ConwayLife.com

You haven't defined what the edge is, and your "enumeration" of cases is provably incomplete, and even if it were complete you still don't have a proof

3c/14 p6300 spaceship

x = 781, y = 123, rule = B3/S23-q4i
49b3o3b3o3b3o653b3o3b3o3b3o$49bobo3bobo3bobo653bobo3bobo3bobo$49b3o3b
3o3b3o653b3o3b3o3b3o4$54b2ob2o663b2ob2o$54b2ob2o663b2ob2o4$25bo11bo705b
o11bo$25bo4b3o4bo705bo4b3o4bo$24bobo9bobo703bobo9bobo$22bo7bobo7bo699b
o7bobo7bo ...

3c/14 p1232 puffer

x = 191, y = 20, rule = B3/S23-q4i
24b3o3b3o3b3o113b3o3b3o3b3o$24bobo3bobo3bobo113bobo3bobo3bobo$24b3o3b
3o3b3o113b3o3b3o3b3o4$29b2ob2o123b2ob2o$29b2ob2o123b2ob2o4$3o4bo4b3o161b
3o4bo4b3o$3o3b3o3b3o161b3o3b3o3b3o$bo4b3o4bo133b3o27bo4b3o4bo$149bo$148b
o$5bo3bo171bo3bo ...

Several partials completed by bespoke oscillators:

p40 ??? rotator

x = 28, y = 28, rule = B3/S23-q4i
8bo4b3o4bo$7bobo9bobo$8bo3bo3bo3bo$9b2o7b2o$10bo7bo$10b2o5b2o$bo10b5o
$obo23bo$bobo21bobo$3b2o19bobo$2b2o2bo16b2o$4bo16bo2b2o$bo2bo18bo$b2o
bo3bo3b3o8bo2bo$bo2bo5b2ob2o4bo3bob2o$4bo8b2o8bo2bo ...

p20 billiard table:
x = 21, y = 24, rule = B3/S23-a5
bo$2bo$3o4$11b2o$9bo2bo$9b2o$2b2o$2bo2bo$3b2obo2bo2b2o$6b7o2b2o$3b3o8b
2o$3bo3b6obobo$4b4o4bobo2bo$9b2o3bob2o$6bob2o3b2o3b2o$6b2o3bo4b2o2bo$
9b2ob4obob2o$10bobo2bobo$10bo2bobobo$11bobob2o$12bo!
…

Optimized(though why did I do this)
x = 18 ...

DYK 93 (pulse dividers) is outdated. Small stable pulse dividers are known for all multipliers not 5 mod 6, as well as 5 and 11.

The p10 can be supported by two copies of Elkies' p5; it hassles the same object as the oscillator in this post 2 days ago and I think there are several wicks posted here containing it, such as xp10 ...

A traffic light wire oscillator of sorts, based on the tl + half-tl reaction. Period 424 shown below:

x = 124, y = 72, rule = B3/S23
92b2o3b2o2b2o2b2o$85b2o5bo3bob4obo2bo$79b2o4bobo5bo2bo6b2o$73b2o4bobo
5bo4b2o3bob2obo2b4o$67b2o4bobo5bo4b2ob2o3b3ob2ob2obo3bo$61b2o4bobo5bo
4b2ob2o4bob3o2bo4bo3bo ...

reduction of my p152 traffic light thing:

x = 70, y = 71, rule = B3/S23
32b2o2$30bo3bo$30bo4bo$32bobobo$33bobobo$34bo4bo$35bo3bo2$30bo5b2o$28b
2obo$27bo7bo$26bobo2bo3bo$26bo2bo4bobo$27b2o6bo$35bo4$62bo$60b2o$62b2o
$57b2o2bo6b2o$22b2o33bobo7bobo$47b2ob2o15bo$20bo3bo23bobobo6b2ob2ob3o
bo ...

gun_64 in 984:

x = 41, y = 24, rule = B3/S23
31b2o$28bo2bobo$26b3o4bo$20b2o3bo3bobobobo$19bo2bobob2o3b2obobo2b2o$
20bobobo3bo3bobobo3bo$18b2obo3b3o6bo2b3o$18b3o6bobo3b2o3bo$18b2o9b2o7b
o$30bo6b3o$36bo3bo$32bo3b5o$12bo17b3o3b2o$10bo3bo3b2o12bo3b5o$14bo3b3o
15bo3bo$8b2o5bo3bo17b3o$8bo6b2o$8bo28b2obo ...

reduction to the other one by using a smaller p4 fountain
x = 68, y = 54, rule = B3/S23
36bob2o9b2obo$36b2obo2b2ob2o2bob2o$39bobobobobobo$36b3obo7bob3o$36bo2b
obo5bobo2bo$39b4o3b4o$38bo3bo3bo3bo$39b2o7b2o$29b2o$29bobo6b4o5b4o$30b
o6bob2o2b3o2b2obo$38b2ob7ob2o$12b2o$11bobo$11bobob2o$12bobobo$14bo ...

