Thread for basic questions

[Book]

By the way, frequency class can be calculated up to 42-43 or so.

But not very meaningfully...

[hotdogPi]

By the way, frequency class can be calculated up to 42-43 or so.

But not very meaningfully...

log2(5.62e14/200) = 41.35
log2(5.62e14/210) = 41.28

You can see that the difference between 200 occurrences and 210 occurrences only differs by 0.07.

[Book]

By the way, frequency class can be calculated up to 42-43 or so.

But not very meaningfully...

log2(5.62e14/200) = 41.35
log2(5.62e14/210) = 41.28

You can see that the difference between 200 occurrences and 210 occurrences only differs by 0.07.

For objects with a small number of occurrences, the relative order of items changes over time, as does FC, which would require maintenance of the list or out-of-date results. Since including FCs for those objects does not contribute to understanding, I opted for less maintentance (who's gonna do it?).

[Bombba]

Is it possible that you can write a program where every finite initial configuration can determine whether this eventually disappears? If so,
how? If not, why not? Is there a difference between a finite grid and an infinite grid?

[C28]

Is it possible that you can write a program where every finite initial configuration can determine whether this eventually disappears? If so,
how? If not, why not? Is there a difference between a finite grid and an infinite grid?

i feel like this falls under the halting problem

[mniemiec]

Is it possible that you can write a program where every finite initial configuration can determine whether this eventually disappears? If so,
how? If not, why not? Is there a difference between a finite grid and an infinite grid?

i feel like this falls under the halting problem

This is only equivalent to the Halting Problem on an infinite grid. On a finite MxN grid, there are only 2^(MN) possible states, so one either has an oscillator of period at most 2^(MN), or an unstable configuration that eventually settles into one. In practice, the upper limit is significantly lower, because in Life (and other isotropic rules), symmetry significantly reduces the number of unique states. Also, Many patterns are unstable, so they can't be a phase in an oscillator. Also, at least in Life, the number of such unstable patterns greatly outnumbers the number of stable patterns, because mechanisms that support oscillation are extremely fragile - even when considering still-lifes as period 1 oscillators (with the empty field being the degenerate case).

[otismo]

What is the most volatile known P7? I was able to assemble this based off of a reaction that Scorbie pointed out:

Code: Select all

x = 31, y = 31, rule = B3/S23
10bo9bo$10bo9bo$10bo9bo3$10b2o2bobo2b2o$10bobobobobobo$9bo2bobobobo2b
o$10b2obo3bob2o$7bo3bo7bo3bo$3o2b2obo13bob2o2b3o$5bo2b2o2bo5bo2b2o2bo
$6b2o3bobo3bobo3b2o$8bo3bo5bo3bo$5b3o15b3o2$5b3o15b3o$8bo3bo5bo3bo$6b
2o3bobo3bobo3b2o$5bo2b2o2bo5bo2b2o2bo$3o2b2obo13bob2o2b3o$7bo3bo7bo3b
o$10b2obo3bob2o$9bo2bobobobo2bo$10bobobobobobo$10b2o2bobo2b2o3$10bo9b
o$10bo9bo$10bo9bo!

Makes a dandy stable agar :

