muzik wrote:I'm pretty sure that the block is the only finite pattern at all with very cell having exactly 3 neighbours.
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$D$D$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$D$2A$CA8D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$2C$C.C$B2C7D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$D$BC.C$2B2C6D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$2C$BC.C$2B2C6D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$B2C$B.C.C$3B2C5D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$B$B3C$B2.C.C$4B2C4D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$B$B$B4C$BC2.C.C$5B2C3D!
x = 30, y = 10, rule = LifeHistory
D19.D$D19.D$D19.D$D19.D$B19.B$B19.B$B19.B$B.4C14.B5C$B2C2.C.C12.B.C2.
C.C$6B2C2D10.6B2C2D!
x = 10, y = 4, rule = B3/S23
2o2b2o2b2o$2b2o2b2o$2o2b2o2b2o$2b2o2b2o!
x = 5, y = 10, rule = B3/S23
2bo$b3o$o3bo$2ob2o$bobo$bobo$2ob2o$o3bo$b3o$2bo!
x = 7, y = 12, rule = LifeHistory
2.3B$.2BA2B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$2B3A
2B$.2BA2B$2.3B!
x = 7, y = 12, rule = LifeHistory
2.3B$D2BA2BD$BF3AFB$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$BF
3AFB$D2BA2BD$2.3B!
x = 7, y = 12, rule = LifeHistory
2.3B$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$2B3A
2B$3BA3B$2.3B!
x = 7, y = 12, rule = LifeHistory
.A3BA$2BDAD2B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$2B
3A2B$2BDAD2B$.A3BA!
x = 7, y = 12, rule = LifeHistory
.A3BA$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$2B3A
2B$3BA3B$.A3BA!
x = 7, y = 12, rule = LifeHistory
DA3BAD$BFBABFB$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$
2B3A2B$BFBABFB$DA3BAD!
x = 7, y = 12, rule = LifeHistory
BA3BAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$2B
3A2B$3BA3B$BA3BAB!
x = 7, y = 12, rule = LifeHistory
BF3BFB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$2B
3A2B$3BA3B$BF3BFB!
x = 7, y = 14, rule = LifeHistory
3D.3D$BA3BAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3B
AB$2B3A2B$3BA3B$BA3BAB$3D.3D!
x = 7, y = 14, rule = LifeHistory
3A.3A$BA3BAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3B
AB$2B3A2B$3BA3B$BA3BAB$3A.3A!
x = 7, y = 14, rule = LifeHistory
3A.3A$BABDBAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA
3BAB$2B3A2B$3BA3B$BABDBAB$3A.3A!
x = 7, y = 14, rule = LifeHistory
3AF3A$BABDBAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA
3BAB$2B3A2B$3BA3B$BABDBAB$3AF3A!
x = 7, y = 14, rule = LifeHistory
7A$BABDBAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB
$2B3A2B$3BA3B$BABDBAB$7A!
x = 7, y = 16, rule = LifeHistory
7B$7A$BA3BAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3B
AB$2B3A2B$3BA3B$BA3BAB$7A$7B!
x = 7, y = 16, rule = LifeHistory
7B$3AD3A$BA3BAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$B
A3BAB$2B3A2B$3BA3B$BA3BAB$3AD3A$7B!
wwei23 wrote:Do any still lifes exist from 9 to 19 cells so that every living cell has exactly two living neighbors and if not, then why?
x = 22, y = 17, rule = B3/S23
16bo$15bobo$4bo10bobo2bo$3bobo6b2obobobobo$3bobo6bo2bobo2bo$b2o3b2o6bo
2bo$o7bo6b2o$b2o3b2o$3bobo$3bobo$4bo10b2o$14bo2bo$14bobo2bo$11b2obobob
2o$11bo2bobo$13bo2bo$14b2o!
x = 290, y = 45, rule = LifeHistory
204.2A$203.A2.A$203.A.A2.A$200.2A.A.A.2A$200.A2.A.A$202.A2.A$203.2A
37.2A$241.A2.A$242.2A$204.A$203.A.A34.4A$203.A.A2.A30.A4.A$200.2A.A.A
.A.A30.4A$200.A2.A.A2.A$202.A2.A34.2A$203.2A34.A2.A$240.2A2$203.A36.
