Thread for basic questions

[gameoflifemaniac]

1. Why is the Caterpilllar so long?
2. Could you post the 0E0P meta-glider and maybe some other metapatterns?

[dvgrn]

1. Why is the Caterpilllar so long?

It's basically because the 17c/45 helix has a lot of *WSSes in it, and each one has to be added to the upship stream in series, and each addition needs some forward glider rakes to collide with some backward glider rakes running on the blinker trails. That's what all the visible big triangles are.

We could probably make a "Caterpillar's little brother" a good bit shorter these days, by creating all the *WSSes with slow salvos. With the gliders all coming from one direction, no incompressible triangles would be needed, so the odds are good that the whole thing would pack together a lot more tightly.

2. Could you post the 0E0P meta-glider and maybe some other metapatterns?

People should be able to make whatever metapatterns they want, by cloning the slmake repository and following calcyman's instructions... and much good may it do them, given that it's so impressively tedious to run even a single cell through one metatick.

metaglider.mc.gz

(made by copying the relevant piece of a meta-Sir-Robin, not the proper way with the script)

(7.69 MiB) Downloaded 564 times

[Ian07]

How do I embed RLEs in comments on Catagolue pages?

[dvgrn]

How do I embed RLEs in comments on Catagolue pages?

Enclose the RLE in triple backticks, similar to on Discord, and add the marker "rle" after the opening triple backticks.

The closing triple backticks should be at the beginning of a new line. See this post for other types of supported markdown, and a link to some experiments I did with comment lines in the RLE.

[Apple Bottom]

Enclose the RLE in triple backticks, similar to on Discord, and add the marker "rle" after the opening triple backticks.

The closing triple backticks should be at the beginning of a new line. See this post for other types of supported markdown, and a link to some experiments I did with comment lines in the RLE.

Also see this document for all the details, straight from the horse's mouth (Calcyman's, that is, not mine).

[wwei23]

What's the largest still life that has ever appeared in Catagolue in any rule in C1? What about if it didn't have to be C1?

[dani]

What's the largest still life that has ever appeared in Catagolue in any rule in C1? What about if it didn't have to be C1?

For both questions, the highest I've seen is this 6178-cell still life in an awesome rule that I totally forgot about until today:

Code: Select all

x = 129, y = 95, rule = B2-a5/S135678
64bo$63b3o$62b5o$61b7o$60b9o$59b11o$58b13o$57b15o$56b17o$55b19o$54b10o
b10o$53b23o$52b25o$48b33o$48b16ob16o$47b35o$46b37o$45b39o$44b41o$43b
43o$42b45o$41b8ob29ob8o$40b49o$39b51o$38b53o$20bo16b55o16bo$19b91o$18b
93o$17b95o$16b97o$15b20ob19ob17ob19ob20o$14b47ob5ob47o$13b103o$12b105o
$11b20ob65ob20o$10b109o$6b117o$6b53ob9ob53o$6b34ob47ob34o$6b117o$6b
117o$6b34ob47ob34o$5b59ob59o$4b36ob47ob36o$3b17ob87ob17o$2b125o$b127o$
18ob45ob45ob18o$b127o$2b125o$3b17ob87ob17o$4b36ob47ob36o$5b59ob59o$6b
34ob47ob34o$6b117o$6b117o$6b34ob47ob34o$6b53ob9ob53o$6b117o$10b109o$
11b20ob65ob20o$12b105o$13b103o$14b47ob5ob47o$15b20ob19ob17ob19ob20o$
16b97o$17b95o$18b93o$19b91o$20bo16b55o16bo$38b53o$39b51o$40b49o$41b8ob
29ob8o$42b45o$43b43o$44b41o$45b39o$46b37o$47b35o$48b16ob16o$48b33o$52b
25o$53b23o$54b10ob10o$55b19o$56b17o$57b15o$58b13o$59b11o$60b9o$61b7o$
62b5o$63b3o$64bo!

[Apple Bottom]

What's the largest still life that has ever appeared in Catagolue in any rule in C1? What about if it didn't have to be C1?

To my knowledge:

• Largest non-oversized in C1: xs2221_y08...7fa, in g4b3678s235678.
• Largest oversized in C1: ov_s68589, in b3-c4is1c2-ck34a.
• Largest non-oversized in any symmetry: xs3446_ygg...311, in r4b41t80s41t81/iiiiC1.
• Largest oversized in any symmetry: ov_s192061, in r7b113t224s113t225/iiiiiC1.

[dani]

Largest oversized in C1: ov_s68589, in b3-c4is1c2-ck34a.

