ConwayLife.com

Posted: **July 11th, 2026, 4:06 am**

B468S02357 wrote: July 11th, 2026, 3:33 am Speed?

x = 89, y = 86, rule = B2i3-jkq4qt5cny7c/S2-ci3-aeky4ciz5cjq6eik7|B2i3-jkq4qt5cny7c/S2-ci3-aeky4ciz5cjq6eik7e
36$18b2o$20bo$14bobo3bo$14bo3b3o2$14bob2o$14bo2bo$14b3o6$3b2ob3o$8bo$
3bo2bobo9b3o$6b2o9bo2bo$bo2bo12bo3bo$bo2bo12b2o$2b3o13bo$18bo$17bobo15b
o$17bobo14b3o$18bo2bo12bobo$33b2o2bo$33b5o$33b2o5$25b2o$24bobo$23b2o$
24b2o4$32b2o$30bo2bo$30b3o$31bo!

2c/76.
Simplified: c/38

Posted: **July 11th, 2026, 5:11 am**

NNlk05 wrote: June 29th, 2026, 12:51 am Was any B1e rule proven TC?

Bump.

Posted: **July 11th, 2026, 10:06 am**

B468S02357 wrote: July 11th, 2026, 3:33 am Speed?

Code: Select all

x = 89, y = 86, rule = B2i3-jkq4qt5cny7c/S2-ci3-aeky4ciz5cjq6eik7|B2i3-jkq4qt5cny7c/S2-ci3-aeky4ciz5cjq6eik7e
36$18b2o$20bo$14bobo3bo$14bo3b3o2$14bob2o$14bo2bo$14b3o6$3b2ob3o$8bo$
3bo2bobo9b3o$6b2o9bo2bo$bo2bo12bo3bo$bo2bo12b2o$2b3o13bo$18bo$17bobo15b
o$17bobo14b3o$18bo2bo12bobo$33b2o2bo$33b5o$33b2o5$25b2o$24bobo$23b2o$
24b2o4$32b2o$30bo2bo$30b3o$31bo!

2c/76o

Edit: Somehow I didn't see that 1and0nlycordershippr had already responded, sorry.

Edit 2: typo

Posted: **July 12th, 2026, 9:30 pm**

Can rules have (countably) infinite neighborhoods and how hard would a rule without a neighborhood range limit be to simulate?
For clarity I don’t mean smooth life and other limits of neighborhoods as cell size goes to zero.
The neighborhood would be the whole board or at least an infinite subset of the board.

Would such a rule even have a speed limit?

Posted: **July 12th, 2026, 10:48 pm**

Rhombicubocta wrote: July 12th, 2026, 9:30 pm Can rules have (countably) infinite neighborhoods and how hard would a rule without a neighborhood range limit be to simulate?

This acts as a emulation of SmoothLife because as the neighbourhoods get bigger the cell acts more and more like a point.

Posted: **July 12th, 2026, 11:56 pm**

Rhombicubocta wrote: July 12th, 2026, 9:30 pm Can rules have (countably) infinite neighborhoods and how hard would a rule without a neighborhood range limit be to simulate?
For clarity I don’t mean smooth life and other limits of neighborhoods as cell size goes to zero.
The neighborhood would be the whole board or at least an infinite subset of the board.

If I understand correctly, an example would be a 2D CA where the neighborhood is all cells within the same row, plus those one cell away.

Code: Select all

x = 54, y = 3, rule = LifeHistory
7.40D$D.D.D2.20DA19D2.D.D.D$7.40D!

I think most cellular automata concepts break down where an infinite neighborhood is involved (speed, period, the notion of finite patterns, etc...). However, you could simulate it by treating each row as a cell in a 1D CA with an infinite number of states. In that case, the 1D CA could still have a sensible speed / speed limit.

If the neighborhood is the whole grid, then position becomes meaningless, since all cells are in each other's neighborhood. A generation of the simulation would take an infinite list of cells, and return an infinite list of cells.