2A$202.A.A34.A2.A$90.D3.D5.D.D7.3D7.3D7.3D17.3D7.3D7.3D7.D.D7.3D10.A
36.2A$90.2D.2D5.D.D7.D10.D8.D19.D.D8.D8.D.D7.D.D7.D$90.D.D.D5.3D7.3D
8.D8.3D17.2D9.D8.D.D7.D.D7.3D8.5A34.4A$90.D3.D6.D10.D8.D8.D19.D.D8.D
8.D.D7.D.D9.D7.A5.A32.A4.A$90.D3.D6.D8.3D8.D8.3D17.D.D7.3D7.3D7.3D7.
3D8.5A34.4A2$203.A36.2A$202.A.A34.A2.A$203.A36.2A$244.A19.2A18.2A$
204.A19.2A17.A.A17.A2.A16.A2.A$203.A.A17.A2.A16.A.A18.A2.A15.A2.A$
203.A.A18.A2.A13.2A3.2A13.3A4.A12.2A4.2A$201.2A3.2A13.3A4.A11.A7.A11.
A8.A10.A8.A$90.4D46.3D47.3D7.A7.A11.A5.A.A11.A7.A12.A5.A.A10.A8.A$61.
A4.2A3.A9.2A3.A3.D49.D.D47.D.D8.2A3.2A13.A3.A.A13.2A3.2A14.A3.A.A12.
2A4.2A$41.A18.A.A4.A2.A.A7.A2.A.A.A2.D.2D46.3D47.3D10.A.A16.A2.A17.A.
A17.A2.A16.A2.A$40.A.A17.A.A2.A4.A2.A6.A2.A.A2.A.D2.D46.D.D47.D12.A.A
17.A.A17.A.A18.A.A16.A2.A$41.A19.A3.2A4.2A8.2A3.A.A.4D46.D.D47.D13.A
19.A19.A20.A18.2A$87.A$3B7.2B8.3B7.3B7.B.B7.3B7.3B7.3B7.3B7.3B7.2B2.
3B3.2B2.2B4.2B2.3B3.2B2.3B3.2B2.B.B3.2B2.3B3.2B2.3B3.2B2.3B3.2B2.3B3.
2B2.3B3.3B.3B13.3B.2B14.3B.3B13.3B.3B13.3B.B.B$B.B8.B10.B9.B7.B.B7.B
9.B11.B7.B.B7.B.B8.B2.B.B4.B3.B5.B4.B4.B4.B4.B2.B.B4.B2.B6.B2.B6.B4.B
4.B2.B.B4.B2.B.B5.B.B.B15.B2.B16.B3.B15.B3.B15.B.B.B$B.B8.B8.3B7.3B7.
3B7.3B7.3B9.B7.3B7.3B8.B2.B.B4.B3.B5.B2.3B4.B2.3B4.B2.3B4.B2.3B4.B2.
3B4.B4.B4.B2.3B4.B2.3B3.3B.B.B13.3B2.B14.3B.3B13.3B.3B13.3B.3B$B.B8.B
8.B11.B9.B9.B7.B.B9.B7.B.B9.B8.B2.B.B4.B3.B5.B2.B6.B4.B4.B4.B4.B4.B4.
B2.B.B4.B4.B4.B2.B.B4.B4.B3.B3.B.B13.B4.B14.B3.B15.B5.B13.B5.B$3B7.3B
7.3B7.3B9.B7.3B7.3B9.B7.3B7.3B7.3B.3B3.3B.3B3.3B.3B3.3B.3B3.3B3.B3.3B
.3B3.3B.3B3.3B3.B3.3B.3B3.3B.3B3.3B.3B13.3B.3B13.3B.3B13.3B.3B13.3B3.
B!
x = 46, y = 13, rule = LifeHistory
3.A$2.A.A6.2A10.2A6.2A10.2A$2.A.A5.A2.A8.A2.A4.A2.A8.A2.A$3.A7.2A10.
2A6.2A10.2A2$.5A5.4A6.4A6.4A6.4A$A5.A3.A4.A4.A4.A4.A4.A4.A4.A$.5A5.4A
6.4A6.4A6.4A2$3.A7.2A8.2A8.2A8.2A$2.A.A6.A9.A10.A9.A$3.A9.A9.A6.A9.A$
12.2A8.2A6.2A8.2A!
x = 7, y = 12, rule = LifeHistory
3.A$2.A.A$3.A2$.5A$A5.A$.5A2$3.A$2.A.A$.A2.A$2.2A!
x = 68, y = 89, rule = LifeHistory
2.A$.A.A9.A18.2A8.2A9.2A8.2A$.A2.A7.A.A16.A2.A6.A2.A7.A2.A6.A2.A$2.A.
