$11bo$7bo$8bo2bo!

Re: 4-Life (LtL R2,S4,B4)

Posted: December 25th, 2020, 10:15 pm

by yujh

Bump! P48:

Code: Select all

x = 88, y = 86, rule = R2,C0,M0,S4..4,B4..4,NM
24b3o$25b2o$9b2obo$9bob2o$9b4o11bo$7bo2bo2bo$26bo$12b2o43b2o4b2o$10b2o
bo6bo34bo4b2o4bo$10bo11bo4bo27bo4b2o4bo$6bo4b2o7b2o33bo4b2o4bo$8bo4bo
7bo6bo26bo4b2o4bo$9bo12bo34b2o4b2o$9bo12bo4bo$8bo8bo$21b3o$6b2o12bo3b
2o2$5bo8bo10bo49b4o$13bob2o7b3o$7bo9bo2b2o52bo4bo$7bob2o6bo3b2o51bo4bo
$8bo5b2o5bo$o74b4o$obo6b2obo62b4o$bo$o73bo4bo$2bo5bobo7bobo53bo4bo$4bo
8bo4b2o$75b4o27$9b4o$68b2o4bo8bo$8bo4bo53bobo7bobo5bo$8bo4bo73bo$86bo$
9b4o62bob2o6bobo$9b4o74bo$66bo5b2o5bo$8bo4bo51b2o3bo6b2obo$8bo4bo52b2o
2bo9bo$61b3o7b2obo$9b4o49bo10bo8bo2$62b2o3bo12b2o$64b3o$70bo8bo$60bo4b
o12bo$23b2o4b2o34bo12bo$21bo4b2o4bo26bo6bo7bo4bo$21bo4b2o4bo33b2o7b2o
4bo$21bo4b2o4bo27bo4bo11bo$21bo4b2o4bo34bo6bob2o$23b2o4b2o43b2o$61bo$
74bo2bo2bo$63bo11b4o$75b2obo$75bob2o$61b2o$61b3o!

Re: 4-Life (LtL R2,S4,B4)

Posted: December 25th, 2020, 11:51 pm

by bubblegum

Another p48:

Code: Select all

x = 86, y = 22, rule = R2,C2,M0,S4..4,B4..4,NM
8$50bo2bo3bo6bo3bo$58bo4bo5bo$6b2o39b3o9bo2bo15b2o$6b2o39b3o9bo2bo15b
2o$58bo4bo5bo$50bo2bo3bo6bo3bo!

EDIT: Also a fragment of some kind of grammar for p120s:

Code: Select all

x = 112, y = 96, rule = R2,C2,M0,S4..4,B4..4,NM
6$6b2o$6b2o$21b2o2$16b2o8b2o2$15bo12bo$29bo$14bo5bo2bo5bo$18bo6bo17$18b
o6bo$14bo5bo2bo5bo$14bo14bo$15bo12bo2$16b2o8b2o2$21b2o29$104b2o$104b2o
4$67b2o22b2o$67b2o22b2o11$67b2o22b2o$67b2o22b2o!

Re: 4-Life (LtL R2,S4,B4)

Posted: January 7th, 2021, 9:50 pm

by FWKnightship

2c/4:

Code: Select all

x = 5, y = 5, rule = R2,C0,M0,S4..4,B4..4,NM
3obo2$o$3bo$2bo!

Re: 4-Life (LtL R2,S4,B4)

Posted: January 7th, 2021, 9:52 pm

by LaundryPizza03

I've seen this rule called "Kaleidoscope of Life" in the literature. But I don't have access to the actual source.

Re: 4-Life (LtL R2,S4,B4)

Posted: January 8th, 2021, 1:39 am

by wildmyron

LaundryPizza03 wrote: January 7th, 2021, 9:52 pm I've seen this rule called "Kaleidoscope of Life" in the literature. But I don't have access to the actual source.

It seems to be freely available from this link:
https://www.sciencedirect.com/science/a ... 8907004022

Wait, that doesn't seem to work. But it did when I followed the first link from this search:
https://scholar.google.com/scholar?hl=e ... Life&btnG=

Re: 4-Life (LtL R2,S4,B4)

