gameoflifemaniac wrote:1. Why is the Caterpilllar so long?
gameoflifemaniac wrote:2. Could you post the 0E0P meta-glider and maybe some other metapatterns?
Ian07 wrote:How do I embed RLEs in comments on Catagolue pages?
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.
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?
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$64bo!
wwei23 wrote:What's the largest still life that has ever appeared in Catagolue in any rule in C1? What about if it didn't have to be C1?
Apple Bottom wrote:Largest oversized in C1: ov_s68589, in b3-c4is1c2-ck34a.
danny wrote:The soup for that one seems to just generate a wickstrecher that doesn't die to create any sort of still life (apgsearch misidentified it, I guess), so I'd say it doesn't count...
ov_s33345|b3-rs2-ckn3-cknqy4-acknqwy5-ejkq6c7-c|C1
ov_s26424|b3-rs2-ckn3-cknqy4-acknqwy5-ejkq6c7-c|C1
ov_s26164|b3-rs2-ckn3-cknqy4-acknqwy5-ejkq6c7-c|C1
ov_s25665|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s24533|b3-ej4e5es23-a4iy6c|C1
ov_s23946|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s23944|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s19733|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s17528|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
ov_s16821|b2cen3ackr4-jkryz5ckqy6-cn7e8s12i3qy4aciw5-jkr6ak|C1
danny wrote:Is it possible for a garden of eden to exist where all cells die of underpopulation or overpopulation, disregarding births?
Is it possible for a garden of eden to die in the next generation?
x = 21, y = 22, rule = B3/S23
4bo2bo2bo2bo2bo$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!
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 haveCode: 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.
dvgrn wrote:On Mon Jan 17, 2000, Stephen Silver wrote:long-lost theorem
danny wrote:Is it currently feasible to run a Sparse Life soup?
Apple Bottom wrote: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...
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 allov_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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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?
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