A7.A.A17.A2.A6.A2.A7.A2.A6.A2.A$3.A9.A19.2A8.2A9.2A8.2A2$.5A5.5A17.4A
6.4A5.4A6.4A$A5.A3.A5.A15.A4.A4.A4.A3.A4.A4.A4.A$.5A5.5A17.4A6.4A5.4A
6.4A2$3.A9.A19.2A8.2A7.2A8.2A$2.A.A7.A.A19.A8.A9.A8.A$3.A8.A.A17.A12.
A5.A12.A$13.A18.2A10.2A5.2A10.2A3$33.2A8.2A10.2A8.2A$32.A2.A6.A2.A8.A
2.A6.A2.A$31.A2.A6.A2.A8.A2.A6.A2.A$32.2A8.2A10.2A8.2A2$32.4A6.4A6.4A
6.4A$31.A4.A4.A4.A4.A4.A4.A4.A$32.4A6.4A6.4A6.4A2$32.2A8.2A8.2A8.2A$
33.A8.A10.A8.A$31.A12.A6.A12.A$31.2A10.2A6.2A10.2A3$2.2A10.2A$.A2.A8.
A2.A$.A2.A8.A2.A$2.2A10.2A2$2.4A6.4A$.A4.A4.A4.A$2.4A6.4A2$2.2A8.2A$.
A2.A6.A2.A$2.2A8.2A19$2.2A8.2A18.2A10.2A$.A2.A6.A2.A16.A2.A8.A2.A$.A
2.A6.A2.A17.A2.A6.A2.A$2.2A8.2A19.2A8.2A2$2.4A6.4A17.4A6.4A$.A4.A4.A
4.A15.A4.A4.A4.A$2.4A6.4A17.4A6.4A2$2.2A8.2A19.2A8.2A$3.A8.A19.A2.A6.
A2.A$.A12.A18.2A8.2A$.2A10.2A2$33.2A10.2A$2.2A8.2A18.A2.A8.A2.A$.A2.A
6.A2.A18.A2.A6.A2.A$.A2.A6.A2.A19.2A8.2A$2.2A8.2A$32.4A6.4A$2.4A6.4A
15.A4.A4.A4.A$.A4.A4.A4.A15.4A6.4A$2.4A6.4A$32.2A8.2A$4.2A8.2A15.A2.A
6.A2.A$5.A8.A17.2A8.2A$3.A12.A$3.2A10.2A!
x = 20, y = 19, rule = LifeHistory
4.BD2B$4.B2AB$4.BA2B3.4BD3B$4.BA3B2.D3AB2A2B$5B2A3B.D2BABABAB$D4A2BA
6BA2B2AB$BA2BABABA4B2A4BD$5BABABA2BA2B4AB$3.3BA2B4A2BA2BAB$4.3B2A4B2A
3BAB$5.3BAB2ABA3B2DB$5.D2BAB2ABA3B$5.2B2A4B2A3B$5.DA2B4A2BA3B$5.BA2BA
2BABABA2B$5.2B2A4BABABAD$6.2BDBD3BA2BAB$12.3B2A2B$13.2BD2B!
x = 20, y = 19, rule = LifeHistory
4.BD2B$4.B2AB$4.BA2B3.4BD3B$4.BA3B2.D3AB2A2B$5B2A3B.D2BABABAB$D4A2BA
6BA2B2AB$BA2BABABA4B2A4BD$5BABABA2BA2B4AB$3.3BA2B4A2BA2BAB$4.3B2A4B2A
3BAB$3.BD3BAB2ABA3B2DB$3.B2A2BAB2ABA3B$3.BA2B2A4B2A3B$3.2B2A2B4A2BA3B
$4.2BA2BA2BABABA2B$5.2B2A4BABABAD$6.2BABA3BA2BAB$7.2B2AD3B2A2B$8.4B.
