Thread for your miscellaneous posts and discussions

[hotdogPi]

Your choice of the word 'transition' to mean "state of cell's neighborhood" (as you seem to claim) strikes me as counterintuitive and confusing. Are there any real "transitions" in this situation? What is "transitioning" here? Can this choice of wording be explained to someone who is familiar with the common English meanings of the word 'transition'?

Discord would interpret this paragraph very differently.

[confocaloid]

Your choice of the word 'transition' to mean "state of cell's neighborhood" (as you seem to claim) strikes me as counterintuitive and confusing. Are there any real "transitions" in this situation? What is "transitioning" here? Can this choice of wording be explained to someone who is familiar with the common English meanings of the word 'transition'?

Discord would interpret this paragraph very differently.

^^ I don't really know how "discord would interpret" what I wrote. I'm not discord. I'm not on discord.

I don't see anything that could be helpfully and correctly described as "transition" in the following table:
https://web.archive.org/web/20241118163 ... bors2.html
There is a table showing current states of some cells. It basically lists all possible conditions of a cell in a two-state CA with Moore neighbourhood, up to rotations and reflections, and ignoring the cell's own current state.

The discussion is about cellular automata. Specifically, the discussion is about ways to explain

• exactly how much a cell in the universe "is allowed to see" about the current states of other cells in the universe (and its own current state),
• exactly how the evolution rules of the cellular automaton are defined (i.e. what sort of a calculation or computation is needed to determine a cell's future state).

The former is basically a question "what are [all possible] cell's conditions?"
The latter is basically a question "how the rules are defined?"

Usually the two questions are interlinked together: the "if-then" rules (prescribing how CA configurations evolve) are written in terms of cell's conditions.
> "If a cell is in such-and-such condition in generation T, then the cell will be in such-and-such state in generation T + 1."

More complete context for the quoted paragraph:

"If a cell would turn on, a cell that is already on with nothing else different is guaranteed to stay on." (There's probably a better wording, and I'm aware my definition is only clearly defined for two-state rules.)

I think one can simply say that the birth conditions must be a subset of the survival conditions.
The birth conditions are (a set of) conditions on states of neighbours of a currently-dead cell, for that cell to become alive in the next generation.
The survival conditions are (a set of) conditions on states of neighbours of a currently-alive cell, for that cell to remain alive in the next generation.

Compare with the following examples (quotes from Life/CA-related sources), which also use the same wording with the same meaning:

[...] While the birth conditions are totalistic (and, in fact, the same as Life's), the survival conditions are not totalistic - i.e. they depend not only on the number of neighbors, but also their relative positions. Birth occurs on any 3 neighbors, while survival occurs on 2-4 neighbors that are orthogonally connected to the original cell (i.e. diagonal neighbors are allowed only if they are themselves adjacent to one or two orthogonal neighbors). Most common patterns are shared by all variants. The variants arise by tweaking three of the survival conditions: [...]

[...] More succinctly, a Life-like cellular automaton emulates a Margolus block cellular automaton if and only if, in its rulestring, B3 = S5, B4 = S4, B5 = S6 = S7, and B1 = B2 = S3. 2x2 can be seen to satisfy these conditions because 4 is neither a birth condition nor a survival condition, 5 is not a birth condition and 6 and 7 are not survival conditions, 3 is a birth condition and 5 is a survival condition, and 3 is not a survival condition and 1 and 2 are not birth conditions. There are 2^12 = 4096 Life-like cellular automata that emulate 2^6 = 64 different Margolus block cellular automata. [...]

edit: fixed superscripts that were broken due to copy/pasting a quote.

---

Edit: By "transition" I mean "state of cell's neighborhood" and not "state of cell and cell's neighborhood". By this logic, B4t and S4t are equivalent. Also, "gnomonic" is a random word that entered my mind once and I just had to use it somewhere hehe sorry

When I read 'gnomonic' I think of the gnomonic projection, but unfortunately it doesn't seem relevant here.

I think any new terminology needs to be reasonably helpful and reasonably self-explanatory.

Your choice of the word 'transition' to mean "state of cell's neighborhood" (as you seem to claim) strikes me as counterintuitive and confusing. Are there any real "transitions" in this situation? What is "transitioning" here? Can this choice of wording be explained to someone who is familiar with the common English meanings of the word 'transition'?

[hotdogPi]

That's because Discord wouldn't interpret that paragraph in a CA context at all — several people on the server have transitioned (in an entirely different context).

I only quoted the last paragraph and not the entire post for a reason.

[confocaloid]

That's because Discord wouldn't interpret that paragraph in a CA context at all — [...]

I fail to see how that relates to the actual discussion at hand (given that the discussion *is* CA-related in an obvious way).

My suggestion would be to read the discussion more carefully, to avoid misinterpreting a CA-related discussion about a specific CA-related topic in a completely irrelevant way.

[...]
Do not test the boundaries on this. Do not discuss gender issues if you are not completely sure that you will not violate this rule.

[hotcrystal0]

That's because Discord wouldn't interpret that paragraph in a CA context at all — several people on the server have transitioned (in an entirely different context).

I only quoted the last paragraph and not the entire post for a reason.

Well, when referring to transition rules, “transition” is being used as a noun, not a verb, which signifies it’s the CA definition.

[CARuler]

@sokwe i don't see why you locked the cgol skyscraper; people only flooded the other threads with more stuff and made more threads; please stop locking threads

[Sokwe]

@sokwe i don't see why you locked the cgol skyscraper;

This was explained at the time. It was a random posts thread, which have been banned for some time.

i only flooded the other threads with more stuff and made more threads

Please do not create new threads simply because another thread was locked. And please do not ever "flood" threads.

please stop locking threads

I will lock threads if I believe they need to be locked. The moderators do not have time to monitor high-volume threads that have a high chance of rule violations.

[Scorbie]

Hey, I read the bounding box discussion but was unsure which thread to continue the discussion so I'm posting here.
Original discussion: viewtopic.php?p=199174#p199174

Here's an alternative definition for the bounding box of a gun:

Assume someone covers the rectangle (x, y, w, h) with a black box and we observe the pattern at gen 0, 1, 2, ... without knowing the pattern inside the rectangle. If the result is indistinguishable from someone manually drawing a glider on some position with the same direction and phase inside the rectangle every p generations, the rectangle is a bounding box for the gun. We are looking for the minimal bounding box for the gun.

This should hopefully be a bit easier to calculate?

(I personally don't care about the names of the terminologies chosen to describe the concept as long as the meaning of the statement is the same. Feel free to substitute for a better name as you see fit. For this post I'll stick with "bounding box" and "minimal bounding box" as implied for the sake of explanation.)


There is one interesting judgement call this proposes.

According to this criterion, the bottom row of gun_184's minimal bounding box is one cell below the clock, but only barely. The row below the clock is distinguishable from an output glider stream only on phases 183, 0, 1, and 2. If the row were indistinguishable, should the minimal bounding box be reduced by one row?

[confocaloid]

Hey, I read the bounding box discussion but was unsure which thread to continue the discussion so I'm posting here.
Original discussion: viewtopic.php?p=199174#p199174
[...]

There was also related discussion in this forum thread:
viewtopic.php?p=199278#p199278
viewtopic.php?p=199308#p199308
viewtopic.php?p=199309#p199309
viewtopic.php?p=199310#p199310
viewtopic.php?p=199311#p199311
viewtopic.php?p=199316#p199316
viewtopic.php?p=199318#p199318
viewtopic.php?p=199321#p199321

It should be possible to implement the usual definition of "the bounding box of a glider gun" per the readme file https://entropymine.com/jason/life/dpguns/readme.txt
I think the main problem is doing that efficiently enough for it to be part of Catagolue code. The input is a RLE (which may be either a glider gun submission, or a glider synthesis submission, or neither). One would need to decide what kinds of submissions to accept (rejecting everything else), and how to transform the accepted submissions into canonical form.
One would also need to handle different cases (such as true period glider gun vs. pseudo period glider gun), and decide how to handle "width = height" and hopefully make it so that it ensures the canonical orientation of guns.