Posted: July 20th, 2022, 3:59 pm

by ihatecorderships

bump!
2 suprisingly new p88s

Code: Select all

x = 140, y = 116, rule = R2,C0,S4,B4
15$22bo2bo30bo2bo$21b2o2b2o28b2o2b2o$19bob2o2b2obo24bob2o2b2obo$20bobo
2bobo26bobo2bobo$18b2obo4bob2o22b2obo4bob2o$17b4o6b4o20b4o6b4o3$17b4o
6b4o20b4o6b4o$18b2obo4bob2o22b2obo4bob2o$20bobo2bobo26bobo2bobo$19bob
2o2b2obo24bob2o2b2obo$21b2o2b2o28b2o2b2o$22bo2bo30bo2bo$92b2o32b2o$91b
o2bo30bo2bo$90b2o2b2o28b2o2b2o$89bo6bo26bo6bo$89bo6bo26bo6bo$90b2o2b2o
28b2o2b2o$33b4o8b4o42bo2bo30bo2bo$33bo2bo8bo2bo43b2o32b2o$33bo2bo8bo2b
o$33b4o8b4o20$102b4o8b4o$102bo2bo8bo2bo$102bo2bo8bo2bo$102b4o8b4o7$91b
o2bo30bo2bo$90b2o2b2o28b2o2b2o$88bob2o2b2obo24bob2o2b2obo$89bobo2bobo
26bobo2bobo$87b2obo4bob2o22b2obo4bob2o$86b4o6b4o20b4o6b4o3$86b4o6b4o
20b4o6b4o$87b2obo4bob2o22b2obo4bob2o$33b4o8b4o40bobo2bobo26bobo2bobo$
33bo2bo8bo2bo39bob2o2b2obo24bob2o2b2obo$33bo2bo8bo2bo41b2o2b2o28b2o2b
2o$33b4o8b4o42bo2bo30bo2bo7$22bo2bo30bo2bo$21b2o2b2o28b2o2b2o$19bob2o
2b2obo24bob2o2b2obo$20bobo2bobo26bobo2bobo$18b2obo4bob2o22b2obo4bob2o$
17b4o6b4o20b4o6b4o3$17b4o6b4o20b4o6b4o$18b2obo4bob2o22b2obo4bob2o$20bo
bo2bobo26bobo2bobo$19bob2o2b2obo24bob2o2b2obo$21b2o2b2o28b2o2b2o$22bo
2bo30bo2bo!

A very cool high-period puffrake

Code: Select all

x = 27, y = 18, rule = R2,C0,S4,B4
3$11bo4bo2$12b4o6$7b2o10b2o$7bo12bo$7b2o10b2o!

Siderake:

Code: Select all

x = 219, y = 841, rule = R2,C0,S4,B4
29$109bo$109bo2$101bobo$101b3o3$99b3o5bo$99b3obo$102bo$102bo2b2o4bo$
110b2o2$108bo$108bo3$93b5o$94bobo10bo5bo2bo$103b2obo9b2o$103bo9bo2b2o$
94bo3bo5b2o5bo4b2o$95bo9bo5bobobo$95bo15b2o2$111b2o16$82b2o$81bobo$80b
o5b2o$88b2o$89b2o2$90bo$85bo2b2o$80b2o2b2o2b4o$80bo3b3obobo$89b2o$82bo
bo4b2o4b2o$83bobo2b2o5bo$85bo2bo8b2o$94bo2bobo$92bobo3b2obo$90b2o2bo3b
2ob2o$91bo2bo5bo$100bobo$100bo$90bob3o2bo3bo$97bob2o$99bo13$94bobo4bob
o$101b4o$101b2obo$100b2o3bo$97bobo$98bo7bo$96bo2bo6bo$97bobo6bo2$102bo
2bo$106bo$102b2o$101bo$107bo$107bo$100bo2$103bo$101bo35$90bo$90b3o$86b
o6bo$92bo$84bo3$80bo9bo$80bo7bo$81bo5bo$85bo4$74bo$75bobo$73bobobo$74b
o2$70b4o2$64bo11b2o$66b2ob2o5bobo$67b3o2$70bo$64bo7b3o$70bob3o$69bob4o
$88bobo$70bo18bo$71b2o15bobo$72bo$73b2o$76bo4bo$74bo$81bo$73bo8b2o2$
73bo9bo$74bob2o4bo$72bo4bo$76b2o5bo2$73bo8bo$73bo8bo$74b2o4b2o$77b2o4$
28b4o21b4o$29b2o$52bo$33bo18bo6bo$59bo$53bo5bo$54bo4bo$56b2o$30bo2bo4$
50b2o$49bo2bo$47b2ob2ob2o17b2o14bobo$45b3ob4ob3o16b2o2b4o8bo$44b3obo4b
ob3o21b2o7bobo$44bob3o4b3obo21bobo$44bob3ob2ob3obo$42b2o2bob6obo2b2o$
42bob2o10b2obo19bo$49bo2bo$47b2o4b2o23bo4bo$42b2o14b2o18bo2bo$45bo10bo
21bo$45bo10bo21b2o$45bo10bo7$56b2o2$54b2o2b2o$53bo6bo$53bo6bo$33bobo
17bobo2bobo$31bo5bo14bo8bo$36b2o15bobo2bobo$37bo15bo6bo$53bo6bo10b3o$
31bo10bo2bo8b2o2b2o9bo4bo$31bobobo6bo25bo$31bob3o2b2o8bo7b2o$41b2o3bob
o25b2o$29bo4bo40bobo$29bo4bo29bo$73bo5bo$30bo4bo34bo3bo5bo7bobo$70bobo
16bo$31bobo2b3o49bobo$31bo33bo11b2o$32bo33b2o11bo$33bo36bo$71bo$34bo3b
o35bo14$44bob2o18b2obo$49bo14bo2$46bobo16bobo$44bo2b2o16b2o2bo3$37bo3b
o30bo3bo2$37bo2bo32bo2bo$37bo3bo30bo3bo$40b2o30b2o$38bo36bo3$28bobo57b
obo$29bo59bo$28bobo57bobo20$43bo26bo$43bo26bo$43bo26bo$43bo26bo2$38b4o
30b4o9$28bobo57bobo$29bo59bo$28bobo57bobo7$56b2o$55bo2bo$53bo6bo$53b2o
4b2o4$52bo8bo$52bo8bo12$49b3o10b3o$49b3o10b3o2$49b2o12b2o$49b2o12b2o$
53b2o4b2o$51bo10bo$28bobo20bo10bo25bobo$29bo21bo10bo26bo$28bobo20bo10b
o25bobo$53b2o4b2o$49b2o12b2o$49b2o12b2o2$49b3o10b3o$49b3o10b3o3$52bob
2o2b2obo3$55bo2bo$54bo4bo$54bo4bo2$54bo4bo3$56b2o8$56b2o$56b2o2$54bo4b
o$56b2o$56b2o$56b2o$28bobo57bobo$29bo59bo$28bobo57bobo11$158bo2bo2bo2b
o$160bo4bo$156bo12bo6$156bo12bo$160bo4bo$158bo2bo2bo2bo13$28bobo57bobo
$29bo59bo$28bobo57bobo4$161bo2bo$160b2o2b2o$158bob2o2b2obo$159bobo2bob
o$157b2o8b2o$159bo2b2o2bo$160bo4bo$162b2o$162b2o8$162b2o$162b2o$160bo
4bo$159bo2b2o2bo$157b2o8b2o$159bobo2bobo$158bob2o2b2obo$160b2o2b2o$
161bo2bo6$28bobo57bobo$29bo59bo$28bobo57bobo2$153bo18bo$155bo14bo$156b
o12bo$151bo22bo$147bo30bo$147b2o28b2o$149bo26bo$145bo2b2o5bo14bo5b2o2b
o$146bo6bo18bo6bo$144bo4bo4bo16bo4bo4bo$150bob2o18b2obo$145bo6bo20bo6b
o10$155b2ob2o6b2ob2o3$155b2o3bo4bo3b2o$155bo5bo2bo5bo$162b2o$156bo12bo
2$157bo10bo2$160bo4bo$28bobo57bobo$29bo59bo67bo10bo$28bobo57bobo$156bo
12bo$155bo6b2o6bo$154bo6bo2bo6bo$152bo7bo4bo7bo$140b2obo8bobo16bobo8bo
