Miscellaneous Discoveries in Other Cellular Automata

confocaloid · Post by **confocaloid** » April 2nd, 2025, 10:23 am

WhiteHawk wrote: April 2nd, 2025, 9:55 am [...]
According to my notes, this means there is now a p13 oscillator for all Isotropic Non-totalistic rules that contain Snarks, Snark64, Herschel Conduits, or the Scorbie Splitter-based reflector (and thereby have a complete infinite set of oscillators above a certain period)

That claim cannot possibly be correct, as stated.

"All isotropic non-totalistic" is way too wide. There are infinitely many isotropic non-totalistic CA. Finitely many are supported in Golly/LifeViewer, but very very many. And very many of those isotropic non-totalistic cellular automata support the Snark, the Snark64, some Herschel conduits, and/or the Scorbie Splitter. There are examples with some higher-range neighbourhood. There are examples with more than two cellstates. There is also some room for interpretation/debate on, for example, what would count as the Snark.

Lots and lots of examples can be provided if requested.

Mostly unrelated, here is a period-40 orthogonal 2c/5 spaceship in a two-state isotropic non-totalistic cellular automaton:

Code: Select all

x = 24, y = 7, rule = R3,C0,S234-467,494,511,B12,104,351-419,421-467,512,NW00000D000D0000000101000101000D01757575010D000075007500000D01757575010D0001010001010000000D000D0000
20b2o$obo16b2ob2o$ob2o14bo4bo$bo15b3o3bo$2bo13bo2bob2o$16bobo$17b2o!

islptng · Post by **islptng** » April 3rd, 2025, 12:21 am

This rule has a P120 4-barrelled gun(it nay be a failedrep but i'm not sure):

Code: Select all

x = 2, y = 5, rule = B2n3aeik4iqrz5ajn6akn8/S2ae3airy4ainqrtz5-ackq6ac7c
2o$2o2$2o$2o!

Block reflects the T with rt 15:

Code: Select all

x = 14, y = 14, rule = B2n3aeik4iqrz5ajn6akn8/S2ae3airy4ainqrtz5-ackq6ac7c
10b2o$10b2o$2o$2o4$8b3o$3b3o3bo$3bobo$4bo7b2o$12b2o$2b2o$2b2o!

Most importantly, It has a SMOSMOS:

Code: Select all

#C P240 Capped SMOSMOS Gun
x = 155, y = 75, rule = B2n3aeik4iqrz5ajn6akn8/S2ae3airy4ainqrtz5-ackq6ac7c
8b2o27b2o77b2o27b2o$8b2o17b2o8b2o77b2o8b2o17b2o$27b2o97b2o6$19b2ob2o
107b2ob2o$19b2ob2o107b2ob2o7$2o151b2o$2o151b2o2$11bo131bo$10bobo129bob
o$10b3o129b3o2$38b2o75b2o$38b2o75b2o2$31b2o89b2o$31b2o9b2o67b2o9b2o$
42b2o21b2o21b2o21b2o$65b2o21b2o3$14b2o123b2o$14b2o123b2o$2b2o35b2o73b
2o35b2o$2b2o35b2o73b2o35b2o3$64b2o23b2o$64b2o23b2o4$57b2o37b2o$57b2o
37b2o2$57b2o37b2o$57b2o37b2o4$33b2o85b2o$33b2o85b2o2$45b2o61b2o$45bobo
59bobo$45b2o61b2o$65b2o21b2o$65b2o21b2o5$31b2o89b2o$31b2o89b2o$49b2o
53b2o$49b2o53b2o7$69b2o13b2o$69b2o13b2o!

b-engine · Post by **b-engine** » April 3rd, 2025, 2:18 am

Replicator in stripes agar in stripes-restricted rule:

Code: Select all

x = 17, y = 10, rule = B2-ei3inqry4ny5r6i/S
8bo$6bobobo$4bobobobobo$2bobobobobobobo$obobobobobobobobo$obobo3bobob
obobo$2bobobobobobobo$4bobobobobo$6bobobo$8bo!

Citation needed · Post by **Citation needed** » April 4th, 2025, 6:09 am

Code: Select all

#C 5×79P5H2V0A1
#C Based on a puffer found by Josh Ball
x = 211, y = 11, rule = B3/S023
7b2o19b2o21b3o19b3o20bo21bo17b3o19b3o20bo21bo$5b2obo19bob2o18b2ob2ob4o
7b4ob2ob2o17b2ob2o2b2o9b2o2b2ob2o14b2o2bo2bobo7bobo2bo2b2o17b4o19b4o$
2bobo5b6o5b6o5bobo11b3ob2o8bo5bo8b2ob3o10bobo3b2o2b3o7b3o2b2o3bobo7b2o
b2o5bo3bo5bo3bo5b2ob2o12bo3bo19bo3bo$b2o4b8obo3bob8o4b2o9bobob4o8bo3b
o8b4obobo8b3o4bo3b4o5b4o3bo4b3o6bo2bo3b2o2bo2b2o3b2o2bo2b2o3bo2bo9b4o
bob9o3b9obob4o$2o2b2ob2ob4o3bobo3b4ob2ob2o2b2o14b2o6bob2ob2obo6b2o15b
obo11b2ob2o11bobo8bo13bo3bo13bo10bo2b2o9b2o3b2o9b2o2bo$2o15bobo15b2o8b
2o9b2o3b2ob2o3b2o9b2o7bo6bo6bo7bo6bo6bo4bo6bo7b2o3b2o7bo6bo8bo6bo8bob
o8bo6bo$17bobo42bobo39bo5bo34b2o3b2o22bo6bo9bobo9bo6bo$18bo44bo41b2ob
2o36b5o41bo$107bo39b3o39bo5bo$190bo3bo$192bo!

WhiteHawk · Post by **WhiteHawk** » April 4th, 2025, 10:02 am

OTT of a 4c/37 ship in B34c57/S234c8 that consumes a ship and a block to output a 180 degree reflected ship, a displaced block, and ablinker.

Code: Select all

x = 10, y = 19, rule = B34c57/S234c8
bo$obo$obo$bo$3bo$2bobo$bo3bo$2bobo2b2o$3bo2bo2bo$7b2o8$2o$2o!

LaundryPizza03 · Post by **LaundryPizza03** » April 4th, 2025, 4:51 pm

p16 replicator hassler:

Code: Select all

x = 22, y = 22, rule = B0236/S2
6bo5bo$5b3o3b3o$6bo5bo$5b3o3b3o$6bo5bo$18bobo$17b5o$18bobo$bobo$5o6bob
o$bobo$18bobo$17b5o$18bobo$bobo$5o$bobo$9bo5bo$8b3o3b3o$9bo5bo$8b3o3b
3o$9bo5bo!

I suspect it cannot be reduced, can you confirm this? I have confirmed this with period-2 eaters.

R2INT · Post by **R2INT** » April 4th, 2025, 9:12 pm

Here is a proof I wrote that disproves the existence of p2 c/2o spaceships in CityBlocks from R2INT's Rule Collection:

R2INT wrote: July 12th, 2024, 7:09 pm [...]
Code: Select all
x = 24, y = 13, rule = B2cik3aekqr4jqrtz5ci8/S01c2cek3aijqy4ajkn5aei6-ek78History
18.2DAD$4.A.C11.2DAC6$12B$12B$12B$5BE6B8.CAD$5.EA.C10.A3.A$6.A.2A!
Each of these figures (top and bottom rows) represent the top-right corner of a theoretical c/2o. For the first figure (top), notice that there is no way to arrange live cells inside of the 4x4 red block in the second phase to get an exact match of the first phase, thus meaning that this frontend doesn't work. For the second figure (bottom), instead of using B3a in the second phase, it is possible to use B2k instead. This also leads to a contradiction, because the marked on cell must be alive, meaning that the yellow cells sticking into the blue forbidden area must be alive for that marked cell to come alive. That completes our proof.
[...]

