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g0t0

Rule B2-a3ijkn/S2ak

Natural object:

p2, p4, p6, p8
c/2o, 2x c/4o

x = 97, y = 78, rule = B2-a3ijkn/S2ak
7$66bo$68bo13b2o$81bo$64bo2bo14bobo$65bo$44b2o$20bo8bobo11b4o$21bo$18b
o$19bo2$29bo$30bo5$18bo$19bo2$17bo$18bo$29bobo2$30bo9$16bo$16bo12bo$
16bo$16bo11bo2bo$16bo$16bo13bo7$16bo$14bo$17bo9bo ...

g0t0

NNlk05 wrote: October 2nd, 2026, 8:52 pm
g0t0 wrote: October 2nd, 2026, 8:33 pm Is this a standalone object or 2 objects in apgsearch?
Code: Select all
x = 7, y = 5, rule = B3/S23
b2ob2o$b2ob2o2$ob3obo$2obob2o!
Its one

Why? (I'm not clear about Catagolue)

g0t0

Is this a standalone object or 2 objects in apgsearch?

Code: Select all

x = 7, y = 5, rule = B3/S23
b2ob2o$b2ob2o2$ob3obo$2obob2o!

g0t0

Code: Select all

x = 20, y = 38, rule = B3/S23
3$6bo4bo$5bo4bo$5b3o2b3o3$6bo4bo$5bo4bo$5b3o2b3o3$6bo4bo$5bo4bo$5b3o2b
3o3$6bo4bo$5bo4bo$5b3o2b3o3$6bo4bo$5bo4bo$5b3o2b3o3$6bo4bo$5bo4bo$5b3o
2b3o3$8b2o$7bo2bo$8b2o!

I don't know what thread fit it.

g0t0

A synthese:

x = 188, y = 132, rule = B3/S23
16$88bo$86bobo$87b2o36$147bobo$147b2o$148bo9$144bo$143bo$143b3o9$137b
2o$138b2o$137bo5$153b3o$153bo$154bo$146b2o$146bobo$146bo26$87b3o$89bo$
88bo!

The reaction from a lucky soup:

x = 15, y = 9, rule = B3/S23
2b3o$bo3bo$o5bo5b3o$bo3bo$2b3o5bo$10bo ...

g0t0

Code: Select all

x = 10, y = 10, rule = B3/S23
4b2o$4bobo$5b2o$7b2o$2o2b2obobo$obob2o2b2o$b2o$3b2o$3bobo$4b2o!

The block is eaten.

g0t0

Doing so at all the corners can cut upper limit?

What if two corners is a same cell?

However, do it at the highest and lowest is correct and can cut the bound to 3n-2.

I actually noticed that 2 cornrers can be the same cell, thus deriving at the limit of 3n-2. But when the population is ...

g0t0

Can someone summarize the known spaceship speed in Just Friends?

Little p3:

Code: Select all

x = 6, y = 5, rule = B2-a/S12
5bo$2b2obo$2obo$3bo$3bo!

g0t0

Proof of pop <= 3n:

https://i.imageupload.app/0e89ffa8e8d7802aa6e8.png

The sum of all numbers is pop and number in every cell <= 3.
Q.E.D.

in fact the 3 is only achieved when a cell has 2 live neighbors and the other 6 will turn alive for next generation.
the corners can’t actually ...

g0t0

NNlk05 wrote: September 25th, 2026, 11:09 am
g0t0 wrote: September 25th, 2026, 2:46 am Conjecture:

For infinite 50% soup, the limit of the density when time->inf exists.
Around 37%, IIRC. In sparser soups, imminent growth and/or the potential quadratic growth may skew it.

This is infinite soup. Quadratic growth can't remain forever.

What does 'Around 37%' means?

g0t0

This is a MAP rule.

It is almost B2/S2-ei but will not born in these cases:

x = 4, y = 4, rule = MAPFCgWSGiASABogGiAgACAAGiASACAAAAAAACAAAAAAABogGiAAACAAIAAgAAAAAAAgACAAAAAAAAAAAAAAAAAAAHistory
2.D$D2A$.2AD$.D!

Common objects: domino, duoplet, flipper, pseudo banana, banana, banana tagalong ...

g0t0

I prove it by enumerating all the case(about 30).

I think LLS can do it fast.

The way is to prove can't stabilize the cell without let it fully turn to the object list.
x = 11, y = 12, rule = LifeHistory
10.B$9.2B$8.3B$7.4B$6.5B$5.A5B$5.6B$4.7B$3.8B$2.9B$.10B$11B!