b2o$141bo2bo7bo20bo7bo2bo$145b2obo9b2o6b2o9bob2o$145b2o8bo14bo8b2o$
140b3o2bo34bo2b3o17$154b4o10b4o$153bo2bobo8bobo2bo$157bobo6bobo$158bo
8bo$93bo62b3o2bo2bo2b3o$95bo$91b2o68bo2bo$92bo$28bobo59bo5b2o61b2o4b2o
$29bo60bo4b3obo$28bobo57b3o3bo4bo$86bo7bo$86b2o6bo$84bo56bo42bo$90b3ob
o45bo44bo$85bo3bo50bo44bo$88b2o50b2o2bo36bo2b2o$88b2o50bobobo36bobobo$
141bob2o36b2obo$89b2o51bo5bo28bo5bo$148bo28bo$144bobo32bobo$147bo30bo$
145b2o32b2o10$100bobo$103bo$98bo$98bo5bo$98bo5bo$101b3o$98b5o45b2o26b
2o$92b2obo6bo43b2o3b2o20b2o3b2o$91bo8bo48bo26bo$92b2o5bo44bo7bo20bo7bo
$144bo6b2o20b2o6bo$28bobo60bo51bo38bo$29bo73bo39bobo34bobo$28bobo68b2o
2b2o45bo24bo$85bo2bo9bo6bo38bo2bo30bo2bo$84bobo11bo6bo38bob2o30b2obo$
84bobo12b2o2b2o$100bo2bo$84bo16b2o3$79b3obo7b2o$83bo2bo3bo2bo$77bo5bob
o4bo2b2o$82b2o11bo$77bo4b3o10bo$78bo3bo6b2o2b2o$80b2o8bo2bo$91b2o12$
92b2o$92b2o$93bo30bobo4b3o$91bo3bo27b2o2bo$91bo3b2o26b2o$96bo27b2obo
29b2o8b2o$93bo31bo30bo4bo2bo4bo$127bo28bo12bo$33bo2bo60bo$33b2obo56bo
2bo57bo16bo$33bob2o47b2o68b2o14b2o$81b2o9bo61b2o14b2o$29b3o49b3o3bo2bo
62bo4bo8bo4bo$30bo$31bo52b2o$29b3o53b2o3bo$89bo6$161b4o$160bo4bo$159bo
6bo$158bo8bo$161bo2bo2$159bo6bo5$37bobo$37bo$38b2o$116bo$89bob2o20bo
48b2o$87b2o2bobo18bobo5bo41b2o$37bo3b2o42bo7bo18bobo47b2o$35bo3bob2o
41bo9b2o14b2o12b2o15b2o17bo4bo$35bo4bo47bo6bo14bo12bo3bo$36bo6bo39bo
37bo5b2o8bo$35bo4bobo40bo2bo7bo16bo11bo13bo5bo16bo4bo$40bo41bo39b2o13b
o24b2o$38bobo51bo20b3o5bobo4bo9b2ob3o18b2o$82b2o32bo4bo5bo34b2o$35bo2b
o43bo7bo26bobobo2bo$36b2o45b2o38bo4bo8b2o$85bo2bo34bo4bo8b2o$25b2obo3b
o52b2o40bo$27bo5bo95bo6bo3bo20bo2bo$18b2o4bo8bo91bo14bo$20bo9bobo127bo
4bo$18bobo4bo134bo4bo$26bob3o$24b2o135bo2bo$24b2o2bo$27bo103b4o$128bo
3b2o3bo$127b2o3b2o3b2o$162b2o$129bo6bo25b2o$130bo4bo26b2o$160bo4bo2$
129bo6bo$160bo4bo$162b2o$162b2o$162b2o$129bo6bo2$35bo29b2o65b2o$34bobo
28b2o$39bo32b2o$33bo31bo9bo$31bo27bo15bo$59bo21bo2bo$33b2o3b2o41bo2bo
11bo12bo22b2o$32b3o44bo3bo9b2o3b2o6b2o3b2o19b2o$66bo3bo22bo18bo19b2o$
26bo55bo11bo16bo18bo4bo$29bo49bobo$25bo2b2o31b3o68b2o$23bo4b2o66b3o8b
3o22b2o$22bo36bo37bo10bo$23bo35bo4bo2$28bo32bo29bo22bo$24bo3bo62bo22bo
3$98bo8bo$96b3o8b3o22b2o$93bo18bo19b2o$99bo6bo$94bo16bo18bo4bo$72b2o
58b2o$71bo2bo21bo3bo4bo3bo22b2o$69bo6bo55b2o$69b2o4b2o20bobo6bobo2$
102b2o2$68bo8bo22b2o2b2o$68bo8bo$100bo4bo2$102b2o4$28bo28bo$28bo28bo$
28bo28bo42bo4bo$29bo2b2o18b2o2bo43bo4bo$30b2o22b2o$65b3o10b3o$65b3o10b
3o2$65b2o12b2o21b2o$65b2o12b2o21b2o$69b2o4b2o25b2o$67bo10bo21bo4bo$67b
o10bo$67bo10bo$67bo10bo21bo4bo$69b2o4b2o25b2o$65b2o12b2o21b2o$65b2o12b
2o21b2o2$65b3o10b3o$65b3o10b3o3$68bob2o2b2obo3$41b4o26bo2bo$41bo2bo25b
o4bo$70bo4bo$40bo4bo$70bo4bo2$41bo2bo$40b2o2b2o26b2o$41bo2bo2$41bo2bo$
41bo2bo4$72b2o$72b2o$37bobo6bobo$35bo4b6o4bo19bo4bo$35b2o12b2o21b2o$
72b2o$72b2o5$35b2o12b2o$35bo4b6o4bo$37bobo6bobo6$41bo2bo$41bo2bo2$41bo
2bo5$42b2o$42b2o$42b2o$40bo4bo3$40bo4bo$42b2o$42b2o$42b2o!