EDIT: 2c/5 partial from rlifesrc:

Code: Select all

x = 29, y = 62, rule = B2cik3aekqr4jqrtz5ci8/S01c2cek3aijqy4ajkn5aei6-ek78
13bobo$5b2obob9obob2o$4b2ob5o5b5ob2o$4bobo4bobobobo4bobo$3b3o6b5o6b3o
$2b2o21b2o$b2ob2o4bobobobobo4b2ob2o$b2obo4b2o7b2o4bob2o$b2o9b2ob2o9b2o
$2bo6bo2bo3bo2bo6bo$9bo2bo3bo2bo$5b3o3bo5bo3b3o$3bo2bo15bo2bo$7b2ob2o
2bo2b2ob2o$4bo3bo4b3o4bo3bo$5bob2ob9ob2obo$4b2o4b9o4b2o$7b2obob5obob2o
$6bob2o2b5o2b2obo$4b5obo2b3o2bob5o$3bo4b13o4bo$4bo5b2ob3ob2o5bo$2b2ob
o4bo7bo4bob2o$2bob3o3bo7bo3b3obo$2bo2b4ob2o5b2ob4o2bo$6b4obo5bob4o$3b
ob3o2bobo3bobo2b3obo$2b2o2bo3bo7bo3bo2b2o$3b2obo15bob2o$5b6o7b6o$2b2o
b4ob2o5b2ob4ob2o$3bob8o3b8obo$2b3ob3ob4ob4ob3ob3o$2ob2ob5obo3bob5ob2o
b2o$bo3b3o2bo3bo3bo2b3o3bo$3bo2b2o3bo5bo3b2o2bo$b3o3bo3b2obob2o3bo3b3o
$2bo2bo6bobobo6bo2bo$4b3o2bobobobobobo2b3o$2b5obobobobobobobob5o$b11o
b3ob11o$2o2b3obo11bob3o2b2o$9o5bo5b9o$3ob3o4bo2bo2bo4b3ob3o$3ob3o3b2o
5b2o3b3ob3o$3ob4o3bobobobo3b4ob3o$3o4bo4b2ob2o4bo4b3o$3o4b3o9b3o4b3o$
6obo13bob6o$3obo2b2o2bo2bo2bo2b2o2bob3o$6obo2bobobobobo2bob6o$3obob3o
b9ob3obob3o$3ob2ob3o2b5o2b3ob2ob3o$6obobob7obobob6o$3o4b2ob9ob2o4b3o$
3obo3bobob5obobo3bob3o$2obo5b11o5bob2o$bobo4bobob5obobo4bobo$b2obob6o
b3ob6obob2o$2b7ob9ob7o$o4b5obob3obob5o4bo$4bo5b2o2bo2b2o5bo!

Code: Select all

x = 29, y = 64, rule = B2cik3aekqr4jqrtz5ci8/S01c2cek3aijqy4ajkn5aei6-ek78
.............................$
.............o.o.............$
.....oo.o.ooooooooo.o.oo.....$
....oo.ooooo.....ooooo.oo....$
....o.o....o.o.o.o....o.o....$
...ooo......ooooo......ooo...$
..oo.....................oo..$
.oo.oo....o.o.o.o.o....oo.oo.$
.oo.o....oo.......oo....o.oo.$
.oo.........oo.oo.........oo.$
..o......o..o...o..o......o..$
.........o..o...o..o.........$
.....ooo...o.....o...ooo.....$
...o..o...............o..o...$
.......oo.oo..o..oo.oo.......$
....o...o....ooo....o...o....$
.....o.oo.ooooooooo.oo.o.....$
....oo....ooooooooo....oo....$
.......oo.o.ooooo.o.oo.......$
......o.oo..ooooo..oo.o......$
....ooooo.o..ooo..o.ooooo....$
...o....ooooooooooooo....o...$
....o.....oo.ooo.oo.....o....$
..oo.o....o.......o....o.oo..$
..o.ooo...o.......o...ooo.o..$
..o..oooo.oo.....oo.oooo..o..$
......oooo.o.....o.oooo......$
...o.ooo..o.o...o.o..ooo.o...$
..oo..o...o.......o...o..oo..$
...oo.o...............o.oo...$
.....oooooo.......oooooo.....$
..oo.oooo.oo.....oo.oooo.oo..$
...o.oooooooo...oooooooo.o...$
..ooo.ooo.oooo.oooo.ooo.ooo..$
oo.oo.ooooo.o...o.ooooo.oo.oo$
.o...ooo..o...o...o..ooo...o.$
...o..oo...o.....o...oo..o...$
.ooo...o...oo.o.oo...o...ooo.$
..o..o......o.o.o......o..o..$
....ooo..o.o.o.o.o.o..ooo....$
..ooooo.o.o.o.o.o.o.o.ooooo..$
.ooooooooooo.ooo.ooooooooooo.$
oo..ooo.o...........o.ooo..oo$
ooooooooo.....o.....ooooooooo$
ooo.ooo....o..o..o....ooo.ooo$
ooo.ooo...oo.....oo...ooo.ooo$
ooo.oooo...o.o.o.o...oooo.ooo$
ooo....o....oo.oo....o....ooo$
ooo....ooo.........ooo....ooo$
oooooo.o.............o.oooooo$
ooo.o..oo..o..o..o..oo..o.ooo$
oooooo.o..o.o.o.o.o..o.oooooo$
ooo.o.ooo.ooooooooo.ooo.o.ooo$
ooo.oo.ooo..ooooo..ooo.oo.ooo$
oooooo.o.o.ooooooo.o.o.oooooo$
ooo....oo.ooooooooo.oo....ooo$
ooo.o...o.o.ooooo.o.o...o.ooo$
oo.o.....ooooooooooo.....o.oo$
.o.o....o.o.ooooo.o.o....o.o.$
.oo.o.oooooo.ooo.oooooo.o.oo.$
..ooooooo.ooooooooo.ooooooo..$
o....ooooo.o.ooo.o.ooooo....o$
?...o.....oo..o..oo.....o...?$
?????????????...?????????????!

b-engine · Post by **b-engine** » April 5th, 2025, 4:07 am

(This should be in Thread for your unsure OCA discoveries, but since that thread doesn't exist I have to post here)

Accidental c/13 diagonal spaceship:

Code: Select all

x = 4, y = 4, rule = B34w/S23-c
2o$obo$o2bo$b3o!

R2INT · Post by **R2INT** » April 5th, 2025, 9:40 am

Here is a 3-state INT rule where spaceships can travel arbitrarily close to, but not exactly at the speed of light.

Code: Select all

x = 106, y = 22, rule = NotExactlyC
21.2A6.AB4.AB.AB4.AB.AB.AB4.AB.AB.AB.AB4.AB.AB.AB.AB.AB4.AB.AB.AB.AB.
AB.AB$7.A.A5.A$B2A18.2B6.2B4.2B.2B4.2B.2B.2B4.2B.2B.2B.2B4.2B.2B.2B.2B
.2B4.2B.2B.2B.2B.2B.2B$A.A$2A3$7.2B5.2A$7.2B5$14.A$6.3A4.A.A7$6.A2.A!
@RULE NotExactlyC
@COLORS
0 0,0,0
1 255,255,255
2 0,255,255
@TABLE
n_states:3
neighborhood:Moore
symmetries:rotate4reflect
var a1 = {0,1,2}
var a2 = a1
var a3 = a2
var a4 = a3
var a5 = a4
var a6 = a5
var a7 = a6
var a8 = a7
var a9 = a8
# infinite photon
0 1,2,0,0,0,0,0,0 1
0 2,1,0,0,0,0,0,0 2
# break photonic frontend
0 0,1,0,1,0,0,0,0 1
# burning
0 0,1,0,0,0,0,0,0 2
# backend
0 2,2,0,2,1,0,0,0 2
0 2,2,0,1,2,0,0,0 2
0 1,0,0,0,0,0,0,0 2
2 2,0,1,0,0,0,0,0 2
0 2,2,1,2,0,2,2,0 1
2 0,1,0,0,0,0,0,0 1
0 2,2,1,0,2,0,0,0 2
1 2,2,0,0,2,0,0,0 1
2 1,1,0,0,0,0,0,0 2
1 2,0,1,2,0,0,0,0 2
0 1,0,0,1,0,0,0,0 2
0 1,0,0,2,0,1,0,0 1
2 1,0,2,1,0,0,0,0 2
0 0,2,2,1,2,2,1,2 1
0 2,2,1,2,0,0,0,0 1
0 1,2,1,2,0,2,2,0 2
2 1,0,2,1,0,2,1,0 1
1 1,2,1,0,2,0,0,0 2
#misic
1 0,0,0,0,0,0,0,0 1
1 2,2,2,2,2,2,2,2 1
1 2,1,0,1,2,0,0,0 1
1 1,0,0,0,0,0,0,0 1
0 2,2,1,1,0,0,0,0 1
2 2,0,1,0,1,0,0,0 2
0 0,1,2,0,1,1,0,0 2
0 2,2,0,2,2,0,0,0 1
2 2,2,2,0,0,0,0,0 2
0 1,2,0,2,0,2,0,0 1
0 0,2,2,2,1,2,0,0 2
1 2,2,0,2,0,2,2,0 2
0 0,1,1,1,0,0,0,0 1
0 2,2,1,0,1,0,0,0 2
1 0,1,0,1,0,0,0,0 2
0 0,2,2,2,0,2,2,2 1
0 2,2,2,0,2,2,0,0 1
0 2,0,0,2,1,2,0,0 1
# c/2
2 2,1,1,2,0,0,0,0 2
0 2,2,0,1,1,0,0,0 2
0 1,1,0,2,2,2,0,0 2
# c/2d
0 2,1,2,0,0,0,0,0 2
2 1,2,0,0,0,0,0,0 1
0 2,1,0,2,0,0,0,0 1
2 1,0,1,0,0,0,0,0 1
1 1,0,1,0,0,0,0,0 2
0 1,2,0,0,2,0,0,0 1
2 1,2,2,2,2,2,2,2 2
1 2,2,1,2,2,0,0,0 1
2 1,1,2,2,2,1,0,0 1
# zebra agar
0 0,1,1,1,0,1,1,1 2
a1 a2,a3,a4,a5,a6,a7,a8,a9 0