Posted: **July 13th, 2026, 10:11 am**

silversmith wrote: July 12th, 2026, 11:56 pm If I understand correctly, an example would be a 2D CA where the neighborhood is all cells within the same row, plus those one cell away.
Code: Select all
x = 54, y = 3, rule = LifeHistory
7.40D$D.D.D2.20DA19D2.D.D.D$7.40D!
I think most cellular automata concepts break down where an infinite neighborhood is involved (speed, period, the notion of finite patterns, etc...). However, you could simulate it by treating each row as a cell in a 1D CA with an infinite number of states. In that case, the 1D CA could still have a sensible speed / speed limit.

If the neighborhood is the whole grid, then position becomes meaningless, since all cells are in each other's neighborhood. A generation of the simulation would take an infinite list of cells, and return an infinite list of cells.

That would be an example. I was thinking of infinite subsets of the grid in general or even the whole grid. If you weighted an infinite neighborhood properly you could guarantee a finite weighted sum of the cells. For example if we weight each neighbor cell by 1/(n^3) where n is the Chebyshev metric from the central cell then even if the neighborhood is the whole grid and all cells are in the on state, the weighted sum still comes out to be approximately 13.15947... or exactly (4(pi)^2)/3 which is finite.

Code: Select all

x = 51, y = 18, rule = B/SSuper
5$32.H13.J$18.B13.H13.J$2.7J9.B13.H13.J$2.J5HJ9.B13.H13.J$2.JH3BHJ9.B
13.H13.J$2.JHBDBHJ9.B$2.JH3BHJ21.5H8.7J$2.J5HJ$2.7J22.3H9.3J.3J$31.H.
H11.J3.J$31.3H9.3J3.J$31.H.H9.J5.J$31.3H9.3J3.J!

There are (2n+1)^2-(2n-1)^2 cells a Chebyshev distance of n away from any cell and the sequence 8+2+8/9+1/2+ ... + [(2n+1)^2-(2n-1)^2]/n^3]. The infinite sum converges to the value give above. Then we just pick an interval of subset of 0 to(4(pi)^2)/3 and use that as your birth conditions and survival conditions. Obviously this would be a nightmare to code up and probably won't be done.

The point is there are ways of weighting to deal with infinite neighborhoods.

As for Silversmith's position becoming meaningless in infinite grids issue, I am not sure I understand that problem.
Conway's game of life takes place on an infinite grid and we can simulate finite patterns so I don't see the issue with infinite grids
and just because the neighborhood is infinite it does not mean we actually have cells an infinite distance apart.
I would appreciate some elaboration on that from silversmith.

Do rules really need speed limits as long as the next step is determined by the rule?

Are there any other issues I have over looked?

I probably should have put this in the advanced questions thread in hindsight.

Posted: **July 14th, 2026, 7:59 am**

Hope it’s not W4124 r=3/2 again…

yyh_baboon wrote: July 14th, 2026, 4:24 am New kind of replicator?
Which rule does it emulate?
Code: Select all
 x = 3, y = 3, rule = B2n3-jkny4i5ekr8/S2aek3-ak4ceiqz5en
3o$obo$2bo!

Edit: Why is W4124 r=3/2 so common? All of non-W90 replicators I find belong to this category.

Posted: **July 14th, 2026, 8:21 am**

yyh_baboon wrote: July 14th, 2026, 7:59 am Hope it’s not W4124 r=3/2 again…
yyh_baboon wrote: July 14th, 2026, 4:24 am New kind of replicator?
Which rule does it emulate?
Code: Select all
 x = 3, y = 3, rule = B2n3-jkny4i5ekr8/S2aek3-ak4ceiqz5en
3o$obo$2bo!

Yes, it is:

Code: Select all

x = 187, y = 187, rule = B2n3-jkny4i5ekr8/S2aek3-ak4ceiqz5enHistory
182.4D$182.2D.2D$182.D2.D$182.3D$172.4D7.D$172.2D.2D$172.D2.D$172.3D$
162.4D7.D$162.2D.2D$162.D2.D$162.3D$152.4D7.D$152.2D.2D$152.D2.D$152.
3D$142.4D7.D$142.2D.2D$142.D2.D$142.3D$132.4D7.D$132.2D.2D$132.D2.D12.
4D$132.3D13.2D.2D$122.4D7.D14.D2.D$122.2D.2D21.3D$122.D2.D23.D$122.3D
$112.4D7.D$112.2D.2D$112.D2.D12.4D$112.3D13.2D.2D$102.4D7.D14.D2.D12.
4D$102.2D.2D21.3D13.2D.2D$102.D2.D23.D14.D2.D$102.3D39.3D$92.4D7.D41.
D$92.2D.2D$51.3A38.D2.D$51.A.A38.3D$53.A28.4D7.D$82.2D.2D$82.D2.D12.4D
$82.3D13.2D.2D$72.4D7.D14.D2.D$72.2D.2D21.3D$72.D2.D23.D$72.3D$62.4D7.
D$62.2D.2D$62.D2.D12.4D$62.3D13.2D.2D$52.4D7.D14.D2.D12.4D$52.2D.2D21.
3D13.2D.2D$52.D2.D23.D14.D2.D$52.3D39.3D$53.D41.D2$100.4D$100.2D.2D$100.
D2.D12.4D$100.3D13.2D.2D$48.4D38.4D7.D14.D2.D$48.2D.2D37.2D.2D21.3D$48.
D2.D38.D2.D12.4D7.D$48.3D39.3D13.2D.2D$49.D41.D14.D2.D$106.3D$96.4D7.
D$96.2D.2D$96.D2.D$96.3D$44.4D49.D$44.2D.2D$44.D2.D54.4D$44.3D55.2D.2D
$45.D56.D2.D$102.3D$50.4D49.D$50.2D.2D$50.D2.D$50.3D$40.4D7.D$40.2D.2D
$40.D2.D$40.3D$41.D4$62.4D$62.2D.2D$36.4D22.D2.D$36.2D.2D21.3D$36.D2.
D12.4D7.D$36.3D13.2D.2D$37.D14.D2.D12.4D$52.3D13.2D.2D$42.4D7.D14.D2.
D$42.2D.2D21.3D$42.D2.D12.4D7.D$42.3D13.2D.2D$32.4D7.D14.D2.D12.4D$32.
2D.2D21.3D13.2D.2D$32.D2.D23.D14.D2.D$32.3D39.3D$33.D30.4D7.D$64.2D.2D
$64.D2.D$64.3D$65.D2$28.4D$28.2D.2D$28.D2.D$28.3D$29.D30.4D$60.2D.2D$
60.D2.D$60.3D$61.D2$24.4D$24.2D.2D$24.D2.D$24.3D$25.D2$30.4D$30.2D.2D
$30.D2.D$30.3D$20.4D7.D$20.2D.2D$20.D2.D$20.3D$21.D6$16.4D$16.2D.2D$16.
D2.D12.4D$16.3D13.2D.2D$17.D14.D2.D$32.3D$22.4D7.D$22.2D.2D$22.D2.D$22.
3D$12.4D7.D$12.2D.2D$12.D2.D$12.3D$13.D6$8.4D$8.2D.2D$8.D2.D$8.3D$9.D
6$4.4D$4.2D.2D$4.D2.D$4.3D$5.D6$4D$2D.2D$D2.D$3D$.D!

Posted: **July 14th, 2026, 8:22 am**

Rhombicubocta wrote: July 13th, 2026, 10:11 am As for Silversmith's position becoming meaningless in infinite grids issue, I am not sure I understand that problem.
Conway's game of life takes place on an infinite grid and we can simulate finite patterns so I don't see the issue with infinite grids
and just because the neighborhood is infinite it does not mean we actually have cells an infinite distance apart.
I would appreciate some elaboration on that from silversmith.

I suppose I had some different assumptions, namely that you were asking for an algorithm to simulate any rule within a given infinite neighborhood. Coming up with a way to simulate a particular CA with an infinite neighborhood is simpler, and avoids the problem I had in mind.

Posted: **July 15th, 2026, 11:56 am**

I was wondering if there is a rule in which the small ships and stable splitters/reflectors/... are common enough to allow soupfind give engineered puffers, rakes, ships, even replicators, etc. These are normally, or as far as what we have seen, only manually created or spawned. And as the name suggests, to maintain symmetry and be not too complex, the rule is best to be Isotropic Non-Totalistic (I don't think Outer-Totalistic rules can be life-emerging anyway).
Note: the rule obviously have to be non-explosive to have these objects spawn from random soups.