edit: another siderake

Code: Select all

x = 63, y = 44, rule = R2,C0,S4,B4
21$9bo2bo2bo2bo23bo2bo2bo2bo$13b2o31b2o$13b2o31b2o$9bo8bo23bo8bo$9bo8b
o23bo8bo$10bo6bo25bo6bo$11bo4bo27bo4bo$11bo4bo27bo4bo2$12b4o29b4o!

Re: 4-Life (LtL R2,S4,B4)

Posted: July 20th, 2022, 5:57 pm

by Period1GliderGun

3-engine 60c/100 spaceship:

Code: Select all

x = 76, y = 64, rule = R2,C2,M0,S4..4,B4..4,NM
31b2o10b2o$31b2o10b2o18$2b4o8b4o40b4o8b4o$2bo2bo8bo2bo40bo2bo8bo2bo$2b
o2bo8bo2bo40bo2bo8bo2bo$2b4o8b4o40b4o8b4o2$31b2o10b2o$31b2o10b2o9$31b
ob2o6b2obo$24bo26bo$25bo10bo2bo10bo$25bo5bo5b2o5bo5bo$25bo24bo$24b2o24b
2o$23bo28bo2$20bo34bo$20bo12bo8bo12bo$26bo4bo12bo4bo$21bo9bo12bo9bo$23b
2o6b2o10b2o6b2o$3b2o26bo4bo2bo4bo26b2o$5b2o24b2o2b2o2b2o2b2o24b2o$31b
2o2b2o2b2o2b2o$o30bo4bo2bo4bo30bo$o8bo13b2o6b2o10b2o6b2o13bo8bo$2bo6b
o11bo9bo12bo9bo11bo6bo$26bo4bo12bo4bo$3bo2bo13bo12bo8bo12bo13bo2bo$20b
o34bo2$23bo28bo$24b2o24b2o$25bo24bo$25bo5bo5b2o5bo5bo$25bo10bo2bo10bo
$24bo26bo$31bob2o6b2obo!

Also my first discovery in LtL.

Re: 4-Life (LtL R2,S4,B4)

Posted: January 19th, 2024, 7:47 am

by Yoel

Esoteric growing gun:

Code: Select all

x = 298, y = 266, rule = R2,C0,M0,S4..4,B4..4,NM
35$140bo10bo$139bobo8bobo$138b2obo8bob2o$138b2o12b2o$137b3o2b3o2b3o2b
3o$140bo10bo5$123bo3bo36bo3bo$128bo34bo$122bo6bo32bo6bo$129bo32bo$129b
o11bo8bo11bo$111b2o2bobobo5bo3b2o11b3o2b3o11b2o3bo5bobobo2b2o$109b2o
12bo4bo16b2o16bo4bo12b2o$103bo3bo76bo3bo$100b4o3bo5bo9bo16bo10bo16bo9b
o5bo3b4o$101b3o5bo28bo14bo28bo5b3o$107bo15bo14bo2bo8bo2bo14bo15bo$100b
3o4b3ob2o10bo15bobo2bo2bo2bobo15bo10b2ob3o4b3o$107bo6bo23b2o4bo2bo4b2o
23bo6bo$103b2o3b2o5bo5bo21bo4bo21bo5bo5b2o3b2o$103bo5bo32bo6bo32bo5bo$
104bo3bo10bo23b2o2b2o23bo10bo3bo$104bo82bo$144bo2bo$145b2o11$95b2o98b
2o$93bo4bo94bo4bo$92bo6bo92bo6bo2$91bo8bo90bo8bo$91bo8bo90bo8bo2$92bo
6bo92bo6bo$93bo4bo94bo4bo$70bo2bo21b2o98b2o21bo2bo$70b2obo144bob2o$70b
2obo144bob2o$69b3o3b2o138b2o3b3o$75bob2o134b2obo3$69b2ob3o142b3ob2o$
73bobobo136bobobo$68bo2bobob2o138b2obobo2bo$68bo154bo$67bo5bo144bo5bo$
67bo5bo144bo5bo$70bo150bo$74bo142bo$67bo7bo140bo7bo2$67bo156bo2$67bo9b
o136bo9bo2$75bo140bo$64bo162bo$62bo5bobob2o144b2obobo5bo2$67bo156bo2$
62bo166bo$63bo4bo154bo4bo$64b4o156b4o$67bo156bo7$56bo178bo$54b3o14b2ob
o142bob2o14b3o$53b4o16b2o142b2o16b4o$52bo4bo12bo150bo12bo4bo$53b2o11bo
5b2o144b2o5bo11b2o$56bo10bo8bo138bo8bo10bo$56bo10bo7bobo136bobo7bo10bo
$56bo10bo5b2o2bobo132bobo2b2o5bo10bo$68bo11bo130bo11bo$68bo11bo130bo
11bo$56bo10bo5b2o2bobo132bobo2b2o5bo10bo$56bo10bo7bobo136bobo7bo10bo$
56bo10bo8bo138bo8bo10bo$53b2o11bo5b2o144b2o5bo11b2o$52bo4bo12bo150bo
12bo4bo$53b4o16b2o142b2o16b4o$54b3o14b2obo142bob2o14b3o$56bo178bo7$67b
o156bo$64b4o156b4o$63bo4bo154bo4bo$62bo166bo2$67bo156bo2$62bo5bobob2o
144b2obobo5bo$64bo162bo$75bo140bo2$67bo9bo136bo9bo2$67bo156bo2$67bo7bo
140bo7bo$74bo142bo$70bo150bo$67bo5bo144bo5bo$67bo5bo144bo5bo$68bo154bo
$68bo2bobob2o138b2obobo2bo$73bobobo136bobobo$69b2ob3o142b3ob2o3$75bob
2o134b2obo$69b3o3b2o138b2o3b3o$70b2obo144bob2o$70b2obo144bob2o$70bo2bo
21b2o98b2o21bo2bo$93bo4bo94bo4bo$92bo6bo92bo6bo2$91bo8bo90bo8bo$91bo8b
o90bo8bo2$92bo6bo92bo6bo$93bo4bo94bo4bo$95b2o98b2o11$145b2o$144bo2bo$
104bo82bo$104bo3bo10bo23b2o2b2o23bo10bo3bo$103bo5bo32bo6bo32bo5bo$103b
2o3b2o5bo5bo21bo4bo21bo5bo5b2o3b2o$107bo6bo23b2o4bo2bo4b2o23bo6bo$100b
3o4b3ob2o10bo15bobo2bo2bo2bobo15bo10b2ob3o4b3o$107bo15bo14bo2bo8bo2bo
14bo15bo$101b3o5bo28bo14bo28bo5b3o$100b4o3bo5bo9bo16bo10bo16bo9bo5bo3b
4o$103bo3bo76bo3bo$109b2o12bo4bo16b2o16bo4bo12b2o$111b2o2bobobo5bo3b2o
11b3o2b3o11b2o3bo5bobobo2b2o$129bo11bo8bo11bo$129bo32bo$122bo6bo32bo6b
o$128bo34bo$123bo3bo36bo3bo5$140bo10bo$137b3o2b3o2b3o2b3o$138b2o12b2o$
138b2obo8bob2o$139bobo8bobo$140bo10bo!