LaundryPizza03 · Post by **LaundryPizza03** » April 5th, 2025, 7:54 pm

Spaceship that has a B0 counterpart, but does not work in any self-complementary rule:

Code: Select all

x = 4, y = 4, rule = B0123cer4acjkntz5-jky6in/S012-e3y4cyz5-kq
3bo$ob2o$b2o$bo!

Code: Select all

x = 4, y = 4, rule = B3-ce4eiqrwy5jy6-in78/S2e3-y4-cjnyz5kqr678
3bo$ob2o$b2o$bo!

confocaloid · Post by **confocaloid** » April 5th, 2025, 8:43 pm

^^ That p12 diagonal c/6 spaceship definitely does work in a self-complementary CA:

Code: Select all

#C Two-state isotropic self-complementary cellular automaton,
#C defined using a weighted neighbourhood (weights in hexadecimal):
#C -- -- 01 01 01 -- --
#C -- -- 01 -- 01 -- --
#C 01 01 15 69 15 01 01
#C 01 -- 69 -- 69 -- 01
#C 01 01 15 69 15 01 01
#C -- -- 01 -- 01 -- --
#C -- -- 01 01 01 -- --
x = 80, y = 43, rule = R3,C0,S0-24,27-45,47-59,61-108,110-127,132-169,172-186,188-274,276-287,292-338,340-358,361-372,376-524,B149-151,164-165,185,233-236,249,337,353-354,393-396,415,464,478,498-499,NW00000101010000000001000100000101156915010101006900690001010115691501010000010001000000000101010000
17b23o$17b23o$17b23o$17b23o$17b23o$17b23o$17b23o$17b23o$17b23o$17b23o$
40o$40o$40o$30o2b8o8b2o$31o2b7o7b2o$32o2b6o6b2o$31ob8o8bo$40o$40o$40o$
40o$40o$40o$40o$40o$40o$40o$40o$40o$40o$40o$40o$40o$40o$40o$40o$40o$
40o$40o$40b40o$40b40o$40b40o$40b40o!
#C [[ GRID THEME MCell ]]

(and neither this "higher-range" CA nor B3-ce4eiqrwy5jy6-in78/S2e3-y4-cjnyz5kqr678 is "merely a rule"; defining a CA also involves telling the underlying tiling/graph, the neighbourhood and the number of cellstates, which is more than writing down the rules).

LaundryPizza03 wrote: April 5th, 2025, 7:54 pm Spaceship that has a B0 counterpart, but does not work in any self-complementary rule:
Code: Select all
x = 4, y = 4, rule = B0123cer4acjkntz5-jky6in/S012-e3y4cyz5-kq
3bo$ob2o$b2o$bo!
Code: Select all
x = 4, y = 4, rule = B3-ce4eiqrwy5jy6-in78/S2e3-y4-cjnyz5kqr678
3bo$ob2o$b2o$bo!

b-engine · Post by **b-engine** » April 5th, 2025, 10:54 pm

I don't know what base is this ant counting in:

Code: Select all

x = 2, y = 1, rule = SemisoAnt:T30,4
EC!

PiSpaceships · Post by **PiSpaceships** » April 6th, 2025, 5:57 am

Crossposting from RARTBT:

PiSpaceships wrote: April 6th, 2025, 5:55 am

LittleLWSS wrote: April 6th, 2025, 4:33 am B2ci3-jnqr4e/S1e2-k3aeiy4etz5ei6i7e(Refterneovarius) -> B2ci3aceiy4e/S1e2-k3aeiy4eqtz6i(Refterneon)

Code: Select all

x = 65, y = 66, rule = B2ci3aceiy4e/S1e2-k3aeiy4eqtz6i
2bo2b3ob2obo5bo2b4o3bo2b2ob2o3b2o2bobo3bo2b3o4b3o2bo$bo4bobo2bo4b2ob4o
4b2o2b2o2bobobob2obobob2o2b3o2b2ob2ob2o$6o3b2obo3bo3bo5bo4bob3obob2obo
b2obo3bo2b2o2bob2o2bo$2o3b2o2bo9bob3obo2bo2bobo2bob4o5bo3b4o3b4ob2o$3b
obo3bo9bob3o3b2obob2o3bobob2ob2ob2o2bobobob2o2bo$bobo3bo2b7ob4o2bob3o
2bo4b2o2bobob3o4bobo4b3o$b3o3bobob2ob3o3b5obob2o2bo4b3o3bo3b2obo3bo2b
4o3bo$b5o3bob3o2bobo12b3obo3b2o3bob2o2bob4obo4bobo$obo4b5o2b2o2b2o2bo
2b2ob4ob2o2b3o2b5o4bob3o2b2ob2obo$6ob2obob4o3b2ob3o2bob3o3bo2b2obob2o
2b2o4bo4bo2b4o$o2b2o3b2obob4obo2b3obob3o2b2obobo4b4o2bobobo5b3o2bo$b4o
3b2o2b2o3b2o3b2ob3ob2ob2o7bo2b2o2bo4b2obo2b5o$3obo4bob3ob3o2bo6bo4bobo
3b2ob2o2b2o2bob2o2bo2b4ob2o$ob2obo5b2o2b3ob4o3bo4b7o5bob3o2bob4ob3ob4o
$2bo2bobo2bo2b7obo3b2o5bo2bo3bo2bob3o2bobo2b3o2bob3o$3obobo2b2o2b3o5bo
2bob7ob2o2b2obob6obo4bobobob2obo$b8ob3o2bo3bobo3b3o2bo10b2ob5ob2o3b3ob
obob2o$4bobo2bo5bo2bobob3ob2ob2obo2bob2o2b7obo2bo4bo3b2obo$3bobob2ob2o
2bobo2b2o6bobobo2b3obob4ob3obobo2bo3bo3bobo$2bo3b6obo2b3o4bob3o3bob2o
5b5ob2o3b2obo3b2ob3o$3bo4bo3b3obo4bob3ob2o2b2obo4bob2o6b3o3bo5b2o$ob4o
b3o2b2o2bobob4obob2o5b2ob5o2b3obob6o4b4o$2obo2b5o2bo3bob2o2b5obob4ob2o
3b2o5b2o2b3o3b2o2b3o$o2b5o4b3o2bo2b2obobob5o3bo3b2o5b3ob2o6b4ob2o$2o3b
o3bob2obob2obo3b5obo2b2o2bo3b3o2b2o2bo3b3obob2o2bo$2bo2b3obobo4bobo3bo
bo2b2obob2o5bo3b3ob2o5bo3bo2bobo$o4bob3ob2o5bo2b2o2b3o2bo4bobobobobo2b
o5bobo2b2obo3bo$2b4ob3obob2o3b2ob5ob2o2b6o3b4obob10obo4b2o$bobob2obo2b
o2b2o2b2obo2b2obo2b3ob2o2b4ob2obob3o3bob2o3b3o$o4b2ob3obob2o4b6o2bobo
3b3ob2obo2b2o3b2ob2obob3ob4o$b5o2bobob2obobobo2bo5b2obo2bo3bo2bobobobo
b2o5bo4b2o$2bob2o3b2o2b2ob7ob3ob3o2b5o2b2obobob3o2bo4b4obobo$bobo4b2o
2b2obo2b2obo3bo2bobob2o2b4o3bob2o2b5obob2obo3bo$bobo4b3o2b6o2bobob3obo
bo3bo3bo3b2o2b3o3b2ob8o$o6bo3bo3b2o2bobobob2o2bo2bobo3b2ob2ob3o5bo2bob
3o3b2o$bo2bobob3obobobo3bo2bob2ob2o2b3obo2b2ob2obob3o6bo3b2o$ob4obob2o
3b10o3bo2b2ob2o2bo2b3ob5ob2obobobobobo$7bob2o3b2o2b3ob2o2bob2obo4b2o2b
2o2bobob2obobo2b2o4b3o$2bo3bo2b2ob2o2b3ob4o4bo2b2o3bo2b3obo3bobobo3b4o
bo3bo$6ob2obo7bob3obo4b3obobo5bob2obo2b2o2b4ob2o4bo$ob2obo3bo4b3obo2b
4o8bo2bo3bo3bobo2bo2b4ob3o3b2o$3b2ob2o4b2obo2bobob3o3bobobob6o3b3o4bob
o2b2o5bo$o3b3obob5o2b2o4bob2o2bob4o3bo4b3o2b6ob4o2bobo$3b2ob2obob2o3b
3ob3o2bob3o2b4o3bo4b6o6bo2b6o$o2b5ob3obo3b2obo2bo2bob3o7b2ob2o2bob6ob
4obobo2bo$b2o3b4o2b2ob3o2b5o2b3o2bo2bobo5bob4o2bo4bobob2o2bo$b3o2bobob
ob3obobob6obo2bo3b3o2b3ob2o2b6o3bo7bo$o4b6o2bo3b4ob3o7bobo3bo3b3o2b2ob
o3bob2ob3o2bo$bo6b6o2b5o4bob2o4bobob2obobo5b2ob10o2bo$4ob4obo2bo8b4ob
2obob4o2b4o5b2o3bo6bob4o$bo3b2obob3ob2obo2b3o3bo4bo4b4o2b5o3bo3bo2b3o
2b2o$bobob3obob5ob3obob4ob2o2bobo2b2o2bo2b2o6b2o4bobobobo$2o2bo2b2o2bo
bo3b3o5b3obo2b2o2b3o3bob5o3bo2b2o2bobob2o$ob3o2bob2obo2b2obobobobo2b3o
4bo2bob6obobob2o7bo$o3bo2b2obo5b2o2bo2bo2bobo2b3ob2o2bo2b3ob3ob3o2b5ob
4o$bobo2b2obob2obo2b3obobo3bo2bob6ob4o3b4o3b2o4b6o$2obobo5b2o2b2o2bo5b
3o2b2obobo4bob2ob2ob3o3b2obo6bo$bo5bo3b2obo2bo2b2obo2bo4b2obo5bobo2b3o
b5o4b2obob2o$2o2bob6o3bobobo2bo2bob2obob2o2b2o2bo2b4ob2ob2ob11o$2o2b3o
b5ob3o2bobo2bobo2b4obobob6obo3bo3bo3bo2b3obo$2b2o3bo2bobo3b2obobob2obo
bo2b2ob4o3b2obob3ob2o3bob2ob3obo$3obobob2obo2b5o4b2o2b4o2bob3ob3obo3b
4obo4b3o2bo$o2bob2o3b2obobo10b2obo2b2o3bo3bob2obo4bobo3bob6o$2obo5bo2b
obobo2bo6bo2b2o2b2o7bob2ob2ob5o4b3o$b2ob2o7bob2o2b3obo2b2ob2o5b3o2b3o
2bob3o4bob2o2b4o$2ob7o2b4obob2obo3b2obo2bo3bob2obo2bob3obo2b7o2b3o!

