indestructible pattern

[genarojm]

Somebody know about indestructible patterns in LIfe?

You know some reference please. Thanks!

[apg]

You have stumbled across an open problem:

Prove that, for any stable pattern, there exists a sequence of gliders that interact with it leaving zero live cells.

In response to this question, Brice Due suggested using a proof by contradiction. He even considered extending it to any pattern.

Dave Greene subsequently wrote:

At least at first glance, this initial line of investigation doesn't look too promising, just because erosion is so far from being inevitable. Even for stable patterns, eaters and boat-bit catchers are fairly common, and even rarer kinds of accretion are possible:

He provided the following example pattern to showcase this:

Code: Select all

#C glider eater/catcher (boat-bit, beehive, and block)
#C Based on Koenig's 16.1262 -> 22.475646 in collision table:
#C http://pentadecathlon.com/lifeNews/2008/02/glider_collisions_with_16_bit.html
x = 22, y = 20, rule = B3/S23
7boo$6bobbo$7boobboo$9boobobboo$5b4o6bobo$4bo3bo6bo$4boo$19boo$boo16bo
bo$obo16bo$bbo$8boo$8bobo7boo$8bo9bobo$18bo3$8boo$8bobo$8bo!

He then commented about the unusual beehive reaction, saying:

... Seems unusual to be able to add six cells with one glider:

The smallest object that I know of that exhibits this reaction is:

Code: Select all

...**......
...*..**...
....**.*...
.***.......
*..*.......
**.........
...........
........***
........*..
.........*.

Brice Due commented that a huge, densely-packed wave of gliders would probably wreak havoc on any pattern:

Code: Select all

x = 22, y = 22, rule = B3/S23
12b3o$8boobbo$3boobboo4bo$3bobo3bo6boo$3bo8bo3bobo$11boo3bo$6b3obbobo$
bboobbo12b3o$boo4bo7boobbo$3bo6boobboo4bo$6bo3bobo3bo$5boo3bo8bo$3obbo
bo10boo$o12b3obbobo$bo7boobbo$4boobboo4bo$4bobo3bo6boo$4bo8bo3bobo$12b
oo3bo$7b3obbobo$7bo$8bo!

And in response to Dave's possible counter-example:

For a proof you'd have to be able to rule out arbitrarily large enclosed spaces containing mechanisms that maintain many copies of the same boundary-wall segment.

Brice suggested the following mechanism of destruction:

But it doesn't matter how many concentric fortress walls you have. All I have to do is send one glider armada to start one burning, then send armadas periodically afterwards. Your pattern will never be able to fully repair the wall. Given infinte time, I can simply send random glider patterns between each armada to statistically reduce the ash between armadas.

When only one glider is allowed to be sent at the pattern at a time, try the following article:

http://b3s23life.blogspot.com/2005/02/g ... terns.html

It is actually a bit out-of-date. Since then, it can be proven possible to make an eater that has an asymptotic rating of 99.999...%

It relies on the highway robber device:

Code: Select all

x = 113, y = 117, rule = B3/S23
64bo$62b3o$38bo22bo$26bo11b3o20boo$24b3o14bo$8bo14bo16boo39boo$8b3o12b
oo56boo5boo$11bo76boo$10boo$$67boo17boo$11boo55bo17boo$11boo17boo36bob
o21boo$30boo37boo21boo4$72bo$72bo$27boo32boo9b3o$27bo20boo11boo11bo$
29bo19bo$28boo16b3o$24boo20bo$24bo$25b3o68bo$27bo66b3o$84b3o6bo$84bo8b
oo$83boo$8boo$7bobo$7bo25boo$6boo25bo$14boo15bobo$14boo15boo65boo$98bo
$96bobo$96boo3$64boo16boo$65bo15bobo$65bobo13bo$66boo12boo3$13boo83boo
bo$12bobo83boboo$12bo$11boo78boo$91boo8$23boo$23boo$35boo$35bobo$37bo$
37boo$$12boo$13bo19boo55b3o$13bobo17bo56bo14boo$14boo15bobo55boo14bo$
26bo4boo70bobo$25bobo75booboo$25bobo78bo$14boo10bo79bobo$13bobo67boo
20boob3o$13bo70bo26bo$7bo4boo70bobo18booboobbo$7b3o17boo56boo18boobob
oo$10bo16bo82bo$o8boo17b3o79bo$3o27bo77boboo$3bo104boobbo$bboo15boo65b
oo23boo$19boo66bo$84b3o$47bo36bo$45b3o$44bo$44boo62boo$50boo56bo$9boo
39boo7bo49b3o$8bobbo45b3o51bo$8bobo45bo26bo$9bo46boo25b3o$86bo6b3o$64b
oo19boo8bo$64bo16boo12boo$62bobo16bo$62boo19bo$82boo6$63bo15boo$63bo
15boo17boo$61b3o34boo$19b3o18boo19bo$19bo20bo$20bo20b3o6boo47boo$43bo
bboobboo47bo$43bobobo38boo12b3o$42boobo23boo16bo14bo$42bobbo23bo14b3o$
43boo25b3o11bo$72bo!

I'll leave this as an 'exercise to the reader' to determine how to make a 99% density eater based on this.



There is no proof of a 100% eater, but I believe that a Universal Constructor surrounded by a wall could constitute such a pattern. However, Dave Greene seems to doubt this:

my instinct is that a stable pattern will never be 100% glider-proof -- there are too many possible lanes of attack

[Macbi]

The rule B35678/S34567 explodes, but because:

Code: Select all

x = 8, y = 8, rule = B35678/S34567
$2b4o$b2o2b2o$bo4bo$bo4bo$b2o2b2o$2b4o!

Is an indestructible patten in that rule the random agar eventually crystallises into lots of copies of that pattern.

[genarojm]

Thank you for your very complete explain. Initially this problem about glider-proof seems more complicated that I had imagined. I have tested these examples and my idea become better to understand this phenomenon on others evolution rules.

As Macbi describes using another life like rule. I have an indestructible pattern (one still life pattern) that resist any collision from any direction for gliders. Of course the universe is yet more limited compared with Life but interesting indeed.

I am constructing computable process by competing patterns and this still life had captured my attention particularity for other reasons. You can see some exercises as:

Virus

Code: Select all

#CXRLE Pos=-40,-20
x = 78, y = 70, rule = B2/S2345678
bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo$6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo2bobo2bo4bo2bo4bo2bo$15bo52bob2o$15bo54b2o$bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo$6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6bo31b2o$38b2o$bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo$18bo34bo13bo$53bo$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$
bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo$7bo20b2o17bo$6bo21b2o16bo$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b3o
2bo2bo$69b2o2$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo$6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$54b2o$6bo48bo$b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo$6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$30bo$31bo35bo$bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo2bo3b2o2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo$46bo$47bo14b2o$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$
bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o$bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo!

Stopping super nova explosions or constructing gaps:

