Still life puzzles
Still life puzzles
One (None exist): 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.)?
And two (None exist): Other than some agars, is the block the only still life where every living cell has exactly three neighbors? If so, then why?
Re: Still life puzzles
- BlinkerSpawn
- Posts: 1992
- Joined: November 8th, 2014, 8:48 pm
- Location: Getting a snacker from R-Bee's
Re: Still life puzzles
I also believe that the only stable patterns with every cell having 3 neighbors consist exclusively of blocks.muzik wrote:I'm pretty sure that the block is the only finite pattern at all with very cell having exactly 3 neighbours.
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 all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$D$D$10D!
For the cell to have 3 live neighbors, (1,0), (0,1), and (1,0) must be ON, but then the pattern contains a block and is invalid, so (0,0) must be OFF:
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$D$2A$CA8D!
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 all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$2C$C.C$B2C7D!
Let's force (2,0) to be ON, then.
By identical logic to the above we can immediately force these cells ON:
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$D$BC.C$2B2C6D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$2C$BC.C$2B2C6D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$B2C$B.C.C$3B2C5D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$B$B3C$B2.C.C$4B2C4D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$B$B$B4C$BC2.C.C$5B2C3D!
Code: Select all
x = 30, y = 10, rule = LifeHistory
D19.D$D19.D$D19.D$D19.D$B19.B$B19.B$B19.B$B.4C14.B5C$B2C2.C.C12.B.C2.
C.C$6B2C2D10.6B2C2D!
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.
Re: Still life puzzles
https://catagolue.appspot.com/census/bs3/C1
Re: Still life puzzles
EDIT: Also I don't know if that's what you meant by 'agars'. I was picturing something like infinite chicken wire:
Code: Select all
x = 10, y = 4, rule = B3/S23
2o2b2o2b2o$2b2o2b2o$2o2b2o2b2o$2b2o2b2o!
Re: Still life puzzles
Code: Select all
x = 5, y = 10, rule = B3/S23
2bo$b3o$o3bo$2ob2o$bobo$bobo$2ob2o$o3bo$b3o$2bo!
Never mind:
Because all the living cells of the seed have three living neighbors, no cells can be on adjacent to any of them. These cells are shown in blue:
Code: Select all
x = 7, y = 12, rule = LifeHistory
2.3B$.2BA2B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$2B3A
2B$.2BA2B$2.3B!
Code: Select all
x = 7, y = 12, rule = LifeHistory
2.3B$D2BA2BD$BF3AFB$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$BF
3AFB$D2BA2BD$2.3B!
Code: Select all
x = 7, y = 12, rule = LifeHistory
2.3B$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$2B3A
2B$3BA3B$2.3B!
Code: Select all
x = 7, y = 12, rule = LifeHistory
.A3BA$2BDAD2B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$2B
3A2B$2BDAD2B$.A3BA!
Code: Select all
x = 7, y = 12, rule = LifeHistory
.A3BA$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$2B3A
2B$3BA3B$.A3BA!
Code: Select all
x = 7, y = 12, rule = LifeHistory
DA3BAD$BFBABFB$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$
2B3A2B$BFBABFB$DA3BAD!
Code: Select all
x = 7, y = 12, rule = LifeHistory
BA3BAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$2B
3A2B$3BA3B$BA3BAB!
Code: Select all
x = 7, y = 12, rule = LifeHistory
BF3BFB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB$2B
3A2B$3BA3B$BF3BFB!
Code: Select all
x = 7, y = 14, rule = LifeHistory
3D.3D$BA3BAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3B
AB$2B3A2B$3BA3B$BA3BAB$3D.3D!
Code: Select all
x = 7, y = 14, rule = LifeHistory
3A.3A$BA3BAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3B
AB$2B3A2B$3BA3B$BA3BAB$3A.3A!
Code: Select all
x = 7, y = 14, rule = LifeHistory
3A.3A$BABDBAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA
3BAB$2B3A2B$3BA3B$BABDBAB$3A.3A!