Re: 4-Life (LtL R2,S4,B4)

Posted: January 20th, 2024, 9:51 am

by confocaloid

p120 gun for a 6c/4o spaceship

Code: Select all

x = 143, y = 73, rule = R2,C0,M0,S4..4,B4..4,NM
5bo2bo133bo$4b2o2b2o$2bob2o2b2obo$3bobo2bobo65b2o$b2obo4bob2o62bo2bo$
4o6b4o60b2o2b2o$73bo6bo$73bo6bo$4o6b4o60b2o2b2o$b2obo4bob2o62bo2bo$3bo
bo2bobo65b2o$2bob2o2b2obo$4b2o2b2o25b2o$5bo2bo25bo2bo$33b2o2b2o$32bo6b
o$32bo6bo$33b2o2b2o$34bo2bo$35b2o5$11b2o22b2o$10bo2bo20bo2bo$9b2o2b2o
18b2o2b2o$8bo6bo16bo6bo$8bo6bo16bo6bo$9b2o2b2o18b2o2b2o$10bo2bo20bo2bo
$11b2o22b2o5$80b2o$77bo$82b2o$78bo4bo$76b3ob2obo$79bo7$112b2o10b2o$
110bobo12bobo$109bo18bo$109bo18bo$110bobo12bobo$93bo2bo15b2o10b2o$93bo
2bo$94b2o2$94b2o2$64bo2bo$63b2o2b2o$61bob2o2b2obo$62bobo2bobo65b2o$60b
2obo4bob2o62bo2bo$59b4o6b4o60b2o2b2o$132bo6bo$132bo6bo$59b4o6b4o13bo3b
o42b2o2b2o$60b2obo4bob2o19bo42bo2bo$62bobo2bobo16bo4bo43b2o$61bob2o2b
2obo$63b2o2b2o18b4o$o63bo2bo!
#C [[ MAXGRIDSIZE 9 THEME MCell ]]

Re: 4-Life (LtL R2,S4,B4)

Posted: January 20th, 2024, 10:00 am

by b-engine

2-engine 84c/140:

Code: Select all

x = 143, y = 54, rule = R2,C2,M0,S4..4,B4..4,NM
7b4o22b4o$9b2o22b2o$11bo20bo$6bo5bo18bo5bo$6bo4bobo16bobo4bo31b2o22b4o
18b4o22b2o$8bo2bobo16bobo2bo33b2o27b2o12b2o27b2o$b3o5b2o2bo16bo2b2o5b
3o$3obo34bob3o$4bo34bo53bo6bo10bo6bo$4bo34bo64b4o$2b2o36b2o62bo2bo$104b
o2bo$104b4o$93bo6bo10bo6bo3$69b2o27b2o12b2o27b2o$69b2o22b4o18b4o22b2o
19$69b2o22b4o18b4o22b2o$69b2o27b2o12b2o27b2o3$93bo6bo10bo6bo$104b4o$104b
o2bo$2b2o36b2o62bo2bo$4bo34bo64b4o$4bo34bo53bo6bo10bo6bo$3obo34bob3o$
b3o5b2o2bo16bo2b2o5b3o$8bo2bobo16bobo2bo33b2o27b2o12b2o27b2o$6bo4bobo
16bobo4bo31b2o22b4o18b4o22b2o$6bo5bo18bo5bo$11bo20bo$9b2o22b2o$7b4o22b
4o!

120c/200:

Code: Select all

x = 435, y = 97, rule = R2,C2,M0,S4..4,B4..4,NM
133bo$133bo$272bo$269bo$135b2o128b2obo$130bo142bo$131bo132bo8bo$133bo
129bo15bo$135bo128bo87bo2bobo2bo$126bo137bo7bo7bo71b2o2b2o$127bo7bo129b
2o13b2o70bo$130bo140b2o78bo10bo$353bo$355bo4bo$356bob2obo$336bobo$o3b
o344bob2o5b3o$o3bo332b2o2bo7bob2o$337bo11bo2bo$2bo225b2ob2o105bobo$2b
o125b2o100bobo106bo2bo5bobo56b4o22b2o$126bo4b4o93b2obo106b2o32bo31b2o
27b2o$130bo2b2o203bo18bo15b3o$133b2o203bo8b3o7bo$135bo196bo14b3o7bo13b
o31bo6bo$131bo6bo193bo5bo32bo24b4o$23bo101b2o4bo240bo23bo2bo$19bo2b2o
107bo7bo196bo7bob3o47bo2bo$19bo119bo89b2o103bo14bo46b4o$19bo5bo106bo6b
o89b3o111bo6bo18bo33bo6bo$24bo104bo211b3o8bo$19bo106b2o2bo96bo111b3ob
o8bo$21b2obo102bo3bo93bo3bo51bo57bo10b3o15b2o34b2o27b2o$222bo2bobob2o
50bo61bo2bob2o20bo36b4o22b2o$220bo9b2o49bo61bo2bo28bo$19b3o105bo6b2o84b
o9b2o112b3o23bo3bo$17bo4bob2o109bo84bo10bo138bo$17bo6bo104bo2bo86bo9b
o19bobo$229bo19bo23bo$223bo2bobo7b4o10b2o21bo$20bobo213bo2bo28bo$236b
o2bo26bo$236b3obobobo27bo$241bo17b3o9bo$259b2o2bo$260b3o$258bo8bo$258b
o$240bo19bo5b2o$258bo$258bo8bo$260b3o$259b2o2bo$241bo17b3o9bo$236b3ob
obobo27bo$236bo2bo26bo$20bobo213bo2bo28bo$223bo2bobo7b4o10b2o21bo$229b
o19bo23bo$17bo6bo104bo2bo86bo9bo19bobo$17bo4bob2o109bo84bo10bo138bo$19b
3o105bo6b2o84bo9b2o112b3o23bo3bo$220bo9b2o49bo61bo2bo28bo$222bo2bobob
2o50bo61bo2bob2o20bo36b4o22b2o$21b2obo102bo3bo93bo3bo51bo57bo10b3o15b
2o34b2o27b2o$19bo106b2o2bo96bo111b3obo8bo$24bo104bo211b3o8bo$19bo5bo106b
o6bo89b3o111bo6bo18bo33bo6bo$19bo119bo89b2o103bo14bo46b4o$19bo2b2o107b
o7bo196bo7bob3o47bo2bo$23bo101b2o4bo240bo23bo2bo$131bo6bo193bo5bo32bo
24b4o$135bo196bo14b3o7bo13bo31bo6bo$133b2o203bo8b3o7bo$130bo2b2o203bo
18bo15b3o$126bo4b4o93b2obo106b2o32bo31b2o27b2o$2bo125b2o100bobo106bo2b
o5bobo56b4o22b2o$2bo225b2ob2o105bobo$337bo11bo2bo$o3bo332b2o2bo7bob2o
$o3bo344bob2o5b3o$336bobo$356bob2obo$355bo4bo$353bo$130bo140b2o78bo10b
o$127bo7bo129b2o13b2o70bo$126bo137bo7bo7bo71b2o2b2o$135bo128bo87bo2bo
bo2bo$133bo129bo15bo$131bo132bo8bo$130bo142bo$135b2o128b2obo$269bo$272b
o$133bo$133bo!