I think the same issues would apply even if the definition of "the bounding box of a glider gun" was changed. I personally would prefer the old definition per https://entropymine.com/jason/life/dpguns/readme.txt (or a consistent clarification of that to account for cases like "width=height" without changing the original meaning), simply to avoid having different "competing" definitions.

[Scorbie]

I personally would prefer the old definition per https://entropymine.com/jason/life/dpguns/readme.txt (or a consistent clarification of that to account for cases like "width=height" without changing the original meaning), simply to avoid having different "competing" definitions.

There was also related discussion in this forum thread:

I skimmed the links. The alternative definition is not "competing" in the sense that it is compatible with the existing definition for all guns shown (and the edge cases you suggested in the original thread.) It works the same for pure and pseudo-period guns.

The judgement call I suggested has to do with where the boundary lies between a forming output glider stream and the rotor.

Anyway, I just brought this up to solve an existing problem of guns. If it doesn't solve the problem I'm not interested in pursuing the idea further. Wish you have a nice day.

[confocaloid]

[...] There is one interesting judgement call this proposes.

According to this criterion, the bottom row of gun_184's minimal bounding box is one cell below the clock, but only barely. The row below the clock is distinguishable from an output glider stream only on phases 183, 0, 1, and 2. If the row were indistinguishable, should the minimal bounding box be reduced by one row?

[...] The judgement call I suggested has to do with where the boundary lies between a forming output glider stream and the rotor. [...]

If I understand the idea, then the row below the clock would be distinguishable from an output glider stream only in phases 183, (184 ≡ 0 (mod 184)), and 1.
It would be indistinguishable in phase 2 (if the row below the clock is the first row below the "black box"), even though the glider is not yet formed in phase 2:

Code: Select all

x = 68, y = 49, rule = DoubleB3S23
2.B$B.B$.2B16$54.A$52.3A$51.A$51.2A$63.A$61.2A$46.3A14.2A$46.A.A13.A$
48.A$47.2A$47.2A.A$47.A3.A$49.A.2A$48.2A.A$49.2A$49.3A$37.2A8.A4.A13.
2A$36.A.A7.A3.2A.A4.2A5.3A$36.A9.A.2A.A.2A3.2A4.A.2A$35.2A10.A5.A9.A.
A$63.A2.A$64.2A2$47.A$46.A.A$45.A$40.A4.A3.2A$40.A.A8.A$39.A.A4.A.B.A
$41.A4.BACA$47.2B!

There may be issues with the idea, due to the possibility of a "heisenburp-type" interaction between "what appears to be a fully-formed output glider leaving the black box" and the rest of the gun.

Even if "what appears to be a fully-formed output glider" is completely outside the "black box", there may be a gun such that simply clearing those five alive cells causes the gun to fail.
I'm not sure if there is a non-contrived example of that problem, but I also don't see how one could possibly eliminate that possibility for some actual record-beating discovery submission.

[Scorbie]

If I understand the idea, then the row below the clock would be distinguishable from an output glider stream only in phases 183, (184 ≡ 0 (mod 184)), and 1.

You're totally right. I somehow missed that.

There may be issues with the idea, due to the possibility of a "heisenburp-type" interaction between "what appears to be a fully-formed output glider leaving the black box" and the rest of the gun.

I can see that this is an edge case that makes my alternative definition differ from the original one.

This made me curious.

If I understand right, your step 1 can be summarised as "ensure that the pattern is a period-N gun". In other words, the pattern must reappear exactly after N ticks (where N needs to be determined), with one or more output gliders appearing on the same lane and moving away from the pattern.

It's possible that a pattern can evolve `N` generations to generate the same pattern with an output glider, but then when evolving another `period` generations can lead to differing intermediate patterns because the presence of the glider may lead to a "heisenburp-type" reaction that isn't necessary for the gun to work. Should you only check generation `i` and `i+period`, or should you compare all generations in range `i..i+period-1` and `i+period..i+2*period-1`?

Edit: this was in the discussion, and the conclusion seems to be yes you should compare all phases. Here's the relevant quote

If necessary, evolve the initial pattern until all sparks die and the pattern becomes a gun.

[CARuler]

i only flooded the other threads with more stuff and made more threads

Please do not create new threads simply because another thread was locked. And please do not ever "flood" threads.

i don't how this happened, i'm sure i typed "people"

[Scorbie]

I was trying to formalize the concept of the gun and bounding box (mostly for my own understanding). I was unsure if the following definition aligns with the current usages or previous mentions of a gun.

Pseudocode conventions:

Code: Select all

`pattern[i]` := the pattern `pattern` after `i` generations
`&`, `|`, `^`, `~` := bitwise operations on one or two patterns

A pattern `x` is a period-`p` gun if it satisfies the following equation for some pattern of a spaceship `g`:

Code: Select all

for all i in 0, 1, 2, ...
x[i + p] = x[i] | g[i + p]
  AND x[i] & g[i + p] = (empty pattern)
  AND (x[i] and g[i + p] are "identifiable from each other")

The bounding box of the gun `x` is calculated as the union of the bounding box of patterns `x[0]`, `x[1]`, ... `x[p - 1]`

Note to language lawyers: I might have been sloppy with the exact semantics of terminology. [s]The words used in this post is intended as a tool to share information, not as a strict usage of language semantics.[/s]
Edit: What I mean by this is that I don't want this post to be cited as usage of a certain terminology when discussing precise language semantics.

see also:

Probably the best idea I was able to imagine so far, in order to guarantee correctness, would be to build a directed graph out of statements of the following form:

A glider g is a visible object (can be identified as a glider) in such-and-such location in phase t,
and the 1-tick successor of g is a visible object (can be identified as a glider) in the same location in phase (t + 1) mod period,
and presence or absence of g in phase t causes presence or absence of the 1-tick successor of g in phase (t+1) mod period and no other changes apart from that.

---

EDIT: here is an example of a problem with pseudo period guns. The gun period is 57, the output glider stream period is 19. There are three different ways to "interpret" this gun as a period-57 gun that shoots glider triplets "xq4_456zy1562zy5247" (rather than single gliders):

