ConwayLife.com

Posted: **March 9th, 2023, 6:27 pm**

hotdogPi wrote: March 8th, 2023, 1:03 pm
AlbertArmStain wrote: March 8th, 2023, 12:56 pm Can we make a log(t!) growth?
https://conwaylife.com/wiki/Tlog(t)_growth

They're equivalent.

What about a t! growth?

Posted: **March 9th, 2023, 6:57 pm**

AlbertArmStain wrote: March 9th, 2023, 6:27 pm
hotdogPi wrote: March 8th, 2023, 1:03 pm
AlbertArmStain wrote: March 8th, 2023, 12:56 pm Can we make a log(t!) growth?
https://conwaylife.com/wiki/Tlog(t)_growth

They're equivalent.
What about a t! growth?

Isn't that faster than quadratic though?
How about sqrt(t)! or log(t)! growth?

Posted: **March 9th, 2023, 8:26 pm**

hotdogPi wrote: March 8th, 2023, 1:03 pm https://conwaylife.com/wiki/Tlog(t)_growth
They're equivalent.

AlbertArmStain wrote: March 9th, 2023, 6:27 pmWhat about a t! growth?

pipsqueek wrote: March 9th, 2023, 6:57 pmIsn't that faster than quadratic though?
How about sqrt(t)! or log(t)! growth?

t! is O(sqrt(t)*(t/e)^t), which is exponential, so not be possible in a CA of any finite number of dimensions
sqrt(t)! is also exponential.
log(t)! is O(t*(log t)^1.5), so it is theoretically possible in a 2D CA like Life.

Posted: **March 13th, 2023, 12:17 pm**

What is the repeat time of the "functionally stable" p8 glider reflector?

Code: Select all

x = 156, y = 148, rule = B3/S23
154bo$153bo$153b3o38$115bo$113b2o$114b2o33$95b2o$95bo$81bobo9bobo$82b
2o9b2o$82bo3$92b2o$92b2o3b2o$96bo2bo2$95bo$82b2o11bo2bo$82bo5b2o3b2ob
2o$83b3o2b2o3b3o$85bo8bo$83b2o$83bo$84bo8b2o$83b2o8b2o9$46b2o$47b2o$
41bo4bo$41b2o$40bobo36$6b3o$8bo$b2o4bo$obo$2bo!
#C [[ ZOOM 6 THEME LifeHistory ]]

Posted: **March 14th, 2023, 8:16 am**

43, excluding output gliders.

Code: Select all

x = 30, y = 29, rule = B3/S23
2bo$obo$b2o7$25b2o$25bo$11bobo9bobo$12b2o9b2o$12bo3$22b2o$22b2o3b2o$26b
o2bo2$25bo$12b2o11bo2bo$12bo5b2o3b2ob2o$13b3o2b2o3b3o$15bo8bo$13b2o$13b
o$14bo8b2o$13b2o8b2o!
[[ PASTEMODE 3 PASTET 50 PASTE 3b$3b$3b! 18 12 ]]

Posted: **March 14th, 2023, 10:01 am**

squareroot12621 wrote: March 14th, 2023, 8:16 am 43, excluding output gliders.

The output gliders are kind of the point, though... and surprisingly, if they're included, the answer still isn't necessarily all that bad.

It looks like the repeat time will generally be limited by the repeat time of the glider inserter being used. With an NW31 you can go as low as 70 ticks, which seems pretty good:

Code: Select all

x = 44, y = 31, rule = B3/S23
15b2o$15b2o2$40b2o$40bo$38bobo$16bob2o6b2o10b2o$15b2o2bo5bo3bo$13bo5bo
4bo5bo$15b3o7bo4bo$2o9bo3b2o10bo2bo6b2o$2o9bobo13bobo7b2o3b2o$15bo12bo
13b2o$15bo$15bo3b2o21bo$27b2o12b2o$27bo5b2o4b2o2bo$28b3o2b2o4bobo$30bo
8bo$28b2o$10b3o15bo$11bo8b2o7bo8b2o$11b3o6bo7b2o8b2o$21b3o$23bo3$5b2o$
4bobo$4bo$3b2o!