Code: Select all

#CXRLE Pos=-45,-23
x = 619, y = 543, rule = B2/S2345678
271bo2bo2$272b2o$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo3$6bo2bo116bo2bo12bo2bo116bo2bo
12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo
116bo2bo12bo2bo116bo2bo$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$
5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo
116bo2bo3$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o
114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$6bo2bo
116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b
6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo3$6bo2bo116bo2bo12bo2bo
116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2b
o12bo2bo116bo2bo12bo2bo116bo2bo$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo
116bo2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2b
o12bo2bo116bo2bo3$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo$5b6o14b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o14b6o$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo$6bo2bo16bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12b
o2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o16bo2bo$5b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o
14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo
3$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2b
o76bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o
14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo
16bo2bo76bo2bo16bo2bo$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo14b2o
60bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b
6o74b6o14b6o10b6o14b6o74b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16b
o2bo13bo2bo59bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo3$6bo2bo16bo2bo
76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo
$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o$6bo2bo16b
o2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16b
o2bo$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16b
o2bo76bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o
74b6o14b6o$6bo2bo16bo2bo17b2o57bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2b
o12bo2bo16bo2bo76bo2bo16bo2bo2$46bo2bo$6bo2bo16bo2bo76bo2bo16bo2bo12bo
2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$5b6o14b6o74b6o14b
6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo
12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$6bo2bo16bo2bo
76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo
$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o$6bo2bo16b
o2bo76bo2bo16bo2bo12bo2bo16bo2bo69bo6bo2bo16bo2bo12bo2bo16bo2bo76bo2bo
16bo2bo$237bo$237bo$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo69bo6bo2b
o16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b
6o14b6o10b6o14b6o74b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo
76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$6bo2bo16bo2bo76bo2bo16bo2bo
12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$5b6o14b6o74b
6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o$6bo2bo16bo2bo76bo2bo
16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo3$6bo2b
o16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2b
o16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o$
6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo
76bo2bo16bo2bo$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo
12bo2bo16bo2bo76bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o
10b6o14b6o74b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo
16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo3$6bo2bo16bo2bo76bo2bo16bo2bo12bo2b
o16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$5b6o14b6o74b6o14b6o
10b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo
12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo6bo69bo2bo16bo2bo$6bo2bo16bo
2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo4bo71bo2bo
16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o3bo70b6o14b6o
$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo
6bo69bo2bo16bo2bo3$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo$5b6o14b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o14b6o$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo$6bo2bo16bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12b
o2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o16bo2bo$5b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o
14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo
3$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o
10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$6bo2bo116bo2b
o12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2b
o116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo3$6bo2bo116bo2bo12bo2bo116bo2bo
12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo
116bo2bo12bo2bo116bo2bo$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$
5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo
116bo2bo3$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o
114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$6bo2bo
116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b
6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo3$6bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$6bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo$5b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$6bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo3$o$2bo615bo$2bo613bo$o615bo$618bo4$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$6bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo3$6bo2b
o116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b
6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$6bo2bo116bo2bo12bo2bo
116bo2bo12bo2bo15b2o6b2o91bo2bo$5b6o6bo107b6o10b6o114b6o10b6o114b6o$6b
o2bo5bo110bo2bo12bo2bo116bo2bo12bo2bo14bo2bo4bo2bo90bo2bo$15bo$17bo$6b
o2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o
114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$6bo2bo116bo2bo12bo
2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116b
o2bo12bo2bo116bo2bo12bo2bo116bo2bo3$6bo2bo116bo2bo12bo2bo116bo2bo12bo
2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo18bo
2bo94bo2bo12bo2bo116bo2bo$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo
$5b6o114b6o10b6o18b2o94b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12b
o2bo116bo2bo3$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo$5b6o14b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o14b6o$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo$6bo2bo16bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12b
o2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o16bo2bo$5b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o
14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo
3$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2b
o76bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o
14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo
16bo2bo76bo2bo16bo2bo$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo
16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o
14b6o10b6o14b6o74b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76b
o2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo3$6bo2bo16bo2bo76bo2bo16bo2bo
12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$5b6o14b6o74b
6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o$6bo2bo16bo2bo76bo2bo
16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$6bo2bo
16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo
16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o$6b
o2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76b
o2bo16bo2bo3$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo
12bo2bo16bo2bo76bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o
10b6o14b6o74b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo
16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo
16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$5b6o14b6o74b6o14b6o
10b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo
12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo3$6bo2bo16bo2b
o76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2b
o$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o$6bo2bo
16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo
16bo2bo$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo
16bo2bo76bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b
6o74b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo
12bo2bo16bo2bo76bo2bo16bo2bo3$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2b
o76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o
14b6o74b6o14b6o10b6o14b6o74b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo
16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$6bo2bo16bo2bo76bo2bo
16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$5b6o
14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o$6bo2bo16bo2bo
76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo
3$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2b
o76bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o
14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo
16bo2bo76bo2bo16bo2bo$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo
16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o
14b6o10b6o14b6o74b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76b
o2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo3$6bo2bo16bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2b
o16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
16bo2bo$5b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o14b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo$6b
o2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo$5b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b
6o10b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o$6bo2bo16bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo
12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo16bo2bo3$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$
5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo
116bo2bo$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o
114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo3$6bo2bo
116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b
6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$6bo2bo116bo2bo12bo2bo
109bo6bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o110bo3b6o10b6o114b6o$6bo2bo
116bo2bo12bo2bo111bo4bo2bo12bo2bo116bo2bo$255bo2$6bo2bo116bo2bo12bo2bo
116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2b
o12bo2bo116bo2bo12bo2bo116bo2bo$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo
116bo2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2b
o12bo2bo116bo2bo3$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo11$6bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$6bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$6bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$
5b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$6bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
3$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o
10b6o114b6o$6bo2bo100b2o14bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$6bo2bo
116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o98bo2bo12b6o10b6o114b6o10b
6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo3$6bo2bo116bo2bo
12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo
116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$6bo2bo116bo2bo12bo2bo116bo2bo
12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo
116bo2bo12bo2bo116bo2bo3$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$
5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo
116bo2bo$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o
114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo3$6bo2bo
16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16b
o2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo16bo2bo$5b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o
10b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o$6bo2bo16bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12b
o2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo16bo2bo$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo$5b6o14b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o14b6o$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo3$6bo2bo16bo2bo76bo2b
o16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo$5b6o
14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o$6bo2bo16bo2bo
76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo
$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo
76bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o74b6o
14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo
16bo2bo76bo2bo16bo2bo3$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2b
o16bo2bo12bo2bo16bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo
2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o10b6o2b6o
2b6o2b6o2b6o2b6o2b6o10b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo
2bo76bo2bo16bo2bo12bo2bo16bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo12bo2bo16bo2bo$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16b
o2bo12bo2bo16bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo
16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o10b6o2b6o2b6o
2b6o2b6o2b6o2b6o10b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo
76bo2bo16bo2bo12bo2bo16bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o12bo2bo16bo2bo3$6bo2bo16bo2bo6bo69bo2bo16bo2bo12bo2bo16bo2bo76bo2bo
16bo2bo12bo2bo16bo2bo12bo2bo44bo2bo12bo2bo16bo2bo$5b6o14b6o3bo70b6o14b
6o10b6o14b6o74b6o14b6o10b6o14b6o10b6o42b6o10b6o14b6o$6bo2bo16bo2bo4bo
71bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo12bo2bo44bo2bo
12bo2bo16bo2bo$6bo2bo16bo2bo6bo69bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo
2bo12bo2bo16bo2bo12bo2bo44bo2bo12bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o
14b6o74b6o14b6o10b6o14b6o10b6o42b6o10b6o14b6o$6bo2bo16bo2bo76bo2bo16bo
2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo12bo2bo44bo2bo12bo2bo16bo
2bo3$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16b
o2bo12bo2bo44bo2bo12bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b
6o10b6o14b6o10b6o42b6o10b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16b
o2bo76bo2bo16bo2bo12bo2bo16bo2bo12bo2bo44bo2bo12bo2bo16bo2bo$6bo2bo16b
o2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo12bo2bo44b
o2bo12bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o
10b6o42b6o10b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo
16bo2bo12bo2bo16bo2bo12bo2bo44bo2bo12bo2bo16bo2bo3$6bo2bo16bo2bo76bo2b
o16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo12bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o
74b6o14b6o10b6o14b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o14b6o$6bo2bo16bo
2bo76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo12bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo16bo2bo$6bo2bo16bo2bo76bo2bo
16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo12bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo12bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b
6o14b6o10b6o14b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o14b6o$6bo2bo16bo2bo
76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo12bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo16bo2bo3$6bo2bo16bo2bo76bo2bo16bo
2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo72bo3bo2bo16bo2bo$5b6o14b
6o74b6o14b6o10b6o14b6o74b6o14b6o10b6o14b6o69bo4b6o14b6o$6bo2bo16bo2bo
76bo2bo16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo70bo5bo2bo16bo
2bo$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo32bo2bo40bo2bo16bo2bo12bo
2bo16bo2bo72bo3bo2bo16bo2bo$5b6o14b6o74b6o14b6o10b6o14b6o74b6o14b6o10b
6o14b6o74b6o14b6o$6bo2bo16bo2bo76bo2bo16bo2bo12bo2bo16bo2bo33b2o41bo2b
o16bo2bo12bo2bo16bo2bo76bo2bo16bo2bo3$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo
16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16b
o2bo$5b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o14b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o$6bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo$6b
o2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo$5b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o14b6o10b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b
6o10b6o14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o14b6o$6bo2bo16bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo16bo2bo
12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo16bo2bo12bo2bo16bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo16bo2bo3$6bo2bo116bo2bo12bo2bo53b2o61bo2bo12bo2bo116bo
2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo52bo2bo60bo
2bo12bo2bo116bo2bo$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o
114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo
2bo3$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b
6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo$6bo2bo116bo
2bo12bo2bo116bo2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo
2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2bo3$6bo2bo116bo2bo12bo2bo116bo
2bo12bo2bo116bo2bo$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo
2bo116bo2bo12bo2bo116bo2bo$6bo2bo116bo2bo12bo2bo116bo2bo12bo2bo116bo2b
o$5b6o114b6o10b6o114b6o10b6o114b6o$6bo2bo116bo2bo12bo2bo116bo2bo12bo2b
o116bo2bo3$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo$5b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$5b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o$6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo140$272b2o2$271bo2bo!

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continue in the next post ...

[genarojm]

or finally implementing MAJORITY gate:

Code: Select all

#CXRLE Pos=-50,-26
x = 421, y = 870, rule = B2/S2345678
94bo2bo2bo234bo2bo2bo$93b9o232b9o$94bo2bo2bo234bo2bo2bo$94bo5bo234bo5b
o$93b3o3b3o232b3o3b3o$94bo5bo234bo5bo$94bo5bo234bo5bo$93b3o3b3o232b3o
3b3o$94bo5bo234bo5bo$94bo5bo234bo5bo$93b3o3b3o232b3o3b3o$94bo5bo234bo
5bo$94bo5bo234bo5bo$93b3o3b3o232b3o3b3o$94bo5bo234bo5bo$94bo2bo2bo234b
o2bo2bo$93b9o232b9o$94bo2bo2bo234bo2bo2bo5$87bo2bo4bo2bo4bo2bo221bo2bo
4bo2bo4bo2bo$86b6o2b6o2b6o219b6o2b6o2b6o$87bo2bo4bo2bo4bo2bo221bo2bo4b
o2bo4bo2bo$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo$86b6o2b6o2b6o219b6o
2b6o2b6o$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo3$87bo2bo5b2o5bo2bo
221bo2bo5b2o5bo2bo$86b6o10b6o219b6o10b6o$87bo2bo4bo2bo4bo2bo221bo2bo4b
o2bo4bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo
12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o
10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b
6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo
2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo
12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12b
o2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo
2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o
$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b
6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo
2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2b
o221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$
87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221b
o2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo
2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b
6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$
86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221b
o2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$15bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo77bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o75b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo2bo2bo7bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo66bo10bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$9o6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo65b3o9bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o$bo2bo2bo6b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o65bo9b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo5bo7bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo66bo10bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo$3o3b3o235b3o$bo5bo237bo$bo5bo7bo2bo156bo2bo66bo10bo2bo5bo
150bo2bo$3o3b3o5b6o4bo149b6o64b3o8b6o2bo151b6o$bo5bo7bo2bo3bo152bo2bo
66bo10bo2bo3bo152bo2bo$bo5bo7bo2bo3bo152bo2bo66bo10bo2bo5bo150bo2bo$3o
3b3o5b6o4bo149b6o64b3o8b6o154b6o$bo5bo7bo2bo156bo2bo66bo10bo2bo156bo2b
o$bo5bo237bo$3o3b3o235b3o$bo5bo7bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo66bo10bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$b
o2bo2bo6b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o65bo9b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$9o6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo65b3o9bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo$bo2bo2bo7bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo66bo
10bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$14b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o75b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o$15bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo77bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo3$87bo2bo12bo2bo221bo2bo12b
o2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2b
o221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$
87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221b
o2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2b
o12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b
6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$
86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo
221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$
87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221b
o2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo
2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b
6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$
86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221b
o2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo
2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo
12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12b
o2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b
6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo4bo2bo4bo2bo221bo2bo3bo2bo5bo
2bo$86b6o10b6o219b6o10b6o$87bo2bo5b2o5bo2bo221bo2bo4b2o6bo2bo3$87bo2bo
4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo$86b6o2b6o2b6o219b6o2b6o2b6o$87bo2bo4b
o2bo4bo2bo221bo2bo4bo2bo4bo2bo$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo
$86b6o2b6o2b6o219b6o2b6o2b6o$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo5$
94bo2bo2bo237bo$93b9o235b3o$94bo2bo2bo237bo$94bo5bo237bo$93b3o3b3o235b
3o$94bo5bo237bo$94bo5bo237bo$93b3o3b3o235b3o$94bo5bo237bo$94bo5bo237bo
$93b3o3b3o235b3o$94bo5bo237bo$94bo5bo237bo$93b3o3b3o235b3o$94bo5bo237b
o$94bo2bo2bo237bo$93b9o235b3o$94bo2bo2bo237bo11$94bo2bo2bo237bo$93b9o
235b3o$94bo2bo2bo237bo$94bo5bo237bo$93b3o3b3o235b3o$94bo5bo237bo$94bo
5bo237bo$93b3o3b3o235b3o$94bo5bo237bo$94bo5bo237bo$93b3o3b3o235b3o$94b
o5bo237bo$94bo5bo237bo$93b3o3b3o235b3o$94bo5bo237bo$94bo2bo2bo237bo$
93b9o235b3o$94bo2bo2bo237bo5$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo$
86b6o2b6o2b6o219b6o2b6o2b6o$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo$
87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo$86b6o2b6o2b6o219b6o2b6o2b6o$
87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo3$87bo2bo5b2o5bo2bo221bo2bo4b2o
6bo2bo$86b6o10b6o219b6o10b6o$87bo2bo4bo2bo4bo2bo221bo2bo3bo2bo5bo2bo$
87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221b
o2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo
2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b
6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$
86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221b
o2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo
2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo
12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12b
o2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b
6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o
10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo
12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12b
o2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2b
o3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo
221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$
87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b
6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo
2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$15bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo77bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo$14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o75b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo2bo2bo7bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo63bo2bo2bo7bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo$9o6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo62b9o6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$b
o2bo2bo6b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o62bo2bo2bo6b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo5bo7bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo63bo5bo7bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo$3o3b3o232b3o3b3o$bo5bo234bo5bo$bo5bo7bo2bo156bo2bo63b
o5bo7bo2bo156bo2bo$3o3b3o5b6o6bo147b6o61b3o3b3o5b6o4bo149b6o$bo5bo7bo
2bo5bo150bo2bo63bo5bo7bo2bo3bo152bo2bo$bo5bo7bo2bo5bo150bo2bo63bo5bo7b
o2bo3bo152bo2bo$3o3b3o5b6o6bo147b6o61b3o3b3o5b6o4bo149b6o$bo5bo7bo2bo
156bo2bo63bo5bo7bo2bo156bo2bo$bo5bo234bo5bo$3o3b3o232b3o3b3o$bo5bo7bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo63bo5bo7bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$bo2bo2bo6b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o62bo2bo2bo6b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o$9o6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo62b9o
6bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$bo2bo2bo7bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo63bo2bo2bo7bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o75b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$15bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo77bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b
6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$
86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo
221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$
87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221b
o2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo
2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b
6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$
86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221b
o2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo
2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo
12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12b
o2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b
6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o
10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo
12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12b
o2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2b
o3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo5bo2bo3b
o2bo221bo2bo5bo2bo3bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o5b2o3b6o
219b6o5b2o3b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo4bo2bo4bo2bo221bo
2bo4bo2bo4bo2bo$86b6o2b6o2b6o219b6o2b6o2b6o$87bo2bo4bo2bo4bo2bo221bo2b
o4bo2bo4bo2bo$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo$86b6o2b6o2b6o
219b6o2b6o2b6o$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo5$97bo240bo$96b
3o238b3o$97bo240bo$97bo240bo$96b3o238b3o$97bo240bo$97bo240bo$96b3o238b
3o$97bo240bo$97bo240bo$96b3o238b3o$97bo240bo$97bo240bo$96b3o238b3o$97b
o240bo$97bo240bo$96b3o238b3o$97bo240bo11$94bo2bo2bo237bo$93b9o235b3o$
94bo2bo2bo237bo$94bo5bo237bo$93b3o3b3o235b3o$94bo5bo237bo$94bo5bo237bo
$93b3o3b3o235b3o$94bo5bo237bo$94bo5bo237bo$93b3o3b3o235b3o$94bo5bo237b
o$94bo5bo237bo$93b3o3b3o235b3o$94bo5bo237bo$94bo2bo2bo237bo$93b9o235b
3o$94bo2bo2bo237bo5$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo$86b6o2b6o
2b6o219b6o2b6o2b6o$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo$87bo2bo4bo
2bo4bo2bo221bo2bo4bo2bo4bo2bo$86b6o2b6o2b6o219b6o2b6o2b6o$87bo2bo4bo2b
o4bo2bo221bo2bo4bo2bo4bo2bo3$87bo2bo5b2o5bo2bo221bo2bo4b2o6bo2bo$86b6o
10b6o219b6o10b6o$87bo2bo4bo2bo4bo2bo221bo2bo3bo2bo5bo2bo$87bo2bo12bo2b
o221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$
87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221b
o2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2b
o12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b
6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$
86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo
221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$
87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221b
o2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo
2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b
6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$
86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221b
o2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo
2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo
12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12b
o2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b
6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o
10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$15bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo77bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo$14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o75b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$4bo10bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo66bo10bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo$3b3o9bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo65b
3o9bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$4bo9b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
65bo9b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o$4bo10bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo66bo10bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$3b3o238b
3o$4bo240bo$4bo10bo2bo5bo150bo2bo66bo10bo2bo156bo2bo$3b3o8b6o2bo151b6o
64b3o8b6o154b6o$4bo10bo2bo3bo152bo2bo66bo10bo2bo5bo150bo2bo$4bo10bo2bo
5bo150bo2bo66bo10bo2bo3bo152bo2bo$3b3o8b6o154b6o64b3o8b6o2bo151b6o$4bo
10bo2bo156bo2bo66bo10bo2bo5bo150bo2bo$4bo240bo$3b3o238b3o$4bo10bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo66bo10bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$4bo9b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o65bo9b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$3b3o9bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo65b3o9bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$4bo10bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo66bo10bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo$14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o75b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$15bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo77bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo3$
87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221b
o2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2b
o12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b
6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$
86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo
221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$
87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221b
o2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo
2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b
6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$
86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221b
o2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo
2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo
12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12b
o2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b
6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o
10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo
12bo2bo$86b6o10b6o219b6o3bo2bo3b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo
2bo4bo2bo4bo2bo221bo2bo5b2o5bo2bo$86b6o10b6o219b6o10b6o$87bo2bo5b2o5bo
2bo221bo2bo12bo2bo3$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo$86b6o2b6o
2b6o219b6o2b6o2b6o$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo$87bo2bo4bo
2bo4bo2bo221bo2bo4bo2bo4bo2bo$86b6o2b6o2b6o219b6o2b6o2b6o$87bo2bo4bo2b
o4bo2bo221bo2bo4bo2bo4bo2bo5$94bo2bo2bo234bo2bo2bo$93b9o232b9o$94bo2bo
2bo234bo2bo2bo$94bo5bo234bo5bo$93b3o3b3o232b3o3b3o$94bo5bo234bo5bo$94b
o5bo234bo5bo$93b3o3b3o232b3o3b3o$94bo5bo234bo5bo$94bo5bo234bo5bo$93b3o
3b3o232b3o3b3o$94bo5bo234bo5bo$94bo5bo234bo5bo$93b3o3b3o232b3o3b3o$94b
o5bo234bo5bo$94bo2bo2bo234bo2bo2bo$93b9o232b9o$94bo2bo2bo234bo2bo2bo
11$97bo240bo$96b3o238b3o$97bo240bo$97bo240bo$96b3o238b3o$97bo240bo$97b
o240bo$96b3o238b3o$97bo240bo$97bo240bo$96b3o238b3o$97bo240bo$97bo240bo
$96b3o238b3o$97bo240bo$97bo240bo$96b3o238b3o$97bo240bo5$87bo2bo4bo2bo
4bo2bo221bo2bo4bo2bo4bo2bo$86b6o2b6o2b6o219b6o2b6o2b6o$87bo2bo4bo2bo4b
o2bo221bo2bo4bo2bo4bo2bo$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo$86b6o
2b6o2b6o219b6o2b6o2b6o$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo3$87bo2b
o12bo2bo221bo2bo6b2o4bo2bo$86b6o5b2o3b6o219b6o10b6o$87bo2bo12bo2bo221b
o2bo5bo2bo3bo2bo$87bo2bo5bo2bo3bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o
10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b
6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2b
o12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo
12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12b
o2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2b
o221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$
87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o
219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo
2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo
221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$
87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221b
o2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2b
o12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b
6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$
86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo
221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$
87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221b
o2bo12bo2bo3$15bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo77bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$14b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o75b6o2b6o
2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
2b6o$bo2bo2bo7bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo66bo
10bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$9o6bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo65b3o9bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo$bo2bo2bo6b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b
6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o65bo9b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$bo5bo7bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo66bo10bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo$3o3b3o235b3o$bo5bo237bo$bo5bo7bo2bo
156bo2bo66bo10bo2bo5bo150bo2bo$3o3b3o5b6o4bo149b6o64b3o8b6o2bo151b6o$b
o5bo7bo2bo3bo152bo2bo66bo10bo2bo3bo152bo2bo$bo5bo7bo2bo3bo152bo2bo66bo
10bo2bo5bo150bo2bo$3o3b3o5b6o4bo149b6o64b3o8b6o154b6o$bo5bo7bo2bo156bo
2bo66bo10bo2bo156bo2bo$bo5bo237bo$3o3b3o235b3o$bo5bo7bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo66bo10bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo$bo2bo2bo6b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o
10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o65bo9b6o2b6o2b6o2b6o2b6o2b6o
2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$9o6bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo65b3o9bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo4bo2bo$bo2bo2bo7bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo2bo4bo2bo66bo10bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo$14b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b6o2b6o2b6o2b
6o2b6o2b6o2b6o2b6o75b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o10b6o2b6o2b
6o2b6o2b6o2b6o2b6o2b6o2b6o2b6o$15bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo4bo2bo4bo2bo4bo2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2b
o4bo2bo4bo2bo77bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4b
o2bo12bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo3$87b
o2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2b
o12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo
12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o
10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b
6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo
2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo
12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12b
o2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo
2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o
$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b
6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo
2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2b
o221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$
87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221b
o2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b6o10b6o$87bo
2bo12bo2bo221bo2bo12bo2bo$87bo2bo12bo2bo221bo2bo12bo2bo$86b6o10b6o219b
6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo3$87bo2bo12bo2bo221bo2bo12bo2bo$
86b6o10b6o219b6o10b6o$87bo2bo12bo2bo221bo2bo12bo2bo$87bo2bo4bo2bo4bo2b
o221bo2bo3bo2bo5bo2bo$86b6o10b6o219b6o10b6o$87bo2bo5b2o5bo2bo221bo2bo
4b2o6bo2bo3$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo$86b6o2b6o2b6o219b
6o2b6o2b6o$87bo2bo4bo2bo4bo2bo221bo2bo4bo2bo4bo2bo$87bo2bo4bo2bo4bo2bo
221bo2bo4bo2bo4bo2bo$86b6o2b6o2b6o219b6o2b6o2b6o$87bo2bo4bo2bo4bo2bo
221bo2bo4bo2bo4bo2bo5$94bo2bo2bo237bo$93b9o235b3o$94bo2bo2bo237bo$94bo
5bo237bo$93b3o3b3o235b3o$94bo5bo237bo$94bo5bo237bo$93b3o3b3o235b3o$94b
o5bo237bo$94bo5bo237bo$93b3o3b3o235b3o$94bo5bo237bo$94bo5bo237bo$93b3o
3b3o235b3o$94bo5bo237bo$94bo2bo2bo237bo$93b9o235b3o$94bo2bo2bo237bo! 

Another results are available from: http://uncomp.uwe.ac.uk/genaro/Diffusio ... 45678.html.

That seems an easy case compared with Life self. Thanks!

[Eylrid]

What I am interested in is an impenetrable wall, one in which you could enclose complete chaos.

I suppose that an indestructible pattern could be repeated to form a chaos wall, or four chaos walls could form a box, which would be an indestructible pattern.

It's easy to build a chaos wall in other rules, but I doubt it is possible in life.

[H. V. McIntosh]

What I am interested in is an impenetrable wall, one in which you could enclose complete chaos. ...(snip)... It's easy to build a chaos wall in other rules, but I doubt it is possible in life.

What would such a wall be like? Presumably it would be a recognizable structure which would retain its characteristics whatever its surroundings. A still life, for example, or at least a still center. If it were large, its density would be a fixed point in the return map, and if small, surrounding it with numerous copies would produce the same result. Would a supposedly interesting rule have such a structure?

It would be interesting to see examples of rules in which there are chaos walls. Actually, Life has one - the vacuum - but it isn't particularly impenetrable; only slowly penetrable. With one-dimensional automata, there are rules with macrocells and membranes - Rule 110 is one of them - whose membranes can be penetrated, but only under relatively uncommon conditions. As I recall, other rules have unbreachable barriers, so maybe this can be realized in two dimensions as well. Could we be shown some of these rules with a chaos wall and examples of the wall?