Code: Select all

x = 500, y = 132, rule = B3/S23
24b2o3b2o5b2o62b2o5b2o3b2o80b2o3b2o5b2o62b2o5b2o3b2o80b2o3b2o5b2o62b2o
5b2o3b2o$19bo3bobo4bo5b2o62b2o5bo4bobo3bo70bo3bobo4bo5b2o62b2o5bo4bobo
3bo70bo3bobo4bo5b2o62b2o5bo4bobo3bo$18bobobo2bob3o78b3obo2bobobo68bobo
bo2bob3o78b3obo2bobobo68bobobo2bob3o78b3obo2bobobo$19b2ob3o2bo82bobob
2ob2o70b2ob3o2bo82bobob2ob2o70b2ob3o2bo82bobob2ob2o$26bo89bo79bo89bo
79bo89bo$17b5ob2o32bob2o2b2o45bo2b8o66b5ob2o32bob2o2b2o45bo2b8o66b5ob
2o32bob2o2b2o45bo2b8o$16bo8b2o30bobo3bo2bo43bo3bo6bo64bo8b2o30bobo3bo
2bo43bo3bo6bo64bo8b2o30bobo3bo2bo43bo3bo6bo$15bob3o2bo2bob2o27bo2b3o3b
2o45b3o2bob2obo62bob3o2bo2bob2o27bo2b3o3b2o45b3o2bob2obo62bob3o2bo2bob
2o27bo2b3o3b2o45b3o2bob2obo$15bobobob2o35b2o49b2ob2obo2bo3bo62bobobob
2o35b2o49b2ob2obo2bo3bo62bobobob2o35b2o49b2ob2obo2bo3bo$14b2o2b2ob2obo
3bo27bo2b2o2bo38b2o8b2obo3bo2b2o60b2o2b2ob2obo3bo27bo2b2o2bo38b2o8b2ob
o3bo2b2o60b2o2b2ob2obo3bo27bo2b2o2bo38b2o8b2obo3bo2b2o$17b2o4b2ob2o24b
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b2o24b2ob2obo41b5o4bobo3bo3bo$18bo7bobo23b3o7b2obo18bo13b3ob3o4bo2bo5b
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3o49bo5bo3bo2bo2b2obob2o7b2o18b2ob4o13b2o2bobobo11bo13bo3b5obo3b3o$5bo
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ob4o7b2o2bobo17b2o7b2obo4bo2bo2bo4bo2bo2b2o3bo13bo11bobobo5bo6bobo$bob
obo2bo2bo2b4o4bobobob3o12bob2o6bo3bob2obobob2o3bobobo5b3o2bo4b2o2bobo
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3bobobo5b3o2bo4b2o2bobo2bo6b5obobo4b5obobo42bobobo2bo2bo2b4o4bobobob3o
12bob2o6bo3bob2obobob2o3bobobo5b3o2bo4b2o2bobo2bo6b5obobo4b5obobo$2b2o
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2bo5bo4bo8bo5bobobo5bo2bo2bobo41b2obobo4b2o4bo3bo2bo5bo11bob2o6bo3bob
2obobo6bobo2b4ob3o2bo5bo4bo8bo5bobobo5bo2bo2bobo$4b2o7bo2b2o2bobo3b5o
13bo8b2obo4bo2bob2o4bobobo2bo3bo8bo3bo9b5obo3bo3b2o4bobob3o41b2o7bo2b
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41b2o7bo2b2o2bobo3b5o13bo8b2obo4bo2bob2o4bobobo2bo3bo8bo3bo9b5obo3bo3b
2o4bobob3o$2b2obo2b3o2bobo2b3ob2o4bo24bob2o5bo4bo6b2o5bo2bo4b3ob3o14bo
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12b2o5b3o2bobo2b3o2bob2obo37bobob3o4b2ob2o39b2ob4ob2o8bo3bo3bobo4b5o
12b2o5b3o2bobo2b3o2bob2obo$o4bob3o7b2o32b2ob3obo4b2o5b2o2bo3bob2o8b2o
15bo9b2ob2o4b3obo2b2o35bo4bob3o7b2o32b2ob3obo4b2o5b2o2bo3bob2o8b2o15bo
9b2ob2o4b3obo2b2o35bo4bob3o7b2o32b2ob3obo4b2o5b2o2bo3bob2o8b2o15bo9b2o
b2o4b3obo2b2o$4o3b3obob2obo2bo34b3ob2ob2obo6bo3bo2bob2ob2o22bob2o4b2o
7b3obobobo37b4o3b3obob2obo2bo34b3ob2ob2obo6bo3bo2bob2ob2o22bob2o4b2o7b
3obobobo37b4o3b3obob2obo2bo34b3ob2ob2obo6bo3bo2bob2ob2o22bob2o4b2o7b3o
bobobo$10bo2b2o2b2obo30bo10bob3o4bob2obo2b3o24b2ob2o3bo2bob2obob3o5bo
47bo2b2o2b2obo30bo10bob3o4bob2obo2b3o24b2ob2o3bo2bob2obob3o5bo47bo2b2o
2b2obo30bo10bob3o4bob2obo2b3o24b2ob2o3bo2bob2obob3o5bo$2b2ob2obo3b4o2b
obo31b3o6b2o2bobo4bo6bo3bo15b2o12bob2o2b2o2bo6b2o40b2ob2obo3b4o2bobo
31b3o6b2o2bobo4bo6bo3bo15b2o12bob2o2b2o2bo6b2o40b2ob2obo3b4o2bobo31b3o
6b2o2bobo4bo6bo3bo15b2o12bob2o2b2o2bo6b2o$2bo5bob2o4b3ob2o12b2o16b2ob
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16b2ob2o3bo2bo3bo5b8o2bo15b2o5b2ob2o2bobo2b4o3bob2o$obo15bobo14bo20bob
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b3o4b2obo44bobo15bobo14bo20bobo2b6o10bo28b2obobobob3o4b2obo$2o11b2o3bo
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o3b2o68bo16b2o12b2o6b2obob2o11bobo3bo3b2o22b2obobo3b2o$50b2o8bo2bobo
10bo3b2o4b2o26bo105b2o8bo2bobo10bo3b2o4b2o26bo105b2o8bo2bobo10bo3b2o4b
2o26bo$55b2o6bobo11b3o145b2o6bobo11b3o145b2o6bobo11b3o$13b3o11bo12bobo
12bo8bo14bo13b3o25b3o59b3o11bo12bobo12bo8bo14bo13b3o25b3o59b3o11bo12bo
bo12bo8bo14bo13b3o25b3o$12b4o11b3o11bobo9bobo39bo11b2o10b2o61b4o11b3o
11bobo9bobo39bo11b2o10b2o61b4o11b3o11bobo9bobo39bo11b2o10b2o$2o9b2o2b
2o13bo9b2obo9b2o32bo4bo15bo10bo3bo46b2o9b2o2b2o13bo9b2obo9b2o32bo4bo
15bo10bo3bo46b2o9b2o2b2o13bo9b2obo9b2o32bo4bo15bo10bo3bo$2o10bob2o13b
2o11bo6b2o6b2o4bo18b2o2bobo19bobo3b3obo2b2o9b2o36b2o10bob2o13b2o11bo6b
2o6b2o4bo18b2o2bobo19bobo3b3obo2b2o9b2o36b2o10bob2o13b2o11bo6b2o6b2o4b
o18b2o2bobo19bobo3b3obo2b2o9b2o$13b3o33bobo4bobo4b3o16b2obo2bo3bobo14b
2o6bo14b2o49b3o33bobo4bobo4b3o16b2obo2bo3bobo14b2o6bo14b2o49b3o33bobo
4bobo4b3o16b2obo2bo3bobo14b2o6bo14b2o$14bo20b2o13b2o3bo10bo19b2o26bo6b
o62bo20b2o13b2o3bo10bo19b2o26bo6bo62bo20b2o13b2o3bo10bo19b2o26bo6bo$
34bo2bo16bob2o7b2o54bo82bo2bo16bob2o7b2o54bo82bo2bo16bob2o7b2o54bo$34b
o2bo12b5o3bo22b2o3b2o27b2o3bo83bo2bo12b5o3bo22b2o3b2o27b2o3bo83bo2bo
12b5o3bo22b2o3b2o27b2o3bo$18bo15bo2bo12bo4b3o10b2o12bo4bo26bo3b2o68bo