The soup for that one seems to just generate a wickstrecher that doesn't die to create any sort of still life (apgsearch misidentified it, I guess), so I'd say it doesn't count...

[Apple Bottom]

The soup for that one seems to just generate a wickstrecher that doesn't die to create any sort of still life (apgsearch misidentified it, I guess), so I'd say it doesn't count...

Aye, that wouldn't count. FWIW, here's the top 10 ov_s* patterns in C1 in rules other than b3-c4is1c2-ck34a:

Code: Select all

ov_s33345|b3-rs2-ckn3-cknqy4-acknqwy5-ejkq6c7-c|C1
ov_s26424|b3-rs2-ckn3-cknqy4-acknqwy5-ejkq6c7-c|C1
ov_s26164|b3-rs2-ckn3-cknqy4-acknqwy5-ejkq6c7-c|C1
ov_s25665|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s24533|b3-ej4e5es23-a4iy6c|C1
ov_s23946|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s23944|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s19733|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s17528|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s16821|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1

[wwei23]

What's the tallest Catagolue page on record?
What's with all the ov_p0s?
Why are there so many PATHOLOGICALS even though LifeViewer shows simple, low period oscillators for some of them?

[dani]

Is it possible for a garden of eden to exist where all cells die of underpopulation or overpopulation, disregarding births?

Is it possible for a garden of eden to die in the next generation?

[dvgrn]

Is it possible for a garden of eden to exist where all cells die of underpopulation or overpopulation, disregarding births?

Is it possible for a garden of eden to die in the next generation?

Sure looks like it. A lot of smallish Gardens of Eden seem to be overpopulated to some degree -- it's harder to arrange a parent that causes a lot of births in precise locations, whereas a sufficiently sparse pattern always has parents.

The following should be an instant-death Garden of Eden, for example:

Code: Select all

x = 21, y = 22, rule = B3/S23
4bo2bo2bo2bo2bo$bo2bo2bo2bo2bo2bo2bo$3b15o$2b17o$4o3bob4o2bob4o$2b4ob
3ob3ob4o$2b7ob3obob3o$5obob2obob8o$2b4ob2obobob2ob2o$7ob2obob8o$2b4ob
6ob5o$6ob6ob7o$2b5ob2obob6o$2b4ob2obobob2ob2o$5obob2obob8o$2b7ob3obob
3o$2b4ob3ob3ob4o$4o3bob4o2bob4o$2b17o$3b15o$bo2bo2bo2bo2bo2bo2bo$4bo2b
o2bo2bo2bo!

This is one of the higher-population examples in Nicolay Beluchenko's Garden of Eden collection, with the usual decorations around the edges to prevent births there.

It looks like it should be easy to generate other similar examples. In fact, Roger Banks' very first Garden_of_Eden_1 can be extended in the same way.

[Caenbe]

Can someone please link the proof of non-existence of p3 phoenixes? I can't find it anywhere.

[dvgrn]

Can someone please link the proof of non-existence of p3 phoenixes? I can't find it anywhere.

Hm, I can't find an online reference either. Here's a copy of the text from the original email:

Subject: phoenices

A phoenix is a pattern all cells of which die in every generation, but
which never dies as a whole. All phoenices, oscillators and spaceships
in this post are assumed to be finite.

It's easy to show that a spaceship cannot be a phoenix (see proof
below), so I'm mainly interested in phoenix oscillators. The existence
of p2 phoenix oscillators is well-known, but what about higher periods?
I can prove that there are no p3 examples (see proof below) but I can't
see any obvious reason why there shouldn't be a p4 phoenix, or a p5
phoenix, for example. I modified a copy of lifesrc to look only for
phoenices, but my small scale searches so far haven't revealed any
meaningful partial results for periods greater than 2, let alone a
complete oscillator.

Has anyone else looked at this problem?

Stephen

Here are the promised proofs:

Theorem A. No phoenix can ever extend more than one space outside its
original bounding box.

Proof. Suppose it is about to extend two spaces to the right of the
original bounding box for the first time. Then we have

Code: Select all

?O.
?O.
?O.

where the ? cells are inside the original bounding box and the O cells
are just outside it. The O cells must be newborn, so all the ? cells
must have been ON in the previous generation in order to give birth to
the central O cell. In the current generation the ? cells are therefore
OFF. So the central O cell has exactly two neighbours and will survive
into the next generation - a contradiction.

Corollary A1. Every phoenix evolves into a phoenix oscillator.

Corollary A2. No spaceship is a phoenix.