Unfortunately the wickstretchers, puffers, and breeders are still nature, but less explosive.

A failed breeder (actually a few puffers) one transition later from Refterneon:

Code: Select all

x = 8, y = 4, rule = B2ci3aceiy4e/S1e2-k3aeiy4eqtz6in
5bo$2o2b3o$5bo!

I'll call it Refteralmostbreederneon.

AforAmpere · Post by **AforAmpere** » April 7th, 2025, 10:36 am

This grows in a 4xn rectangle in a sort of chaotic log-growth style for a pretty long time before deciding to randomly explode at gen 195506237:

Code: Select all

x = 1, y = 4, rule = B2eik3eijn4n5iy6k/S1e2ek3jr4a5ijq6a
o$o$o$o!

confocaloid · Post by **confocaloid** » April 7th, 2025, 11:22 am

AforAmpere wrote: April 7th, 2025, 10:36 am This grows in a 4xn rectangle in a sort of chaotic log-growth style for a pretty long time before deciding to randomly explode at gen 195506237:
Code: Select all
x = 1, y = 4, rule = B2eik3eijn4n5iy6k/S1e2ek3jr4a5ijq6a
o$o$o$o!

Here is a copy of a later generation, before "explosion":

Code: Select all

#C [[ SHOWGENSTATS ]]
#CXRLE Pos=-113,0 Gen=195505000
x = 227, y = 4, rule = B2eik3eijn4n5iy6k/S1e2ek3jr4a5ijq6a
110bobobobo$obobobobobobobobobo2bobobobobobo2bobobobobo5bobobo3bobo4bo
bobobo3bo5bobo2bobobo2bobo5bobo4bobob2o3b2obobo4bobo5bobo2bobobo2bobo
5bo3bobobobo4bobo3bobobo5bobobobobo2bobobobobobo2bobobobobobobobobobo$
obobobobobobobobobo2bobobobobobo2bobobobobo5bobobo3bobo4bobobobo3bo5bo
bo2bobobo2bobo5bobo4bobob2o3b2obobo4bobo5bobo2bobobo2bobo5bo3bobobobo
4bobo3bobobo5bobobobobo2bobobobobobo2bobobobobobobobobobo$110bobobobo!

b-engine · Post by **b-engine** » April 7th, 2025, 6:23 pm

This failed replicator become four blocks and two cis-mirrored bookends. Both blocks and bookends induce weird catalysis before stabilization:

Code: Select all

x = 3, y = 2, rule = B3-ckqy4eq5eikry6c/S236c
bo$3o!

However this rule is explosive all because of those failed replicators reincarnating themselves.

islptng · Post by **islptng** » April 8th, 2025, 12:17 am

This rule, featuring 6 natural spaceships including a SMOSMOS, labelled "Packet":

Code: Select all

x = 83, y = 20, rule = B3-cjn4-aktz5aceky6-ek/S2ace3-akq4inrtw5ejny6-en7c
3bo12b3o17b2o11bo14b2o9b2o4bo$b3o12bo3bo14b3o10b3o13b2o9b2o3b3o$b3o12b
2ob2o15b2o10bo15bo2b2o3b2o2bo3b3o$3o16b2o12bo32b3o3b3o$32b3o31bo7bo$
32b3o11$2o46bo16bo15bo$obo14b2o14b2o13bobo13bobo13b3o$2o14bobo13bo15b
2o14b2o15bo$o16b2o14b2o13bobo14b2o14bo!

Code: Select all

#R B3-cjn4-aktz5aceky6-ek/S2ace3-akq4inrtw5ejny6-en7c
! [[ RANDOMIZE ]]

BTW The SMOSMOS's rulespace is abundant with oblique ships!

Banananananan · Post by **Banananananan** » April 8th, 2025, 1:56 am

Odd SMOO in a speciation variant

Code: Select all

x = 49, y = 63, rule = B2cei3-eijr4eirtwz5ceiqy6-en7c/S1c2-c3-aiqy4eikntw5enqr6-a
39$21bo$20bo$21bo11$21bo$20bo$21bo!

dl-rs · Post by **dl-rs** » April 8th, 2025, 9:46 am

PiSpaceships wrote: April 6th, 2025, 5:57 am Crossposting from RARTBT:

PiSpaceships wrote: April 6th, 2025, 5:55 am

LittleLWSS wrote: April 6th, 2025, 4:33 am B2ci3-jnqr4e/S1e2-k3aeiy4etz5ei6i7e(Refterneovarius) -> B2ci3aceiy4e/S1e2-k3aeiy4eqtz6i(Refterneon)