Posted: **March 18th, 2023, 4:02 pm**

is there a weld that can allow the 2 p10 domino sparkers in this p190 partial to both work, and thus complete it?

Code: Select all

x = 36, y = 54, rule = B3/S23
30b2o$29bobo$27b3o$27b2ob4o$28bobo3bo$29bo2bo2bo$29b6o2$26b2o2b3o$26b
2ob2ob3o$16b2o9b2obo4bo$bo2bo11b2o9b2o2b5o$ob2obo16bo4b2obo$bo2bo16bo
bo3b3ob2ob2o$bo2bo18bo4bo3bobo$ob2obo17bo5b2obobo$bo2bo14bo3bo6bobob2o
$19bo3bo6bobo$23bo5b2obo$23bo4bo3bob2o$21bobo3b6ob2o$22bo4b5o$3bo8bo14b
3ob5o$2bobo7bo14b2ob4obo$2b2o7bo14b5ob3o$26b2ob4o2bo$29b6o$13b3o13b6o
$13b3o10b2ob4o2bo$2b2o8bobo11b5ob3o$2bobo7b2o13b2ob4obo$3bo23b3ob5o$27b
5o$22b3o2b6ob2o$24bo3bo3bob2o$23bobo3b2obo$23b2o5bobo$bo2bo18b2o5bobo
b2o$ob2obo17bobo3b2obobo$bo2bo19bo3bo3bobo$bo2bo17b3o2b3ob2ob2o$ob2ob
o21b2obo$bo2bo11b2o9b2o2b5o$16b2o9b2obo4bo$26b2ob2ob3o$26b2o2b3o2$29b
6o$29bo2bo2bo$28bobo3bo$27b2ob4o$27b3o$29bobo$30b2o!

Posted: **March 20th, 2023, 7:01 am**

Why can a Klein bottle only have a shift of one?

Posted: **March 20th, 2023, 7:44 am**

Should we add this to the wiki for chucklebait?

Posted: **March 20th, 2023, 3:28 pm**

A "what if" question: What could be the consequences, if at design stage Catagolue apgcodes were designed in such a way that period-2 oscillators would have multiple tabulations according to the minimum population, similarly to the still lifes?

For instance, prefixes "xd3_", "xd6_", "xd14_" could be used for p2 oscillators with minpop 3, 6, 14 respectively (instead of just one prefix/tabulation "xp2_").

(A motivation for the question is that p2 ash is common, and p2 intermediate targets are common in slow salvos. Higher-period oscillators are much less common in B3/S23, so for this question one may assume that higher prefixes "xp3_", "xp4_", ... remain as they are.)

Posted: **March 20th, 2023, 7:44 pm**

confocaloid wrote: March 20th, 2023, 3:28 pmA "what if" question: What could be the consequences, if at design stage Catagolue apgcodes were designed in such a way that period-2 oscillators would have multiple tabulations according to the minimum population, similarly to the still lifes?

For instance, prefixes "xd3_", "xd6_", "xd14_" could be used for p2 oscillators with minpop 3, 6, 14 respectively (instead of just one prefix/tabulation "xp2_").

(A motivation for the question is that p2 ash is common, and p2 intermediate targets are common in slow salvos. Higher-period oscillators are much less common in B3/S23, so for this question one may assume that higher prefixes "xp3_", "xp4_", ... remain as they are.)

Why not just do this in general? E.g. oscillators as xp2_3_..., spaceships as xq4_5_... etc. It would make it much easier to search through results for oscillators and spaceships of a particular size, within their given period and/or velocity.

Posted: **March 20th, 2023, 8:32 pm**

muzik wrote: March 20th, 2023, 7:01 am Why can a Klein bottle only have a shift of one?

Consider the following 4*4 pattern on a Klein bottle (Klein bottles don't work in LifeViewer, so run these patterns in Golly):

Code: Select all

x = 4, y = 4, rule = LifeHistory:K4*,4
4D$B.A$B3A$B2.A!