Code: Select all

x = 225, y = 225, rule = B3/S23
8b3o7b3o15b3o7b3o15b3o7b3o15b3o7b3o15b3o7b3o15b3o7b3o15b3o7b3o15b3o7b
3o3$9b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b
3o5b3o$8b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o
15b5o3b5o$7b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o
4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o$7b3obobobobob3o13b
3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobo
bobob3o13b3obobobobob3o13b3obobobobob3o$5b2obo2b2o3b2o2bob2o9b2obo2b2o
3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o
9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o$o3b4o3b2o
3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b
4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o3bo$o2b2obo3b3o3b3o
3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2o
bo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o
3bob2o2bo$o2b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b
2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob
2o3b2obo4b2o5b2o4bob2o3b2obo4b2o2bo$3b2ob5obo3bob5ob2o5b2ob5obo3bob5ob
2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob
5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o$4bo2b5o5b5o2bo7bo2b5o5b5o2bo
7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo
7bo2b5o5b5o2bo$5b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o
9b2o15b2o9b2o15b2o2$5b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o
15b2o9b2o15b2o9b2o15b2o$4bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo
2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo$3b
2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o
5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob
2o$o2b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4b
ob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo
4b2o5b2o4bob2o3b2obo4b2o2bo$o2b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o
5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o
3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o2bo$o3b4o3b2o3b2o3b
4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o
3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o3bo$5b2obo2b2o3b2o2bob2o9b
2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b
2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o$
7b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obo
bobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o$7b2o4bobo4b
2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b
2o13b2o4bobo4b2o13b2o4bobo4b2o$8b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b
5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o$9b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o
17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o6$9b3o5b3o17b3o5b3o17b3o5b3o17b3o
5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o$8b5o3b5o15b5o3b5o15b5o3b5o15b
5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o$7b2o4bobo4b2o13b2o4bobo4b2o
13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o
13b2o4bobo4b2o$7b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obob
obobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob
3o$5b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo
2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2b
ob2o9b2obo2b2o3b2o2bob2o$o3b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o
3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b
4o3b2o3b2o3b4o3bo$o2b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o
3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o
5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o2bo$o2b2o4bob2o3b2obo4b2o5b2o
4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2o
bo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o2bo$
3b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob
2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob
5ob2o$4bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o
5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo$5b2o15b2o9b2o15b2o9b
2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o2$5b2o15b2o9b2o15b
2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o$4bo2b5o5b5o2b
o7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2b
o7bo2b5o5b5o2bo7bo2b5o5b5o2bo$3b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2o
b5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b
2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o$o2b2o4bob2o3b2obo4b2o5b2o4bob2o3b2o
bo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o
4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o2bo$o2b2obo3b
3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob
2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b
3o3b3o3bob2o2bo$o3b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o
3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b
2o3b4o3bo$5b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o
9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o
3b2o2bob2o9b2obo2b2o3b2o2bob2o$7b3obobobobob3o13b3obobobobob3o13b3obob
obobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob
3o13b3obobobobob3o$7b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo
4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o$8b5o3b5o
15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o$9b3o5b
3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o6$9b
3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o$
8b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b
5o$7b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b
2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o$7b3obobobobob3o13b3obobob
obob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o
13b3obobobobob3o13b3obobobobob3o$5b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bo
b2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo
2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o$o3b4o3b2o3b2o3b
4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o
3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o3bo$o2b2obo3b3o3b3o3bob2o
5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o
3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o
2bo$o2b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o
4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2o
bo4b2o5b2o4bob2o3b2obo4b2o2bo$3b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2o
b5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b
2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o$4bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o
5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o
5b5o2bo$5b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b
2o9b2o15b2o2$5b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b
2o15b2o9b2o15b2o$4bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o
2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo$3b2ob5obo
3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5o
bo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o$o2b
2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b
2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b
2o4bob2o3b2obo4b2o2bo$o2b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo
3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3b
ob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o2bo$o3b4o3b2o3b2o3b4o7b4o
3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b
2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o3bo$5b2obo2b2o3b2o2bob2o9b2obo2b
2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob
2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o$7b3obob
obobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob
3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o$7b2o4bobo4b2o13b2o
4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o
4bobo4b2o13b2o4bobo4b2o$8b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o
15b5o3b5o15b5o3b5o15b5o3b5o$9b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b
3o17b3o5b3o17b3o5b3o17b3o5b3o6$9b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b
3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o$8b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o
15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o$7b2o4bobo4b2o13b2o4bobo4b2o13b2o
4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o
4bobo4b2o$7b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobo
b3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o$5b
2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b
2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b
2obo2b2o3b2o2bob2o$o3b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b
4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o
3b2o3b4o3bo$o2b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bo
b2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo
3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o2bo$o2b2o4bob2o3b2obo4b2o5b2o4bob2o
3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o
5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o2bo$3b2ob
5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b
2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o
$4bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2b
o7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo$5b2o15b2o9b2o15b2o9b2o15b
2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o2$5b2o15b2o9b2o15b2o9b
2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o$4bo2b5o5b5o2bo7bo
2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo
2b5o5b5o2bo7bo2b5o5b5o2bo$3b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5ob
o3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob
5obo3bob5ob2o5b2ob5obo3bob5ob2o$o2b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo
4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4b
ob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o2bo$o2b2obo3b3o
3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o
5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o
3b3o3bob2o2bo$o3b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b
2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o
3b4o3bo$5b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b
2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b
2o2bob2o9b2obo2b2o3b2o2bob2o$7b3obobobobob3o13b3obobobobob3o13b3obobob
obob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o
13b3obobobobob3o$7b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b
2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o$8b5o3b5o15b
5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o$9b3o5b3o
17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o6$9b3o
5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o$8b