[Eylrid]

Here is an example of one built from a circle pattern posted by Macbi in B35678/S34567:

Code: Select all

x = 106, y = 106, rule = B35678/S34567
31b4o4b4o4b4o4b4o4b4o4b4o$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o2b2o$30bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo$30bo4bo2bo4bo2bo4bo2bo4bo
2bo4bo2bo4bo$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o$31b4o4b
4o4b4o4b4o4b4o4b4o$25b4o48b4o$24b2o2b2o46b2o2b2o$24bo4bo46bo4bo$24bo4b
o46bo4bo$24b2o2b2o46b2o2b2o$25b4o48b4o$19b4o60b4o$18b2o2b2o58b2o2b2o$
18bo4bo58bo4bo$18bo4bo58bo4bo$18b2o2b2o58b2o2b2o$19b4o60b4o$13b4o72b4o
$12b2o2b2o70b2o2b2o$12bo4bo70bo4bo$12bo4bo70bo4bo$12b2o2b2o70b2o2b2o$
13b4obo70b4o$7b4o84b4o$6b2o2b2o82b2o2b2o$6bo4bo82bo4bo$6bo4bo82bo4bo$
6b2o2b2o82b2o2b2o$7b4o84b4o$b4o96b4o$2o2b2o94b2o2b2o$o4bo94bo4bo$o4bo
94bo4bo$2o2b2o94b2o2b2o$b4o96b4o3$b4o96b4o$2o2b2o94b2o2b2o$o4bo94bo4bo
$o4bo94bo4bo$2o2b2o94b2o2b2o$b4o96b4o3$b4o96b4o$2o2b2o94b2o2b2o$o4bo
94bo4bo$o4bo94bo4bo$2o2b2o94b2o2b2o$b4o96b4o3$b4o96b4o$2o2b2o94b2o2b2o
$o4bo94bo4bo$o4bo94bo4bo$2o2b2o94b2o2b2o$b4o96b4o3$b4o96b4o$2o2b2o94b
2o2b2o$o4bo94bo4bo$o4bo94bo4bo$2o2b2o94b2o2b2o$b4o96b4o3$b4o96b4o$2o2b
2o94b2o2b2o$o4bo94bo4bo$o4bo94bo4bo$2o2b2o94b2o2b2o$b4o96b4o$7b4o84b4o
$6b2o2b2o82b2o2b2o$6bo4bo82bo4bo$6bo4bo82bo4bo$6b2o2b2o82b2o2b2o$7b4o
84b4o$13b4o72b4o$12b2o2b2o70b2o2b2o$12bo4bo70bo4bo$12bo4bo70bo4bo$12b
2o2b2o70b2o2b2o$13b4o72b4o$19b4o60b4o$18b2o2b2o58b2o2b2o$18bo4bo58bo4b
o$18bo4bo58bo4bo$18b2o2b2o58b2o2b2o$19b4o60b4o$25b4o48b4o$24b2o2b2o46b
2o2b2o$24bo4bo46bo4bo$24bo4bo46bo4bo$24b2o2b2o46b2o2b2o$25b4o48b4o$31b
4o4b4o4b4o4b4o4b4o4b4o$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b
2o$30bo4bo2bo4bo2bo4bo2bo4bo2bo4bo2bo4bo$30bo4bo2bo4bo2bo4bo2bo4bo2bo
4bo2bo4bo$30b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o$31b4o4b4o
4b4o4b4o4b4o4b4o!

I just noticed that with this particle chaos field, one of Macbi's circles shows up in the middle at gen 382

[Eylrid]

I am pretty new to life, would what I'm calling chaos, be called soup? Or is soup something different?

[Lewis]

I just noticed that with this particle chaos field, one of Macbi's circles shows up in the middle at gen 382

After leaving it for a while, lots of the circles start to appear. I think for patterns like this, the whole inside of the octagon will always become filled with the circles and either still or oscillating parts in between them.

[Macbi]

I am pretty new to life, would what I'm calling chaos, be called soup? Or is soup something different?

Soup is often used when talking about random starting patterns, as in http://www.conwaylife.com/soup. Once a pattern has begun to evolve it is no longer purely random, so I'm not sure if it is still "soup", chaos is a fine name for it.

I think for patterns like this, the whole inside of the octagon will always become filled with the circles and either still or oscillating parts in between them.

That's is what tends to happen in that rule. Of course, you sometimes get mutants like this:

Code: Select all

x = 8, y = 7, rule = B35678/S34567
b4o$2o2b3o$o5b2o$o6bo$2o5bo$b3o2b2o$3b4o!

You might even be able to generate a computer, using the gaps between the circles as thin wires to send signals down.

What I am interested in is an impenetrable wall, one in which you could enclose complete chaos.

It seems there are two types of indestructible structures, one to keep chaos contained, and one to keep some area safe against outside chaos. They should look the same, except at the corners. I'm pretty sure life has no indestructable patterns, but glider-proofing might be possible, provided we have enough time to recover between each glider. What about a perimeter made of lots of copies of a simple still life, so that if a glider hits it will only damage a small section of wall. Then we have a ship of some kind go slowly around the perimeter, detecting and repairing any damage to the wall. We get a problem when the glider hits the same point that the ship is dealing with, so it becomes a similar problem to building a device to smush a sparse random input stream of gliders into a fixed period stream. If these problems are overcome, it might even be possible to make a wall invulnerable to any spaceships from some pre-defined set.

[Eylrid]

*snip*
There is no proof of a 100% eater, but I believe that a Universal Constructor surrounded by a wall could constitute such a pattern. However, Dave Greene seems to doubt this:

my instinct is that a stable pattern will never be 100% glider-proof -- there are too many possible lanes of attack

A Universal Constructor surrounded by a wall would need some way to detect damage and translate that into a repair. It wouldn't be able to recover as fast as the incoming gliders could damage.

It seems there are two types of indestructible structures, one to keep chaos contained, and one to keep some area safe against outside chaos. They should look the same, except at the corners. I'm pretty sure life has no indestructable patterns, but glider-proofing might be possible, provided we have enough time to recover between each glider. What about a perimeter made of lots of copies of a simple still life, so that if a glider hits it will only damage a small section of wall. Then we have a ship of some kind go slowly around the perimeter, detecting and repairing any damage to the wall. We get a problem when the glider hits the same point that the ship is dealing with, so it becomes a similar problem to building a device to smush a sparse random input stream of gliders into a fixed period stream. If these problems are overcome, it might even be possible to make a wall invulnerable to any spaceships from some pre-defined set.

This runs into similar problems as the Universal Constructor.


As for the completely indestructible wall, it is not possible in life. Any pattern, when faced with a solid line of live cells up against it would have death along its edge from over crowding, eroding it's structure.

[Macbi]

A Universal Constructor surrounded by a wall would need some way to detect damage and translate that into a repair. It wouldn't be able to recover as fast as the incoming gliders could damage.

True, I do think it may be possible to make an pattern that can defend itself against any single glider though.

As for the completely indestructible wall, it is not possible in life. Any pattern, when faced with a solid line of live cells up against it would have death along its edge from over crowding, eroding it's structure.

While I agree with you, there are plenty of patterns that kill an advancing line, i.e. a line of blocks two spaces apart:

Code: Select all

oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo
oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo
..................................................
..................................................
oooooooooooooooooooooooooooooooooooooooooooooooooo

[Eylrid]

A Universal Constructor surrounded by a wall would need some way to detect damage and translate that into a repair. It wouldn't be able to recover as fast as the incoming gliders could damage.

True, I do think it may be possible to make an pattern that can defend itself against any single glider though.

As for the completely indestructible wall, it is not possible in life. Any pattern, when faced with a solid line of live cells up against it would have death along its edge from over crowding, eroding it's structure.

While I agree with you, there are plenty of patterns that kill an advancing line, i.e. a line of blocks two spaces apart:

Code: Select all

oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo
oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo
..................................................
..................................................
oooooooooooooooooooooooooooooooooooooooooooooooooo

Hmm. Interesting.


While it's true that walls can be constructed to stand up to specific attacks, an indestructible wall would have to stand up to all possible attacks.

[Eylrid]

I just noticed that with this particle chaos field, one of Macbi's circles shows up in the middle at gen 382

After leaving it for a while, lots of the circles start to appear. I think for patterns like this, the whole inside of the octagon will always become filled with the circles and either still or oscillating parts in between them.

At 44009 it is a stable 1440 oscillator (If I did my math right). I believe it stabilizes before this, but I haven't yet found the exact stabilization point.

Here it is at 44009:

Code: Select all

x = 112, y = 112, rule = B35678/S34567
$34b2o6b2o6b2o6b2o6b2o6b2o$32b6o2b6o2b6o2b6o2b6o2b6o$32b2o2b6o2b6o2b6o
2b6o2b6o2b2o$31b2o4b4o4bo2bo4bo2bo4b4o4b4o4b2o$31b2o4b4o4b4o4b4o4b4o4b
4o4b2o$30b4o2b2o2b2o2b6o2b2o2b2o2b2o2b2o2b2o2b2o2b4o$28b9ob15o4b4o4b5o
b11o$26b11ob9o2b4o4b4o4bob17o$26b2o2b2o2b3ob8o4b4o2b2o2b2o2b10o2b4o2b
2o$25b2o4bo2b5o2b5o4b7o4b12o4b2o4b2o$25b2o4b7o4b5o2b8o4b7o2b3o4b2o4b2o
$24b4o2b2o2b2obo4b3ob4o4b4o2b2o2b3o4b3o2b4o2b4o$22b3ob5o4bob2o2b4ob4ob
10o4b2o4b6o2b9o$20b5ob3obo4bob10o2b6ob3obo4b3o2b5ob3o3b8o$20b2o2b5ob2o
2b2ob6o2bo4b5ob3ob2o2b2ob5o2b5ob6o2b2o$19b2o4bob8ob10o4b3o3b3o2b4o5bo
4b8obo4b2o$19b2o4bob4ob3ob3o2b2o2b2o2b7o2b9o3bo4b8obo4b2o$18b4o2b2ob4o
b3ob6o4b4ob2o2b2ob6o2b6o2b2o2b3ob4o2b4o$16b3ob6o6b3ob2o2b2o4b6o4b7o4b
14ob12o$14b5ob12o2b3o4b2o2b3o2b2o4b3ob3o4b4o4b10ob10o$14b2o2b19o4b6o4b
2o2b4ob4o2b12o2b2o2b3o2b3o2b2o$13b2o4bo3b15o2b2ob4o4b16o3b2o2b4o2bo4bo
4bo4b2o$13b2o4bob4o2b2o2b10ob2o2b2o2b4o4b3o5b5o4b3o2bo4bo4bo4b2o$12b4o
2b6o4b6ob6obo4b10ob3o5b5o4b7o2b3o2b3o2b4o$10b14o4b10o2b3o4b7o2b9ob6o2b
26o$8b8o2b7o2b10o4b3o2b5obo4b5o2b2ob2o2b4o2b4o3b3o2b5ob7o$8b2o2b7o3b6o
2b2o2b3o4b6ob3obo4bo2bo4b3o4b2o4bob5ob4ob7o2b2o$7b2o4b12o2b4o4b3o2b7ob
6o2b5o4b3o4b2o4bob5ob6o2b3o4b2o$7b2o4b18o4b8ob13ob4o2b5o2b4o2b8ob6ob4o
4b2o$6b4o2b5ob5ob8o2b4o2b3ob4o2b22o2b8o2b2o3b5o2b2o2b4o$4b9o2b13o2b5o
2b2ob3ob3o4b4o2b10ob9ob3o4b6obo4b5ob3o$2b7ob9o2b3o2b8o4bob3ob3o4bobo4b
ob7ob3o2b4ob3o4b6obo4bob9o$2b2o2b3ob3o2b3o4bo4b7o4bob3ob4o2b4o4b4o4b4o
4b3o3b2o2b10o2b2ob5o2b2o$b2o4b5o4b2o4bo4b4o2b2o2b8o2b4o2b2o2b2o2b9o4b
6ob5o2b9ob5o4b2o$b2o4b5o4b3o2b3o2b2o2b8o2b4o4b2o4b4o4b9o2b2ob9o4bob3o
2b5obo4b2o$2b2o2b7o2b7ob8o2b4o4b3o4b2o4b4o4b7ob4o2b5o2b2o4bob3o2b8o2b
2o$2b8o2b18o4b3o4b4o2b4o2b2o2b2o2b4o2b4o2b2ob4o4b2o2b11o2b7o$3b6o4b3ob
13o4b4o2b14o4b4obo4b2o4b3o2bo4b7ob4obo4bo3bo$3b3o2bo4b7ob5o3b2o2b12ob
8o4b4obo4b2o4b3ob3o2b8ob6o4bo3bo$2b5ob2o2b10o4b8ob3o4b7o2b4o2b2o2b4o2b
4o2b4ob10o2b4o2b3o2b7o$2b2o2b7o2b15o5b6ob10o2b4o4b6o2b7ob3o3b3o4b2o4b
7o2b2o$b2o4b5o4bo2b4o2b13o2b2ob3ob2o2b4o2bo4b3obo4bob3ob10o4b2o4bob4o
4b2o$b2o4b5o4bo2b3o4bo2b2o2b4o4b5obo4b3ob3o2b2o3bo4bob5o2b8o2b4o2b2ob
4o4b2o$2b2o2b7o2b7o4b4o4b3o4b5obo4b3ob6ob5o2b4o2bo4b3o3b5ob11o2b2o$2b
6o4b4o2b5o2b5o4b4o2b5o2b2o2b2o3b6ob14o4bob3ob8ob3o4b5o$3bob3o4b3o4bob
10o2b2o2b5o3b11ob2o2b7o3b7o2b6ob8ob9obo$3bob10o4bob5ob7o4b10o4b4obo4bo
5b3o3b7ob6o4b7o2b4obo$2b9o2b3o2b10o2b2obo4b4o2b4o4b4obo4b16o4b16o4b6o$
2b2o2b4o4b9o3bo4b4o2b4o4bob7ob4o2b5o2b4o2b3o2b4o2b3o2b8o4b2o2b2o$b2o4b
obo4bo2b8obo4b7o2bo4b3o2b4ob10o4b2o4b7o4bo4b3ob4o2b2o4b2o$b2o4bob2o2b
7ob4ob2o2b4o6b2o2b3o4b3ob3ob6o4b2o4b7o4bo4b4o2b6o4b2o$2b2o2b8ob10o2b7o
b5ob4obo4b3ob7o2b2o2b4o2b5o2b2o2b3o2b2o2b2ob7o2b2o$2b5ob6ob3o2b2o2b3ob
2o2b2ob10ob2o2b4ob6o4b13o4b9o4b13o$3bob9o2bo4bo2b3obo4bob5o2b3o2b6o2b
6o4b11obo4b9o4b3o3b3o2bo$3bob12o4bo2b3obo4b3o2bo4b4ob2o2b4o2b4o2b9o2b
4o2b7o2b2o2b10o2bo$2b6o6b4o2b2o2b3ob2o2b7o4b4obo4b2o4b6o3b4o4bob4o4bo
4b7o2b8o$2b2o2b2ob4ob12o2b8o2b2o2b5obo4b2o4b3o2b8o4bo4b4obo4bo2b3o4b3o
2b2o$b2o4b3o2b8ob11o2bo4b6o3b2o2b4o2b3o4b4o2b2o2b5ob7o2b5obo4b2o4b2o$b
2o4b2o4b3ob3ob11o2bo4bo2b11o2b4obo4b3o4b4ob3ob4o2b4ob3ob2o2b3o4b2o$2b
2o2b3o4b9o2b4ob7o2b2ob4o2b5o4bo3b2o2b4o4b4ob3o3bo4b3ob12o2b2o$2b5ob2o
2b2o2b2o2bo4b3ob5ob5ob3o4b4o4b13o2b5ob7o4b4o2b3ob2o2b6o$3bob8o4bo2bo4b
15ob3o4b5o2b6o2b4ob4ob3ob4o2b2o2b2o2b2ob3obo4b4o$3bob4o3bo4b5o2b7ob2o
2b4ob4o2b14o2b4o2b3ob3ob3o4b4o4bob3obo4b4o$2b12o2b4ob4o2b4obo4b3o4b6o
3b5o2b4ob3ob7ob3o4bo2bo4bob3ob2o2b6o$2b2o2b15o5b7o4bob5ob16o2b5ob2o2b
2o2b4o2b6o2b6o2b5o2b2o$b2o4b8ob14o2b2o2b8ob10ob4o4b4obo4b13ob7o2b4obo
4b2o$b2o4bo3b4o3b11o4b4o2b8o2b11o4b6o4b3ob3o3b3ob3ob9obo4b2o$2b2o2b4o
3b13o2bo4bobo4bob2o2b4o2b5o2b2o2b4o2b2o2b6ob7ob3o3b10o2b2o$2b5o2b5o2b
4ob2o2b2ob2o2b2obo4bobo4b2o4b3o4b6o4b5ob3ob4o4b9o4b7o$3b3o4b3o4b3obo4b
ob9o2b2obo4b2o4b3o4bob4o4b14ob4o2b5ob8obo$3b3o4b3o4b3obo4bob16o2b4o2b
5o2b8o2b8o2b5ob3o4b13obo$2b5o2b5o2b4ob2o2b2ob25o3b8o2b4o3b3o4b4ob3o4b
3o2b4o2b5o$2b2o2b4o3b13ob2o2b2ob2o2b5ob2o2b4ob4o3b3o4bob3ob3o4b6ob2o2b
3o4bob4o2b2o$b2o4b7o6b6obo4b3o4bo4bo4b14o4bob3ob4o2b2ob4o2b6o4bob3o4b
2o$b2o4b7o6b6obo4b3o4bob4o4bo2b12o2b2ob3o4b13o2b4o2b2ob3o4b2o$2b2o2b2o
b8o2b7ob2o2b5o2b4o2b2o2b7o2b10o2b6o2b2o2b2o3b3ob2o2b10o2b2o$2b10o2b3ob
2o2b2ob7o3b4obo4b7obo4bo3b4ob5o2b4o4b3ob3obo4bob11o$4b9ob3obo4bob3o3b
8obo4bo3b3obo4bo3b4ob4o4b3o4b3ob3obo4bob4o2b3o$6b4o2b2o4bo4bob14ob2o2b
11o2b14o4b4o2b4ob6o2b4o2b4o$7b2o4bo4b2o2b16o2b22ob2o2b2ob2o2b21obo4b2o
$7b2o4bo5b7o2b4o2b2ob12ob12obo4bob6ob4o2b3o2b5ob3o4b2o$8b2o2b2o8b4o4bo
4bob8o4b2o2b4o2b3obo4bob6ob3o4bo4b9o2b2o$8b5o5b5o4b4o4bob4ob8o4b2o4bo
2b2o2b9ob3o4bo4bob11o$10b3o2b8ob8o2b2ob4ob4o2b2o4b2o4b3ob7o2b3ob4o2b3o
2b2ob5ob3o$12b4o2b7o2b3ob14o4b2o2b4o2b4ob6o4bob2o2b4ob4ob2o2b4o$13b2o
4bob3o4b5o2b10o4b5o2b7ob6o4bobo4b3ob3o2bo4b2o$13b2o4bob3o4b2o2b2ob3o2b
3ob2o2b2o2bo4bob8o2b2o2b2obo4b10o4b2o$14b2o2b2ob4o2b2o4bob18o4bob2o2b
3o4b4ob3o2b12o2b2o$14b7ob7o4b7ob5o2b6o2b4o4b2o4b4ob12ob8o$16b14o2b2o2b
16ob7o4b3o2b5ob7o2b5o2b3o$18b4o2b4ob4o4b6o2b4ob3ob7o2b7ob5o2b4o2b2o2b
4o$19b2o4b3o4bo4bob3o4b3ob7o2b10ob3obo4b3o2bo4b2o$19b2o4b3o4b2o2b6o4b
3ob6o4b3o2b4ob3obo4b3o2bo4b2o$20b2o2b4ob8o2b4o2b11o4b2o4b3ob3ob2o2b4o
2b2o2b2o$20b5o2bob7o4bob10ob4o2b3o4b3ob4ob15o$22b14o4bob4o3b3o3b8o2b4o
2b17o$24b4o2b2ob4o2b4o2b4ob16o2b12o2b4o$25b2o4b11o4b3ob12o2bo4b3ob3o2b
o4b2o$25b2o4b3o5b3o4b3ob8o3b4o4b10o4b2o$26b2o2b8ob4o2b2ob3ob2o2b6o2b2o
2b2o2b2ob5o2b2o$26b5o2b5ob12obo4b4o4b4o4bob3ob5o$28b3o2b5ob7o2b5o4b4o
4b4o4b4o2b3o$30b4o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b4o$31b2o4b
4o4b4o4b4o4b4o4b4o4b2o$31b2o4b4o4b4o4bo2bo4bo2bo4b4o4b2o$32b2o2b6o2b6o
2b6o2b6o2b6o2b2o$32b6o2b6o2b6o2b6o2b6o2b6o$34b2o6b2o6b2o6b2o6b2o6b2o!

Here it is 48 ticks later at 44057 very similar, but with two areas of difference (One at the bottom, above and between the 2nd and 3rd bottom rings from the left. The other is halfway up from the 2nd bottom ring from the right.):