What this really is is a grid that looks like this:

Code: Select all

x = 32, y = 32, rule = LifeHistory
32D$B.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A$B3AB3AB3AB3AB3AB3AB3AB3A$B2.AB2.A
B2.AB2.AB2.AB2.AB2.AB2.A$32D$.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B$3AB3AB
3AB3AB3AB3AB3AB3AB$A2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.B$32D$B.A.B.A.B.A.B
.A.B.A.B.A.B.A.B.A$B3AB3AB3AB3AB3AB3AB3AB3A$B2.AB2.AB2.AB2.AB2.AB2.AB
2.AB2.A$32D$.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B$3AB3AB3AB3AB3AB3AB3AB3AB
$A2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.B$32D$B.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A
$B3AB3AB3AB3AB3AB3AB3AB3A$B2.AB2.AB2.AB2.AB2.AB2.AB2.AB2.A$32D$.A.B.A
.B.A.B.A.B.A.B.A.B.A.B.A.B$3AB3AB3AB3AB3AB3AB3AB3AB$A2.BA2.BA2.BA2.BA
2.BA2.BA2.BA2.B$32D$B.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A$B3AB3AB3AB3AB3AB
3AB3AB3A$B2.AB2.AB2.AB2.AB2.AB2.AB2.AB2.A$32D$.A.B.A.B.A.B.A.B.A.B.A.
B.A.B.A.B$3AB3AB3AB3AB3AB3AB3AB3AB$A2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.B!

If we shift the twisted row over by 1, we get the following grid:

Code: Select all

x = 33, y = 32, rule = LifeHistory
.32D$.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A$.B3AB3AB3AB3AB3AB3AB3AB3A$.B2.A
B2.AB2.AB2.AB2.AB2.AB2.AB2.A$32D$.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B$3AB
3AB3AB3AB3AB3AB3AB3AB$A2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.B$.32D$.B.A.B.A.
B.A.B.A.B.A.B.A.B.A.B.A$.B3AB3AB3AB3AB3AB3AB3AB3A$.B2.AB2.AB2.AB2.AB
2.AB2.AB2.AB2.A$32D$.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B$3AB3AB3AB3AB3AB
3AB3AB3AB$A2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.B$.32D$.B.A.B.A.B.A.B.A.B.A.
B.A.B.A.B.A$.B3AB3AB3AB3AB3AB3AB3AB3A$.B2.AB2.AB2.AB2.AB2.AB2.AB2.AB
2.A$32D$.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B$3AB3AB3AB3AB3AB3AB3AB3AB$A2.
BA2.BA2.BA2.BA2.BA2.BA2.BA2.B$.32D$.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A$.
B3AB3AB3AB3AB3AB3AB3AB3A$.B2.AB2.AB2.AB2.AB2.AB2.AB2.AB2.A$32D$.A.B.A
.B.A.B.A.B.A.B.A.B.A.B.A.B$3AB3AB3AB3AB3AB3AB3AB3AB$A2.BA2.BA2.BA2.BA
2.BA2.BA2.BA2.B!

Code: Select all

x = 4, y = 4, rule = LifeHistory:K4*+1,4
4D$B.A$B3A$B2.A!

In the unshifted grid, the blue lines and the middle of the R lined up with each other, but here, no column lines up with its counterpart. It is a different grid.

And if we shift it by 2, we get this grid:

Code: Select all

x = 34, y = 32, rule = LifeHistory
2.32D$2.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A$2.B3AB3AB3AB3AB3AB3AB3AB3A$2.
B2.AB2.AB2.AB2.AB2.AB2.AB2.AB2.A$32D$.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B
$3AB3AB3AB3AB3AB3AB3AB3AB$A2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.B$2.32D$2.B.
A.B.A.B.A.B.A.B.A.B.A.B.A.B.A$2.B3AB3AB3AB3AB3AB3AB3AB3A$2.B2.AB2.AB
2.AB2.AB2.AB2.AB2.AB2.A$32D$.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B$3AB3AB3A
B3AB3AB3AB3AB3AB$A2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.B$2.32D$2.B.A.B.A.B.A
.B.A.B.A.B.A.B.A.B.A$2.B3AB3AB3AB3AB3AB3AB3AB3A$2.B2.AB2.AB2.AB2.AB2.
AB2.AB2.AB2.A$32D$.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B$3AB3AB3AB3AB3AB3AB
3AB3AB$A2.BA2.BA2.BA2.BA2.BA2.BA2.BA2.B$2.32D$2.B.A.B.A.B.A.B.A.B.A.B
.A.B.A.B.A$2.B3AB3AB3AB3AB3AB3AB3AB3A$2.B2.AB2.AB2.AB2.AB2.AB2.AB2.AB
2.A$32D$.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B$3AB3AB3AB3AB3AB3AB3AB3AB$A2.
BA2.BA2.BA2.BA2.BA2.BA2.BA2.B!