Edit 1: to be precise, such a rule should have naturally generating objects that are kind of pathological, similar to an engineered orthogonoid in certain engineerable rules. It is expected that running an enormous-sized soup with the rule will eventually give patterns that exhibit intellectual behaviour, or at least form competitions between different engineered replicators.

Note: the above text is also in this thread of mine: https://conwaylife.com/forums/viewtopic.php?t=7326
I purposely posted it again here so that it gets more views, and it might also fit in this topic.

Posted: **July 15th, 2026, 4:38 pm**

pifricted wrote: July 14th, 2026, 8:21 am
yyh_baboon wrote: July 14th, 2026, 7:59 am Hope it’s not W4124 r=3/2 again…
yyh_baboon wrote: July 14th, 2026, 4:24 am New kind of replicator?
Which rule does it emulate?
Code: Select all
 x = 3, y = 3, rule = B2n3-jkny4i5ekr8/S2aek3-ak4ceiqz5en
3o$obo$2bo!

Corderized:

Code: Select all

x = 31, y = 46, rule = B2n3-jkny4i5ekr8/S2aek3-ak4ceiqz5en
23bo$22b3o$21b2o2bo$23b3o4$29bo2$29b2o12$2bo$b2o$2obo$bobo$2b2o3$26b3o
$7bobo16bobo$9bo18bo$29bo11$12b2o$12bo$12b3o$15bo!

Posted: **July 16th, 2026, 4:22 pm**

A few unrelated questions.

Has anyone tried to simulate cellular automata in a 3D hexagonal prism based tessellation?

Can anything be said about the fate any explosions in explosive rules and do we actually know they explode forever or just assume so based on the fact the simulations just keep trending up in population?

Can a rule in theory have only growing patterns, but not be explosive?

Can a INT rule or OT rule exist where gardens of Eden are impossible and are any known?

Edit1: another question added so I don’t spam this thread.

Are there any search methods or programs for patterns in 3D rules?

Posted: **July 16th, 2026, 4:51 pm**

Rhombicubocta wrote: July 16th, 2026, 4:22 pm Can a INT rule or OT rule exist where gardens of Eden are impossible and are any known?

If I understand things well enough, a boring answer would be B/S012345678 - since nothing changes in that rule, everything is its own parent and exists at every generation. And reading Garden of Eden, because nothing in that rule has multiple parents, it has no GoEs. Wiki: "a cellular automaton has a Garden of Eden if and only if it has two different finite configurations that evolve into the same configuration in one step. "

Posted: **July 16th, 2026, 10:01 pm**

Rhombicubocta wrote: July 16th, 2026, 4:22 pm Can a rule in theory have only growing patterns, but not be explosive?

Can a INT rule or OT rule exist where gardens of Eden are impossible and are any known?

Edit1: another question added so I don’t spam this thread.

Are there any search methods or programs for patterns in 3D rules?

Kinda?

NNlk05 wrote: June 29th, 2026, 1:25 am This got to be the least explosive B1e rule I seen.
Even if there's lots of unbounded growth, at least it don't explode outwards at c.
Code: Select all
x = 64, y = 64, rule = B1e2-ac3-ai4-a5-aei78/S01234-aw5-ai678
!
[[ RANDOMIZE RANDSEED 137 RANDHEIGHT 256 RANDWIDTH 256 ]]

Posted: **July 17th, 2026, 1:28 am**

Rhombicubocta wrote: July 16th, 2026, 4:22 pm
Can a INT rule or OT rule exist where gardens of Eden are impossible and are any known?

Trivial example:B/S012345678
Edit:Another question: Do unsynthesizable spaceships exist in Life?

Posted: **July 17th, 2026, 3:44 am**

yyh_baboon wrote: July 17th, 2026, 1:28 am Edit:Another question: Do unsynthesizable spaceships exist in Life?

It should, but as far as I know, no example has been found yet.

Posted: **July 20th, 2026, 3:17 pm**

eRroR_6o6 wrote: March 27th, 2024, 3:46 pm Is B45678/S2345 omniperiodic?