5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o$
7b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o
13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o$7b3obobobobob3o13b3obobobob
ob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o
13b3obobobobob3o13b3obobobobob3o$5b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bo
b2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo
2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o$o3b4o3b2o3b2o3b
4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o
3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o3bo$o2b2obo3b3o3b3o3bob2o
5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o
3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o
2bo$o2b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o
4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2o
bo4b2o5b2o4bob2o3b2obo4b2o2bo$3b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2o
b5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b
2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o$4bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o
5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o
5b5o2bo$5b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b
2o9b2o15b2o2$5b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b
2o15b2o9b2o15b2o$4bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o
2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo$3b2ob5obo
3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5o
bo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o$o2b
2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b
2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b
2o4bob2o3b2obo4b2o2bo$o2b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo
3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3b
ob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o2bo$o3b4o3b2o3b2o3b4o7b4o
3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b
2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o3bo$5b2obo2b2o3b2o2bob2o9b2obo2b
2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob
2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o$7b3obob
obobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob
3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o$7b2o4bobo4b2o13b2o
4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o
4bobo4b2o13b2o4bobo4b2o$8b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o
15b5o3b5o15b5o3b5o15b5o3b5o$9b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b
3o17b3o5b3o17b3o5b3o17b3o5b3o6$9b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b
3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o$8b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o
15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o$7b2o4bobo4b2o13b2o4bobo4b2o13b2o
4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o
4bobo4b2o$7b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobo
b3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o$5b
2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b
2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b
2obo2b2o3b2o2bob2o$o3b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b
4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o
3b2o3b4o3bo$o2b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bo
b2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo
3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o2bo$o2b2o4bob2o3b2obo4b2o5b2o4bob2o
3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o
5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o2bo$3b2ob
5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b
2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o
$4bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2b
o7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo$5b2o15b2o9b2o15b2o9b2o15b
2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o2$5b2o15b2o9b2o15b2o9b
2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o$4bo2b5o5b5o2bo7bo
2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo
2b5o5b5o2bo7bo2b5o5b5o2bo$3b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5ob
o3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob
5obo3bob5ob2o5b2ob5obo3bob5ob2o$o2b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo
4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4b
ob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o2bo$o2b2obo3b3o
3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o
5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o
3b3o3bob2o2bo$o3b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b
2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o
3b4o3bo$5b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b
2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b
2o2bob2o9b2obo2b2o3b2o2bob2o$7b3obobobobob3o13b3obobobobob3o13b3obobob
obob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o
13b3obobobobob3o$7b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b
2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o$8b5o3b5o15b
5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o$9b3o5b3o
17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o6$9b3o
5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o$8b
5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o$
7b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o
13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o$7b3obobobobob3o13b3obobobob
ob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o
13b3obobobobob3o13b3obobobobob3o$5b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bo
b2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo
2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o$o3b4o3b2o3b2o3b
4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o
3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o3bo$o2b2obo3b3o3b3o3bob2o
5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o
3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o
2bo$o2b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o
4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2o
bo4b2o5b2o4bob2o3b2obo4b2o2bo$3b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2o
b5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b
2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o$4bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o
5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o
5b5o2bo$5b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b
2o9b2o15b2o2$5b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b
2o15b2o9b2o15b2o$4bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o
2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo$3b2ob5obo
3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5o
bo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o$o2b
2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b
2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b
2o4bob2o3b2obo4b2o2bo$o2b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo
3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3b
ob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o2bo$o3b4o3b2o3b2o3b4o7b4o
3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b
2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o3bo$5b2obo2b2o3b2o2bob2o9b2obo2b
2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob
2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o$7b3obob
obobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob
3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o$7b2o4bobo4b2o13b2o
4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o
4bobo4b2o13b2o4bobo4b2o$8b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o
15b5o3b5o15b5o3b5o15b5o3b5o$9b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b
3o17b3o5b3o17b3o5b3o17b3o5b3o6$9b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b
3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o$8b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o
15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o$7b2o4bobo4b2o13b2o4bobo4b2o13b2o
4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o
4bobo4b2o$7b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobo
b3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o$5b
2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b
2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b
2obo2b2o3b2o2bob2o$o3b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b
4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o
3b2o3b4o3bo$o2b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bo
b2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo
3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o2bo$o2b2o4bob2o3b2obo4b2o5b2o4bob2o
3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o
5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o2bo$3b2ob
5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b
2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o
$4bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2b
o7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo$5b2o15b2o9b2o15b2o9b2o15b
2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o2$5b2o15b2o9b2o15b2o9b
2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o9b2o15b2o$4bo2b5o5b5o2bo7bo
2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo2b5o5b5o2bo7bo
2b5o5b5o2bo7bo2b5o5b5o2bo$3b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5ob
o3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob5obo3bob5ob2o5b2ob
5obo3bob5ob2o5b2ob5obo3bob5ob2o$o2b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo
4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4b
ob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o5b2o4bob2o3b2obo4b2o2bo$o2b2obo3b3o
3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o
5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o3b3o3bob2o5b2obo3b3o
3b3o3bob2o2bo$o3b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b
2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o3b4o7b4o3b2o3b2o
3b4o3bo$5b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b
2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b2o2bob2o9b2obo2b2o3b
2o2bob2o9b2obo2b2o3b2o2bob2o$7b3obobobobob3o13b3obobobobob3o13b3obobob
obob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o13b3obobobobob3o
13b3obobobobob3o$7b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b
2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o13b2o4bobo4b2o$8b5o3b5o15b
5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o15b5o3b5o$9b3o5b3o
17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o17b3o5b3o3$8b3o
7b3o15b3o7b3o15b3o7b3o15b3o7b3o15b3o7b3o15b3o7b3o15b3o7b3o15b3o7b3o!