2BD2B!
x = 20, y = 19, rule = LifeHistory
4.BD2B$4.B2AB$4.BA2B3.4BD3B$4.BA3B2.D3AB2A2B$5B2A3B.D2BABABAB$D4A2BA
6BA2B2AB$BA2BABABA4B2A4BD$5BABABA2BA2B4AB$3.3BA2B4A2BA2BAB$3.D3B2A4B
2A3BAB$3.BA3BAB2ABA3B2DB$3.B2A2BAB2ABA3B$3.BA2B2A4B2A3B$3.2B2A2B4A2BA
3B$4.2BA2BA2BABABA2B$5.2B2A4BABABAD$6.2BABA3BA2BAB$7.2B3A3B2A2B$8.4BD
2BD2B!
x = 20, y = 19, rule = LifeHistory
4.BD2B$4.B2AB$4.BA2B3.4BD3B$4.BA3B2.D3AB2A2B$5B2A3B.D2BABABAB$D4A2BA
6BA2B2AB$BA2BABABA4B2A4BD$5BABABA2BA2B4AB$3.3BA2B4A2BA2BAB$3.D3B2A4B
2A3BAB$3.BA3BAB2ABA3B2DB$3.B2A2BAB2ABA3B$3.BA2B2A4B2A3B$3.2B2A2B4A2BA
3B$4.2BA2BA2BABABA2B$4.D2B2A4BABABAD$6.2BABA3BA2BAB$6.D2B3A3B2A2B$8.
4BD2BD3B!
x = 20, y = 19, rule = LifeHistory
4.BA2B$4.B2AB$4.BA2B3.4BA3B$4.BA3B2.4AB2A2B$5B2A3B.A2BABABAB$5A2BA6BA
2B2AB$BA2BABABA4B2A4BA$5BABABA2BA2B4AB$3.3BA2B4A2BA2BAB$3.A3B2A4B2A3B
AB$3.BAD2BAB2ABA3B2AB$3.B2A2BAB2ABA3B$3.BA2B2A4B2A3B$3.2B2A2B4A2BA3B$
4.2BA2BA2BABABA2B$4.A2B2A4BABAB2A$6.2BABAD2BA2BAB$6.A2B3A3B2A2B$8.4BA
2BA3B!
BlinkerSpawn wrote:muzik wrote:I'm pretty sure that the block is the only finite pattern at all with very cell having exactly 3 neighbours.
I also believe that the only stable patterns with every cell having 3 neighbors consist exclusively of blocks.
Here I will attempt to construct a pattern with every cell having 3 neighbors and containing no blocks.
Set your coordinate system so that the lower left corner of the pattern's bounding box is at (0,0), with coordinates increasing going up and to the right:Code: Select allx = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$D$D$10D!
Assume (0,0) is ON.
For the cell to have 3 live neighbors, (1,0), (0,1), and (1,0) must be ON, but then the pattern contains a block and is invalid, so (0,0) must be OFF:Code: Select allx = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$D$2A$CA8D!
Let's say (1,0) is ON instead.
There are four possible neighbors for (1,0): (0,1), (1,1), (2,1), and (2,0), but one of these must be (0,1) because the other three neighbors constitute a block. In addition, allowing (1,1) to be ON creates B3a at (0,0) so it is OFF and the other two neighbors must therefore be ON. Similar logic applies to (0,1), resulting in a ship:Code: Select allx = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$2C$C.C$B2C7D!
But (2,0) has two neighbors, and giving it a third causes (2,1) to have four neighbors and die, so this solution is also unworkable, and neither (1,0) nor (0,1) can be on in any solution. (This logic is reflection-invariant and so applies to both cases)
Let's force (2,0) to be ON, then.
By identical logic to the above we can immediately force these cells ON:Code: Select allx = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$D$BC.C$2B2C6D!
To prevent the contradiction in the previous case, though, (2,2) must stay OFF, forcing (1,1)'s two neighbors to be (2,1) and (2,0), creating B3a on (0,1). Therefore, (2,0) and (0,2) don't work either:Code: Select allx = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$2C$BC.C$2B2C6D!
Similarly, (3,0) creates this:Code: Select allx = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$B2C$B.C.C$3B2C5D!
(4,0) doesn't work:Code: Select allx = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$B$B3C$B2.C.C$4B2C4D!
This is the only way (5,0) can be done without creating birth at (2,1) or death at (3,2), but (1,1) and (1,2) are still unrescuable:Code: Select allx = 10, y = 10, rule = LifeHistory
D$D$D$D$D$B$B$B4C$BC2.C.C$5B2C3D!