15bo2bo12bo4b3o10b2o12bo4bo26bo3b2o68bo15bo2bo12bo4b3o10b2o12bo4bo26bo
3b2o$17b3o15b2o14b3obo4b2o6b2o9b3o4bo26bo73b3o15b2o14b3obo4b2o6b2o9b3o
4bo26bo73b3o15b2o14b3obo4b2o6b2o9b3o4bo26bo$17b2obo32bobo6bo16bo6b2o
25bo6bo66b2obo32bobo6bo16bo6b2o25bo6bo66b2obo32bobo6bo16bo6b2o25bo6bo$
16b2o2b2o37bo41bo4bo10bo68b2o2b2o37bo41bo4bo10bo68b2o2b2o37bo41bo4bo
10bo$17b4o34bob2o40b2o4bo6b2o2bob3o66b4o34bob2o40b2o4bo6b2o2bob3o66b4o
34bob2o40b2o4bo6b2o2bob3o$17b3o37bob2o39b2o4bo4bo3bo71b3o37bob2o39b2o
4bo4bo3bo71b3o37bob2o39b2o4bo4bo3bo$57bobo54b2o111bobo54b2o111bobo54b
2o$36b2o18b2o2bo50b3o92b2o18b2o2bo50b3o92b2o18b2o2bo50b3o$30b2o4bobo
11bo8b2o12bo126b2o4bobo11bo8b2o12bo126b2o4bobo11bo8b2o12bo$11bob2o3b2o
3b2obo3b2o5b2o12b2o19b2o46bo60bob2o3b2o3b2obo3b2o5b2o12b2o19b2o46bo60b
ob2o3b2o3b2obo3b2o5b2o12b2o19b2o46bo$11bo3bo6bo3bo23b2o20bobo7bo31b2o
3bobo59bo3bo6bo3bo23b2o20bobo7bo31b2o3bobo59bo3bo6bo3bo23b2o20bobo7bo
31b2o3bobo$11bo14bo7b2o46b3o34bobo59bo14bo7b2o46b3o34bobo59bo14bo7b2o
46b3o34bobo$11bobo2b6o2bobo8bo11bo15bob2o18bo23bob2o4b3ob2o58bobo2b6o
2bobo8bo11bo15bob2o18bo23bob2o4b3ob2o58bobo2b6o2bobo8bo11bo15bob2o18bo
23bob2o4b3ob2o$9bobob2o3b2o3b2obobo3b3o11bobo14bobo18b2o20b2obo3b4o2bo
bo2bo54bobob2o3b2o3b2obobo3b3o11bobo14bobo18b2o20b2obo3b4o2bobo2bo54bo
bob2o3b2o3b2obobo3b3o11bobo14bobo18b2o20b2obo3b4o2bobo2bo$6bo10bo2bo
11bo14bo13b2obobo36b2o6bo2b2o2b2o3b2o51bo10bo2bo11bo14bo13b2obobo36b2o
6bo2b2o2b2o3b2o51bo10bo2bo11bo14bo13b2obobo36b2o6bo2b2o2b2o3b2o$6bobob
o3bob2o2b2obo3bobo16bo14bo40bo5b3obob2obo2b3o53bobobo3bob2o2b2obo3bobo
16bo14bo40bo5b3obob2obo2b3o53bobobo3bob2o2b2obo3bobo16bo14bo40bo5b3obo
b2obo2b3o$6bobobo5b2o2b2o22b3o14bo2bo5b2o30bobobob3o7b2o2bo5bo47bobobo
5b2o2b2o22b3o14bo2bo5b2o30bobobob3o7b2o2bo5bo47bobobo5b2o2b2o22b3o14bo
2bo5b2o30bobobob3o7b2o2bo5bo$9bob3obo2b2o2bob2o3bobo16b3o11bobo5bobo
13bo13b2o2bob3o4b2ob2o3bo4b3o7bo42bob3obo2b2o2bob2o3bobo16b3o11bobo5bo
bo13bo13b2o2bob3o4b2ob2o3bo4b3o7bo42bob3obo2b2o2bob2o3bobo16b3o11bobo
5bobo13bo13b2o2bob3o4b2ob2o3bo4b3o7bo$5b2o2bob3obobo2bobob4o3bo40bo12b
3o13bob2obo2b3o2bobo2b2o4bo10b3o36b2o2bob3obobo2bobob4o3bo40bo12b3o13b
ob2obo2b3o2bobo2b2o4bo10b3o36b2o2bob3obobo2bobob4o3bo40bo12b3o13bob2ob
o2b3o2bobo2b2o4bo10b3o$5b3ob2ob2obo6bobobob3o13b3o25b2o11b2o14bo3b2o7b
o2b2o6b2o7b2o3bo35b3ob2ob2obo6bobobob3o13b3o25b2o11b2o14bo3b2o7bo2b2o
6b2o7b2o3bo35b3ob2ob2obo6bobobob3o13b3o25b2o11b2o14bo3b2o7bo2b2o6b2o7b
2o3bo$6bo2b2o2bobob4obo5bo17bob3o43b2o6b3obobo4b2o3bo14bo3bobo36bo2b2o
2bobob4obo5bo17bob3o43b2o6b3obobo4b2o3bo14bo3bobo36bo2b2o2bobob4obo5bo
17bob3o43b2o6b3obobo4b2o3bo14bo3bobo$5b2o2bo4bo8bobobo2b3o17bo36b2o5bo
bo7bobo2bo2bo2b3o4b3o8b5ob2o34b2o2bo4bo8bobobo2b3o17bo36b2o5bobo7bobo
2bo2bo2b3o4b3o8b5ob2o34b2o2bo4bo8bobobo2b3o17bo36b2o5bobo7bobo2bo2bo2b
3o4b3o8b5ob2o$5bo4bobobob7o5bobo2bo11bob3o5b3obo5bo21b2o7bo9bobob4o8bo
2bo8bo40bo4bobobob7o5bobo2bo11bob3o5b3obo5bo21b2o7bo9bobob4o8bo2bo8bo
40bo4bobobob7o5bobo2bo11bob3o5b3obo5bo21b2o7bo9bobob4o8bo2bo8bo$7bo6bo
bo3bobo2b2obo2b2o10b5o7b2o2b2o5bo29b2o8bobo5b2o6bo2bo7bobo3b4o34bo6bob
o3bobo2b2obo2b2o10b5o7b2o2b2o5bo29b2o8bobo5b2o6bo2bo7bobo3b4o34bo6bobo
3bobo2b2obo2b2o10b5o7b2o2b2o5bo29b2o8bobo5b2o6bo2bo7bobo3b4o$6b2o4b2o
4bobo4bo2bo14b3o9b2o2bobo2b3o40bo5bo2bo6bo2bo5b3ob3o4bo32b2o4b2o4bobo
4bo2bo14b3o9b2o2bobo2b3o40bo5bo2bo6bo2bo5b3ob3o4bo32b2o4b2o4bobo4bo2bo
14b3o9b2o2bobo2b3o40bo5bo2bo6bo2bo5b3ob3o4bo$17b2ob2o4b2o28b6o21bo24b
3o3b2o3b2o2bo2bo5bobo2b4obobo42b2ob2o4b2o28b6o21bo24b3o3b2o3b2o2bo2bo
5bobo2b4obobo42b2ob2o4b2o28b6o21bo24b3o3b2o3b2o2bo2bo5bobo2b4obobo$21b
o15b2o17b2o2b2o20bobob2o22bo12bobo5b2o9bobo46bo15b2o17b2o2b2o20bobob2o
22bo12bobo5b2o9bobo46bo15b2o17b2o2b2o20bobob2o22bo12bobo5b2o9bobo$21bo
b2o4b2o7bo17b5o8bo12bobobobo32b2obo7bob2o2bobo3b3o44bob2o4b2o7bo17b5o
8bo12bobobobo32b2obo7bob2o2bobo3b3o44bob2o4b2o7bo17b5o8bo12bobobobo32b
2obo7bob2o2bobo3b3o$9b2o4b2o3b2obo4bo2bo6bobo14b2obo11b2o7b2obobobobo
2bo27bobo9bobob3o4bo4bo2bo28b2o4b2o3b2obo4bo2bo6bobo14b2obo11b2o7b2obo
bobobo2bo27bobo9bobob3o4bo4bo2bo28b2o4b2o3b2obo4bo2bo6bobo14b2obo11b2o
7b2obobobobo2bo27bobo9bobob3o4bo4bo2bo$10bo4bobobo3bobo3bobo2b2o3b2o
15b2o11b2o8bo2bo2b2ob4o14bo10b3o2b2o7bo4bo4bo4bo3b3o27bo4bobobo3bobo3b
obo2b2o3b2o15b2o11b2o8bo2bo2b2ob4o14bo10b3o2b2o7bo4bo4bo4bo3b3o27bo4bo
bobo3bobo3bobo2b2o3b2o15b2o11b2o8bo2bo2b2ob4o14bo10b3o2b2o7bo4bo4bo4bo
3b3o$8bo4b3obob4ob2o2bo2bobo2bo44b2o4bo11b2o3b5o8b2o3b4o4b2o2bobo2bobo
bo2b2o5bo24bo4b3obob4ob2o2bo2bobo2bo44b2o4bo11b2o3b5o8b2o3b4o4b2o2bobo
2bobobo2b2o5bo24bo4b3obob4ob2o2bo2bobo2bo44b2o4bo11b2o3b5o8b2o3b4o4b2o