Cheers !

[Herschel of Ostropol]

Is the block the only still life where one cell can be remove and the still life heals itself?

[hotdogPi]

Is the block the only still life where one cell can be remove and the still life heals itself?

No. Long ship.

Code: Select all

x = 4, y = 4, rule = B3/S23
2o$o$bobo$2b2o!

[GUYTU6J]

Is the block the only still life [motif] where one cell can be [removed] and the still life heals itself?

No. Long ship.

Code: Select all

x = 4, y = 4, rule = B3/S23
2o$o$bobo$2b2o!

And there are more:

Does there exist a still life (other than block) that eventually (or instantly) repairs itself after killing (altering) any single cell?

Long ship, tub on long long house,two long long houses:

Code: Select all

x = 55, y = 7, rule = B3/S23
14b2o3b2o3b2o3b2o6b2o3b2o4b2o3b2o$2o5b2o5bo5bo3bo2bo2bo6bo2bo2bo4bo2bo
2bo$o6bobo5b5o5b5o8b2ob2o6b5o$bobo4bobo$2b2o5b2o6bo9bo10b5o6b5o$16bobo
7bobo8bo2bo2bo4bo2bo2bo$17bo9bo9b2o3b2o4b2o3b2o!

Sadly, these other examples does not see applications in catalysis. I would like to see a still life that has a beehive-like tip with the property in question; this will become a possible completion for a p41 partial.

[Herschel of Ostropol]

How is a 30 x 30 square of cells not a solution to the grandfather problem?

[hotdogPi]

How is a 30 x 30 square of cells not a solution to the grandfather problem?

Code: Select all

x = 32, y = 28, rule = B3/S23
32o3$32o3$32o3$32o3$32o3$32o3$32o3$32o3$32o3$32o!

[Herschel of Ostropol]

How is a 30 x 30 square of cells not a solution to the grandfather problem?

Code: Select all

x = 32, y = 28, rule = B3/S23
32o3$32o3$32o3$32o3$32o3$32o3$32o3$32o3$32o3$32o!