Code: Select all

x = 65, y = 66, rule = B2ci3aceiy4e/S1e2-k3aeiy4eqtz6i
2bo2b3ob2obo5bo2b4o3bo2b2ob2o3b2o2bobo3bo2b3o4b3o2bo$bo4bobo2bo4b2ob4o
4b2o2b2o2bobobob2obobob2o2b3o2b2ob2ob2o$6o3b2obo3bo3bo5bo4bob3obob2obo
b2obo3bo2b2o2bob2o2bo$2o3b2o2bo9bob3obo2bo2bobo2bob4o5bo3b4o3b4ob2o$3b
obo3bo9bob3o3b2obob2o3bobob2ob2ob2o2bobobob2o2bo$bobo3bo2b7ob4o2bob3o
2bo4b2o2bobob3o4bobo4b3o$b3o3bobob2ob3o3b5obob2o2bo4b3o3bo3b2obo3bo2b
4o3bo$b5o3bob3o2bobo12b3obo3b2o3bob2o2bob4obo4bobo$obo4b5o2b2o2b2o2bo
2b2ob4ob2o2b3o2b5o4bob3o2b2ob2obo$6ob2obob4o3b2ob3o2bob3o3bo2b2obob2o
2b2o4bo4bo2b4o$o2b2o3b2obob4obo2b3obob3o2b2obobo4b4o2bobobo5b3o2bo$b4o
3b2o2b2o3b2o3b2ob3ob2ob2o7bo2b2o2bo4b2obo2b5o$3obo4bob3ob3o2bo6bo4bobo
3b2ob2o2b2o2bob2o2bo2b4ob2o$ob2obo5b2o2b3ob4o3bo4b7o5bob3o2bob4ob3ob4o
$2bo2bobo2bo2b7obo3b2o5bo2bo3bo2bob3o2bobo2b3o2bob3o$3obobo2b2o2b3o5bo
2bob7ob2o2b2obob6obo4bobobob2obo$b8ob3o2bo3bobo3b3o2bo10b2ob5ob2o3b3ob
obob2o$4bobo2bo5bo2bobob3ob2ob2obo2bob2o2b7obo2bo4bo3b2obo$3bobob2ob2o
2bobo2b2o6bobobo2b3obob4ob3obobo2bo3bo3bobo$2bo3b6obo2b3o4bob3o3bob2o
5b5ob2o3b2obo3b2ob3o$3bo4bo3b3obo4bob3ob2o2b2obo4bob2o6b3o3bo5b2o$ob4o
b3o2b2o2bobob4obob2o5b2ob5o2b3obob6o4b4o$2obo2b5o2bo3bob2o2b5obob4ob2o
3b2o5b2o2b3o3b2o2b3o$o2b5o4b3o2bo2b2obobob5o3bo3b2o5b3ob2o6b4ob2o$2o3b
o3bob2obob2obo3b5obo2b2o2bo3b3o2b2o2bo3b3obob2o2bo$2bo2b3obobo4bobo3bo
bo2b2obob2o5bo3b3ob2o5bo3bo2bobo$o4bob3ob2o5bo2b2o2b3o2bo4bobobobobo2b
o5bobo2b2obo3bo$2b4ob3obob2o3b2ob5ob2o2b6o3b4obob10obo4b2o$bobob2obo2b
o2b2o2b2obo2b2obo2b3ob2o2b4ob2obob3o3bob2o3b3o$o4b2ob3obob2o4b6o2bobo
3b3ob2obo2b2o3b2ob2obob3ob4o$b5o2bobob2obobobo2bo5b2obo2bo3bo2bobobobo
b2o5bo4b2o$2bob2o3b2o2b2ob7ob3ob3o2b5o2b2obobob3o2bo4b4obobo$bobo4b2o
2b2obo2b2obo3bo2bobob2o2b4o3bob2o2b5obob2obo3bo$bobo4b3o2b6o2bobob3obo
bo3bo3bo3b2o2b3o3b2ob8o$o6bo3bo3b2o2bobobob2o2bo2bobo3b2ob2ob3o5bo2bob
3o3b2o$bo2bobob3obobobo3bo2bob2ob2o2b3obo2b2ob2obob3o6bo3b2o$ob4obob2o
3b10o3bo2b2ob2o2bo2b3ob5ob2obobobobobo$7bob2o3b2o2b3ob2o2bob2obo4b2o2b
2o2bobob2obobo2b2o4b3o$2bo3bo2b2ob2o2b3ob4o4bo2b2o3bo2b3obo3bobobo3b4o
bo3bo$6ob2obo7bob3obo4b3obobo5bob2obo2b2o2b4ob2o4bo$ob2obo3bo4b3obo2b
4o8bo2bo3bo3bobo2bo2b4ob3o3b2o$3b2ob2o4b2obo2bobob3o3bobobob6o3b3o4bob
o2b2o5bo$o3b3obob5o2b2o4bob2o2bob4o3bo4b3o2b6ob4o2bobo$3b2ob2obob2o3b
3ob3o2bob3o2b4o3bo4b6o6bo2b6o$o2b5ob3obo3b2obo2bo2bob3o7b2ob2o2bob6ob
4obobo2bo$b2o3b4o2b2ob3o2b5o2b3o2bo2bobo5bob4o2bo4bobob2o2bo$b3o2bobob
ob3obobob6obo2bo3b3o2b3ob2o2b6o3bo7bo$o4b6o2bo3b4ob3o7bobo3bo3b3o2b2ob
o3bob2ob3o2bo$bo6b6o2b5o4bob2o4bobob2obobo5b2ob10o2bo$4ob4obo2bo8b4ob
2obob4o2b4o5b2o3bo6bob4o$bo3b2obob3ob2obo2b3o3bo4bo4b4o2b5o3bo3bo2b3o
2b2o$bobob3obob5ob3obob4ob2o2bobo2b2o2bo2b2o6b2o4bobobobo$2o2bo2b2o2bo
bo3b3o5b3obo2b2o2b3o3bob5o3bo2b2o2bobob2o$ob3o2bob2obo2b2obobobobo2b3o
4bo2bob6obobob2o7bo$o3bo2b2obo5b2o2bo2bo2bobo2b3ob2o2bo2b3ob3ob3o2b5ob
4o$bobo2b2obob2obo2b3obobo3bo2bob6ob4o3b4o3b2o4b6o$2obobo5b2o2b2o2bo5b
3o2b2obobo4bob2ob2ob3o3b2obo6bo$bo5bo3b2obo2bo2b2obo2bo4b2obo5bobo2b3o
b5o4b2obob2o$2o2bob6o3bobobo2bo2bob2obob2o2b2o2bo2b4ob2ob2ob11o$2o2b3o
b5ob3o2bobo2bobo2b4obobob6obo3bo3bo3bo2b3obo$2b2o3bo2bobo3b2obobob2obo
bo2b2ob4o3b2obob3ob2o3bob2ob3obo$3obobob2obo2b5o4b2o2b4o2bob3ob3obo3b
4obo4b3o2bo$o2bob2o3b2obobo10b2obo2b2o3bo3bob2obo4bobo3bob6o$2obo5bo2b
obobo2bo6bo2b2o2b2o7bob2ob2ob5o4b3o$b2ob2o7bob2o2b3obo2b2ob2o5b3o2b3o
2bob3o4bob2o2b4o$2ob7o2b4obob2obo3b2obo2bo3bob2obo2bob3obo2b7o2b3o!

Unfortunately the wickstretchers, puffers, and breeders are still nature, but less explosive.

A failed breeder (actually a few puffers) one transition later from Refterneon:

Code: Select all

x = 8, y = 4, rule = B2ci3aceiy4e/S1e2-k3aeiy4eqtz6in
5bo$2o2b3o$5bo!

I'll call it Refteralmostbreederneon.

This rule is actually very interesting. Natural quadratic growths appear often... so it should be explosive.

Code: Select all

x = 11, y = 3, rule = B2ci3aceiy4e/S1e2-k3aeiy4eqtz6i
bo$3o7bo$bo8bo!

WhiteHawk · Post by **WhiteHawk** » April 9th, 2025, 8:23 am

quadratic growth. Is the underlying block puffer corderizable?