2bobo2bobobo2b2o5bo$8b2o3b2o2bo13bob3o6b2o43bobo10bo2bo5bo7bo3b2o2bo4b
2o2bob4obob3o3bob2obo23b2o3b2o2bo13bob3o6b2o43bobo10bo2bo5bo7bo3b2o2bo
4b2o2bob4obob3o3bob2obo23b2o3b2o2bo13bob3o6b2o43bobo10bo2bo5bo7bo3b2o
2bo4b2o2bob4obob3o3bob2obo$9bo3b4ob8obobo12b2o4b2o38b2o10bobob2ob2o8bo
5bobo4b2o2bo7bo3b3o5bo2bo21bo3b4ob8obobo12b2o4b2o38b2o10bobob2ob2o8bo
5bobo4b2o2bo7bo3b3o5bo2bo21bo3b4ob8obobo12b2o4b2o38b2o10bobob2ob2o8bo
5bobo4b2o2bo7bo3b3o5bo2bo$9bobo3bo2bobo2bobobobob3o14bobo7b2o38b2o2bob
obo11b2o10b2o2bob2o6bo5bobobobobo20bobo3bo2bobo2bobobobob3o14bobo7b2o
38b2o2bobobo11b2o10b2o2bob2o6bo5bobobobobo20bobo3bo2bobo2bobobobob3o
14bobo7b2o38b2o2bobobo11b2o10b2o2bob2o6bo5bobobobobo$8bo3bo5bobo2bobo
2bob2o2bo13bo9bo14bo23bobobo4bo10b4o10bo4bobo4b2ob2o4bobob2o20bo3bo5bo
bo2bobo2bob2o2bo13bo9bo14bo23bobobo4bo10b4o10bo4bobo4b2ob2o4bobob2o20b
o3bo5bobo2bobo2bob2o2bo13bo9bo14bo23bobobo4bo10b4o10bo4bobo4b2ob2o4bob
ob2o$8bo4bob2obo2b2o2bobo4b3o24b3o12bo19bo2bo2b2obo2b2o10b2o11bobobo2b
3o3bobo3bob2o24bo4bob2obo2b2o2bobo4b3o24b3o12bo19bo2bo2b2obo2b2o10b2o
11bobobo2b3o3bobo3bob2o24bo4bob2obo2b2o2bobo4b3o24b3o12bo19bo2bo2b2obo
2b2o10b2o11bobobo2b3o3bobo3bob2o$11bo3b2obo6bobo4bo28bo10b3o18bobobo5b
o2b2o4bobo5bo8b2ob2obobo3bo2bobo2bo2b2o2b2o23bo3b2obo6bobo4bo28bo10b3o
18bobobo5bo2b2o4bobo5bo8b2ob2obobo3bo2bobo2bo2b2o2b2o23bo3b2obo6bobo4b
o28bo10b3o18bobobo5bo2b2o4bobo5bo8b2ob2obobo3bo2bobo2bo2b2o2b2o$9b3ob
3o4b4o6b3o45bobo12bobo2b4obo2b2o4bo2b2o3bo7bo5bo2b2obo2b2ob4o3bo2bobo
20b3ob3o4b4o6b3o45bobo12bobo2b4obo2b2o4bo2b2o3bo7bo5bo2b2obo2b2ob4o3bo
2bobo20b3ob3o4b4o6b3o45bobo12bobo2b4obo2b2o4bo2b2o3bo7bo5bo2b2obo2b2ob
4o3bo2bobo$9bo2b2o2bo3b4o3bo2b2o3bo43b2o13bobobo2bobo2b2o4b4o3b2o8b5o
3bo3b2o6b2o3bobo2bo19bo2b2o2bo3b4o3bo2b2o3bo43b2o13bobobo2bobo2b2o4b4o
3b2o8b5o3bo3b2o6b2o3bobo2bo19bo2b2o2bo3b4o3bo2b2o3bo43b2o13bobobo2bobo
2b2o4b4o3b2o8b5o3bo3b2o6b2o3bobo2bo$12b3o14b3o3b3o41bo16bo4bo4bo7b2o2b
3o17b3o3b4o2bob2ob5o22b3o14b3o3b3o41bo16bo4bo4bo7b2o2b3o17b3o3b4o2bob
2ob5o22b3o14b3o3b3o41bo16bo4bo4bo7b2o2b3o17b3o3b4o2bob2ob5o$14bob2o8b
2obo8bo29b2o25bo4b3obobo9bobo10b3o9b2o6bo3b2o29bob2o8b2obo8bo29b2o25bo
4b3obobo9bobo10b3o9b2o6bo3b2o29bob2o8b2obo8bo29b2o25bo4b3obobo9bobo10b
3o9b2o6bo3b2o$16b12o9b2o29bo15bo7b2o3bobo2b2obo7bob2o5b2o5bo2bob2o2b2o
bo8b4o2b2o28b12o9b2o29bo15bo7b2o3bobo2b2obo7bob2o5b2o5bo2bob2o2b2obo8b
4o2b2o28b12o9b2o29bo15bo7b2o3bobo2b2obo7bob2o5b2o5bo2bob2o2b2obo8b4o2b
2o$13bob2obob4obob2obo39bo14bo7bobo9b2o5bobo7bo8b2ob2o3bo2b8obo5bo25bo
b2obob4obob2obo39bo14bo7bobo9b2o5bobo7bo8b2ob2o3bo2b8obo5bo25bob2obob
4obob2obo39bo14bo7bobo9b2o5bobo7bo8b2ob2o3bo2b8obo5bo$14bobo10bobo3b2o
5b2o8b2o14b5o12b3o7bobob4o2bobo5bo2bo2b2o4b3o13bobo2b4o9bobo24bobo10bo
bo3b2o5b2o8b2o14b5o12b3o7bobob4o2bobo5bo2bo2b2o4b3o13bobo2b4o9bobo24bo
bo10bobo3b2o5b2o8b2o14b5o12b3o7bobob4o2bobo5bo2bo2b2o4b3o13bobo2b4o9bo
bo$33b2o4bobo9bo13bo28bo4b3ob3o5bo2bo10bo5b2ob4obobo16b2o43b2o4bobo9bo
13bo28bo4b3ob3o5bo2bo10bo5b2ob4obobo16b2o43b2o4bobo9bo13bo28bo4b3ob3o
5bo2bo10bo5b2ob4obobo16b2o$22b2o15b2o10bobo12b3o26b4o3bobo7bo2bo15b2ob
o2bob2o51b2o15b2o10bobo12b3o26b4o3bobo7bo2bo15b2obo2bob2o51b2o15b2o10b
obo12b3o26b4o3bobo7bo2bo15b2obo2bob2o$21b5o26b2o3bo11bo33bo8bo2bo75b5o
26b2o3bo11bo33bo8bo2bo75b5o26b2o3bo11bo33bo8bo2bo$20bobo2bo6b2o22bo2bo
6b4o27b2ob5o8b3o29bobo4bo37bobo2bo6b2o22bo2bo6b4o27b2ob5o8b3o29bobo4bo
37bobo2bo6b2o22bo2bo6b4o27b2ob5o8b3o29bobo4bo$20bo3b3o4b2ob2o20bo2bo6b
o3b2o26bobo3bo18bo21bo4b2o38bo3b3o4b2ob2o20bo2bo6bo3b2o26bobo3bo18bo
21bo4b2o38bo3b3o4b2ob2o20bo2bo6bo3b2o26bobo3bo18bo21bo4b2o$21b3o2bo5bo
2bo21bobo7b3o2bo13bobo9bo3b2o18b3o20b3ob3o39b3o2bo5bo2bo21bobo7b3o2bo
13bobo9bo3b2o18b3o20b3ob3o39b3o2bo5bo2bo21bobo7b3o2bo13bobo9bo3b2o18b
3o20b3ob3o$23b4o5bo2bo33bob2o14b2o10b3o19b4o24b2o7b2o33b4o5bo2bo33bob
2o14b2o10b3o19b4o24b2o7b2o33b4o5bo2bo33bob2o14b2o10b3o19b4o24b2o7b2o$
16b2o8bo6b2o4b2o28bo17bo6bo6bo18b2o10b2o6bo7b2o9bo26b2o8bo6b2o4b2o28bo
17bo6bo6bo18b2o10b2o6bo7b2o9bo26b2o8bo6b2o4b2o28bo17bo6bo6bo18b2o10b2o
6bo7b2o9bo$14b2ob2o3b2o2b2o10bo2bo26b2o22bobo24b3o10b2o5bobo13bo28b2ob
2o3b2o2b2o10bo2bo26b2o22bobo24b3o10b2o5bobo13bo28b2ob2o3b2o2b2o10bo2bo
26b2o22bobo24b3o10b2o5bobo13bo$14b2o8b4o12b2o51b2o25b2o24bo3bo4bo2bo
25b2o8b4o12b2o51b2o25b2o24bo3bo4bo2bo25b2o8b4o12b2o51b2o25b2o24bo3bo4b
o2bo$11b4o8b2o14b2ob2o77b4o11b2o2b2o5b4o30b4o8b2o14b2ob2o77b4o11b2o2b
2o5b4o30b4o8b2o14b2ob2o77b4o11b2o2b2o5b4o$11b2o2b2o3b2ob2o14b2o3bo15b
2o60b3o11b4o5b2o2b2o30b2o2b2o3b2ob2o14b2o3bo15b2o60b3o11b4o5b2o2b2o30b
2o2b2o3b2ob2o14b2o3bo15b2o60b3o11b4o5b2o2b2o$12bo8b2o6b2o7b3o3bo15bo4b