And (6,0) has to be one of these but I don't know how to carry the logic past that:Code: Select allx = 30, y = 10, rule = LifeHistory
D19.D$D19.D$D19.D$D19.D$B19.B$B19.B$B19.B$B.4C14.B5C$B2C2.C.C12.B.C2.
C.C$6B2C2D10.6B2C2D!
I'm pretty sure some sort of proof-by-induction is possible along these lines.
If I could prove in each step that not just the end cells but each successive diagonal must be clear then the solution should just reduce to showing that each attempt to follow the instructions just creates the next level of ship and the proof would trivially follow from that and the logic used above.
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DB$D2B$10D!
x = 70, y = 10, rule = LifeHistory
D19.D19.D19.D$D19.D19.D19.D$D19.D19.D19.D$D19.D19.D19.D$D19.D19.D19.D
$D19.D19.D19.D$D19.D19.D19.D$DB3A15.DB2A16.DBA.A15.DB.2A$D2BA16.D2B2A
15.D2B2A15.D2B2A$10D10.10D10.10D10.10D!
x = 50, y = 10, rule = LifeHistory
D19.D19.D$D19.D19.D$D19.D19.D$D19.D19.D$D19.D19.D$D19.D19.D$D19.D19.D
$DB3A15.DB2A16.DBA.A$D2BA16.D2B2A15.D2B2A$10D10.10D10.10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DBA$D2BA$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DBAF$D2BA$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DBAFA$D2BEA$10D!
x = 50, y = 10, rule = LifeHistory
D19.D19.D$D19.D19.D$D19.D19.D$D19.D19.D$D19.D19.D$D19.D19.D$D2A17.DA.
A16.D.2A$DBAFA15.DBAFA15.DBAFA$D2B2A15.D2B2A15.D2B2A$10D10.10D10.10D!
x = 30, y = 10, rule = LifeHistory
D19.D$D19.D$D19.D$D19.D$D19.D$D19.D$DA.A16.D.2A$DBAFA15.DBAFA$D2B2A
15.D2B2A$10D10.10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D2.A$DBAFA$D2B2A$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D2.A$DBAFA$D2BAE$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB$DB$D3B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB2E$DBAE$D3B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB$D2B$D3B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB$D2B$D3BA$10D!
x = 70, y = 10, rule = LifeHistory
D19.D19.D19.D$D19.D19.D19.D$D19.D19.D19.D$D19.D19.D19.D$D19.D19.D19.D
$D19.D19.D19.D$DB18.DB18.DB18.DB$D2B3A14.D2B2A15.D2BA.A14.D2B.2A$D3BA
15.D3B2A14.D3B2A14.D3B2A$10D10.10D10.10D10.10D!
x = 50, y = 10, rule = LifeHistory
D19.D19.D$D19.D19.D$D19.D19.D$D19.D19.D$D19.D19.D$D19.D19.D$DB18.DB
18.DB$D2B3A14.D2B2A15.D2BA.A$D3BA15.D3B2A14.D3B2A$10D10.10D10.10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB$D2BA$D3BA$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB$D2BAF$D3BA$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB$D2BAFA$D3B2A$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB2.A$D2BAFA$D3B2A$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB2.A$D2BAFA$D3BAE$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$DB$DB$D2B$D4B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$DB$DB$D2BA$D4B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$DB$DBA$D2BA$D4B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$DB$DBAF$D2BA$D4B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$DB2A$DBAFA$D2B2A$D4B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D.3F$DBAE2F$DBAFEF$D2B2AF$D4B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D.3F$DBEA2F$DBAFAF$D2BAEF$D4B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DA3F$DB2A2F$DBAFAF$D2B2AF$D4BA$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DE3F$DB2A2F$DBAFAF$D2B2AF$D4BE$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$DB$D2B$D3B$D4B$10D!
x = 15, y = 5, rule = LifeHistory
7.D$8.D$B4.5D2.B$B7.D3.2B$3B4.D4.3B!
x = 130, y = 10, rule = LifeHistory
D19.D19.D19.D19.D19.D19.D$D19.D19.D19.D19.D19.D19.D$D19.D19.D19.D19.D
19.D19.D$D19.D19.D19.D19.D19.D19.D$D19.D19.D19.D19.D19.D19.DB$DB18.DB
18.DB18.DB18.DB18.DB18.DB$D2B17.D2B17.D2B17.D2B17.D2B2.A14.D2B2.A14.D
2B$D3B16.D3BA15.D3BAF14.D3BAFA13.D3BAFA13.D3BAFA13.D3B$D4BA14.D4BA14.