The red cells can't be alive ...

g0t0

Conjecture:

For infinite 50% soup, the limit of the density when time->inf exists.

g0t0

x = 0, y = 0, rule = B34/S2-a3
!
[[ RANDOMIZE ]]

Although this rule does not seem to cause infinite growth, in this pattern actually leads to infinite growth without any regularity.

x = 5, y = 5, rule = B34/S2-a3
5o$2ob2o$2ob2o$b3o$2bo!

I originally posted this in sandbox, but I think ...

g0t0

I love searching rules like this that generate THOUSANDS of objects per soup, yet are still miraculously stable:

x = 16, y = 16, rule = B3_S12-ae34ceit
obo4bo2b4obo$2b2obobobo5bo$bo2b2o5b2o$ob2ob2ob2o3b2o$bo6bobo$bobo2b3ob
obob2o$3o2bo2b3obobo$2o3bo4b2ob2o$bo2bob2o3b2o2bo$o2b2o2b2o2bo2bo$bo2b ...

g0t0

EDIT by dvgrn: There has been a Discord suggestion to standardize "B2ex3-lS23" to canonical rulestring "B2en3-a/S23" in following posts.

@RULE B2ex3-lS23
@TABLE
n_states:2
neighborhood:Moore
symmetries:rotate4reflect
0,1,0,1,0,0,0,0,0,1
0,0,1,0,0,0,1,0,0,1
0,1,1,0,1,0,0,0,0,1
0,1,1,0,0,1,0,0,0 ...

g0t0

x = 12, y = 10, rule = 2-a3-aei4-aceik/2-a3-akn45/4
3.C$10.B$.BC2.C3.ABA$2A.A.B.C.ACA$.AB.B3CA.2A$2.AB.3A.BA$3.ABACABA$4.
ACACA$4.2AC2A$5.3A!

Similar rule that differs by one transition that also harbors a RRO with interesting spark, but has ships and guns naturally.

x = 9, y = 11, rule = 2 ...

g0t0

How to download LLS in China?
There is not gitlab.com.

g0t0

HerscheltheHerschel wrote: October 20th, 2023, 12:42 pm A completely stable still life
Code: Select all
x = 7, y = 6, rule = B3/S23
2b2o$bo2bo$obobo$o2bobo$b2o2bo$5b2o!

Another completely stable still life

Code: Select all

x = 9, y = 6, rule = B3/S23
2b2o3b2o$bo2bobobo$obobobo$o2bobobo$b2o2bobo$5b2o!

g0t0

2 slightly different 2c/4o's in one of the original rules:

x = 71, y = 44, rule = B3468/S268
21b3o34b3o$9b7o4b2o3bo20b7o4b2o3bo$7b2o4b2o2b6ob2obo16b2o4b2o2b6ob2obo
$5b2o3bobo2b2o6b2o2bobo12b2o3bobo2b2o6b2o2bobo$4bo4b3ob2o2bo5b2obobobo
10bo4b3ob2o2bo5b2obobobo ...

g0t0

5 gliders with same directions:

Code: Select all

x = 7, y = 4, rule = B3/S23
bo$3o$o3b3o$5bo!

g0t0

x = 98, y = 91, rule = B3/S23
3$89b2ob2o$88bobobobo$87bo3bo2bo$86bo7b2o$85bo$84bo$83bo$82bo$81bo$80b
o$79bo$78bo$77bo$76bo$75bo$74bo$73bo$72bo$71bo$70bo$69bo$68bo$67bo$66b
o$65bo$64bo$63bo$62bo$61bo$60bo$59bo$58bo$57bo$56bo$55bo$54bo$53bo$52b
o$51bo$50bo$49bo$48bo$47bo$46bo$45bo$44bo$43bo$42bo$41bo ...

g0t0

18 cells block to pulsar:

x = 433, y = 63, rule = LifeHistory
29$52.2A16.3B$40.C10.ACAB15.4B20.3B19.3B18.3B18.3B18.3B21.3B$23.C6.AC
6.2A11.2A2B15.4B20.4B18.4B17.4B17.4B17.4B20.4B24.3B19.3B$21.2A6.A.A5.
A.A9.2A3B.2B11.2A3B.2B18.4B18.4B17.4B17.4B17.4B20.4B24.4B18.4B16.3B15.
3B19.3B$21.2A6.2A6.2A9 ...

g0t0

exactly two subsets (the standard definition) -- O(n^2)
two or three subsets -- NP-complete
two or three or four subsets (i.e. any number of subsets) -- [open problem]

For Lifewiki definition(two or three or four subsets), it's an open problem, so why it is possible to determine whether a ...

g0t0

https://conwaylife.com/forums/viewtopic.php?t=5342

Another rule.

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