2o30bobo23bo12bo3bo41bo8b2o6b2o7b3o3bo15bo4b2o30bobo23bo12bo3bo41bo8b
2o6b2o7b3o3bo15bo4b2o30bobo23bo12bo3bo$3b2o7b4o13b2o8b2o3bo16b3o2bo31b
2o30bo14bobo25b2o7b4o13b2o8b2o3bo16b3o2bo31b2o30bo14bobo25b2o7b4o13b2o
8b2o3bo16b3o2bo31b2o30bo14bobo$3b2o7bo2b3o21b2ob2o20b2o32bo30bo7b2o7bo
26b2o7bo2b3o21b2ob2o20b2o32bo30bo7b2o7bo26b2o7bo2b3o21b2ob2o20b2o32bo
30bo7b2o7bo$12b3o3bo21b2o6bo10b3o2bo63b2o6b2o44b3o3bo21b2o6bo10b3o2bo
63b2o6b2o44b3o3bo21b2o6bo10b3o2bo63b2o6b2o$13bo2bobo19bo2bo5b3o8bo3bob
o37b2o25b2o4b3ob3o41bo2bobo19bo2bo5b3o8bo3bobo37b2o25b2o4b3ob3o41bo2bo
bo19bo2bo5b3o8bo3bobo37b2o25b2o4b3ob3o$13b5o21b2o5bo2b2o7b5ob2o39bo24b
o4b2o4bo41b5o21b2o5bo2b2o7b5ob2o39bo24bo4b2o4bo41b5o21b2o5bo2b2o7b5ob
2o39bo24bo4b2o4bo$15b2o42bo42bobo29bo4bobo43b2o42bo42bobo29bo4bobo43b
2o42bo42bobo29bo4bobo$22b2obo2bob2o26bobo3b4o35bo18b2o68b2obo2bob2o26b
obo3b4o35bo18b2o68b2obo2bob2o26bobo3b4o35bo18b2o$21bobob4ob2o5bo19b3ob
3o4bo52bobo4b2o61bobob4ob2o5bo19b3ob3o4bo52bobo4b2o61bobob4ob2o5bo19b
3ob3o4bo52bobo4b2o$15b4o2bobo13b3o11bo5bobo2b4obobo25b3o23b2o5b2o3bobo
10bobo36b4o2bobo13b3o11bo5bobo2b4obobo25b3o9bo13b2o5b2o3bobo10bobo36b
4o2bobo13b3o11bo5bobo2b4obobo25b3o9bo13b2o5b2o3bobo10bobo$11bob8o2bo3b
2ob2o8bo8b2o5b2o9bobo25b6o31bob2obob4obob2obo31bob8o2bo3b2ob2o8bo8b2o
5b2o9bobo25b6o7b2o22bob2obob4obob2obo31bob8o2bo3b2ob2o8bo8b2o5b2o9bobo
25b6o7b2o22bob2obob4obob2obo$9b4o8bob2o2b2obo2bo5b2o2b3o2b3o6bob2o2bob
o3b2o27b2obo22b2o9b12o32b4o8bob2o2b2obo2bo5b2o2b3o2b3o6bob2o2bobo3b2o
27b2obo5b2o15b2o9b12o32b4o8bob2o2b2obo2bo5b2o2b3o2b3o6bob2o2bobo3b2o
27b2obo5b2o15b2o9b12o$5b2ob2o3bo6b2o9b3o9b2o2b3o6bobob3o4bo32bobo21bo
8bob2o8b2obo26b2ob2o3bo6b2o9b3o9b2o2b3o6bobob3o4bo32bobo21bo8bob2o8b2o
bo26b2ob2o3bo6b2o9b3o9b2o2b3o6bobob3o4bo32bobo21bo8bob2o8b2obo$4bob2ob
2obo2b4o3b3o19bo2bo8bo4bo4bo35bo22b3o3b3o14b3o23bob2ob2obo2b4o3b3o19bo
2bo8bo4bo4bo35bo22b3o3b3o14b3o23bob2ob2obo2b4o3b3o19bo2bo8bo4bo4bo35bo
22b3o3b3o14b3o$4bobobo3b2o6b2o3bo3b5o7bo2bo4bobo3b2o2bobo2bobobo33b2o
23bo3b2o2bo3b4o3bo2b2o2bo20bobobo3b2o6b2o3bo3b5o7bo2bo4bobo3b2o2bobo2b
obobo33b2o23bo3b2o2bo3b4o3bo2b2o2bo20bobobo3b2o6b2o3bo3b5o7bo2bo4bobo
3b2o2bobo2bobobo33b2o9bo13bo3b2o2bo3b4o3bo2b2o2bo$2b2o2bo2bo3b4ob2o2bo
b2o2bo5bo5bo2bobo3bo5b2o2bob4o2bobo60b3o6b4o4b3ob3o18b2o2bo2bo3b4ob2o
2bob2o2bo5bo5bo2bobo3bo5b2o2bob4o2bobo60b3o6b4o4b3ob3o18b2o2bo2bo3b4ob
2o2bob2o2bo5bo5bo2bobo3bo5b2o2bob4o2bobo41bobo16b3o6b4o4b3ob3o$3bob2o
2b2o2bo2bobo2bo3bobob2ob2o7bobo5b3o3b2o2bo5bobobo60bo4bobo6bob2o3bo21b
ob2o2b2o2bo2bobo2bo3bobob2ob2o7bobo5b3o3b2o2bo5bobobo60bo4bobo6bob2o3b
o21bob2o2b2o2bo2bobo2bo3bobob2ob2o7bobo5b3o3b2o2bo5bobobo42b2o16bo4bob
o6bob2o3bo$3bo5b2obo3bobo3b3o2bobobo23b2o2bob2o2bo2bo59b3o4bobo2b2o2bo
b2obo4bo18bo5b2obo3bobo3b3o2bobobo23b2o2bob2o2bo2bo59b3o4bobo2b2o2bob
2obo4bo18bo5b2obo3bobo3b3o2bobobo23b2o2bob2o2bo2bo59b3o4bobo2b2o2bob2o
bo4bo$4b3obobo4b2ob2o4bobo4bo24bo4bobobo62bo2b2obo2bobo2bobo5bo3bo19b
3obobo4b2ob2o4bobo4bo24bo4bobobo62bo2b2obo2bobo2bobo5bo3bo19b3obobo4b
2ob2o4bobo4bo24bo4bobobo62bo2b2obo2bobo2bobo5bo3bo$6bobobobo5bo6b2obo
2b2o23bobobo2b2o64b3obobobobo2bobo2bo3bobo22bobobobo5bo6b2obo2b2o23bob
obo2b2o64b3obobobobo2bobo2bo3bobo22bobobobo5bo6b2obo2b2o23bobobo2b2o
64b3obobobobo2bobo2bo3bobo$8bo5b3o3bo7bo2b2o3b3o5bobo7b2ob2obobo70bobo
b8ob4o3bo24bo5b3o3bo7bo2b2o3b3o5bobo7b2ob2obobo70bobob8ob4o3bo24bo5b3o
3bo7bo2b2o3b3o5bobo7b2ob2obobo70bobob8ob4o3bo$8bob2obo3b3obob4obo2b2o
5bo3bobo2bo5bo5bo2bo64b3obo13bo2b2o3b2o23bob2obo3b3obob4obo2b2o5bo3bob
o2bo5bo5bo2bo64b3obo13bo2b2o3b2o23bob2obo3b3obob4obo2b2o5bo3bobo2bo5bo
5bo2bo64b3obo13bo2b2o3b2o$9bo5b2o2bobobo2bobo2b2o3bobo4bo2bo7b5o3b2o
62bo2bobo2bo2b2ob4obob3o4bo24bo5b2o2bobobo2bobo2b2o3bobo4bo2bo7b5o3b2o
62bo2bobo2bo2b2ob4obob3o4bo24bo5b2o2bobobo2bobo2b2o3bobo4bo2bo7b5o3b2o
62bo2bobo2bo2b2ob4obob3o4bo$10b3o3bo4bo4bo4bo8bo2bo12bo70b2o2bobo3bobo
3bobobo4bo27b3o3bo4bo4bo4bo8bo2bo12bo70b2o2bobo3bobo3bobobo4bo27b3o3bo
4bo4bo4bo8bo2bo12bo70b2o2bobo3bobo3bobobo4bo$12bo2bo4bo4b3obobo6b3o2b
2o86bo2bo4bobo4b2o4b2o28bo2bo4bo4b3obobo6b3o2b2o86bo2bo4bobo4b2o4b2o
28bo2bo4bo4b3obobo6b3o2b2o86bo2bo4bobo4b2o4b2o$16b3o3bobo2b2obo6b3o2b
3o87b2o4b2ob2o43b3o3bobo2b2obo6b3o2b3o87b2o4b2ob2o43b3o3bobo2b2obo6b3o
2b3o87b2o4b2ob2o$18bobo9b2o5b2o149bobo9b2o5b2o149bobo9b2o5b2o$18bobob
4o2bobo5bo151bobob4o2bobo5bo151bobob4o2bobo5bo$19bo4b3ob3o158bo4b3ob3o
158bo4b3ob3o$20b4o3bobo160b4o3bobo160b4o3bobo$28bo12b2o155bo12b2o155bo
12b2o$22b2ob4obo161b2ob4obo161b2ob4obo$21bobobo2bob3o158bobobo2bob3o
158bobobo2bob3o$22bo3bobo4bo5bo2bo149bo3bobo4bo5bo2bo149bo3bobo4bo5bo
2bo$27b2o3b2o5b2o156b2o3b2o5b2o156b2o3b2o5b2o!