I don't think this question was ever answered. There was a reply in a separate thread, which showed some oscillators with prime periods, but I don't know what does that have to do with omniperiodicity. Right now I'm making a wiki page for Walled Cities and I started to wonder the same thing: is this rule omniperiodic?

From the research on hollow rectangles we know that possible periods seem to grow without bounds, but that is far from proving omniperiodic. Catagolue doesn't help much either, as it currently contains only soups 2x128 which can only produce still lives.

Any ideas?

Posted: **July 20th, 2026, 9:02 pm**

dvgrn wrote: July 16th, 2013, 11:49 am
DivusIulius wrote:I'm not sure if the gliders come from infinity. How might I verify this?
Maybe just use shift.py to move each glider 10 ticks diagonally in the appropriate direction, and see if you still get the same final pattern. In point of fact, you don't:
Code: Select all
x = 15, y = 33, rule = B3/S238
13bo$12bo$12b3o3$2bobo$3b2o$3bo16$8b3o$8bo$9bo5$3o$2bo$bo!
So you'd have add a kickback and turn this into a five-glider construction.

I was very surprised to see so many pulsars in the final output, by the way -- until the extra "8" in the rule string caught my eye!

My glider-rewinder script might work, too -- as you step backwards there will come a point when the script refuses to rewind one of the gliders. I've been threatening to get back to write a version that rewinds to N ticks but throws up a warning message if some objects can't be rewound. It wouldn't be terribly difficult, but it seems I haven't found the time yet...!

I actually find it interesting there aren't any known oscillators in B3/S238 which convert pulsars back to Pi heptominos (there are alien pulsar hasslers of multiple periods). Could someone go looking for some potential reactions/partials?

Posted: **July 24th, 2026, 9:56 am**

DryLife without death and Plow World always have same behavior but DryLife without death left antidot inside:
(Red: pattern in gen 100 in Plow World)

Code: Select all

# [[ STOP 100 ]]
x = 53, y = 67, rule = B37/S012345678History
21.D9.D$20.3D.2D.2D.3D$17.D.7D.7D.D$15.23D$15.23D$14.25D$15.23D$14.25D
$15.23D$14.25D$2.D12.23D12.D$.3D.2D.3D4.23D4.3D.2D.3D$10D.D.27D.D.10D
$.51D$2.49D$.15D.19D.15D$2.14D2.17D2.14D$.51D$2.49D$53D$9D.33D.9D$9D2.
31D2.9D$2.49D$.51D$2.49D$.51D$.51D$.2D.22DC22D.2D$3.D.21DC21D.D$4.22D
C22D$5.21DC21D$4.22DC22D$4.5D.16DC16D.5D$11.15DC15D$4.5D.16DC16D.5D$4.
22DC22D$5.21DC21D$4.22DC22D$3.D.21DC21D.D$.2D.22DC22D.2D$.51D$.51D$2.
49D$.51D$2.49D$9D2.31D2.9D$9D.33D.9D$53D$2.49D$.51D$2.14D2.17D2.14D$.
15D.19D.15D$2.49D$.51D$10D.D.27D.D.10D$.3D.2D.3D4.23D4.3D.2D.3D$2.D12.
23D12.D$14.25D$15.23D$14.25D$15.23D$14.25D$15.23D$15.23D$17.D.7D.7D.D
$20.3D.2D.2D.3D$21.D9.D!

Can we prove it?

Posted: **July 24th, 2026, 7:41 pm**

How was the ship in gems (B3457/S4568) found?

Code: Select all

x = 12, y = 14, rule = B3457/S4568
5b2o$3bo4bo$3b2o2b2o$b3o4b3o$b3o4b3o$2ob6ob2o$3ob4ob3o$ob3o2b3obo$2ob6ob2o$ob
obo2bobobo$2b2ob2ob2o$2b8o$4b4o$4bo2bo!

Posted: **July 24th, 2026, 9:27 pm**

Not sure if this counts as a basic question, but is there a polyglot ship other than the glider that works in both B3/S23 and B3/S23-a5?