Code: Select all

44057 (48 later):
x = 113, y = 113, rule = B35678/S34567
2$35b2o6b2o6b2o6b2o6b2o6b2o$33b6o2b6o2b6o2b6o2b6o2b6o$33b2o2b6o2b6o2b
6o2b6o2b6o2b2o$32b2o4b4o4bo2bo4bo2bo4b4o4b4o4b2o$32b2o4b4o4b4o4b4o4b4o
4b4o4b2o$31b4o2b2o2b2o2b6o2b2o2b2o2b2o2b2o2b2o2b2o2b4o$29b9ob15o4b4o4b
5ob11o$27b11ob9o2b4o4b4o4bob17o$27b2o2b2o2b3ob8o4b4o2b2o2b2o2b10o2b4o
2b2o$26b2o4bo2b5o2b5o4b7o4b12o4b2o4b2o$26b2o4b7o4b5o2b8o4b7o2b3o4b2o4b
2o$25b4o2b2o2b2obo4b3ob4o4b4o2b2o2b3o4b3o2b4o2b4o$23b3ob5o4bob2o2b4ob
4ob10o4b2o4b6o2b9o$21b5ob3obo4bob10o2b6ob3obo4b3o2b5ob3o3b8o$21b2o2b5o
b2o2b2ob6o2bo4b5ob3ob2o2b2ob5o2b5ob6o2b2o$20b2o4bob8ob10o4b3o3b3o2b4o
5bo4b8obo4b2o$20b2o4bob4ob3ob3o2b2o2b2o2b7o2b9o3bo4b8obo4b2o$19b4o2b2o
b4ob3ob6o4b4ob2o2b2ob6o2b6o2b2o2b3ob4o2b4o$17b3ob6o6b3ob2o2b2o4b6o4b7o
4b14ob12o$15b5ob12o2b3o4b2o2b3o2b2o4b3ob3o4b4o4b10ob10o$15b2o2b19o4b6o
4b2o2b4ob4o2b12o2b2o2b3o2b3o2b2o$14b2o4bo3b15o2b2ob4o4b16o3b2o2b4o2bo
4bo4bo4b2o$14b2o4bob4o2b2o2b10ob2o2b2o2b4o4b3o5b5o4b3o2bo4bo4bo4b2o$
13b4o2b6o4b6ob6obo4b10ob3o5b5o4b7o2b3o2b3o2b4o$11b14o4b10o2b3o4b7o2b9o
b6o2b26o$9b8o2b7o2b10o4b3o2b5obo4b5o2b2ob2o2b4o2b4o3b3o2b5ob7o$9b2o2b
7o3b6o2b2o2b3o4b6ob3obo4bo2bo4b3o4b2o4bob5ob4ob7o2b2o$8b2o4b12o2b4o4b
3o2b7ob6o2b5o4b3o4b2o4bob5ob6o2b3o4b2o$8b2o4b18o4b8ob13ob4o2b5o2b4o2b
8ob6ob4o4b2o$7b4o2b5ob5ob8o2b4o2b3ob4o2b22o2b8o2b2o3b5o2b2o2b4o$5b9o2b
13o2b5o2b2ob3ob3o4b4o2b10ob9ob3o4b6obo4b5ob3o$3b7ob9o2b3o2b8o4bob3ob3o
4bobo4bob7ob3o2b4ob3o4b6obo4bob9o$3b2o2b3ob3o2b3o4bo4b7o4bob3ob4o2b4o
4b4o4b4o4b3o3b2o2b10o2b2ob5o2b2o$2b2o4b5o4b2o4bo4b4o2b2o2b8o2b4o2b2o2b
2o2b9o4b6ob5o2b9ob5o4b2o$2b2o4b5o4b3o2b3o2b2o2b8o2b4o4b2o4b4o4b9o2b2ob
9o4bob3o2b5obo4b2o$3b2o2b7o2b7ob8o2b4o4b3o4b2o4b4o4b7ob4o2b5o2b2o4bob
3o2b8o2b2o$3b8o2b18o4b3o4b4o2b4o2b2o2b2o2b4o2b4o2b2ob4o4b2o2b11o2b7o$
4b6o4b3ob13o4b4o2b14o4b4obo4b2o4b3o2bo4b7ob4obo4bo3bo$4b3o2bo4b7ob5o3b
2o2b12ob8o4b4obo4b2o4b3ob3o2b8ob6o4bo3bo$3b5ob2o2b10o4b8ob3o4b7o2b4o2b
2o2b4o2b4o2b4ob10o2b4o2b3o2b7o$3b2o2b7o2b15o5b6ob10o2b4o4b6o2b7ob3o3b
3o4b2o4b7o2b2o$2b2o4b5o4bo2b4o2b13o2b2ob3ob2o2b4o2bo4b3obo4bob3ob10o4b
2o4bob4o4b2o$2b2o4b5o4bo2b3o4bo2b2o2b4o4b5obo4b3ob3o2b2o3bo4bob5o2b8o
2b4o2b2ob4o4b2o$3b2o2b7o2b7o4b4o4b3o4b5obo4b3ob6ob5o2b4o2bo4b3o3b5ob
11o2b2o$3b6o4b4o2b5o2b5o4b4o2b5o2b2o2b2o3b6ob14o4bob3ob8ob3o4b5o$4bob
3o4b3o4bob10o2b2o2b5o3b11ob2o2b7o3b7o2b6ob8ob9obo$4bob10o4bob5ob7o4b
10o4b4obo4bo5b3o3b7ob6o4b7o2b4obo$3b9o2b3o2b10o2b2obo4b4o2b4o4b4obo4b
16o4b16o4b6o$3b2o2b4o4b9o3bo4b4o2b4o4bob7ob4o2b5o2b4o2b3o2b4o2b3o2b8o
4b2o2b2o$2b2o4bobo4bo2b8obo4b7o2bo4b3o2b4ob10o4b2o4b7o4bo4b3ob4o2b2o4b
2o$2b2o4bob2o2b7ob4ob2o2b4o6b2o2b3o4b3ob3ob6o4b2o4b7o4bo4b4o2b6o4b2o$
3b2o2b8ob10o2b7ob5ob4obo4b3ob7o2b2o2b4o2b5o2b2o2b3o2b2o2b2ob7o2b2o$3b
5ob6ob3o2b2o2b3ob2o2b2ob10ob2o2b4ob6o4b13o4b9o4b13o$4bob9o2bo4bo2b3obo
4bob5o2b3o2b6o2b6o4b11obo4b9o4b3o3b3o2bo$4bob12o4bo2b3obo4b3o2bo4b4ob
2o2b4o2b4o2b9o2b4o2b7o2b2o2b10o2bo$3b6o6b4o2b2o2b3ob2o2b7o4b4obo4b2o4b
6o6bo4bob4o4bo4b7o2b8o$3b2o2b2ob4ob12o2b8o2b2o2b5obo4b2o4b3o2b8o4bo4b
4obo4bo2b3o4b3o2b2o$2b2o4b3o2b8ob11o2bo4b6o3b2o2b4o2b3o4b4o2b2o2b5ob7o
2b5obo4b2o4b2o$2b2o4b2o4b3ob3ob11o2bo4bo2b11o2b4obo4b3o4b4ob3ob4o2b4ob
3ob2o2b3o4b2o$3b2o2b3o4b9o2b4ob7o2b2ob4o2b5o4bo3b2o2b4o4b4ob3o3bo4b3ob
12o2b2o$3b5ob2o2b2o2b2o2bo4b3ob5ob5ob3o4b4o4b13o2b5ob7o4b4o2b3ob2o2b6o
$4bob8o4bo2bo4b15ob3o4b5o2b6o2b4ob4ob3ob4o2b2o2b2o2b2ob3obo4b4o$4bob4o
3bo4b5o2b7ob2o2b4ob4o2b14o2b4o2b3ob3ob3o4b4o4bob3obo4b4o$3b12o2b4ob4o
2b4obo4b3o4b6o3b5o2b4ob3ob7ob3o4bo2bo4bob3ob2o2b6o$3b2o2b15o5b7o4bob5o
b16o2b5ob2o2b2o2b4o2b6o2b6o2b5o2b2o$2b2o4b8ob14o2b2o2b8ob10ob4o4b4obo
4b13ob7o2b4obo4b2o$2b2o4bo3b4o3b11o4b4o2b8o2b11o4b6o4b3ob3o3b3ob3ob9ob
o4b2o$3b2o2b4o3b13o2bo4bobo4bob2o2b4o2b5o2b2o2b4o2b2o2b6ob7ob3o3b10o2b
2o$3b5o2b5o2b4ob2o2b2ob2o2b2obo4bobo4b2o4b3o4b6o4b5ob3ob4o4b9o4b7o$4b
3o4b3o4b3obo4bob9o2b2obo4b2o4b3o4bob4o4b14ob4o2b5ob8obo$4b3o4b3o4b3obo
4bob16o2b4o2b5o2b8o2b8o2b5ob3o4b13obo$3b5o2b5o2b4ob2o2b2ob25o3b8o2b4o
3b3o4b4ob3o4b3o2b4o2b5o$3b2o2b4o3b13ob2o2b2ob2o2b5ob2o2b4ob4o3b3o4bob
3ob3o4b6ob2o2b3o4bob4o2b2o$2b2o4b7o6b6obo4b3o4bo4bo4b14o4bob3ob4o2b2ob
4o2b6o4bob3o4b2o$2b2o4b7o6b6obo4b3o4bob4o4bo2b12o2b2ob3o4b13o2b4o2b2ob
3o4b2o$3b2o2b2ob8o2b7ob2o2b5o2b4o2b2o2b7o2b10o2b6o2b2o2b2o3b3ob2o2b10o
2b2o$3b10o2b3ob2o2b2ob7o3b4obo4b7obo4bo3b4ob5o2b4o4b3ob3obo4bob11o$5b
9ob3obo4bob3o3b8obo4bo3b3obo4bo3b4ob4o4b3o4b3ob3obo4bob4o2b3o$7b4o2b2o
4bo4bob14ob2o2b11o2b14o4b4o2b4ob6o2b4o2b4o$8b2o4bo4b2o2b16o2b22ob2o2b
2ob2o2b21obo4b2o$8b2o4bo5b7o2b4o2b2ob12ob12obo4bob6ob4o2b3o2b5ob3o4b2o
$9b2o2b2o8b4o4bo4bob8o4b2o2b4o2b3obo4bob6ob3o4bo4b9o2b2o$9b5o5b5o4b4o
4bob4ob8o4b2o4bo2b2o2b9ob3o4bo4bob11o$11b3o2b8ob8o2b2ob4ob4o2b2o4b2o4b
3ob7o2b3ob4o2b3o2b2ob5ob3o$13b4o2b7o2b3ob14o4b2o2b4o2b4ob6o4bob2o2b4ob
4ob2o2b4o$14b2o4bob3o4b5o2b10o4b5o2b7ob6o4bobo4b3ob3o2bo4b2o$14b2o4bob
3o4b2o2b2ob3o2b3ob2o2b2o2bo4bob8o2b2o2b2obo4b10o4b2o$15b2o2b2ob4o2b2o
4bob18o4bob2o2b3o4b4ob3o2b12o2b2o$15b7ob7o4b7ob5o2b6o2b4o4b2o4b4ob12ob
8o$17b14o2b2o2b16ob7o4b3o2b5ob7o2b5o2b3o$19b4o2b4ob4o4b6o2b4ob3ob7o2b
7ob5o2b4o2b2o2b4o$20b2o4b3o4bo4bob3o4b3ob7o2b10ob3obo4b3o2bo4b2o$20b2o
4b3o4b2o2b6o4b3ob6o4b3o2b4ob3obo4b3o2bo4b2o$21b2o2b4ob8o2b4o2b11o4b2o
4b3ob3ob2o2b4o2b2o2b2o$21b5o2bob7o4bob10ob4o2b3o4b3ob4ob15o$23b14o4bob
4o3b3o3b8o2b4o2b17o$25b4o2b2ob4o2b4o2b4ob16o2b12o2b4o$26b2o4b11o4b3ob
12o2bo4b3ob3o2bo4b2o$26b2o4b3o5b3o4b3ob8o3b4o4b10o4b2o$27b2o2b8ob4o2b
2ob3ob2o2b6o2b2o2b2o2b2ob5o2b2o$27b5o2b5ob12obo4b4o4b4o4bob3ob5o$29b3o
2b5ob14o4b4o4b4o4b4o2b3o$31b4o2b2o2b2o2b6o2b2o2b2o2b2o2b2o2b2o2b2o2b4o
$32b2o4b4o4b4o4b4o4b4o4b4o4b2o$32b2o4b4o4b4o4bo2bo4bo2bo4b4o4b2o$33b2o
2b6o2b6o2b6o2b6o2b6o2b2o$33b6o2b6o2b6o2b6o2b6o2b6o$35b2o6b2o6b2o6b2o6b
2o6b2o!

And 96 ticks after the first at 44105 with only one area of difference (The one at the bottom):