Given a p57 pseudo-period p19 gun, is treating the gun as a p57 triplet glider stream gun and treating the gun as the following equivalent?

Code: Select all

pattern0[19] = pattern1[0] + glider[19]
pattern0[20] = pattern1[1] + glider[20]
...
pattern0[37] = pattern1[18] + glider[37]
...


pattern1[19] = pattern2[0] + glider[19]
pattern1[20] = pattern2[1] + glider[20]
...
pattern1[37] = pattern2[18] + glider[37]
...


pattern2[19] = pattern0[0] + glider[19]
pattern2[20] = pattern0[1] + glider[20]
...
pattern2[37] = pattern0[18] + glider[37]
...

[confocaloid]

Life, except if B7 is triggered a neutrino is created instead, which passes through everything and is traveling in the direction of the empty cell in the B7. If a neutrino encounters a cell which would trigger B5, B6, B7, or B8, it does so (turns the cell on) and destroys itself. Neutrinos can pass through one another, and they travel at the speed of light. I would also like a ruletable where neutrinos do not cause any interactions and just notate B7.

Testing possible interactions between neutrinos (fortunately or unfortunately, these don't pass through each other, and don't always vanish when colliding either).

[EDIT: looks like this wouldn't work as intended ("pre-heads" will cause unwanted interactions with already existing neutrinos) so one would need a third universe for "pre-heads" and "pre-tails".]
Some CA like this could be running in one of two "weakly interacting universes" (with B3/S23 in the other universe). The interactions could be as follows:

• the condition B7|A7 ("a dead cell with precisely seven alive neighbours") in the two-state universe would create a "tail" (2) in the four-state universe,
• every dead cell with at least one alive neighbour in the two-state universe would create a "pre-head" (3) in the four-state universe,
• (optional) presence or absence of "head" (1) in the four-state universe could sometimes affect the cell in the two-state universe,
• (optional) "head" (1) in the four-state universe can be turned into "zero" (0) for some cell conditions in the two-state universe.

Code: Select all

x = 131, y = 24, rule = TestingNeutrinos
3.C9.C$4.B8.B13$51.B38.B38.B$51.AB37.AB36.BAB$51.B38.B$2.B3.B15.B21.B
39.B39.B$.2B3.2B13.2B20.BA38.BA38.BA$2BA3.A2B11.2BA21.B39.B39.B2$27.A
2B$27.2B$27.B!

@RULE TestingNeutrinos

0 = zero, 1 = head, 2 = tail, 3 = pre-head

@COLORS
0 48 48 48
1 240 48 48
2 240 240 48
3 48 240 48

@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect

var p={0,1,2,3}
var q=p
var r=p
var s=p
var t=p
var u=p
var v=p
var w=p

0, 0,1,0,1,0,0,0,0, 1
0, 0,1,1,2,0,0,0,0, 1
0, 3,0,2,0,0,0,0,0, 2
0, 3,2,0,0,0,0,0,0, 2
0, 0,2,1,2,0,0,0,0, 1
0, 2,1,0,0,0,0,0,0, 2
0, 0,1,0,0,0,0,0,0, 1
0, 0,1,2,2,0,0,0,0, 2
0, 1,q,r,s,t,u,v,w, 2
1, p,q,r,s,t,u,v,w, 2
2, 3,q,r,s,t,u,v,w, 2
2, p,3,r,s,t,u,v,w, 2
2, p,q,r,s,t,u,v,w, 0
3, 2,q,r,s,t,u,v,w, 1
3, p,2,r,s,t,u,v,w, 1
3, p,q,r,s,t,u,v,w, 0

[confocaloid]

I don't see any signals in the posted pattern.

Terminology is supposed to be helpful. Terminology is needed to be able to communicate interesting ideas. In this case the jargon is confusing and fails to communicate any interesting idea. The same for many other instances of unnecessary jargon.

p56 R-swooper - the number of signal converters is frightening:

Code: Select all

x = 40, y = 42, rule = B3/S23
16b3o$15bo$14b2o3bo$12b3obo8b2o$2o9b2obobobo4bo2bo$bo8bobo2bo9bo$bobo
8b2o5bo5bo2b2o$2b2o2bo5bo5b2o8bobo$6bo9bo2bobo8bo$5bo2bo4bobobob2o9b2o
$5b2o8bob3o$12bo3b2o8bo3b2o5b2o$16bo7b3o3b2o5b2o$13b3o7bo$23b2o$19bo$
18bo2bo11bobo$18bo2bo$19b4o7b3o3b3o$29bo9bo$19b6o4b3o5b3o$19bo3bo6bo7b
o$19bo$20bobo$19bo2bo7b2o5b2o$20b2o8b2o5b2o$7bo13b2o$7b3o10b3o$10bo8b
2ob2o$9b2o8b2ob2o$19b2ob2o$21bo$24bo$13bo9bobo$12bobo7bo2bo$12b2o9b2o
3$6b2o$7bo15b2o$4b3o16b2o$4bo!

[Period1GliderGun]

I did not mean to resurrect the long-dead (and arguably pointless) signal debate. I just meant to highlight the pre-phi -> angel -> 42P38 spark reaction.

[confocaloid]

I did not mean to resurrect the long-dead (and arguably pointless) signal debate. I just meant to highlight the pre-phi -> angel -> 42P38 spark reaction.

Neither of three intermediate described objects is a signal.
Furthermore, to my knowledge, there is currently no sufficient known technology to use either of those three described objects as an intermediate in conduit tracks for actually carrying some signals.

This is why I wrote it's confusing. It is unclear why the word 'signal' seemed relevant at all to insert it into the supplied description.

[Period1GliderGun]

To reiterate and hopefully close, I do not mean to use the term "signal" in a way that could be confusing. Perhaps a better term would be "output converter."