D4BA14.D4B2A13.D4B2A13.D4BAE13.D5B$10D10.10D10.10D10.10D10.10D10.10D
10.10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB$DB$D2BA$D3B$D5B$10D!
x = 110, y = 10, rule = LifeHistory
D19.D19.D19.D19.D19.D$D19.D19.D19.D19.D19.D$D19.D19.D19.D19.D19.D$D
19.D19.D19.D19.D19.D$DB18.DB18.DB18.DB18.DB18.DB$DB3A15.DB2A16.DB2A
16.DBA.A15.DBA.A15.DB.2A$D2BA16.D2B2A15.D2BA16.D2B2A15.D2BA16.D2B2A$D
3B16.D3B16.D3BA15.D3B16.D3BA15.D3B$D5B14.D5B14.D5B14.D5B14.D5B14.D5B$
10D10.10D10.10D10.10D10.10D10.10D!
x = 15, y = 5, rule = LifeHistory
7.D$8.D$B4.5D.B$2B6.D2.2B$4B3.D3.4B!
x = 30, y = 10, rule = LifeHistory
D19.D$D19.D$D19.D$D19.D$DB18.DB$DBA.A15.DBA.A$D2B2A15.D2BA$D3B16.D3BA
$D5B14.D5B$10D10.10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB$DBAFA$D2BA$D3B$D5B$10D!
x = 30, y = 10, rule = LifeHistory
D19.D$D19.D$D19.D$D19.D$DB18.DB$DBAFA15.DBAFA$D2B2A15.D2BAF$D3BF15.D
3BA$D5B14.D5B$10D10.10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB2A$DBEFA$D2B2A$D3BF$D5B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D.3F$DBAE2F$DBAFEF$D2B2AF$D3BF$D5B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$DA3F$DBEA2F$DBAFAF$D2BAEF$D3BFA$D5B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$DA3F$DB2A2F$DBAFAF$D2B2AF$D3BFA$D5B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB$DBEFA$D2BAF$D3BE$D5B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB2A$DBAFA$D2BAFA$D3B2A$D5B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D.3F$DB2A2F$DBAFA2F$D2BAFAF$D3B2AF$D5B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$DA3F$DB2A2F$DBAFA2F$D2BAFAF$D3B2AF$D5BA$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$DA3F$DB2A2F$DBAFA2F$D2BAFAF$D3B2AF$D5BA$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB$DB$D3B$D3B$D5B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB$D2B$D3B$D4B$D5B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$DB$DB$D2B$D3B$D4B$D6B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$DB$D2B$D2B$D3B$D5B$D6B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$DB$D2B$D3B$D4B$D5B$D6B$10D!
x = 21, y = 21, rule = LifeHistory
B2$B2$B2$B$B$B$B$B$2B$B.B$B2.B$B3.B$B4.B$B5.B$B6.B$B7.BA.A$B8.B2A$15B
.B.B.B!
x = 21, y = 21, rule = LifeHistory
B2$B2$B2$B$B$B$B$B$2B$B.B$B2.B$B3.B$B4.B$B5.B$B6.B$B7.BA.AE$B8.B2A$
15B.B.B.B!
x = 21, y = 21, rule = LifeHistory
B2$B2$B2$B$B$B$B$B$2B$B.B$B2.B$B3.B$B4.B$B5.B$B6.B2ED$B7.BAD2A$B8.B2A
$15B.B.B.B!
x = 21, y = 21, rule = LifeHistory
B2$B2$B2$B$B$B$B$B$2B$B.B$B2.B$B3.B$B4.B$B5.B2ED$B6.BAD2A$B7.B2A$B8.
2B$15B.B.B.B!
x = 21, y = 21, rule = LifeHistory
B2$B2$B2$B$B$B$B$B$2B$B.B$B2.B$B3.B$B4.B2ED$B5.BAD2A$B6.B2A$B7.2B$B8.