Code: Select all

x = 113, y = 114, rule = B35678/S34567
2$35b2o6b2o6b2o6b2o6b2o6b2o$33b6o2b6o2b6o2b6o2b6o2b6o$33b2o2b6o2b6o2b
6o2b6o2b6o2b2o$32b2o4b4o4bo2bo4bo2bo4b4o4b4o4b2o$32b2o4b4o4b4o4b4o4b4o
4b4o4b2o$31b4o2b2o2b2o2b6o2b2o2b2o2b2o2b2o2b2o2b2o2b4o$29b9ob15o4b4o4b
5ob11o$27b11ob9o2b4o4b4o4bob17o$27b2o2b2o2b3ob8o4b4o2b2o2b2o2b10o2b4o
2b2o$26b2o4bo2b5o2b5o4b7o4b12o4b2o4b2o$26b2o4b7o4b5o2b8o4b7o2b3o4b2o4b
2o$25b4o2b2o2b2obo4b3ob4o4b4o2b2o2b3o4b3o2b4o2b4o$23b3ob5o4bob2o2b4ob
4ob10o4b2o4b6o2b9o$21b5ob3obo4bob10o2b6ob3obo4b3o2b5ob3o3b8o$21b2o2b5o
b2o2b2ob6o2bo4b5ob3ob2o2b2ob5o2b5ob6o2b2o$20b2o4bob8ob10o4b3o3b3o2b4o
5bo4b8obo4b2o$20b2o4bob4ob3ob3o2b2o2b2o2b7o2b9o3bo4b8obo4b2o$19b4o2b2o
b4ob3ob6o4b4ob2o2b2ob6o2b6o2b2o2b3ob4o2b4o$17b3ob6o6b3ob2o2b2o4b6o4b7o
4b14ob12o$15b5ob12o2b3o4b2o2b3o2b2o4b3ob3o4b4o4b10ob10o$15b2o2b19o4b6o
4b2o2b4ob4o2b12o2b2o2b3o2b3o2b2o$14b2o4bo3b15o2b2ob4o4b16o3b2o2b4o2bo
4bo4bo4b2o$14b2o4bob4o2b2o2b10ob2o2b2o2b4o4b3o5b5o4b3o2bo4bo4bo4b2o$
13b4o2b6o4b6ob6obo4b10ob3o5b5o4b7o2b3o2b3o2b4o$11b14o4b10o2b3o4b7o2b9o
b6o2b26o$9b8o2b7o2b10o4b3o2b5obo4b5o2b2ob2o2b4o2b4o3b3o2b5ob7o$9b2o2b
7o3b6o2b2o2b3o4b6ob3obo4bo2bo4b3o4b2o4bob5ob4ob7o2b2o$8b2o4b12o2b4o4b
3o2b7ob6o2b5o4b3o4b2o4bob5ob6o2b3o4b2o$8b2o4b18o4b8ob13ob4o2b5o2b4o2b
8ob6ob4o4b2o$7b4o2b5ob5ob8o2b4o2b3ob4o2b22o2b8o2b2o3b5o2b2o2b4o$5b9o2b
13o2b5o2b2ob3ob3o4b4o2b10ob9ob3o4b6obo4b5ob3o$3b7ob9o2b3o2b8o4bob3ob3o
4bobo4bob7ob3o2b4ob3o4b6obo4bob9o$3b2o2b3ob3o2b3o4bo4b7o4bob3ob4o2b4o
4b4o4b4o4b3o3b2o2b10o2b2ob5o2b2o$2b2o4b5o4b2o4bo4b4o2b2o2b8o2b4o2b2o2b
2o2b9o4b6ob5o2b9ob5o4b2o$2b2o4b5o4b3o2b3o2b2o2b8o2b4o4b2o4b4o4b9o2b2ob
9o4bob3o2b5obo4b2o$3b2o2b7o2b7ob8o2b4o4b3o4b2o4b4o4b7ob4o2b5o2b2o4bob
3o2b8o2b2o$3b8o2b18o4b3o4b4o2b4o2b2o2b2o2b4o2b4o2b2ob4o4b2o2b11o2b7o$
4b6o4b3ob13o4b4o2b14o4b4obo4b2o4b3o2bo4b7ob4obo4bo3bo$4b3o2bo4b7ob5o3b
2o2b12ob8o4b4obo4b2o4b3ob3o2b8ob6o4bo3bo$3b5ob2o2b10o4b8ob3o4b7o2b4o2b
2o2b4o2b4o2b4ob10o2b4o2b3o2b7o$3b2o2b7o2b15o5b6ob10o2b4o4b6o2b7ob3o3b
3o4b2o4b7o2b2o$2b2o4b5o4bo2b4o2b13o2b2ob3ob2o2b4o2bo4b3obo4bob3ob10o4b
2o4bob4o4b2o$2b2o4b5o4bo2b3o4bo2b2o2b4o4b5obo4b3ob3o2b2o3bo4bob5o2b8o
2b4o2b2ob4o4b2o$3b2o2b7o2b7o4b4o4b3o4b5obo4b3ob6ob5o2b4o2bo4b3o3b5ob
11o2b2o$3b6o4b4o2b5o2b5o4b4o2b5o2b2o2b2o3b6ob14o4bob3ob8ob3o4b5o$4bob
3o4b3o4bob10o2b2o2b5o3b11ob2o2b7o3b7o2b6ob8ob9obo$4bob10o4bob5ob7o4b
10o4b4obo4bo5b3o3b7ob6o4b7o2b4obo$3b9o2b3o2b10o2b2obo4b4o2b4o4b4obo4b
16o4b16o4b6o$3b2o2b4o4b9o3bo4b4o2b4o4bob7ob4o2b5o2b4o2b3o2b4o2b3o2b8o
4b2o2b2o$2b2o4bobo4bo2b8obo4b7o2bo4b3o2b4ob10o4b2o4b7o4bo4b3ob4o2b2o4b
2o$2b2o4bob2o2b7ob4ob2o2b4o6b2o2b3o4b3ob3ob6o4b2o4b7o4bo4b4o2b6o4b2o$
3b2o2b8ob10o2b7ob5ob4obo4b3ob7o2b2o2b4o2b5o2b2o2b3o2b2o2b2ob7o2b2o$3b
5ob6ob3o2b2o2b3ob2o2b2ob10ob2o2b4ob6o4b13o4b9o4b13o$4bob9o2bo4bo2b3obo
4bob5o2b3o2b6o2b6o4b11obo4b9o4b3o3b3o2bo$4bob12o4bo2b3obo4b3o2bo4b4ob
2o2b4o2b4o2b9o2b4o2b7o2b2o2b10o2bo$3b6o6b4o2b2o2b3ob2o2b7o4b4obo4b2o4b
6o3b4o4bob4o4bo4b7o2b8o$3b2o2b2ob4ob12o2b8o2b2o2b5obo4b2o4b3o2b8o4bo4b
4obo4bo2b3o4b3o2b2o$2b2o4b3o2b8ob11o2bo4b6o3b2o2b4o2b3o4b4o2b2o2b5ob7o
2b5obo4b2o4b2o$2b2o4b2o4b3ob3ob11o2bo4bo2b11o2b4obo4b3o4b4ob3ob4o2b4ob
3ob2o2b3o4b2o$3b2o2b3o4b9o2b4ob7o2b2ob4o2b5o4bo3b2o2b4o4b4ob3o3bo4b3ob
12o2b2o$3b5ob2o2b2o2b2o2bo4b3ob5ob5ob3o4b4o4b13o2b5ob7o4b4o2b3ob2o2b6o
$4bob8o4bo2bo4b15ob3o4b5o2b6o2b4ob4ob3ob4o2b2o2b2o2b2ob3obo4b4o$4bob4o
3bo4b5o2b7ob2o2b4ob4o2b14o2b4o2b3ob3ob3o4b4o4bob3obo4b4o$3b12o2b4ob4o
2b4obo4b3o4b6o3b5o2b4ob3ob7ob3o4bo2bo4bob3ob2o2b6o$3b2o2b15o5b7o4bob5o
b16o2b5ob2o2b2o2b4o2b6o2b6o2b5o2b2o$2b2o4b8ob14o2b2o2b8ob10ob4o4b4obo
4b13ob7o2b4obo4b2o$2b2o4bo3b4o3b11o4b4o2b8o2b11o4b6o4b3ob3o3b3ob3ob9ob
o4b2o$3b2o2b4o3b13o2bo4bobo4bob2o2b4o2b5o2b2o2b4o2b2o2b6ob7ob3o3b10o2b
2o$3b5o2b5o2b4ob2o2b2ob2o2b2obo4bobo4b2o4b3o4b6o4b5ob3ob4o4b9o4b7o$4b
3o4b3o4b3obo4bob9o2b2obo4b2o4b3o4bob4o4b14ob4o2b5ob8obo$4b3o4b3o4b3obo
4bob16o2b4o2b5o2b8o2b8o2b5ob3o4b13obo$3b5o2b5o2b4ob2o2b2ob25o3b8o2b4o
3b3o4b4ob3o4b3o2b4o2b5o$3b2o2b4o3b13ob2o2b2ob2o2b5ob2o2b4ob4o3b3o4bob
3ob3o4b6ob2o2b3o4bob4o2b2o$2b2o4b7o6b6obo4b3o4bo4bo4b14o4bob3ob4o2b2ob
4o2b6o4bob3o4b2o$2b2o4b7o6b6obo4b3o4bob4o4bo2b12o2b2ob3o4b13o2b4o2b2ob
3o4b2o$3b2o2b2ob8o2b7ob2o2b5o2b4o2b2o2b7o2b10o2b6o2b2o2b2o3b3ob2o2b10o
2b2o$3b10o2b3ob2o2b2ob7o3b4obo4b7obo4bo3b4ob5o2b4o4b3ob3obo4bob11o$5b
9ob3obo4bob3o3b8obo4bo3b3obo4bo3b4ob4o4b3o4b3ob3obo4bob4o2b3o$7b4o2b2o
4bo4bob14ob2o2b11o2b14o4b4o2b4ob6o2b4o2b4o$8b2o4bo4b2o2b16o2b22ob2o2b
2ob2o2b21obo4b2o$8b2o4bo5b7o2b4o2b2ob12ob12obo4bob6ob4o2b3o2b5ob3o4b2o
$9b2o2b2o8b4o4bo4bob8o4b2o2b4o2b3obo4bob6ob3o4bo4b9o2b2o$9b5o5b5o4b4o
4bob4ob8o4b2o4bo2b2o2b9ob3o4bo4bob11o$11b3o2b8ob8o2b2ob4ob4o2b2o4b2o4b
3ob7o2b3ob4o2b3o2b2ob5ob3o$13b4o2b7o2b3ob14o4b2o2b4o2b4ob6o4bob2o2b4ob
4ob2o2b4o$14b2o4bob3o4b5o2b10o4b5o2b7ob6o4bobo4b3ob3o2bo4b2o$14b2o4bob
3o4b2o2b2ob3o2b3ob2o2b2o2bo4bob8o2b2o2b2obo4b10o4b2o$15b2o2b2ob4o2b2o
4bob18o4bob2o2b3o4b4ob3o2b12o2b2o$15b7ob7o4b7ob5o2b6o2b4o4b2o4b4ob12ob
8o$17b14o2b2o2b16ob7o4b3o2b5ob7o2b5o2b3o$19b4o2b4ob4o4b6o2b4ob3ob7o2b
7ob5o2b4o2b2o2b4o$20b2o4b3o4bo4bob3o4b3ob7o2b10ob3obo4b3o2bo4b2o$20b2o
4b3o4b2o2b6o4b3ob6o4b3o2b4ob3obo4b3o2bo4b2o$21b2o2b4ob8o2b4o2b11o4b2o
4b3ob3ob2o2b4o2b2o2b2o$21b5o2bob7o4bob10ob4o2b3o4b3ob4ob15o$23b14o4bob
4o3b3o3b8o2b4o2b17o$25b4o2b2ob4o2b4o2b4ob16o2b12o2b4o$26b2o4b11o4b3ob
12o2bo4b3ob3o2bo4b2o$26b2o4b3o5b3o4b3ob8o3b4o4b10o4b2o$27b2o2b8ob4o2b
6ob2o2b6o2b2o2b2o2b2ob5o2b2o$27b5o2b5ob12obo4b4o4b4o4bob3ob5o$29b3o2b
5ob14o4b4o4b4o4b4o2b3o$31b4o2b2o2b2o2b6o2b2o2b2o2b2o2b2o2b2o2b2o2b4o$
32b2o4b4o4b4o4b4o4b4o4b4o4b2o$32b2o4b4o4b4o4bo2bo4bo2bo4b4o4b2o$33b2o
2b6o2b6o2b6o2b6o2b6o2b2o$33b6o2b6o2b6o2b6o2b6o2b6o$35b2o6b2o6b2o6b2o6b
2o6b2o!

[Macbi]

The oscar.py script in Golly, tells me that it is actually period 720, but you can get much larger periods using different seeds inside the octagon.
Also, another mutant:

Code: Select all

x = 9, y = 6, rule = B35678/S34567
b7o$2o2bo2b2o$o7bo$o7bo$2o2bo2b2o$b7o!

There's probably a grammar for them.

[apg]

A Universal Constructor surrounded by a wall would need some way to detect damage and translate that into a repair.

Indeed. That's difficult, but theoretically possible.

It wouldn't be able to recover as fast as the incoming gliders could damage.

Again, I mean a device that can absorb all gliders, as long as they arrive sufficiently far apart. Existing eaters also have recovery times; this one takes 16 generations to recover:

Code: Select all

x = 50, y = 24, rule = B3/S23
6bo$7bo27bobo$5b3o6boo20boo6boo$14bobo19bo7bobo$10bo5bo23bo5bo$11bo4bo
boo21bo4boboo$9b3oboobobo20b3oboobobo$14bobobo25bobobo$14bobbo26bobbo$
3boo7bobo18boo7bobo$bbobbo6boo18bobbo6boo$bobobbo24bobobbo$obboobo23bo
bboobo$boo3b3o3boo17boo3b3o3boo$3b3o3bobboo19b3o3bobboo$3bobb4o23bobb
4o$4boo28boo$b3obb4o21b3obb4o$bobboo3bo3boo16bobboo3bo3boo$bboobboobob
obbo17boobboobobobbo$4bobbobob3o20bobbobob3o$4boobbo25boobbo$9b3o27b3o
$11bo29bo!

