Forums for Conway's Game of Life
https://conwaylife.com/forums/
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.gameoflifemaniac wrote:1. Why is the Caterpilllar so long?
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.gameoflifemaniac wrote:2. Could you post the 0E0P meta-glider and maybe some other metapatterns?
Enclose the RLE in triple backticks, similar to on Discord, and add the marker "rle" after the opening triple backticks.Ian07 wrote:How do I embed RLEs in comments on Catagolue pages?
Also see this document for all the details, straight from the horse's mouth (Calcyman's, that is, not mine).dvgrn wrote: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.
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:wwei23 wrote: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?
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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$64bo!
To my knowledge:wwei23 wrote:What's the largest still life that has ever appeared in Catagolue in any rule in C1? What about if it didn't have to be C1?
The soup for that one seems to just generate a wickstrecher that doesn't die to create any sort of still life (apgsearch misidentified it, I guess), so I'd say it doesn't count...Apple Bottom wrote:Largest oversized in C1: ov_s68589, in b3-c4is1c2-ck34a.
Aye, that wouldn't count. FWIW, here's the top 10 ov_s* patterns in C1 in rules other than b3-c4is1c2-ck34a:danny wrote:The soup for that one seems to just generate a wickstrecher that doesn't die to create any sort of still life (apgsearch misidentified it, I guess), so I'd say it doesn't count...
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ov_s33345|b3-rs2-ckn3-cknqy4-acknqwy5-ejkq6c7-c|C1
ov_s26424|b3-rs2-ckn3-cknqy4-acknqwy5-ejkq6c7-c|C1
ov_s26164|b3-rs2-ckn3-cknqy4-acknqwy5-ejkq6c7-c|C1
ov_s25665|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s24533|b3-ej4e5es23-a4iy6c|C1
ov_s23946|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s23944|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s19733|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s17528|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s16821|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
Sure looks like it. A lot of smallish Gardens of Eden seem to be overpopulated to some degree -- it's harder to arrange a parent that causes a lot of births in precise locations, whereas a sufficiently sparse pattern always has parents.danny wrote:Is it possible for a garden of eden to exist where all cells die of underpopulation or overpopulation, disregarding births?
Is it possible for a garden of eden to die in the next generation?
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x = 21, y = 22, rule = B3/S23
4bo2bo2bo2bo2bo$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!Hm, I can't find an online reference either. Here's a copy of the text from the original email:Caenbe wrote:Can someone please link the proof of non-existence of p3 phoenixes? I can't find it anywhere.
On Mon Jan 17, 2000, Stephen Silver wrote: 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
where the ? cells are inside the original bounding box and the O cellsCode: Select all
?O. ?O. ?O.
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):
If x is of type Y then it has at least two Y neighbours and so at leastCode: Select all
..?? .Zx? .???
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:
where I have marked in the three X parents of the leftmost Y. But now theCode: Select all
..Y? .ZX? .YY? .XX? .???
leftmost X has no room for its own W parents.
So the counterexample does not exist.
Corollary B1. There is no p3 phoenix.
Thanks. This definitely seems like it should be on LifeWiki. Would it be appropriate to use your post as a citation?dvgrn wrote:On Mon Jan 17, 2000, Stephen Silver wrote: long-lost theorem
How sparse?danny wrote:Is it currently feasible to run a Sparse Life soup?
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).Apple Bottom wrote:Aye, that wouldn't count. FWIW, here's the top 10 ov_s* patterns in C1 in rules other than b3-c4is1c2-ck34a:danny wrote: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...
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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
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............................*.......*.......................................................*.......*.......................................................*.......*.......................................................*.......*.......................................................*.......*...........................Not automatically, no. The recipes on b3s23/SS are usually very dirty, whereas slmake needs clean edgy syntheses.Rhombic wrote:Is slmake updated with the recipes found on the Catagolue b3s23/SS census?
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).A for awesome wrote: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?