Note. The theorem holds in a number of other cellular automata.
The proof requires only that births not be possible with less than
3 neighbours and that survival occurs with a particular arrangement
of 2 neighbours.

Theorem B. If an oscillator is such that no cell is ON in more than one
phase then it is either a still life or a statorless p2.

Proof. Suppose there is a counterexample. Cells ON in some chosen phase
will be said to be of type Z. Those ON in the previous phase will be called
type Y, those on in the phase before that will be type X, and those of the
phase before that type W. Since the period is at least 3 these types are
all distinct, except that we may have W=Z.
In the following diagrams . marks a cell that is definitely not in the
rotor (and is therefore permanently off), while known rotor cells are marked
Z, Y, X or W according to their type. Cells which are unknown or not
discussed here are marked with a ?.
Consider the leftmost column of the rotor, and in particular the uppermost
rotor cell of this column. We can assume this cell is of type Z. Three of
its neighbours will be of type Y, namely its parents.
Consider the cell to the right of the Z cell (marked x here):

Code: Select all

..??
.Zx?
.???

If x is of type Y then it has at least two Y neighbours and so at least
four (to kill it off). It also has three X neighbours (its parents).
Together with its Z neighbour and its non-rotor neighbour this is a total
of nine neighbours. This contradiction shows that x is not of type Y, so
we have the following diagram:

Code: Select all

..Y?
.ZX?
.YY?
.XX?
.???

where I have marked in the three X parents of the leftmost Y. But now the
leftmost X has no room for its own W parents.
So the counterexample does not exist.

Corollary B1. There is no p3 phoenix.

[Caenbe]

long-lost theorem

Thanks. This definitely seems like it should be on LifeWiki. Would it be appropriate to use your post as a citation?

[dani]

Is it currently feasible to run a Sparse Life soup?

[wwei23]

Is it currently feasible to run a Sparse Life soup?

How sparse?

[77topaz]

The soup for that one seems to just generate a wickstrecher that doesn't die to create any sort of still life (apgsearch misidentified it, I guess), so I'd say it doesn't count...

Aye, that wouldn't count. FWIW, here's the top 10 ov_s* patterns in C1 in rules other than b3-c4is1c2-ck34a:

Code: Select all

ov_s33345|b3-rs2-ckn3-cknqy4-acknqwy5-ejkq6c7-c|C1
ov_s26424|b3-rs2-ckn3-cknqy4-acknqwy5-ejkq6c7-c|C1
ov_s26164|b3-rs2-ckn3-cknqy4-acknqwy5-ejkq6c7-c|C1
ov_s25665|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s24533|b3-ej4e5es23-a4iy6c|C1
ov_s23946|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s23944|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s19733|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s17528|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s16821|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1

Unfortunately, it looks like most of those are misidentified wickstretchers that grow forever. The B3-ej4e5e/S23-a4iy6c soup does actually produce a very large still life, though (from a wickstretcher that is stopped).

[cvojan]

For some reason, afind likes to spam still-lives. I mean, thousands of still lives. I am running a width 6 odd-bilateral search for period 5 oscillators, and this is the closest I got to an oscillator, which can be reduced in an obvious way:

Code: Select all

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..............................**.**............................................................................................................................***.............................................................***............................................................*****.............................
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Is there some sort of way to reduce the still-live count? That would be nice if I could.

[Rhombic]

Is slmake updated with the recipes found on the Catagolue b3s23/SS census?

[calcyman]

Is slmake updated with the recipes found on the Catagolue b3s23/SS census?

Not automatically, no. The recipes on b3s23/SS are usually very dirty, whereas slmake needs clean edgy syntheses.

[praosylen]

Is a rule which contains oscillators of every period except 1 considered omniperiodic? In essence, does the vacuum count as a p1 oscillator for the purposes of determining omniperiodicity?

A rule with these properties would have to be quite strange. I could imagine a B2a rule with a small photon or 2c/3, two p2 reflectors, one normal, one phase-shifting, for it, allowing loops of all sufficiently high periods, and (somehow?) other oscillators at all lower periods — including p3, which is quite a rare period in B2a rules lacking still lives. A three-state rule with these properties could be quite a bit easier (although very much still not easy) to find.

[Macbi]

Is a rule which contains oscillators of every period except 1 considered omniperiodic? In essence, does the vacuum count as a p1 oscillator for the purposes of determining omniperiodicity?

I think the vacuum counts as a p1 oscillator (unless of course the rule has B0 and not S8, in which case the vacuum is p2).

However, I would say that the vacuum is not a strict still life, for the same reason that 1 isn't prime.

[dani]

Can a universal GoE working in all outer totalistic rules exist?