Does that have a grandfather?

[Macbi]

How is a 30 x 30 square of cells not a solution to the grandfather problem?

Code: Select all

x = 32, y = 28, rule = B3/S23
32o3$32o3$32o3$32o3$32o3$32o3$32o3$32o3$32o3$32o!

Does that have a grandfather?

Code: Select all

x = 36, y = 32, rule = B3/S23
10b2o$2b2ob2obo14bobo2bo2b2obo$9b5ob2o2b2obo5bo$bo2bo2bo4bo2b2ob2o2bo
2b2o2bobo2bo$11bo2bob2ob2o12bo$2bo2bo2bo8bo2b2o3b2o$3ob2ob2ob2ob2o7b3o
2b6obo$2b2ob4o13b2ob2ob2ob3o$3b2o4b6o2bo2b3o2b2o5bo$o14b2ob2o9bo$bo7b
2obob2ob2obo9bo2bobo$4bo2bo5b2o2bo5bo2b2o$2b2ob2obo2bo8b2ob2ob2ob2ob2o
bo$4ob2o16b5o$2bo2bo2bo2bo2b2o2b3obo5b3ob2obo$8b2ob2obob2obobo7bo2b2ob
o$3bo2bob6obob2ob2obobobobo2b2o$7bo6b2o2bo2b2o5b4o2bo$b2ob2o18bobo$17b
o12bobo$ob4o2bo2bo2b2o2bobo4b4o5bo$b2o2bob2ob2ob2o2bobob4o2bobobobo$2o
2b2ob2ob2ob2o4b2ob2ob2o$3ob2o2bo2bo2b6o5b2ob5o2bo$bo20bo6bo2b2o$bo8bo
2bobo2b2o2bo6bo3b2o$4bo2bo8bo8b2ob6obo$bob2ob2ob2ob2o2bo2bob2ob2obo$2b
2ob3o12b5obobobo2b2o$3b2o3b12o5bob3o$18bo12b2o$bo6b2o2bob2o2bo2b2o3b2o
!

[Wyirm]

There may be an easier to construct/extend alternative:

Code: Select all

x = 40, y = 30, rule = B3/S23
2bo34bo$2bo34bo$40o$2b36o$2bo34bo3$2bo34bo$2b36o$40o$2bo34bo3$2bo34bo$
2b36o$40o$2bo34bo3$2bo34bo$40o$2b36o$2bo34bo3$2bo34bo$2b36o$40o$2bo34b
o$2bo34bo!

[Macbi]

Further back:

Code: Select all

x = 32, y = 32, rule = B3/S23
2bo13b2o2b2o8b2o$o4b2obo2b4o4bo3b4o$ob2ob4ob2o2bo2bobo2b2o2b4o$6bo2b2o
b4obo6bobo4bo$b2obo2b2o4bo2b3o2bobob2o2b2o$4bob4o2bo4b2obobobo2bobo$b
2o2bo9b2obob2o2b3obobo$4b2o2bo2bobo4bo2bobob4o$obo4b4o3b3ob2ob2o$7bo2b
o2bo8bo$4b2obob4ob2o3bobob5obobo$b2o3bo4bo2b2o2bob2obobo2b4o$bo2bo2bo
2bo5b3o3b2obobo$3obo7b3o7b2o5b3o$o2bobob2o3b2o3bo3bo3bob2ob2o$4b4o2bo
4bo2b3obobo4b2o$bo3b2o4bo4bo3bo3bobobo2bo$4bo4b4ob3o2b2o4b3o$2b2o5bo2b
o3b2o2bo4b2o$b3o2bob2o5bo3bo2b2o5bobo$ob2o2bobobob2obo8bobo2bo$b3o2bob
2o2b2obobo2bo2bo2bobobo$o8bobo2bo2bo2b3obo3bo$2b3o4bo4bob2o3bobo2bo$3b
o4bob2o4bo2bobo2bo2b2obo$bo2b2o2bobobob2o2bo5bobo$4b2o5b3o2bob2o3bo2b
3obo$b2o2bob2o4bo4b2obo6b2o$b2o2b2o2b3ob2obo3bo2b2o$2bo4bo2bo2bob2obo
2b2ob2o5bo$5bo3bo2b2o2bo4b2o3bob2o$o2b2o4bo2bo6bo3b2obobobo!