Code: Select all

x = 122, y = 128, rule = B34qz8/S236i8
7bo$6bobo$5b2ob2o$18bo9b2o$18bo9b2o$18bo9bo2bo$10b2ob2o10b2ob2o2bo$7b
obo5bo7b2ob2o2b2obo$6b6o11b2obo6bo$6b4ob2o14bo4bo$3ob2ob2o3bobo9bobob
o$6bo6b2o11bo2bo$6bobo3b3o12b3o$11b3o5b3o6b2o$11b3o$30bo$24b2o3bobo11b
2o$24b2o4b2o11b2o$5b2ob2o$6bobo$7bo30b2o$38b2o3$30b3o3$54b2o$54b2o3$49b
2o$49b2o3$41b3o3$65b2o$65b2o3$60b2o$60b2o3$52b3o3$76b2o$76b2o3$71b2o$
71b2o$55b3o2$64b2o$65bo$47b2o7bo8b2o$47b2o4bo5bo5b2o20b2o$46bo6bo5bo6b
o20b2o$47b2o15b2o$47b2o15b2o$52bob2ob2obo21b2o$54b2ob2o23b2o$53b3ob3o
6b3o$53b3ob3o$52bobo3bobo$53bo5bo$59b2o$59b2o37b2o$58bo2bo36b2o$59b2o
$53bo$50bobob2o37b2o$48bo3bo40b2o$48bo$48bo4bo$52bobo$51bo$52b2o$109b
2o$109b2o3$104b2o$104b2o6$120b2o$120b2o3$115b2o$115b2o9$104b3o$104bo2b
o$103bo3bo$108bo$101b2o3b2o$99bo5bo$99bo4bo$99bo5bo$101b2o3b2o$108bo$
103bo3bo$104bo2bo$104b3o7$102b2o$102b2o!

confocaloid · Post by **confocaloid** » April 9th, 2025, 8:43 am

Potentially useful glider-emitting interaction between two puffer engines

Code: Select all

x = 75, y = 60, rule = B34qz8/S236i8
17bo$16b3o$11b2ob6o$12bob2o3b2o$20b2o$14b2o3b2o$15bo3bo$8bo$7b3o$6bobo
bo$5b2o4bo2bo$8bo5bo$14bo$8b2o12b3o$4b2o8bo$5b2o7bo$4bo9bo4$15bo3bo$2o
12b2o3b2o$13b2o5b2o$14b2o3b2o$15b5o$16b3o$17bo7$67bo$66b3o$61b2ob6o$
62bob2o3b2o$70b2o$64b2o3b2o$65bo3bo$58bo$57b3o$56bobobo$55b2o4bo2bo$
58bo5bo$64bo$58b2o12b3o$54b2o8bo$55b2o7bo$54bo9bo4$65bo3bo$50b2o12b2o
3b2o$63b2o5b2o$64b2o3b2o$65b5o$66b3o$67bo!

WhiteHawk wrote: April 9th, 2025, 8:23 am quadratic growth. Is the underlying block puffer corderizable?
Code: Select all
x = 122, y = 128, rule = B34qz8/S236i8

WhiteHawk · Post by **WhiteHawk** » April 9th, 2025, 8:51 am

confocaloid wrote: April 9th, 2025, 8:43 am Potentially useful glider-emitting interaction between two puffer engines
Code: Select all
x = 75, y = 60, rule = B34qz8/S236i8
17bo$16b3o$11b2ob6o$12bob2o3b2o$20b2o$14b2o3b2o$15bo3bo$8bo$7b3o$6bobo
bo$5b2o4bo2bo$8bo5bo$14bo$8b2o12b3o$4b2o8bo$5b2o7bo$4bo9bo4$15bo3bo$2o
12b2o3b2o$13b2o5b2o$14b2o3b2o$15b5o$16b3o$17bo7$67bo$66b3o$61b2ob6o$
62bob2o3b2o$70b2o$64b2o3b2o$65bo3bo$58bo$57b3o$56bobobo$55b2o4bo2bo$
58bo5bo$64bo$58b2o12b3o$54b2o8bo$55b2o7bo$54bo9bo4$65bo3bo$50b2o12b2o
3b2o$63b2o5b2o$64b2o3b2o$65b5o$66b3o$67bo!
WhiteHawk wrote: April 9th, 2025, 8:23 am quadratic growth. Is the underlying block puffer corderizable?
Code: Select all
x = 122, y = 128, rule = B34qz8/S236i8

Wow! B+G=180G

Code: Select all

x = 183, y = 151, rule = B34qz8/S236i8
125bo$124b3o$119b2ob6o$120bob2o3b2o$128b2o$122b2o3b2o$123bo3bo$116bo$
115b3o$114bobobo$113b2o4bo2bo$116bo5bo$122bo$116b2o12b3o$112b2o8bo$113b
2o7bo$112bo9bo4$123bo3bo$108b2o12b2o3b2o$121b2o5b2o$122b2o3b2o$123b5o
$124b3o$125bo7$175bo$174b3o$169b2ob6o$170bob2o3b2o$178b2o$172b2o3b2o$
173bo3bo$166bo$165b3o$164bobobo$163b2o4bo2bo$166bo5bo$172bo$166b2o12b
3o$162b2o8bo$163b2o7bo$162bo9bo4$173bo3bo$158b2o12b2o3b2o$171b2o5b2o$
172b2o3b2o$173b5o$174b3o$175bo32$17bo$16b3o$11b2ob6o$12bob2o3b2o$20b2o
$14b2o3b2o$15bo3bo$8bo$7b3o$6bobobo$5b2o4bo2bo$8bo5bo$14bo$8b2o12b3o$
4b2o8bo$5b2o7bo$4bo9bo4$15bo3bo$2o12b2o3b2o$13b2o5b2o$14b2o3b2o$15b5o
$16b3o$17bo7$67bo$66b3o$61b2ob6o$62bob2o3b2o$70b2o$64b2o3b2o$65bo3bo$
58bo$57b3o$56bobobo$55b2o4bo2bo$58bo5bo$64bo$58b2o12b3o$54b2o8bo$55b2o
7bo$54bo9bo4$65bo3bo$50b2o12b2o3b2o$63b2o5b2o$64b2o3b2o$65b5o$66b3o$67b
o!

EDIT:

islptng wrote: April 8th, 2025, 12:17 am This rule, featuring 6 natural spaceships including a SMOSMOS, labelled "Packet":
Code: Select all
x = 83, y = 20, rule = B3-cjn4-aktz5aceky6-ek/S2ace3-akq4inrtw5ejny6-en7c
3bo12b3o17b2o11bo14b2o9b2o4bo$b3o12bo3bo14b3o10b3o13b2o9b2o3b3o$b3o12b
2ob2o15b2o10bo15bo2b2o3b2o2bo3b3o$3o16b2o12bo32b3o3b3o$32b3o31bo7bo$
32b3o11$2o46bo16bo15bo$obo14b2o14b2o13bobo13bobo13b3o$2o14bobo13bo15b
2o14b2o15bo$o16b2o14b2o13bobo14b2o14bo!
Code: Select all
#R B3-cjn4-aktz5aceky6-ek/S2ace3-akq4inrtw5ejny6-en7c
! [[ RANDOMIZE ]]
BTW The SMOSMOS's rulespace is abundant with oblique ships!

Some discoveries. There aren't many objects other than ships in this rule.

Code: Select all

x = 154, y = 60, rule = B3-cjn4-aktz5aceky6-ek/S2ace3-akq4inrtw5ejny6-en7c
95bo$48bobo6bo9bobo23bo$48b3o6b3o7b3o12b3o7bob2o$47b3o6b3o7b3o13b2o9b
2obo$47bobo8bo9bo17b2o7bo$85b3o5bo8$152b2o$153bo$4o147b3o$b3o$2bo8$80b
obo2$78bo$78b3o$79bo12$55bo$55b2obo$55bo14$96b3o$96bo$96b2o!

Failed gun?

Code: Select all

x = 7, y = 6, rule = B3-cjn4-aktz5aceky6-ek/S2ace3-akq4inrtw5ejny6-en7c
3bo2$b2ob2o$2o3b2o$7o$bo3bo!

Yoel · Post by **Yoel** » April 10th, 2025, 3:22 am

A 90c/180 orthogonal spaceship in a non-isotropic version of Day & Night that preserves rotational, but not mirror symmetry, becomes a puffer when flipped.

Code: Select all

x = 200, y = 200, rule = DN-x4z:T200,200
54$83bo43bo$83bo2b2o35b2obobo$82bo5bo27bo6b6o$81bo2b7obobob7o5bo4b6o3b
ob5obo$79b2ob12ob16o3b7o2b9o$79b54o$79b3o2b49o$79b3o4b12o2b3obob10o2b
14o$89b2o3bob3o3bo3b8o3bob9o2bo$88bo3bo2bo11b2ob2o6b8obobo$107bo10b2ob
2o4bo$122bo73$122bo$107bo10b2ob2o4bo$88bo3bo2bo11b2ob2o6b8obobo$89b2o
3bob3o3bo3b8o3bob9o2bo$79b3o4b12o2b3obob10o2b14o$79b3o2b49o$79b54o$79b
2ob12ob16o3b7o2b9o$81bo2b7obobob7o5bo4b6o3bob5obo$82bo5bo27bo6b6o$83bo
2b2o35b2obobo$83bo43bo!