Code: Select all
x = 7, y = 14, rule = LifeHistory
3AF3A$BABDBAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA
3BAB$2B3A2B$3BA3B$BABDBAB$3AF3A!
Code: Select all
x = 7, y = 14, rule = LifeHistory
7A$BABDBAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3BAB
$2B3A2B$3BA3B$BABDBAB$7A!
Code: Select all
x = 7, y = 16, rule = LifeHistory
7B$7A$BA3BAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$BA3B
AB$2B3A2B$3BA3B$BA3BAB$7A$7B!
Code: Select all
x = 7, y = 16, rule = LifeHistory
7B$3AD3A$BA3BAB$3BA3B$2B3A2B$BA3BAB$B2AB2AB$2BABA2B$2BABA2B$B2AB2AB$B
A3BAB$2B3A2B$3BA3B$BA3BAB$3AD3A$7B!
- gameoflifeboy
- Posts: 474
- Joined: January 15th, 2015, 2:08 am
Re: Still life puzzles
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. I could find three at 20 cells though: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?
Code: Select all
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!
Re: Still life puzzles
Code: Select all
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!
Code: Select all
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!
Code: Select all
x = 7, y = 12, rule = LifeHistory
3.A$2.A.A$3.A2$.5A$A5.A$.5A2$3.A$2.A.A$.A2.A$2.2A!
Code: Select all
x = 68, y = 89, rule = LifeHistory
2.A$.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!
Re: Still life puzzles
Code: Select all
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!
Code: Select all
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!
Code: Select all
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!
EDIT:
I was wrong:
Code: Select all
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!
Coolout Conjecture Counterexample, even if made internally stable:
Here red means bad cell.
Code: Select all
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$8.4BA
2BA3B!
And Catagolue for 12, 13, none.
Re: Still life puzzles
Force (2,0) to be on:BlinkerSpawn wrote:I also believe that the only stable patterns with every cell having 3 neighbors consist exclusively of blocks.muzik wrote:I'm pretty sure that the block is the only finite pattern at all with very cell having exactly 3 neighbours.
Here I will attempt to construct a pattern with every cell having 3 neighbors and containing no blocks.
Set your coordinate system so that the lower left corner of the pattern's bounding box is at (0,0), with coordinates increasing going up and to the right:Assume (0,0) is ON.Code: Select all
x = 10, y = 10, rule = LifeHistory D$D$D$D$D$D$D$D$D$10D!
For the cell to have 3 live neighbors, (1,0), (0,1), and (1,0) must be ON, but then the pattern contains a block and is invalid, so (0,0) must be OFF:Let's say (1,0) is ON instead.Code: Select all
x = 10, y = 10, rule = LifeHistory D$D$D$D$D$D$D$D$2A$CA8D!
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: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)Code: Select all
x = 10, y = 10, rule = LifeHistory D$D$D$D$D$D$D$2C$C.C$B2C7D!
Let's force (2,0) to be ON, then.
By identical logic to the above we can immediately force these cells ON:To prevent the contradiction in the previous case, though, (2,2) must stay OFF, forcing (1,1)'s two neighbors to be (2,1) and (2,0), creating B3a on (0,1). Therefore, (2,0) and (0,2) don't work either:Code: Select all
x = 10, y = 10, rule = LifeHistory D$D$D$D$D$D$D$D$BC.C$2B2C6D!
Similarly, (3,0) creates this:Code: Select all
x = 10, y = 10, rule = LifeHistory D$D$D$D$D$D$D$2C$BC.C$2B2C6D!
(4,0) doesn't work:Code: Select all
x = 10, y = 10, rule = LifeHistory D$D$D$D$D$D$D$B2C$B.C.C$3B2C5D!
This is the only way (5,0) can be done without creating birth at (2,1) or death at (3,2), but (1,1) and (1,2) are still unrescuable:Code: Select all
x = 10, y = 10, rule = LifeHistory D$D$D$D$D$D$B$B3C$B2.C.C$4B2C4D!
