ConwayLife.com

iNoMed wrote: July 29th, 2022, 4:36 am I believe this 66-cell p146 Pi hassler variant eliminates S4c from the equation, not sure if it's actually endemic though:

Code: Select all

x = 24, y = 32, rule = B3/S23
2bo$2b3o$5bo7b2o$4b2o7bo$11bobo$11b2o3$16b2o$16b2o2$5b2o$2bo3bo10bo$b
2o3bo9bobo$2bob2o11b2o8$22b2o$18b2obobo$18b2obo$22bo$2b2o14b2ob2o$bobo
15bobo$bo11b2o4bobo$2o11bo6bo$14b3o$16bo!

pzq_alex wrote: July 29th, 2022, 7:36 am Notice that this is (roughly) equivalent to a set covering problem, where each object “covers” a certain set of transitions and costs a certain number of cells, and we want to minimize the cost (number of cells).

confocaloid wrote: July 29th, 2022, 5:06 am Edit:

pzq_alex wrote: July 29th, 2022, 7:36 am Notice that this is (roughly) equivalent to a set covering problem, where each object “covers” a certain set of transitions and costs a certain number of cells, and we want to minimize the cost (number of cells).

At least before getting sufficiently close to an optimal solution where one cell may belong to two or more recognizable sub-objects at once and a single high-period evolutionary sequence may cover most transitions.

Inferno wrote: September 14th, 2022, 12:59 am 61-cell pattern endemic to B3/S23, which contains a p129 r-pentomino hassler with an unnamed p2 oscillator which disallows S4c.

Code: Select all

x = 65, y = 35, rule = B3/S23
46b2o$43b2o2bo$42bo2b2o$42b2o$46b3o$42b2obo2bo$26bo14bobobobo$24b3o15b
o3bo$23bo$23b2o$2o$bo$bobo$2b2o2$20b2o$19b2o$20bo6$44bo$44b2o$43b2o2$
61b2o$61bobo$63bo$63b2o$40b2o$41bo$38b3o$38bo!

x = 71, y = 31, rule = B3/S23
26bo$24b3o$23bo$23b2o$2o$bo$bobo$2b2o2$20b2o$19b2o$20bo6$44bo$44b2o$43b
2o2$61b2o$61bobo$63bo4bo$63bobobobo$40b2o22b2obo2bo$41bo26b3o$38b3o23b
2o$38bo25bo2b2o$65b2o2bo$68b2o!

carsoncheng wrote: September 14th, 2022, 2:15 am

Inferno wrote: September 14th, 2022, 12:59 am61-cell pattern endemic to B3/S23, which contains a p129 r-pentomino hassler with an unnamed p2 oscillator which disallows S4c.

Code: Select all

x = 65, y = 35, rule = B3/S23
46b2o$43b2o2bo$42bo2b2o$42b2o$46b3o$42b2obo2bo$26bo14bobobobo$24b3o15b
o3bo$23bo$23b2o$2o$bo$bobo$2b2o2$20b2o$19b2o$20bo6$44bo$44b2o$43b2o2$
61b2o$61bobo$63bo$63b2o$40b2o$41bo$38b3o$38bo!

3-cell reduction by welding the two oscillators, making the minpop 58:

Code: Select all

x = 71, y = 31, rule = B3/S23
26bo$24b3o$23bo$23b2o$2o$bo$bobo$2b2o2$20b2o$19b2o$20bo6$44bo$44b2o$43b
2o2$61b2o$61bobo$63bo4bo$63bobobobo$40b2o22b2obo2bo$41bo26b3o$38b3o23b
2o$38bo25bo2b2o$65b2o2bo$68b2o!

x = 68, y = 31, rule = B3/S23
26bo$24b3o$23bo$23b2o$2o$bo$bobo$2b2o2$20b2o$19b2o$20bo6$44bo$44b2o$
43b2o2$61b2o$61bobo$63bo2b2o$63bobobo$40b2o19b2o2bo$41bo18bo5bo$38b3o
20b2obobo$38bo23bob2o$62bo$61b2o!

LaundryPizza03 wrote: September 11th, 2023, 1:57 pm Cross-posting from discord a 94-cell endemic still life found by AlbertArmStain on August 23:

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x = 24, y = 12, rule = B/S012345678
8bo$4bobo5bobobo3bo$3b2obo4bo3bo6bo$4bobobobobobob2o2b2o$2b3o2b2o6b2o
2b2o2bo$6b7o2bobo2b2obo$3bob2ob3o4bo2bob2o$13obob2o2b2o$3bo2bob2obobob
o6bo$b2o3b2o2bob2obo$bo3bo$2o2bo!

yujh wrote: August 22nd, 2023, 11:02 pm

yujh wrote: May 22nd, 2022, 9:21 am 122

some slight reductions to that:

Code: Select all

x = 24, y = 12, rule = B/S012345678
8bo$4bobo5bobobo3bo$3b2obo4bo3bo6bo$4bobobobobobob2o2b2o$2b3o2b2o6b2o2b2o2bo$
6b7o2bobo2b2obo$3bob2ob3o4bo2bob2o$13obob2o2b2o$3bo2bob2obobobo6bo$b2o3b2o2bo
b2obo$bo3bo$2o2bo!

x = 14, y = 16, rule = B/S012345678
5bo$4bo$3b4o$4bobobo2bo$3obobo5bo$obo2bobo2bo2bo$2b3obo5b2o$obob3o4b2o
$ob3ob3ob3o$2b4obo2b2o$2b5ob2o$bobo5bo$obob3ob2o$8b3o$2b2o5bo$2b2o!