Now, the "leg" and "nose" of the R line up with their counterparts. Now, if we mark a new column, we can see that it is effectively an unshifted Klein bottle:

Code: Select all

x = 34, y = 32, rule = LifeHistory
2.32D$3.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA$3.C2A.C2A.C2A.C2A.C2A.C2A.C2A.
C2A$3.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A$32D$.AB2.AB2.AB2.AB2.AB2.AB2.AB
2.AB$2AC.2AC.2AC.2AC.2AC.2AC.2AC.2AC$A.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B$
2.32D$3.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA$3.C2A.C2A.C2A.C2A.C2A.C2A.C2A.
C2A$3.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A$32D$.AB2.AB2.AB2.AB2.AB2.AB2.AB
2.AB$2AC.2AC.2AC.2AC.2AC.2AC.2AC.2AC$A.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B$
2.32D$3.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA$3.C2A.C2A.C2A.C2A.C2A.C2A.C2A.
C2A$3.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A$32D$.AB2.AB2.AB2.AB2.AB2.AB2.AB
2.AB$2AC.2AC.2AC.2AC.2AC.2AC.2AC.2AC$A.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B$
2.32D$3.BA2.BA2.BA2.BA2.BA2.BA2.BA2.BA$3.C2A.C2A.C2A.C2A.C2A.C2A.C2A.
C2A$3.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B.A$32D$.AB2.AB2.AB2.AB2.AB2.AB2.AB
2.AB$2AC.2AC.2AC.2AC.2AC.2AC.2AC.2AC$A.B.A.B.A.B.A.B.A.B.A.B.A.B.A.B!

Code: Select all

x = 4, y = 4, rule = LifeHistory:K4*,4
4D$BA$C2A$B.A!

This means that there are only two shifts mod 2: 0 and 1, and every other shift is just equivalent to one of these, but with the point of the twist differing. Without limiting the possible patterns, you can limit the shift to 0 or 1, so of course a programmer would do this to save effort.

As for why you can't have a shift on the untwisted edge, that's a little simpler. Adding a shift requires the two edges to be distinguished, so that there is a distinct "left" and "right" edge. If you cross the right edge you move down, and if you cross the left you move up.
But there is really only one untwisted edge (a bit like a Möbius strip). If you stood next to the right edge, put your hand on it and crossed the bottom edge, you would end up with that same hand on the left edge.
As a result, because there is only one edge, they both have to do the same thing when you cross them, and they both can't shift you in the same direction. You can't make it into a grid:

Code: Select all

x = 16, y = 17, rule = LifeHistory
4D$B.A.4D$B3AB.A.4D$B2.AB3AB.A.4D$4.B2.AB3AB.A$8.B2.AB3A$12.B2.A$5.B$
4.3B$5.B$12.4D$8.4D.A.B$4.4D.A.B3AB$4D.A.B3ABA2.B$.A.B3ABA2.B$3ABA2.B
$A2.B!

Code: Select all

x = 16, y = 19, rule = LifeHistory
4D$B.A.4D$B3AB.A.4D$B2.AB3AB.A.4D$4DB2.AB3AB.A$.A.B4DB2.AB3A$3AB.A.B
4DB2.A$A2.B3AB.A.B4D$4DA2.B3AB.A.B$B.A.4DA2.B3AB$B3AB.A.4DA2.B$B2.AB
3AB.A.4D$4DB2.AB3AB.A$.A.B4DB2.AB3A$3AB.A.B4DB2.A$A2.B3AB.A.B4D$4.A2.
B3AB.A.B$8.A2.B3AB$12.A2.B!