gun_496 reduction

x = 50, y = 49, rule = B3/S23
31bo$29b2o$24b2o5b2o$23bobo4bo$23bo$18bob2ob2o9bo3b2o$18b2obo11bobo2bo
$21bo12b2o3b3o$21b2o13b3o3bo$6b2o4bo3b2o18bo2bo2bo$6bo3b3o3bo20bob2ob
2o$3b2obo2bo3b2obo22bobo2bo$3b2obobo2b2o2bo21b3o3bo$5b2ob2obobo12bo10b
2ob2ob2o$5bo5b3o12b3o12bobo ...

reductions to gun_2604 and gun_2852

x = 49, y = 40, rule = B3/S23
21b2ob2o$20bobobo14bo$20bo3bo2bo9b3o$12b2o4b2obo2bobobo7bo$6b2o3bo2bo
2bobob3o2bobo7b2o$6bo4bo2bo3bo5b3ob2o$7b3obobo6b2obo9b3o$9bo2b3o3bobo
b2ob2obobobo3bo3bo6b2o$12b2ob5o4bobobo8bo2b2o4bobo$8bo15bo9bo12bo$8bo
13bobo8bobo2bo2bobobo ...

Is there a better/smaller sparker for reducing the guntrue_5580 solution currently in Catagolue

x = 59, y = 46, rule = B3/S23
42b2o$42b2o$24bo$17bo4b3o17bo$16bobo2bo19bobo$15bo2bo2bob2o10b2o3bo3b
o$15bobob2obobo10b2o2b2obob2o2bo3b2o$14b2obo4bo16bo2bob4obo2bo$17bo4b
2o14b2ob6ob2o3b3o ...

Maybe an oscillator could be made with this? You need a constant supply of LWSS and MWSS (to delete the blocks) I know there is a better way to delete the blocks but this is just a demo of my idea. It may be discovered already but it seems pretty original.

x = 95, y = 110, rule = B3/S23
64bo30b ...

58P5H1V1 to two gliders:


x = 127, y = 133, rule = LifeHistory
73.2A$73.A.A$75.A4.2A$71.4A.2A2.A2.A$71.A2.A.A.A.A.2A$73.BABABA.A$74.
B2ABA.A$75.2B.BA$74.3B$65.2A6.4B$66.A6.B2A3B$66.A.AB3.B2A3B$67.2AB.10B
$69.13B$69.14B$69.15B$71.8B2.4B$71.6B5.4B$70.9B4.4B$69.4B4.2A5.4B$68.
4B5.A7.4B$67.4B7.3A5 ...

In the Density page, in the Densities of other objects section, it says on the second line:
The maximum average density of an oscillating agar is conjectured but not proven to be 1/2. The current upper bound is 1176/2087≈0.563, proven by Keith Amling in 2024.[5]
However, I am pretty sure that it ...

poorly built gun:

x = 293, y = 53, rule = MVS
73.3A45.3A52.A11.A11.A11.A$174.B3AB7.B3AB7.B3AB7.B3AB$71.A5.A41.A5.A
48.2A.2A7.2A.2A7.2A.2A7.2A.2A$2C69.A5.A41.A5.A47.A.A.A.A5.A.A.A.A5.A.
A.A.A5.A.A.A.A$2C69.A5.A41.A5.A50.A11.A11.A11.A$71.A5.A41.A5.A44.A47.
A$169.ABA45.ABA71.2C$73.3A45.3A45.ABA45 ...

aircraft carrier reduction: any glider-synthesizable object can be done in 3 cells per turn

Is it possible for pseudo still life components to be connected orthogonaly?

It seems that all definitions of strict still life assume by default that islands (polyplets) are indivisible - is there a proof for that?


It is possible.

x = 10, y = 10, rule = LifeHistory
4.A$2.3A$.A$.A.2A2C$2A ...

p38 reduction (octamer -> dimer):

Here is a list of traffic light and honey farm pushes from the same program I found the complete ones about a month ago, but these don't have a completion yet. They are sorted first by object type, then larger offset, then smaller offset, then number of generations.

If it's a honey farm, it ...

SE5T179, a composite H -> teardrop -> G from known conduits:

x = 53, y = 55, rule = LifeHistory
12.2A$11.B2AB5.2A$12.3B5.A$13.B3.BA.A$9.7B.B2A$8.10B$8.7B2AB$8.6BA2BA
$6.2AB.5B2AB$5.A.AB.8B$5.A4.8B3.2B$4.2A5.12B$11.14B10.A$11.15B8.A.A$
9.18B6.2BAB$7.21B6.2B$7.2BC19B3.4B$6.3BCBC17B3.5B.B$7.2B3C17B3 ...

1) It does not grow infinitely, because the loaf fuse will eventually run out and then the resulting crash destroys both guns
2) if MCPS is limited, why is the Summers/Nivash logarithmic growth existing even relevant? you can't get unbounded L/MCPS with bounded MCPS even if you do have the ...

- If you think this is too much, a reduction to 256 cells also seems valid (although it does disqualify two large objects mentioned in the article).

This eliminates the Summers/Nivasch logarithmic growth, which has a much higher initial population. What is the highest L/MCPS you can think of ...