And (6,0) has to be one of these but I don't know how to carry the logic past that:Code: Select all
x = 10, y = 10, rule = LifeHistory D$D$D$D$D$B$B$B4C$BC2.C.C$5B2C3D!
I'm pretty sure some sort of proof-by-induction is possible along these lines.Code: Select all
x = 30, y = 10, rule = LifeHistory D19.D$D19.D$D19.D$D19.D$B19.B$B19.B$B19.B$B.4C14.B5C$B2C2.C.C12.B.C2. C.C$6B2C2D10.6B2C2D!
If I could prove in each step that not just the end cells but each successive diagonal must be clear then the solution should just reduce to showing that each attempt to follow the instructions just creates the next level of ship and the proof would trivially follow from that and the logic used above.
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DB$D2B$10D!
Code: Select all
x = 70, y = 10, rule = LifeHistory
D19.D19.D19.D$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$10D10.10D10.10D10.10D!
The others have a cell in common:
Code: Select all
x = 50, y = 10, rule = LifeHistory
D19.D19.D$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$10D10.10D10.10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DBA$D2BA$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DBAF$D2BA$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DBAFA$D2BEA$10D!
Code: Select all
x = 50, y = 10, rule = LifeHistory
D19.D19.D$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$10D10.10D10.10D!
Code: Select all
x = 30, y = 10, rule = LifeHistory
D19.D$D19.D$D19.D$D19.D$D19.D$D19.D$DA.A16.D.2A$DBAFA15.DBAFA$D2B2A
15.D2B2A$10D10.10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D2.A$DBAFA$D2B2A$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D2.A$DBAFA$D2BAE$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB$DB$D3B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB2E$DBAE$D3B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB$D2B$D3B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB$D2B$D3BA$10D!
Code: Select all
x = 70, y = 10, rule = LifeHistory
D19.D19.D19.D$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$10D10.10D10.10D10.10D!
Code: Select all
x = 50, y = 10, rule = LifeHistory
D19.D19.D$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$10D10.10D10.10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB$D2BA$D3BA$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB$D2BAF$D3BA$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB$D2BAFA$D3B2A$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB2.A$D2BAFA$D3B2A$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$DB2.A$D2BAFA$D3BAE$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$DB$DB$D2B$D4B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$DB$DB$D2BA$D4B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$DB$DBA$D2BA$D4B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$DB$DBAF$D2BA$D4B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$DB2A$DBAFA$D2B2A$D4B$10D!
Gray would kill yellow:
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D.3F$DBAE2F$DBAFEF$D2B2AF$D4B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D.3F$DBEA2F$DBAFAF$D2BAEF$D4B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DA3F$DB2A2F$DBAFAF$D2B2AF$D4BA$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DE3F$DB2A2F$DBAFAF$D2B2AF$D4BE$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$DB$D2B$D3B$D4B$10D!
Code: Select all
x = 15, y = 5, rule = LifeHistory
7.D$8.D$B4.5D2.B$B7.D3.2B$3B4.D4.3B!
Code: Select all
x = 130, y = 10, rule = LifeHistory
D19.D19.D19.D19.D19.D19.D$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$10D10.10D10.10D10.10D10.10D10.10D
10.10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB$DB$D2BA$D3B$D5B$10D!
Code: Select all
x = 110, y = 10, rule = LifeHistory
D19.D19.D19.D19.D19.D$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!
Code: Select all
x = 15, y = 5, rule = LifeHistory
7.D$8.D$B4.5D.B$2B6.D2.2B$4B3.D3.4B!
Code: Select all
x = 30, y = 10, rule = LifeHistory
D19.D$D19.D$D19.D$D19.D$DB18.DB$DBA.A15.DBA.A$D2B2A15.D2BA$D3B16.D3BA
$D5B14.D5B$10D10.10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB$DBAFA$D2BA$D3B$D5B$10D!