NimbleRogue wrote: December 23rd, 2023, 6:47 pm What is the endemic periodic pattern with the lowest score, where the score is the sum of the total cells on for every generation of it's cycle?

x = 73, y = 30, rule = B3/S23
26bo$24b3o$23bo$23b2o$2o$bo$bobo$2b2o2$20b2o$19b2o$20bo6$44bo$44b2o$
43b2o$67bo$61b2o3bobo$61bobobobobo$63bobo3bo$63bobobobob2o$40b2o22bo5b
obo$41bo23b2ob2o$38b3o25bobo$38bo27bobo$67bo!

hotdogPi wrote: August 23rd, 2025, 11:31 am In the 2024 newjslife stamp collection (https://github.com/carson-cheng/newjslife/tree/main), which contains everything that's been posted on the forum until mid-2024, all p2 oscillators work with S8. I can't quite find a simple proof that p2 oscillators in Life can't fail with S8, but given how many are in that collection, I believe it to be the case. (The converse is not true; there are some B3/S238 p2s that fail in Life.)

x = 14, y = 12, rule = B3/S23
4bo4bo$3bob2obobob2o$3bob3o2bobo$2obo6bobo$obo3b3o3b2o$2bobob3o2bo$bob
2ob4obo$bo7bobobo$2b4o6b2o$obo2b4o$2o3b2o$5bo!

vilc wrote: August 23rd, 2025, 11:54 am Here is an example of a p2 oscillator which triggers the S8 transition, found with LLS.

NooneAtAll3 wrote: August 23rd, 2025, 10:40 am what's the minpop for p2 life-endemic pattern?

rabbit wrote: August 23rd, 2025, 12:30 pm

vilc wrote: August 23rd, 2025, 11:54 am Here is an example of a p2 oscillator which triggers the S8 transition, found with LLS.

Searching for a 13x13 pattern centered around the 3x3 live box yielded 0 results with RLS, so this may be one of the smallest examples.

whatislife wrote: January 16th, 2026, 10:51 pm ...
and S7c:

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x = 13, y = 12, rule = B3/S23
7b2ob2o$6bobobo$5bobo4bo$4bob3o2b2o$3bo2bobobo$2bo5bobo$bob2ob2obo$obo
bo2b2o$b2ob2obo$3bobo$3bo4bo$2b2o3b2o!

They are not proven to be minimal, but those are the only rotors I could get out of RLS at 12x12 and 13x13 respectively.

x = 12, y = 13, rule = B3/S23
7bo$6bobo$5bo2bo2bo$4bo4b3o$3bob2o$2bob3ob2o$bo2b3o2bo$o7bob2o$b2ob2o
2bob2o$3b2obo$b2o2bo$bo2bo$2b2o!

x = 12, y = 13, rule = B3/S23
6bo2b2o$4b3o2bo$3bo7bo$3bob2ob4o$4bob3o$6b4o$4bo5bo$3bo2bo$b2o3b4o$4ob
2o$3bobobo$3bo2b2o$2b2o!

WhiteHawk wrote: March 25th, 2026, 11:45 pm Unsynthesizable oscillator 1 has B8, but is massive. What is the smallest p2 oscillator that triggers B8 in life? (Pedestrian Life has a very small p2 which uses B8)

x = 11, y = 15, rule = B3/S23
4b2o$4bobob2o$b2obob2obo$o2bo$2o4b3o$4b3o2bo$2ob2ob2o2bo$o3b3o2b2o$b4o
$7bo$ob2ob2o$2ob3o$6b3o$5bo2bo$6b2o!

x = 11, y = 12, rule = B3/S23
b2o3bob2o$bobo2b2obo$3bo$bo2bob3o$b2ob3o2bo$4b4o2bo$6bo2b2o$2b2o$bob4o
$obo2bo$obo4bo$bo4b2o!

x = 12, y = 13, rule = B3/S23
2o5b2o$bo4bo2bo$bob2o$2bo2b3obo$5bobobo$2bo2b3o2bo$2b2obo$5bob2obo$5b
o2b2obo$6b2o2b2o$8bo$5bobo$5b2o!

NimbleRogue wrote: December 23rd, 2023, 6:47 pm What is the endemic periodic pattern with the lowest score, where the score is the sum of the total cells on for every generation of it's cycle?

x = 3, y = 4, rule = B3/S23
o$2o$b2o$2o!