There is one other case to consider, which is when the length of the untwisted edge is even, and the shift is exactly half, so the edges can't be said to move you "up" or "down". This doesn't work either. If you start by heading straight to the right and keep going until you reach your original position, either you will have been reflected across a vertical axis, or you will have not.
The first case is a problem because you are now heading to the left, so you must have been turned around while staying on the same row, which is obviously very bad. The second case is a little subtler. Consider this diagram:

Code: Select all

x = 50, y = 10, rule = LifeHistory
10D10.10D10.9DE$B19.B19.B$B19.B19.B$B11.B7.B11.B7.B$BC11.B6.C12.B6.B$
BE8.5B5.E9.5B5.B$B12.B6.B12.B6.B$B11.B7.B11.B7.B$B19.B19.B$B19.B19.B
8.C!

As you can see, the yellow and white cells are separated from each other after they cross the left edge. If we try to resolve this by making some areas of the left edge go to other areas of the left edge, it only moves the discontinuity.

By the way, just as an aside, Klein bottles and asymmetric rules are a stupid combination. In these rules, patterns cross the edge and then behave differently, which defeats the whole purpose of a Klein bottle.
Of course, people may still want to keep them for the same reasons as B0 rule tables.

Posted: **March 21st, 2023, 1:30 pm**

mniemiec wrote: March 20th, 2023, 7:44 pm
confocaloid wrote: March 20th, 2023, 3:28 pmA "what if" question: What could be the consequences, if at design stage Catagolue apgcodes were designed in such a way that period-2 oscillators would have multiple tabulations according to the minimum population, similarly to the still lifes?
Why not just do this in general? E.g. oscillators as xp2_3_..., spaceships as xq4_5_... etc. It would make it much easier to search through results for oscillators and spaceships of a particular size, within their given period and/or velocity.

Yes, a general two-way split (by period and by minimum population) would probably be more convenient from the user's viewpoint. Although apgcodes would become slightly longer. While "xp15_4r4z4r4" is shorter than "pentadecathlon", "xp15_12_4r4z4r4" would be longer than "pentadecathlon".

To make things easier to understand / preserve partial compatibility with other formats, maybe one could introduce a combination of the Pentadecathlon ID and the apgcodes. This would also reflect the displacement for spaceships (so that c/6o, 2c/6o and (2,1)c/6 would be three different tabulations).
For example, "12P15_4r4z4r4" could refer to the pentadecathlon (which is again shorter than "pentadecathlon").
Similarly, "34P3H1V0_mhqkzarahh0heezdhb5" would then refer to the dart, etc. -- the prefix is the Pentadecathlon ID (without the part after the dot) and the suffix is the apgcode suffix.

(In my "what if" question above, I asked about the p2 case specifically, because it seems like there are very many p2 oscillators and p2 constellations that are catalogued in Catagolue/Shinjuku/somewhere else using their apgcodes, which dumps them all in the same tabulation. While the general two-way split seems to require substantial changes to the apgcode format, one can imagine a limited solution for the p1/p2 special case, that mostly keeps things as they are, and just introduces one other prefix (e.g. "xd", by interpreting "d" as "double" and re-interpreting "s" in "xs" as "single"). I do not know what could be consequences.)

Posted: **March 21st, 2023, 3:57 pm**

mniemiec wrote: March 20th, 2023, 7:44 pmWhy not just do this in general? E.g. oscillators as xp2_3_..., spaceships as xq4_5_... etc. It would make it much easier to search through results for oscillators and spaceships of a particular size, within their given period and/or velocity.

confocaloid wrote: March 21st, 2023, 1:30 pm Yes, a general two-way split (by period and by minimum population) would probably be more convenient from the user's viewpoint. Although apgcodes would become slightly longer. While "xp15_4r4z4r4" is shorter than "pentadecathlon", "xp15_12_4r4z4r4" would be longer than "pentadecathlon".

Catagolue doesn't seem to be too concerned about minimum size. Soups are stored as a character matrix, rather than being encoded as an RLE, even though converting to/from RLE is extremely easy. This adds a much larger increase in space for each soup than a 2-3-character increase to each oscillator and spaceship, even though those are usually vastly outnumbered by still-lifes (which won't change). Even worse, if a pattern occurs in 100 soups, the extra space consumed by the soup is replicated a hundred-fold.