Code: Select all

x = 200, y = 200, rule = DN-x4z:T200,200
200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$
200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$
200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$
200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$83ob43ob
72o$83ob2o2b35o2bobob71o$82ob5ob27ob6o6b71o$81ob2o7bobobo7b5ob4o6b3obo
5bob69o$79o2bo12bo16b3o7b2o9b68o$79o54b67o$79o3b2o49b67o$79o3b4o12b2o
3bobo10b2o14b68o$89o2b3obo3b3ob3o8b3obo9b2ob69o$88ob3ob2ob11o2bo2b6o8b
obob70o$107ob10o2bo2b4ob72o$122ob77o$200o$200o$200o$200o$200o$200o$
200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$
200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$
200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$
200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$
200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$122ob77o$107ob10o2bo
2b4ob72o$88ob3ob2ob11o2bo2b6o8bobob70o$89o2b3obo3b3ob3o8b3obo9b2ob69o$
79o3b4o12b2o3bobo10b2o14b68o$79o3b2o49b67o$79o54b67o$79o2bo12bo16b3o7b
2o9b68o$81ob2o7bobobo7b5ob4o6b3obo5bob69o$82ob5ob27ob6o6b71o$83ob2o2b
35o2bobob71o$83ob43ob72o$200o$200o$200o$200o$200o$200o$200o$200o$200o$
200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$
200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$
200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o$200o!

This rule differs from Day & Nights by the following modification of the 4z transition:

Code: Select all

0 0 1       ? ? ?
1 0 1  ==>  ? 1 ?
1 0 0       ? ? ?

1 1 0       ? ? ?
0 0 0  ==>  ? 1 ?
0 1 1       ? ? ?

1 0 0       ? ? ?
1 0 1  ==>  ? 0 ?
0 0 1       ? ? ?

0 1 1       ? ? ?
0 0 0  ==>  ? 0 ?
1 1 0       ? ? ?

0 0 1       ? ? ?
1 1 1  ==>  ? 0 ?
1 1 0       ? ? ?

1 1 0       ? ? ?
0 1 0  ==>  ? 0 ?
0 1 1       ? ? ?

1 0 0       ? ? ?
1 1 1  ==>  ? 1 ?
0 0 1       ? ? ?

0 1 1       ? ? ?
0 1 0  ==>  ? 1 ?
1 1 0       ? ? ?

Here is the ruletable:

Code: Select all

@RULE DN-x4z
@COLORS
1 255 255 255
@TABLE
n_states:2
neighborhood:Moore
symmetries:none
var A={0,1}
var B=A
var C=A
var D=A
var E=A
var F=A
var G=A
var H=A
# Birth conditions
0,1,0,0,0,0,0,1,1,1
0,1,1,1,0,0,0,0,0,1
0,0,0,1,1,1,0,0,0,1
0,0,0,0,0,1,1,1,0,1
0,0,0,0,1,0,1,0,1,1
0,0,1,0,0,0,1,0,1,1
0,0,1,0,1,0,0,0,1,1
0,0,1,0,1,0,1,0,0,1
0,1,0,0,0,1,0,1,0,1
0,1,0,1,0,0,0,1,0,1
0,1,0,1,0,1,0,0,0,1
0,0,0,1,0,1,0,1,0,1
0,0,0,0,0,0,1,1,1,1
0,1,1,0,0,0,0,0,1,1
0,0,1,1,1,0,0,0,0,1
0,0,0,0,1,1,1,0,0,1
0,1,0,1,1,0,0,0,0,1
0,0,0,1,0,1,1,0,0,1
0,0,0,0,0,1,0,1,1,1
0,1,1,0,0,0,0,1,0,1
0,1,0,0,0,0,1,1,0,1
0,1,0,1,0,0,0,0,1,1
0,0,1,1,0,1,0,0,0,1
0,0,0,0,1,1,0,1,0,1
0,1,0,0,1,0,0,1,0,1
0,1,0,1,0,0,1,0,0,1
0,0,0,1,0,1,0,0,1,1
0,0,1,0,0,1,0,1,0,1
0,1,1,0,1,0,0,0,0,1
0,0,0,1,1,0,1,0,0,1
0,0,0,0,0,1,1,0,1,1
0,0,1,0,0,0,0,1,1,1
0,1,0,0,0,0,1,0,1,1
0,0,1,1,0,0,0,0,1,1
0,0,1,0,1,1,0,0,0,1
0,0,0,0,1,0,1,1,0,1
0,1,1,0,0,0,1,0,0,1
0,0,0,1,1,0,0,0,1,1
0,0,1,0,0,1,1,0,0,1
0,0,0,0,1,0,0,1,1,1
0,1,0,0,1,0,0,0,1,1
0,0,1,1,0,0,1,0,0,1
0,0,0,0,1,1,0,0,1,1
0,0,1,0,0,0,1,1,0,1
0,1,1,0,0,1,0,0,0,1
0,0,0,1,1,0,0,1,0,1
0,1,0,0,0,1,1,0,0,1
0,0,0,1,0,0,0,1,1,1
0,1,0,0,0,1,0,0,1,1
0,0,1,1,0,0,0,1,0,1
0,1,0,0,1,1,0,0,0,1
0,0,0,1,0,0,1,1,0,1
0,1,0,0,1,0,1,0,0,1
0,0,0,1,0,0,1,0,1,1
0,0,1,0,0,1,0,0,1,1
0,0,1,0,1,0,0,1,0,1