I find it interesting that the densities of the first generations are 0.376 and 0.363. These are suspiciously close to 0.370, the fixed-point density of Life if you were to randomly permute the cells every generation.

[mniemiec]

Further back:I find it interesting that the densities of the first generations are 0.376 and 0.363. These are suspiciously close to 0.370, the fixed-point density of Life if you were to randomly permute the cells every generation.

This is not surprising. Life cells survive if they have 2 or 3 live neighbors, which means a density of 3/9 or 4/9 within their own neighborhood. Cells are born with 3, at a density of 3/9. The average of these three is 0.37037.

[Random life lover]

Has anyone done research on this kind of grid before?

UvO5x.jpg (30.31 KiB) Viewed 1063 times

where the octagon and the squares can have same or different rules.

[GUYTU6J]

Has anyone done research on this kind of grid before?
...
where the octagon and the squares can have same or different rules.

Hello, you can try TiledCA.

[dvgrn]

Hello, you can try TiledCA.

Ready also allows CA simulations on arbitrary tilings -- there are some sample patterns that run on Penrose tilings, for example.

Ready can also generate tiling meshes of whatever size you want, but last time I investigated it looked like there would be some coding involved, one way or another.

[Wyirm]

Couldn't this be run by a three-state rule where state 2 is Moore neighborhood, and state 3 is Von-Neumann? Another possible option would be using custom neighborhood LTL unit cells, but that might be harder to construct. Side question, aren't Penrose tilings by definition aperiodic, and thus impossible to support infinite planes, and even finite planes requiring massive computational capabilities?

[dvgrn]

Couldn't this be run by a three-state rule where state 2 is Moore neighborhood, and state 3 is Von-Neumann?

Sure, a rule table could be made to work in various ways, the only limitation being that you'd always have to start with a checkerboard of two different cell states -- it makes it a little awkward to draw in initial states manually, so no doubt you'd have a script to "checkerify" an initial two-state pattern and switch to the rule.

Could even create icons in Golly that showed the octagonal and square cells (with gaps in between).

Side question, aren't Penrose tilings by definition aperiodic, and thus impossible to support infinite planes, and even finite planes requiring massive computational capabilities?

Simulating an unbounded plane containing a Penrose tiling with (almost) all OFF cells would actually not be too terribly difficult. Penrose tilings can be "inflated" and "deflated", so a simulation algorithm could figure out what specific tiles are in a given area, only when your pattern or your viewpoint travels to that region and you actually need to know.

Now, there are an infinite number of different infinite Penrose tilings, so if you want to simulate a specific one that isn't just a repeated dissection of a single dart or kite (for example) then you'd theoretically have to store a lot of information... but here again there are shortcuts. Roughly speaking, each "decision point" in a Penrose tiling (where there are two or more possibilities as to what tile is at a given location) forces a larger and larger region of tiles to be placed in a specific way. In practice, you can store all details needed to simulate an incredibly huge Penrose tiling, in just a few kilobytes of information.

-- Obviously if half the tiles are ON cells, in this incredibly huge tiling, that's another matter! But that's just the same limitation that Golly has: it does just fine simulating ridiculously large almost-empty spaces, but if you fill even a relatively small space with chaotic stuff, that takes more memory and it will bog down.

[Herschel of Ostropol]

If I reversed engineered, i.e. designed, a soup for an object (e.g. Sir Robin, a gun) would that count as natural?

[hotdogPi]

If I reversed engineered, i.e. designed, a soup for an object (e.g. Sir Robin, a gun) would that count as natural?

No. As you say, reverse engineered.

[Sokwe]

If I reversed engineered, i.e. designed, a soup for an object (e.g. Sir Robin, a gun) would that count as natural?

No. From the wiki (with added emphasis):

an object is said to occur naturally if it has been found in the ash of an asymmetric random soup at least once

A reverse-engineered soup isn't random. For example, a reverse-engineered 16x16 soup that produces a 2-engine Cordership is known, but the ship has not yet occurred naturally.