[Eylrid]

A Universal Constructor surrounded by a wall would need some way to detect damage and translate that into a repair.

Indeed. That's difficult, but theoretically possible.

It wouldn't be able to recover as fast as the incoming gliders could damage.

Again, I mean a device that can absorb all gliders, as long as they arrive sufficiently far apart. Existing eaters also have recovery times; this one takes 16 generations to recover:

Code: Select all

x = 50, y = 24, rule = B3/S23
6bo$7bo27bobo$5b3o6boo20boo6boo$14bobo19bo7bobo$10bo5bo23bo5bo$11bo4bo
boo21bo4boboo$9b3oboobobo20b3oboobobo$14bobobo25bobobo$14bobbo26bobbo$
3boo7bobo18boo7bobo$bbobbo6boo18bobbo6boo$bobobbo24bobobbo$obboobo23bo
bboobo$boo3b3o3boo17boo3b3o3boo$3b3o3bobboo19b3o3bobboo$3bobb4o23bobb
4o$4boo28boo$b3obb4o21b3obb4o$bobboo3bo3boo16bobboo3bo3boo$bboobboobob
obbo17boobboobobobbo$4bobbobob3o20bobbobob3o$4boobbo25boobbo$9b3o27b3o
$11bo29bo!

Indeed it may be possible to create something that is slow salvo proof.

I strung together a chain of overwriters (posted by KnightLife in another thread) to create a repairable line of blocks. One of the gliders from each reaction triggers the next, with an extra block added to eat the other glider:

Code: Select all

x = 134, y = 95, rule = B3/S23
13b2o$13b2o$bo$2bo$3o3$4b2o4b2o$3bo2bo3b2o$3bo2bo$4b2o$20b2o$20b2o8b2o
$30b2o6$21b2o4b2o$20bo2bo3b2o$20bo2bo$21b2o$37b2o$37b2o8b2o$47b2o6$38b
2o4b2o$37bo2bo3b2o$37bo2bo$38b2o$54b2o$54b2o8b2o$64b2o6$55b2o4b2o$54bo
2bo3b2o$54bo2bo$55b2o$71b2o$71b2o8b2o$81b2o6$72b2o4b2o$71bo2bo3b2o$71b
o2bo$72b2o$88b2o$88b2o8b2o$98b2o6$89b2o4b2o$88bo2bo3b2o$88bo2bo$89b2o$
105b2o$105b2o8b2o$115b2o6$106b2o4b2o$105bo2bo3b2o$105bo2bo$106b2o$122b
2o$122b2o8b2o$132b2o6$123b2o4b2o$122bo2bo3b2o$122bo2bo$123b2o!

The blocks are rather far apart, but it could be the basis of self-repair.

[H. V. McIntosh]

With one-dimensional automata, there are rules with macrocells and membranes - Rule 110 is one of them - whose membranes can be penetrated, but only under relatively uncommon conditions.

Rule 110's left membrane is the sequence x10, which is the vertical edge of a large evolutionary triangle, and is only semipermeable since there is no matching right membrane and the essential 0 in the wall eventually erodes.

The essence of this membrane is that x10 always becomes 1, so that a glider or simply a varying pattern on the left has no influence on the wall or anything further to the right. For a two dimensional lattice, a similar principle should be operative, so it is a question of whether Life or some other rule contains such transitions. For Life, probably not; it is a matter of checking the neighborhoods. This could be done by a search program, such as reading a de Bruijn diagram, or by scanning a prospective border looking for neighborhoods which were insensitive to the contents of the left column, say. Even without the benefit of a de Bruijn diagram, searches looking for still lifes, oscillators, etc., could be adapted to this new goal.

Supposing nothing serviceable is found. There might be a second generation wall which restores itself when breached on the first generation. Or after the third generation, although the complexity of the search rapidly escalates. Mostly, that means working with ever larger neighborhoods. Semipermeability is also an option. Suppose that a wall with low or minimum penetrability is constructed; one could hope for the best, that during the course of most evolutions, even one which has been purposefully designed, no breaching attack occurs.

[genarojm]

Yes, some walls there are in rule 110. Indeed, whether this configuration x10 become be x10* (with a very long right part). Any glider or pattern coming of the left side they cannot destroy this wall. That is the same case when a big triangle emerge on Rule 110.

[Axaj]

One rule to note would be 2/2. It is easy to see why 1-cell thick walls cannot be destroyed.

Code: Select all

x = 44, y = 24, rule = B2/S2
4bo34bo$2bob2o32b2obo$b2o38b2o$4b36o$2obo36bob2o$bobo36bobo$3bo36bo$3b
o36bo$3bo36bo$3bo36bo$3bo36bo$3bo16b2o18bo$3bo15bo20bo$3bo36bo$3bo36bo
$3bo36bo$3bo36bo$3bo36bo$bobo36bobo$2obo36bob2o$4b36o$b2o38b2o$2bob2o
32b2obo$4bo34bo!

[Sokwe]

One rule to note would be 2/2. It is easy to see why 1-cell thick walls cannot be destroyed.

Indeed, although it should be noted that the indestructibility of it is dependent on the two rows of dead cells surrounding the row of live cells. Unfortunately there is no way to make such a pattern that is indestructible from the 'outside', as the corners of the box can be hit by spaceships from an arbitrary distance to destroy it.

Code: Select all

x = 34, y = 24, rule = B2/S2
14bo14bo$o11bob2o12b2obo$2bo8b2o18b2o$2bo11b16o$o9b2obo16bob2o$11bobo
16bobo$13bo16bo$13bo16bo$13bo16bo$13bo16bo$13bo16bo$13bo16bo$13bo16bo$
13bo16bo$13bo16bo$13bo16bo$13bo16bo$13bo16bo$11bobo16bobo$10b2obo16bob
2o$14b16o$11b2o18b2o$12bob2o12b2obo$14bo14bo!

[Axaj]

One rule to note would be 2/2. It is easy to see why 1-cell thick walls cannot be destroyed.

Indeed, although it should be noted that the indestructibility of it is dependent on the two rows of dead cells surrounding the row of live cells. Unfortunately there is no way to make such a pattern that is indestructible from the 'outside', as the corners of the box can be hit by spaceships from an arbitrary distance to destroy it.

Code: Select all

x = 34, y = 24, rule = B2/S2
14bo14bo$o11bob2o12b2obo$2bo8b2o18b2o$2bo11b16o$o9b2obo16bob2o$11bobo
16bobo$13bo16bo$13bo16bo$13bo16bo$13bo16bo$13bo16bo$13bo16bo$13bo16bo$
13bo16bo$13bo16bo$13bo16bo$13bo16bo$13bo16bo$11bobo16bobo$10b2obo16bob
2o$14b16o$11b2o18b2o$12bob2o12b2obo$14bo14bo!

Yes, but as this is a B2 rule it has c/1 wickstretchers (meaning that no pattern can catch up to it):

Code: Select all

x = 17, y = 16, rule = B2/S2
2bo11bo$o15bo$o15bo$2bo11bo$3b11o2$4bo7bo$2bo4b3o4bo$2bo4bobo4bo$4bo7b
o2$3b11o$2bo11bo$o15bo$o15bo$2bo11bo!

[xnihilozero]

I found a pattern that contains chaos. The chaos sticks to the walls, but patterns with two axes of symmetry (one in small spaces) can crystallize spaceship collisions in the center until the space is filled. Then inverse spaceships often create inverse crystals and the process repeats. This pattern works in some nearby rules as well.

Code: Select all

x = 78, y = 78, rule = B0167/S023
5bo66bo$6bo64bo$7bo62bo$7bo62bo$5b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$o3bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo3bo$bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$2b2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$4bo2bo62bo2bo
$4bo2bo62bo2bo$5b2o64b2o$4bo2bo62bo2bo$4bo2bo62bo2bo$5b2o64b2o$4bo2bo
62bo2bo$4bo2bo62bo2bo$5b2o64b2o$4bo2bo33bo10bo17bo2bo$4bo2bo32b3o8b3o
16bo2bo$5b2o64b2o$4bo2bo62bo2bo$4bo2bo20bo41bo2bo$5b2o20b3o41b2o$4bo2b
o62bo2bo$4bo2bo62bo2bo$5b2o64b2o$4bo2bo62bo2bo$4bo2bo12bo29bo19bo2bo$
5b2o12b3o27b3o19b2o$4bo2bo62bo2bo$4bo2bo62bo2bo$5b2o64b2o$4bo2bo30bo
31bo2bo$4bo2bo29b3o30bo2bo$5b2o64b2o$4bo2bo62bo2bo$4bo2bo62bo2bo$5b2o
64b2o$4bo2bo62bo2bo$4bo2bo21bo26bo13bo2bo$5b2o21b3o24b3o13b2o$4bo2bo
33bo28bo2bo$4bo2bo32b3o27bo2bo$5b2o12bo51b2o$4bo2bo10b3o49bo2bo$4bo2bo
62bo2bo$5b2o64b2o$4bo2bo62bo2bo$4bo2bo44bo17bo2bo$5b2o44b3o17b2o$4bo2b
o62bo2bo$4bo2bo62bo2bo$5b2o64b2o$4bo2bo20bo11bo29bo2bo$4bo2bo19b3o9b3o
28bo2bo$5b2o64b2o$4bo2bo62bo2bo$4bo2bo10bo34bo16bo2bo$5b2o10b3o32b3o
16b2o$4bo2bo62bo2bo$4bo2bo62bo2bo$5b2o64b2o$4bo2bo62bo2bo$4bo2bo62bo2b
o$5b2o64b2o$4bo2bo62bo2bo$4bo2bo62bo2bo$5b2o64b2o$4bo2bo62bo2bo$4bo2bo
62bo2bo$2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo2bo2bo2bo2bo$o3bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo3bo$5b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$7bo62bo$7bo62bo$6bo64bo$5bo66bo!

[p46beth]

A Universal Constructor surrounded by a wall would need some way to detect damage and translate that into a repair. It wouldn't be able to recover as fast as the incoming gliders could damage.

True, I do think it may be possible to make an pattern that can defend itself against any single glider though.

As for the completely indestructible wall, it is not possible in life. Any pattern, when faced with a solid line of live cells up against it would have death along its edge from over crowding, eroding it's structure.

While I agree with you, there are plenty of patterns that kill an advancing line, i.e. a line of blocks two spaces apart:

Code: Select all

oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo
oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo..oo
..................................................
..................................................
oooooooooooooooooooooooooooooooooooooooooooooooooo

Hmm. Interesting.


While it's true that walls can be constructed to stand up to specific attacks, an indestructible wall would have to stand up to all possible attacks.

What would be possible, is a wall that can sustain arbitrary amounts of chaos--if the wall were sufficiently thick.

As for other rules, B45678/S2345 naturally forms walls that are immune to chaos on their interiors

Now, for life, a SLOW glider-proof structure:

A Universal Constructor surrounded by a wall would need some way to detect damage and translate that into a repair.

Indeed. That's difficult, but theoretically possible.

It wouldn't be able to recover as fast as the incoming gliders could damage.

Again, I mean a device that can absorb all gliders, as long as they arrive sufficiently far apart.

Would if the "wall" being repaired were a 99.99999% slow-glider eater? That would significantly cut down on the number and frequency of situations in which the UCC would need to repair anything, thus making it much easier to program. I still haven't learned enough about programming universal constructors to make such a pattern, but it seems feasible after seeing the gemini (although, of course, the UCC used in the gemini may not be the best suited to this particular task.)