2B$15B.B.B.B!
x = 21, y = 21, rule = LifeHistory
B2$B2$B2$B$B$B$B2A$B2A$3B$B.2B$B2.2B$B3.2B$B4.2B$B5.2B$B6.2B$B7.2B$B
8.2B$15B.B.B.B!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DB$D2B$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DB$D2BA$10D!
x = 70, y = 10, rule = LifeHistory
D19.D19.D19.D$D19.D19.D19.D$D19.D19.D19.D$D19.D19.D19.D$D19.D19.D19.D
$D19.D19.D19.D$D19.D19.D19.D$DB3A15.DB2A16.DBA.A15.DB.2A$D2BA16.D2B2A
15.D2B2A15.D2B2A$10D10.10D10.10D10.10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DBA.A$D2B2A$10D!
x = 50, y = 10, rule = LifeHistory
D19.D19.D$D19.D19.D$D19.D19.D$D19.D19.D$D19.D19.D$D19.D19.D$D2A17.DA.
A16.D.2A$DBA.A15.DBA.A15.DBA.A$D2B2A15.D2B2A15.D2B2A$10D10.10D10.10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D2.A$DBA.A$D2B2A$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D2.A$DBA.C$D2BAE$10D!
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DB$D3B$10D!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B$10B.2A$11BCA$13B$14B$15B$16B$17B$18B$19B$
20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B$10BA$11BC$13B$14B$15B$16B$17B$18B$19B$20B$
21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B$10B2A$11BC$13B$14B$15B$16B$17B$18B$19B$20B$
21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B$9BF2A$9B2FC$10B3F$14B$15B$16B$17B$18B$19B$
20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B$9BF2A$7B4FC$7BF2A3F$7BF2AF3B$7B4F4B$16B$17B
$18B$19B$20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B$9BF2A$7B4FC$7BF2A4F$7BF2AF2AF$7B4F2AFB$10B
4F2B$17B$18B$19B$20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B$9BF2A$7B4FC$7BF2A4F$7BF2AF2AF$7B4F2AFB$7BF
2A4F2B$7BF2AF6B$7B4F7B$19B$20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B$9BF2A$7B4FC$7BF2A4F$7BF2AF2AF$7B4F2AFB$7BF
2A4F2B$7BF2AF2AF3B$7B4F2AF4B$10B4F5B$20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B$10BA.A$11BCA$13B$14B$15B$16B$17B$18B$19B$
20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B$9BFAFA$9B2FCA$9B4F$14B$15B$16B$17B$18B$19B$
20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B2A$9BFAFA$9B2FCA$9B4F$14B$15B$16B$17B$18B$
19B$20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$8BF2A$8B2FAFA$9B2FCA$9B4F$14B$15B$16B$17B$18B$
19B$20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$8BF2A$6B4FAFA$6BF2A2FCA$6BF2A4F$6B4F4B$15B$16B
$17B$18B$19B$20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$8BF2A$6B4FAFA$6BF2ADFCA$6BF2A4F$6B4F4B$15B$16B
$17B$18B$19B$20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B2.A$9BFAFA$9B2FCA$9B4F$14B$15B$16B$17B$18B$
19B$20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B2.A2F$9BFAFAF$9B2FCAF$9B4F$14B$15B$16B$17B$
18B$19B$20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B2.A2F$9BFAFAF$9B2FCAF$9B4FA$14B$15B$16B$17B$
18B$19B$20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B2.A2F$9BFAFAF$9B2FCAF$9B4FA$12B2F$15B$16B$
17B$18B$19B$20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B2.A2F$9BFAFAF$9B2FCAF$9B4FA$9BF2A2F$9BF2AF2B
$9B4F3B$17B$18B$19B$20B$21B$22B!
x = 22, y = 21, rule = LifeHistory
B$2B$3B$4B$5B$6B$7B$8B$9B2.A2F$9BFAFAF$9B2FCAF$9BFD2FA$9BF2A2F$9BF2AF
2B$9B4F3B$17B$18B$19B$20B$21B$22B!
wwei23 wrote:Do still lives exist in B/S4?
x = 32, y = 32, rule = B/S4:T32,32
15bo$15b2o$15b2o$16bo$16b2o$16b2o$16bo$16b2o$16b2o$16bo$15b2o$15b2o$
15bo$14b2o$3b2ob2o6b2o$11o4bob2o$2o7b6ob6o7b3o$12b2obo4b11o$15b2o6b2ob
2o$15b2o$15bo$14b2o$14b2o$14bo$13b2o$13b2o$14bo$13b2o$13b2o$14bo$14b2o
$14b2o!