[confocaloid]

To reiterate and hopefully close, I do not mean to use the term "signal" in a way that could be confusing. Perhaps a better term would be "output converter."

I think that one way to actually explain/illustrate/demonstrate "how the oscillator works" would be to show several consecutive modifications, where some of optional/variable components are removed/replaced:

Code: Select all

x = 140, y = 42, rule = B3/S23
16b3o47b3o47b3o$15bo49bo49bo$14b2o3bo44b2o3bo44b2o3bo$12b3obo8b2o35b3o
bo8b2o35b3obo8b2o$2o9b2obobobo4bo2bo23b2o9b2obobobo4bo2bo23b2o9b2obobo
bo4bo2bo$bo8bobo2bo9bo25bo8bobo2bo9bo25bo8bobo2bo9bo$bobo8b2o5bo5bo2b
2o21bobo8b2o5bo5bo2b2o21bobo8b2o5bo5bo2b2o$2b2o2bo5bo5b2o8bobo21b2o2bo
5bo5b2o8bobo21b2o2bo5bo5b2o8bobo$6bo9bo2bobo8bo25bo9bo2bobo8bo25bo9bo
2bobo8bo$5bo2bo4bobobob2o9b2o23bo2bo4bobobob2o9b2o23bo2bo4bobobob2o9b
2o$5b2o8bob3o35b2o8bob3o35b2o8bob3o$12bo3b2o8bo3b2o5b2o23bo3b2o8bo3b2o
5b2o23bo3b2o8bo3b2o5b2o$16bo7b3o3b2o5b2o27bo7b3o3b2o5b2o27bo7b3o3b2o5b
2o$13b3o7bo39b3o7bo39b3o7bo$23b2o48b2o48b2o$19bo49bo49bo$18bo2bo11bobo
32bo2bo11bobo32bo2bo11bobo$18bo2bo46bo2bo46bo2bo$19b4o7b3o3b3o30b4o7b
3o3b3o30b4o7b3o3b3o$29bo9bo39bo9bo39bo9bo$19b6o4b3o5b3o29b6o4b3o5b3o
29b6o4b3o5b3o$19bo3bo6bo7bo30bo3bo6bo7bo30bo3bo6bo7bo$19bo49bo49bo$20b
obo47bobo47bobo$19bo2bo7b2o5b2o30bo2bo7b2o5b2o30bo2bo7b2o5b2o$20b2o8b
2o5b2o31b2o8b2o5b2o31b2o8b2o5b2o$21b2o48b2o34bo13b2o$20b3o47b3o34b3o
10b3o$19b2ob2o45b2ob2o36bo8b2ob2o$19b2ob2o45b2ob2o35b2o8b2ob2o$19b2ob
2o45b2ob2o45b2ob2o$21bo49bo49bo$74bo49bo$73bobo37bo9bobo$63b2o7bo2bo
36bobo7bo2bo$64bo8b2o37b2o9b2o$61b3o$61bo$106b2o$73b2o32bo15b2o$73b2o
29b3o16b2o$104bo!

The word 'component' is very general, which is appropriate in cases like this I believe. It's not really about any kind of communication or circuitry or logic or conversions or whatever. It's just the general idea/approach of combining known (or not-so-well-known) components in various ways. There are several interacting parts, and it makes sense to consider each of those parts separately / try to combine them in different ways.

[hotcrystal0]

wwei said this on the Discord:

Also some more details about the original stories thread that I would like to post more publicly.
This is basically what I did during the vast majority of the time I spent there:

1. Take a random soup
2. Run it for any amount of time
3. Find a patch of chaos
4. "Cut" a rectangle out of this patch of chaos
5. Apply "glue" to turn this rectangle into a still life; the more "chaos cells" in your rectangle, the better

There are also rules on glue: you can't have free-floating glue, meaning that from any glue cell, a king (no pun intended) has to be able to make it to a chaos cell without ever entering a dead cell; you can bring in still lives "from outside" BUT in the stories thread, your still life supply is limited, since you also have to harvest those from the soups

Often, I would spend half an hour or more deciding on which rectangle I wanted to cut from which generation of the soup, and sometimes I would even pull out literal JLS to help me with this process. I even posted my notes at least once (viewtopic.php?f=12&t=2915&p=204327&hilit=notes#p204327). So clearly this thread is CA-related, and clearly it requires an insane amount of effort from me. Since I thought that this thread might be challenged, I had this argument prepared in advance to counter the most common lock reasons ("low effort" or "not CA-related").
There's also the gender aspect of it. I have been questioning my gender for ages now and have been too nervous to follow the "standard" advice of "just experiment". This thread gave me a solution in the form of "I 'roleplay' as trans-me". My main character looked like this:

Code: Select all

x = 5, y = 5, rule = LifeSuper
3.2S$2.C.C$.M.M$.C$2S!

So losing the ability to post in this thread was a HUGE blow to me.

Really, the real problem was that a moderator saw Confocaloid's posts and realized mentions of other people were all over the place, so they knew there were probably "potentially rule-violating jokes" there.
I said this:

I think it's time to consider how to make a roleplay that captures this essence of the old "Stories told through structures in CGoL" but without any "potentially rule-violating jokes" about other people.
The making Mysterious Fragments was the best part of it. The worst part? That was definitely the fact that in the late roleplay era, there was an argument like... every three posts.
I'm glad [Sokwe] put a stop to that.
But guess what? By that point, the thread had already drifted far from its original scope. [Sokwe's] ideas for the reboot, which I laid out in the reboot [thread] when I made it, were meant to be like its original scope.
Just storytelling. Nothing too crazy.
A second reboot that captures the essence of that thread in the roleplay era but also prevents rule 1 violations would be needed.
There's a reason why I'm currently doing owner keep-away with the reboot. I tried to create something, and I failed.

[confocaloid]

wwei said this on the Discord:

[...][...]
Often, I would spend half an hour or more deciding on which rectangle I wanted to cut from which generation of the soup, and sometimes I would even pull out literal JLS to help me with this process. I even posted my notes at least once (viewtopic.php?f=12&t=2915&p=204327&hilit=notes#p204327). So clearly this thread is CA-related, and clearly it requires an insane amount of effort from me. Since I thought that this thread might be challenged, I had this argument prepared in advance to counter the most common lock reasons ("low effort" or "not CA-related").
[...][...]

Really, the real problem was that a moderator saw Confocaloid's posts and realized mentions of other people were all over the place, so they knew there were probably "potentially rule-violating jokes" there.
[...][...]

Since there was a mention of my username in the above, here are some questions from me (to those people who are potentially interested in potentially attempting to restart something similar to that thread).

• Were the "ground rules" of that forum thread ever written down before, in a way that would be sufficiently clear for those readers who don't yet know and understand the intended idea? (This question is more or less: are "outsiders" welcome? Are "outsiders" supposed to be able to understand what is going on in the thread?)
• From what was posted above, it seems clear that at least one user (is|was) willing to put in significant efforts into the thread. However, that doesn't mean others would be willing/likely to put in comparable efforts to keep the thread in a sufficiently good state. Does it seem a reasonable expectation to assume that most users active in the thread would put in comparable efforts to keep the thread in a good state? (If not, then it might be the problem of trying to swim against the tide.)

An out-of-context quote from an old discussion, re: "the only one who will contribute" etc.:

Agree.

Then please test out dvgrn's and my scripts. Try adding ships to the database on dvgrn's page, because if I am the only one who will contribute, then this will be pointless.

[hotcrystal0]

It crashes into sixteen pixels.

Next:

Code: Select all

x = 9, y = 4, rule = B3/S23
3o4b2o$2bo4b2o$2bo$bo!

Seriously? I warned you about the post cooldown rule and you didn't listen. Post reported.

[Aleph]

Next:

Code: Select all

x = 6, y = 5, rule = B3/S23
5bo$5bo$5bo2$6o!

I had a funny response to this one that I didn't post because I didn't have a good follow-up RLE. Surprisingly, this response is something that actually happened.

Having learned earlier today that Life exists, I scribble in Kongregate and find a "new" still life.

[WhiteHawk]

Off-topic in this thread. Request admin to move to appropriate thread.