EDIT:
Probably known p28:

Code: Select all

x = 5, y = 5, rule = R2,C0,S4,B4
2bo$o2b2o$o3bo$2bobo$b2o!

Re: 4-Life (LtL R2,S4,B4)

Posted: February 4th, 2024, 11:46 pm

by AlephAlpha

2c/2:

Code: Select all

x = 9, y = 7, rule = R2,C0,S4,B4
2o$o$o6b2o2$2b2o2$5b2o!

Re: 4-Life (LtL R2,S4,B4)

Posted: December 7th, 2025, 2:44 pm

by speedydelete

Adjustable-period gun based off of a (non-failed) replicator:

Code: Select all

x = 56, y = 32, rule = R2,C2,S4,B4
2o52b2o$2o52b2o7$12b2o4b2o$10bo4b2o4bo$10bo4b2o4bo$10bo4b2o4bo$10bo4b
2o4bo$12b2o4b2o5$12b2o4b2o$10bo4b2o4bo$10bo4b2o4bo$10bo4b2o4bo$10bo4b
2o4bo$12b2o4b2o7$2o$2o!

And a p40:

Code: Select all

x = 56, y = 24, rule = R2,C2,S4,B4
49bo2bo$49bo2bo$48b2o2b2o$46b3o4b3o$2o$2o17b2o$19b2o25b3o4b3o$48b2o2b
2o$49bo2bo$49bo2bo5$49bo2bo$49bo2bo$48b2o2b2o$19b2o25b3o4b3o$2o17b2o$
2o$46b3o4b3o$48b2o2b2o$49bo2bo$49bo2bo!

Re: 4-Life (LtL R2,S4,B4)

Posted: May 11th, 2026, 7:39 pm

by speedydelete

Periodic splitter:

Code: Select all

x = 494, y = 313, rule = R2,C2,S4,B4
190b2o28b2o$190b2o28b2o9$199b4o6b4o2$198bo4bo4bo4bo$198bo4bo4bo4bo2$199b
4o6b4o$199b4o6b4o2$198bo4bo4bo4bo$198bo4bo4bo4bo2$199b4o6b4o33$190b2o
$190b2o15$123b2o$121bo4bo$120bo6bo2$119bo8bo$119bo8bo2$120bo6bo$121bo
4bo$123b2o3$131bo14bo2$128b3o2b2o8b2o2b3o$128b3o2b2o8b2o2b3o2$131bo14b
o$138b2o$137bo2bo$137bo2bo$138b2o$131bo14bo$492b2o$128b3o2b2o8b2o2b3o
342b2o$128b3o2b2o8b2o2b3o141b2o$290bo2bo$131bo14bo142b2o2b2o$288bo6bo
$288bo6bo$123b2o52b2o110b2o2b2o$121bo4bo48bo4bo109bo2bo$120bo6bo46bo6b
o109b2o2$119bo8bo44bo8bo$119bo8bo44bo8bo2$120bo6bo46bo6bo$121bo4bo48b
o4bo$123b2o52b2o21$23b2o$22bo2bo$21b2o2b2o$o19bo6bo$20bo6bo$b3o17b2o2b
2o300b2o$b3o18bo2bo299bo4bo$23b2o299bo6bo$o$323bo8bo$323bo8bo2$324bo6b
o$325bo4bo$327b2o65$424b4o$424bo2bo$424bo2bo$424b4o5$409bo2bo$406bo8b
o2$403b3o10b3o$403b3o10b3o2$406bo8bo$409bo2bo3$409bo2bo$406bo8bo2$403b
3o10b3o$403b3o10b3o2$406bo8bo$409bo2bo5$370b4o50b4o$370bo2bo50bo2bo$370b
o2bo50bo2bo$370b4o50b4o7$320bo2bo$320bo2bo$319b2o2b2o$317b3o4b3o3$317b
3o4b3o$319b2o2b2o$320bo2bo$320bo2bo23$330b4o6b4o2$329bo4bo4bo4bo$329b
o4bo4bo4bo2$329bo4bo4bo4bo$331b2o8b2o$330bo2bo6bo2bo$330b4o6b4o$336b2o
$335bo2bo$334bo4bo$334bo4bo$335bo2bo$336b2o$330b4o6b4o$330bo2bo6bo2bo
$331b2o8b2o$329bo4bo4bo4bo2$329bo4bo4bo4bo$329bo4bo4bo4bo$320bo2bo26b
o2bo$320bo2bo6b4o6b4o6bo2bo$319b2o2b2o24b2o2b2o$317b3o4b3o20b3o4b3o3$
317b3o4b3o20b3o4b3o$319b2o2b2o24b2o2b2o$320bo2bo26bo2bo$320bo2bo26bo2b
o!