#C [[ THUMBNAIL THUMBSIZE 2 ]]
wwei23 wrote:Does an eater exist that can eat a glider, a lightweight spaceship, a middleweight spaceship, and a heavyweight spaceship?
gameoflifeboy wrote:I've been searching B3/S2 for years to try to answer this. I'm already pretty sure the answer is "no", because the only available islands seem to be preblocks and rings of cells joined orthogonally or diagonally.
dvgrn wrote:wwei23 wrote:Do still lives exist in B/S4?
Interesting question... there are enough possibilities that I can't instantly prove it's impossible...
x = 18, y = 18, rule = B/S4:T18,18
9bo$8bobo$7b5o$6b2o3b2o$5b2o5b2o$4b2o7b2o$3b2o9b2o$2b2o11b2o$b2o13b2o$
obo13bo$b2o13b2o$2b2o11b2o$3b2o9b2o$4b2o7b2o$5b2o5b2o$6b2o3b2o$7b5o$8b
obo!
#C [[ THUMBNAIL THUMBSIZE 2 ]]
x = 3, y = 2, rule = B/S4History
.CA$3A!
#C [[ THUMBNAIL ]]
x = 3, y = 2, rule = B/S4History
..2A$.CEA$2A!
#C [[ THUMBNAIL ]]
dvgrn wrote:Q.E.D., right?
dvgrn wrote:wwei23 wrote:Does an eater exist that can eat a glider, a lightweight spaceship, a middleweight spaceship, and a heavyweight spaceship?
This one I think you need to be a little more specific about. Otherwise the answer is a trivial "yes". Gliders come in at a different angle from spaceships, so maybe you want to require that the first cell that interacts has to be the same in all four cases, or something like that?
wwei23 wrote:The XWSSes have to be on the same path. The glider must hit the same spot.
x = 97, y = 24, rule = B3/S23
bo$2bo$3o7$11b2o$10bo2bo$10bo2bo$11b2o!
x = 100, y = 100, rule = B3/S23
7bo$8bo$4bo3bo$5b4o$17b2o$16bo2bo$16bo2bo$17b2o$20$
7bo$8bo$3bo4bo$4b5o$17b2o$16bo2bo$16bo2bo$17b2o$20$
7bo$8bo$2bo5bo$3b6o$17b2o$16bo2bo$16bo2bo$17b2o!
dvgrn wrote:wwei23 wrote:The XWSSes have to be on the same path. The glider must hit the same spot.
An eater with that constraint can almost certainly be built somehow -- or a multi-input converter, with the same signal output for any of the four inputs.
However, it would probably take several thousand ticks for the Giant Multi-Eater to recover after any meal. Mostly for that reason, nobody may actually want to complete a construction along these lines. It seems like the kind of thing that might remain forever in the "We Could If We Wanted To But It Would Be Big And Ugly" category.
If you want a reasonable-sized eater that recovers reasonably quickly, the answer might be "no" at the moment. But it's vaguely possible that some existing weird still lifes with very slow eater2-like action might be sufficiently omnivorous. Anyway, "yes" could possibly be only a Bellman search away.
One more question: does this gliderCode: Select allx = 97, y = 24, rule = B3/S23
bo$2bo$3o7$11b2o$10bo2bo$10bo2bo$11b2o!
strike in the "same spot" as these *WSSes?Code: Select allx = 100, y = 100, rule = B3/S23
7bo$8bo$4bo3bo$5b4o$17b2o$16bo2bo$16bo2bo$17b2o$20$
7bo$8bo$3bo4bo$4b5o$17b2o$16bo2bo$16bo2bo$17b2o$20$
7bo$8bo$2bo5bo$3b6o$17b2o$16bo2bo$16bo2bo$17b2o!
wwei23 wrote:dvgrn wrote:One more question: does this glider... strike in the "same spot" as these *WSSes?
Basically first interaction must be the same.
wwei23 wrote:Do any still lifes exist from 9 to 19 cells so that every living cell has exactly two living neighbors and if not, then why(I've also apgsearched and turned up empty-handed.)?
wwei23 wrote:Other than some agars, is the block the only still life where every living cell has exactly three neighbors? If so, then why?
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