Posted: **March 22nd, 2023, 7:11 am**

What is the fastest way to find a spaceship in any Cellular Automata? Do you need a script or just naturally find it in soups?

Posted: **March 22nd, 2023, 7:36 am**

Drelectron8 wrote: March 22nd, 2023, 7:11 am What is the fastest way to find a spaceship in any Cellular Automata? Do you need a script or just naturally find it in soups?

"Fastest" is difficult to give a definite answer for across such an impossibly wide range as "any Cellular Automaton".

There's an easy recommendation for "simplest option if it works": use apgsearch to run a soup-search haul of the rule that you're interested in. If an "xq" object shows up, then you've found a natural spaceship.

However, there are lots and lots of explosive CA rules that apgsearch can't census effectively, and other CA rules that basically never produce natural spaceships from soup, and still other CA rules that apgsearch simply doesn't support ... that nonetheless support an endless variety of spaceships.

To find spaceships outside of apgsearch's "home range", you're better off with a search program like LLS (Logic Life Search), gfind, etc. -- see this Search Software LifeWiki page for a description of options.

Posted: **March 22nd, 2023, 8:31 pm**

mniemiec wrote: March 21st, 2023, 3:57 pm Catagolue doesn't seem to be too concerned about minimum size. Soups are stored as a character matrix, rather than being encoded as an RLE, even though converting to/from RLE is extremely easy. This adds a much larger increase in space for each soup than a 2-3-character increase to each oscillator and spaceship, even though those are usually vastly outnumbered by still-lifes (which won't change). Even worse, if a pattern occurs in 100 soups, the extra space consumed by the soup is replicated a hundred-fold.

They're not stored as character matrices; they're stored as hash preimages. They're only converted to ASCII patterns in the frontend to make it convenient for copying into simulation software such as Golly. Also, the list of soups in which a pattern has occurred is gzip-compressed at rest to minimise unnecessary storage overhead.

Posted: **March 23rd, 2023, 1:36 pm**

Is it possible to build a caber tosser (or sawtooth) in discrete cellular automata such that
1) its expansion factor is not an integer, and
2) the generations at which the pattern emits an output (or reaches a fixed minimum population) can be serially calculated with a closed-form expression that
a. is non-recursive,
b. is not piecewise, and
c. involves no rounding operations (floor/ceiling/nearest)
?

If not, what conditon in 2) should be relaxed if the non-integer e.f. requirement in 1) is insisted?

Posted: **March 24th, 2023, 2:06 am**

GUYTU6J wrote: March 23rd, 2023, 1:36 pm Is it possible to build a caber tosser (or sawtooth) in discrete cellular automata such that
1) its expansion factor is not an integer, and
2) the generations at which the pattern emits an output (or reaches a fixed minimum population) can be serially calculated with a closed-form expression that
a. is non-recursive,
b. is not piecewise, and
c. involves no rounding operations (floor/ceiling/nearest)
?

If not, what conditon in 2) should be relaxed if the non-integer e.f. requirement in 1) is insisted?

Does logarithmic_width.mc count? It's a sawtooth in the Wiki definition (which includes replicators), and it is governed by the formula:

a(n) = v1*w1^n+v3*w2^n+v2*w3^n, where v1,2,3 are the roots of (-1+9*x-31*x^2+31*x^3): [v1=0.6114919920, v2=0.1942540040 - 0.1225496913*I, v3=conjugate(v2)] and w1,2,3 are the roots of (-1-x^2+x^3): [w1=1.4655712319, w2=-0.2327856159 - 0.7925519925*I, w3=conjugate(w2)]. - Gerry Martens, Jun 27 2015

(from oeis.org)
It then reaches a minimum population of 4,496 in generation 240*a(3n)-815, starting from n=2.

If you want an actual caber tossing pattern, I think it should be possible to construct one using the irrational glider stream. For example, we could have one copy bouncing off boats from a boat puffer (if you're a little fancier, you could make one with irrational-density push reactions instead), where the caber-tossed glider is reflected off of these sideways gliders. Those that don't instead crash into another copy of the glider stream which is eating up another line of blocks or something.

: Caber tosser.png (34.44 KiB) Viewed 2416 times

The blue gliders are delayed from the green gliders so that they perfectly match up with the red gliders.