# Adding non-reflective B4z

0,1,0,0,1,1,0,0,1,1
0,0,1,1,0,0,1,1,0,1

0,1,1,1,1,1,1,0,0,1
0,0,0,1,1,1,1,1,1,1
0,1,1,0,0,1,1,1,1,1
0,1,1,1,1,0,0,1,1,1
0,1,0,0,1,1,1,1,1,1
0,1,1,1,0,0,1,1,1,1
0,1,1,1,1,1,0,0,1,1
0,0,1,1,1,1,1,1,0,1
0,1,0,1,1,1,1,1,0,1
0,1,0,1,0,1,1,1,1,1
0,1,1,1,0,1,0,1,1,1
0,1,1,1,1,1,0,1,0,1
0,0,1,0,1,1,1,1,1,1
0,1,1,0,1,0,1,1,1,1
0,1,1,1,1,0,1,0,1,1
0,0,1,1,1,1,1,0,1,1
0,0,1,1,1,0,1,1,1,1
0,1,1,0,1,1,1,0,1,1
0,1,1,1,1,0,1,1,0,1
0,1,0,1,1,1,1,0,1,1
0,0,1,1,0,1,1,1,1,1
0,1,1,0,1,1,0,1,1,1
0,1,0,1,1,0,1,1,1,1
0,1,1,1,0,1,1,0,1,1
0,0,1,1,1,1,0,1,1,1
0,1,1,0,1,1,1,1,0,1
0,1,0,1,1,1,0,1,1,1
0,1,1,1,0,1,1,1,0,1
0,1,0,1,1,1,1,1,1,1
0,1,1,1,0,1,1,1,1,1
0,1,1,1,1,1,0,1,1,1
0,1,1,1,1,1,1,1,0,1
0,0,1,1,1,1,1,1,1,1
0,1,1,0,1,1,1,1,1,1
0,1,1,1,1,0,1,1,1,1
0,1,1,1,1,1,1,0,1,1
0,1,1,1,1,1,1,1,1,1
# Survival conditions
1,1,0,0,0,0,0,1,1,1
1,1,1,1,0,0,0,0,0,1
1,0,0,1,1,1,0,0,0,1
1,0,0,0,0,1,1,1,0,1
1,0,0,0,1,0,1,0,1,1
1,0,1,0,0,0,1,0,1,1
1,0,1,0,1,0,0,0,1,1
1,0,1,0,1,0,1,0,0,1
1,1,0,0,0,1,0,1,0,1
1,1,0,1,0,0,0,1,0,1
1,1,0,1,0,1,0,0,0,1
1,0,0,1,0,1,0,1,0,1
1,0,0,0,0,0,1,1,1,1
1,1,1,0,0,0,0,0,1,1
1,0,1,1,1,0,0,0,0,1
1,0,0,0,1,1,1,0,0,1
1,1,0,1,1,0,0,0,0,1
1,0,0,1,0,1,1,0,0,1
1,0,0,0,0,1,0,1,1,1
1,1,1,0,0,0,0,1,0,1
1,1,0,0,0,0,1,1,0,1
1,1,0,1,0,0,0,0,1,1
1,0,1,1,0,1,0,0,0,1
1,0,0,0,1,1,0,1,0,1
1,1,0,0,1,0,0,1,0,1
1,1,0,1,0,0,1,0,0,1
1,0,0,1,0,1,0,0,1,1
1,0,1,0,0,1,0,1,0,1
1,1,1,0,1,0,0,0,0,1
1,0,0,1,1,0,1,0,0,1
1,0,0,0,0,1,1,0,1,1
1,0,1,0,0,0,0,1,1,1
1,1,0,0,0,0,1,0,1,1
1,0,1,1,0,0,0,0,1,1
1,0,1,0,1,1,0,0,0,1
1,0,0,0,1,0,1,1,0,1
1,1,1,0,0,0,1,0,0,1
1,0,0,1,1,0,0,0,1,1
1,0,1,0,0,1,1,0,0,1
1,0,0,0,1,0,0,1,1,1
1,1,0,0,1,0,0,0,1,1
1,0,1,1,0,0,1,0,0,1
1,0,0,0,1,1,0,0,1,1
1,0,1,0,0,0,1,1,0,1
1,1,1,0,0,1,0,0,0,1
1,0,0,1,1,0,0,1,0,1
1,1,0,0,0,1,1,0,0,1
1,0,0,1,0,0,0,1,1,1
1,1,0,0,0,1,0,0,1,1
1,0,1,1,0,0,0,1,0,1
1,1,0,0,1,1,0,0,0,1
1,0,0,1,0,0,1,1,0,1
1,1,0,0,1,0,1,0,0,1
1,0,0,1,0,0,1,0,1,1
1,0,1,0,0,1,0,0,1,1
1,0,1,0,1,0,0,1,0,1
1,1,1,1,1,0,0,0,0,1
1,0,0,1,1,1,1,0,0,1
1,0,0,0,0,1,1,1,1,1
1,1,1,0,0,0,0,1,1,1
1,1,0,0,0,0,1,1,1,1
1,1,1,1,0,0,0,0,1,1
1,0,1,1,1,1,0,0,0,1
1,0,0,0,1,1,1,1,0,1
1,0,1,0,1,0,1,0,1,1
1,1,0,1,0,1,0,1,0,1
1,0,1,1,0,0,0,1,1,1
1,1,1,0,1,1,0,0,0,1
1,0,0,1,1,0,1,1,0,1
1,1,0,0,0,1,1,0,1,1
1,0,1,1,0,1,0,1,0,1
1,1,0,0,1,1,0,1,0,1
1,1,0,1,0,0,1,1,0,1
1,1,0,1,0,1,0,0,1,1
1,0,0,1,0,1,0,1,1,1
1,1,1,0,0,1,0,1,0,1
1,1,0,1,1,0,0,1,0,1
1,1,0,1,0,1,1,0,0,1
1,1,1,0,1,0,0,1,0,1
1,1,0,1,1,0,1,0,0,1
1,0,0,1,0,1,1,0,1,1
1,0,1,0,0,1,0,1,1,1
1,1,0,1,0,0,1,0,1,1
1,0,1,1,0,1,0,0,1,1
1,0,1,0,1,1,0,1,0,1
1,1,0,0,1,0,1,1,0,1
1,0,1,1,1,0,0,0,1,1
1,0,1,0,1,1,1,0,0,1
1,0,0,0,1,0,1,1,1,1
1,1,1,0,0,0,1,0,1,1
1,0,1,0,0,0,1,1,1,1
1,1,1,0,1,0,0,0,1,1
1,0,1,1,1,0,1,0,0,1
1,0,0,0,1,1,1,0,1,1
1,1,0,0,1,0,0,1,1,1
1,1,1,1,0,0,1,0,0,1
1,0,0,1,1,1,0,0,1,1
1,0,1,0,0,1,1,1,0,1
1,1,1,1,0,1,0,0,0,1
1,0,0,1,1,1,0,1,0,1
1,1,0,0,0,1,1,1,0,1
1,1,0,1,0,0,0,1,1,1
1,1,0,0,0,1,0,1,1,1
1,1,1,1,0,0,0,1,0,1
1,1,0,1,1,1,0,0,0,1
1,0,0,1,0,1,1,1,0,1
1,1,0,0,1,1,1,0,0,1
1,0,0,1,0,0,1,1,1,1
1,1,1,0,0,1,0,0,1,1
1,0,1,1,1,0,0,1,0,1
1,1,0,1,1,0,0,0,1,1
1,0,1,1,0,1,1,0,0,1
1,0,0,0,1,1,0,1,1,1
1,1,1,0,0,0,1,1,0,1
1,1,1,0,1,0,1,0,0,1
1,0,0,1,1,0,1,0,1,1
1,0,1,0,0,1,1,0,1,1
1,0,1,0,1,0,0,1,1,1
1,1,0,0,1,0,1,0,1,1
1,0,1,1,0,0,1,0,1,1
1,0,1,0,1,1,0,0,1,1
1,0,1,0,1,0,1,1,0,1

# Making S4z non-reflective 

1,1,1,0,0,1,1,0,0,1
1,0,0,1,1,0,0,1,1,1

1,1,1,1,1,1,1,0,0,1
1,0,0,1,1,1,1,1,1,1
1,1,1,0,0,1,1,1,1,1
1,1,1,1,1,0,0,1,1,1
1,1,0,0,1,1,1,1,1,1
1,1,1,1,0,0,1,1,1,1
1,1,1,1,1,1,0,0,1,1
1,0,1,1,1,1,1,1,0,1
1,1,0,1,1,1,1,1,0,1
1,1,0,1,0,1,1,1,1,1
1,1,1,1,0,1,0,1,1,1
1,1,1,1,1,1,0,1,0,1
1,0,1,0,1,1,1,1,1,1
1,1,1,0,1,0,1,1,1,1
1,1,1,1,1,0,1,0,1,1
1,0,1,1,1,1,1,0,1,1
1,0,1,1,1,0,1,1,1,1
1,1,1,0,1,1,1,0,1,1
1,1,1,1,1,0,1,1,0,1
1,1,0,1,1,1,1,0,1,1
1,0,1,1,0,1,1,1,1,1
1,1,1,0,1,1,0,1,1,1
1,1,0,1,1,0,1,1,1,1
1,1,1,1,0,1,1,0,1,1
1,0,1,1,1,1,0,1,1,1
1,1,1,0,1,1,1,1,0,1
1,1,0,1,1,1,0,1,1,1
1,1,1,1,0,1,1,1,0,1
1,1,0,1,1,1,1,1,1,1
1,1,1,1,0,1,1,1,1,1
1,1,1,1,1,1,0,1,1,1
1,1,1,1,1,1,1,1,0,1
1,0,1,1,1,1,1,1,1,1
1,1,1,0,1,1,1,1,1,1
1,1,1,1,1,0,1,1,1,1
1,1,1,1,1,1,1,0,1,1
1,1,1,1,1,1,1,1,1,1
1,A,B,C,D,E,F,G,H,0

As expected, some oscillators in this rule also don't work when flipped:

Code: Select all

x = 51, y = 30, rule = DN-x4z
7$13b2o12bo11b3o$14b2o8bo2b2o11b2o$12b3o10bob2o12b2o$11b2o12bo$12b2o
27bo10$12b2o27bo$11b2o12bo$12b3o10bob2o12b2o$14b2o8bo2b2o11b2o$13b2o
12bo11b3o!

confocaloid · Post by **confocaloid** » April 10th, 2025, 3:37 am

Yoel wrote: April 10th, 2025, 3:22 am [...] the following modification of the 4z transition: [...]

The notation '4z' can be plausibly interpreted as denoting an (incompletely specified) isotropic condition of a cell.
Namely, '4z' can be plausibly read as referring to the cell condition telling that states of neighbours of a cell match those of some rotation or reflection of the following 3-by-3 neighbourhood configuration, without telling the state of the middle cell itself:

Code: Select all

1 1 0
0 ? 0
0 1 1

As far as I can tell, there is no plausible consistent way to interpret '4z' as denoting a transition.

Moreover, the code snippet you posted after the quoted sentence appears to list eight different rules, making things even more confusing than they were before.

Yoel · Post by **Yoel** » April 10th, 2025, 4:36 am

confocaloid wrote: April 10th, 2025, 3:37 am As far as I can tell, there is no plausible consistent way to interpret '4z' as denoting a transition.

Moreover, the code snippet you posted after the quoted sentence appears to list eight different rules, making things even more confusing than they were before.

Technically correct or not (by whose standards?), everyone in this forum seems to call such elements of the Hensel notation "transitions". Entire threads are dedicated to "one transition away" from Life, "two transitions away", etc.

My code snippet fully describes this modification of Day & Night. Since it's not the isotropic 4z, but a non-reflective version of it split between the birth and survival transition rules (as this rule is self-complementary), I have fully described the behavior of this non-isotropic rule modification.

ConwayLife.com

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