Posted: **July 25th, 2026, 5:32 am**

Rhombicubocta wrote: July 24th, 2026, 7:41 pm How was the ship in gems (B3457/S4568) found?
Code: Select all
x = 12, y = 14, rule = B3457/S4568
5b2o$3bo4bo$3b2o2b2o$b3o4b3o$b3o4b3o$2ob6ob2o$3ob4ob3o$ob3o2b3obo$2ob6ob2o$ob
obo2bobobo$2b2ob2ob2o$2b8o$4b4o$4bo2bo!

It was found by David Eppstein using a program he wrote - named gsearch. Essentially, gsearch systematically evolves all (small) patterns within a given bounding box (including all the corresponding symmetrical patterns) in a specified life like rule and identifies any pattern that eventually repeats (so it can find oscillators, spaceships, and some puffers and replicators up to a maximum period). It only outputs one pattern for each spatial and time period. Eppstein ran search sweeps at fairly small search widths with gsearch, gfind and some other programs across all life-like rules that we're responsible for finding many thousands more small patterns than had been known about before his work.

I can no longer find a reference to this discovery online as Eppstein's website is offline now (and his glider db has been offline for quite a long time), but you can find a brief description of the program from his search software page and the source code on the way back machine. There is also some scattered discussion of gsearch to be found on the forums here.

Posted: **July 25th, 2026, 7:29 am**

Rhombicubocta wrote: July 24th, 2026, 7:41 pm How was the ship in gems (B3457/S4568) found?
Code: Select all
x = 12, y = 14, rule = B3457/S4568
5b2o$3bo4bo$3b2o2b2o$b3o4b3o$b3o4b3o$2ob6ob2o$3ob4ob3o$ob3o2b3obo$2ob6ob2o$ob
obo2bobobo$2b2ob2ob2o$2b8o$4b4o$4bo2bo!

I think by soup serach, but not apgsearch.

hotcrystal0 wrote: July 24th, 2026, 9:27 pm Not sure if this counts as a basic question, but is there a polyglot ship other than the glider that works in both B3/S23 and B3/S23-a5?

I think LLS can find polyglot patterns, but I con't find it now.

Posted: **July 27th, 2026, 8:59 am**

Are there rules where diagonally-symmetric patterns explode, but orthogonally-symmetric patterns do not?

Code: Select all

x = 652, y = 39, rule = B2-ae3-cij4a5aj6e7e8/S01e2ai3ar4ar5air6ae7c8
4obob6obo3b2o$2bo2bo2bo3bo4b3o$5b3o4bo3b4o$b2o2bob3o2bo4b3o$5bob2o2b3o
2b3o$o3bob2ob5o2b3o$b3obob4o2bo2b4o$b4ob4o2b4o2b2o$3bob2o3b2o2b6o$obob
3o2bob3obobo$3o3bo10b3o$3b2obobobo2b2ob2o$2bob3o2bo2b2o2b4o$obobob2o3b
o4b2o$b2obobob6o2bobo$3b3ob2o2bo2bo2bo$3ob2o3bob2obo$b2o4bobobob3o3bo$
o2bo5bo3bob2o2bo$2b2o2b2obob2o2bob2o$o2bo5bo3bob2o2bo$b2o4bobobob3o3bo
$3ob2o3bob2obo$3b3ob2o2bo2bo2bo$b2obobob6o2bobo$obobob2o3bo4b2o$2bob3o
2bo2b2o2b4o$3b2obobobo2b2ob2o$3o3bo10b3o$obob3o2bob3obobo$3bob2o3b2o2b
6o$b4ob4o2b4o2b2o$b3obob4o2bo2b4o$o3bob2ob5o2b3o$5bob2o2b3o2b3o630b3o$
b2o2bob3o2bo4b3o$5b3o4bo3b4o$2bo2bo2bo3bo4b3o$4obob6obo3b2o!

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Re: Thread for basic non-CGOL questions

Re: Thread for basic non-CGOL questions

Re: Thread for basic non-CGOL questions

Re: Thread for basic non-CGOL questions

Re: Thread for basic non-CGOL questions

Re: Thread for basic non-CGOL questions

Re: Thread for basic non-CGOL questions

Re: Thread for basic non-CGOL questions

Re: Thread for basic non-CGOL questions

Re: Thread for basic non-CGOL questions