Posted: **March 24th, 2023, 1:46 pm**

is it possible to hack ntzfind to search in OT, INT, and maybe even B0 rules?

Posted: **March 25th, 2023, 12:14 pm**

get_snackeTWO wrote: March 24th, 2023, 1:46 pm is it possible to hack ntzfind to search in OT, INT, and maybe even B0 rules?

ntzfind supports all life-like rules (and hence outer totalistic) as far as I know. and the name, ntzfind is short for non-totalistic zfind (so of course it supports INT rules) but I don't think it works with B0 rules. but could probably be adjusted to do so

Posted: **March 25th, 2023, 4:21 pm**

pipsqueek wrote: March 25th, 2023, 12:14 pm ntzfind supports all life-like rules (and hence outer totalistic) as far as I know. and the name, ntzfind is short for non-totalistic zfind (so of course it supports INT rules) but I don't think it works with B0 rules. but could probably be adjusted to do so

oh. when i looked at the final ntzfind script i saw the rule set as "B3/S23" so i thought it was only for Life.

Posted: **March 28th, 2023, 8:35 pm**

what is the largest known naturally occurring non-extensible spaceship in any INT rule?

Posted: **March 28th, 2023, 9:35 pm**

pipsqueek wrote: March 28th, 2023, 8:35 pm what is the largest known naturally occurring non-extensible spaceship in any INT rule?

Does "largest" mean largest by bounding box or by population? Does "naturally occurring" mean it's on Catagolue? Would spaceships from symmetric soups count?

I was thinking maybe some random ship from ZombieLife might qualify, but then it seemed more likely that something out of the whitespace rulespace would probably come out ahead:

Code: Select all

x = 23, y = 23, rule = B34ejkw5ci6ci7c/S2cn3-jk4aer5i6-ak78
3o$3o$3o19$21b2o$21b2o!

There are much bigger whitespace spaceships, and I suspect that a lot of them appeared naturally from small asymmetric soups, but it's hard to know for sure because a lot of the whitespace rules aren't particularly Catagolue-searchable.

Anyone have a definite candidate for largest known natural INT spaceship?

Posted: **April 1st, 2023, 6:56 pm**

Code: Select all

x = 117, y = 50, rule = B3/S23
29bob2o27bo48bob2o$29b2obo76b2obo$60bo$27b5o75b5o$27bo4bo2b2o23bo46bo
4bo2b2o$30bo2bo2bo73bo2bo2bo$30b2obobo24bo49b2obobo$27bo5bob2o70bo5bob
2o$26bobo4bo26bo45bobo4bo$26bo2bo2b2o72bo2bo2b2o$27b2o31bo46b2o2$60bo
2$60bo2$60bo2$60bo$19b2o78b2o$19b2o39bo38b2o2$60bo2$60bo2$60bo2$5b2o
22b2o29bo24b2o22b2o$4bo2bo21bo54bo2bo21bo$5b2o23b3o27bo24b2o23b3o$32bo
79bo$60bo2$60bo2$60bo$22b2o78b2o$22bo37bo41bo$23b3o77b3o$b2o22bo34bo
44bo$obo$2bo57bo2$60bo2$60bo$83bobo$60bo22b2o$84bo!

The pattern above displays two different generations (T = 0 on the left, T = 200 on the right) of a single well-known pattern.
(The pattern is the rectifier, a 180-degree reflector with the output glider on a transparent lane.)
The pattern below is an unmodified copy of the generation T = 200.

Questions:

(Q1) Is it possible to rewind the pattern shown below for 20 ticks?
(Q2) Is it possible to rewind the pattern shown below for 200 ticks?
(Q3) Is the pattern shown below rewindable to infinity?

(For each question: If "yes", how? If "no", why?)

Code: Select all

x = 34, y = 50, rule = B3/S23
26bob2o$26b2obo2$24b5o$24bo4bo2b2o$27bo2bo2bo$27b2obobo$24bo5bob2o$23b
obo4bo$23bo2bo2b2o$24b2o9$16b2o$16b2o8$2b2o22b2o$bo2bo21bo$2b2o23b3o$
29bo6$19b2o$19bo$20b3o$22bo7$obo$2o$bo!

ConwayLife.com

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