Code: Select all
x = 30, y = 10, rule = LifeHistory
D19.D$D19.D$D19.D$D19.D$DB18.DB$DBAFA15.DBAFA$D2B2A15.D2BAF$D3BF15.D
3BA$D5B14.D5B$10D10.10D!
Object 3x2 43:
2 and 2 for yellow:
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB2A$DBEFA$D2B2A$D3BF$D5B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D.3F$DBAE2F$DBAFEF$D2B2AF$D3BF$D5B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$DA3F$DBEA2F$DBAFAF$D2BAEF$D3BFA$D5B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$DA3F$DB2A2F$DBAFAF$D2B2AF$D3BFA$D5B$10D!
Object 3x3 337:
2 and 2 for yellow:
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB$DBEFA$D2BAF$D3BE$D5B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB2A$DBAFA$D2BAFA$D3B2A$D5B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D.3F$DB2A2F$DBAFA2F$D2BAFAF$D3B2AF$D5B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$DA3F$DB2A2F$DBAFA2F$D2BAFAF$D3B2AF$D5BA$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$DA3F$DB2A2F$DBAFA2F$D2BAFAF$D3B2AF$D5BA$10D!
(2,2) must be off:
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB$DB$D3B$D3B$D5B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$DB$D2B$D3B$D4B$D5B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$DB$DB$D2B$D3B$D4B$D6B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$DB$D2B$D2B$D3B$D5B$D6B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$DB$D2B$D3B$D4B$D5B$D6B$10D!
- BlinkerSpawn
- Posts: 1992
- Joined: November 8th, 2014, 8:48 pm
- Location: Getting a snacker from R-Bee's
Re: Still life puzzles
Say we've disproved a diagonal. We force the base of the next diagonal ON and build the claw using the same logic as the previous proofs:
Code: Select all
x = 21, y = 21, rule = LifeHistory
B2$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$15B
.B.B.B!
Code: Select all
x = 21, y = 21, rule = LifeHistory
B2$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!
Code: Select all
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
$15B.B.B.B!
But the logic works the exact same way at the next location too:
Code: Select all
x = 21, y = 21, rule = LifeHistory
B2$B2$B2$B$B$B$B$B$2B$B.B$B2.B$B3.B$B4.B$B5.B2ED$B6.BAD2A$B7.B2A$B8.
2B$15B.B.B.B!
Code: Select all
x = 21, y = 21, rule = LifeHistory
B2$B2$B2$B$B$B$B$B$2B$B.B$B2.B$B3.B$B4.B2ED$B5.BAD2A$B6.B2A$B7.2B$B8.
2B$15B.B.B.B!
We can, in fact, slide the claw all the way up, forcing every cell along the new diagonal OFF.
The "block theorem" finishes off the diagonal:
Code: Select all
x = 21, y = 21, rule = LifeHistory
B2$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$15B.B.B.B!
Re: Still life puzzles
Here's my proof of the claw theorem:
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DB$D2B$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DB$D2BA$10D!
Code: Select all
x = 70, y = 10, rule = LifeHistory
D19.D19.D19.D$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$10D10.10D10.10D10.10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DBA.A$D2B2A$10D!
Code: Select all
x = 50, y = 10, rule = LifeHistory
D19.D19.D$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$10D10.10D10.10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D2.A$DBA.A$D2B2A$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D2.A$DBA.C$D2BAE$10D!
Code: Select all
x = 10, y = 10, rule = LifeHistory
D$D$D$D$D$D$D$DB$D3B$10D!
Re: Still life puzzles
non-block part : white cell = on
(SW edge of bounding diamond of non-block part : Y=-X)
(S-most ON cell on SW edge of bounding diamond of non-block part = origin)
blue area : no non-block part ...(a)
IF (1,0)(0,1)(1,1) are ON
Code: Select all
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!
THEREFORE (-1,1) is ON
Code: Select all
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!
Code: Select all
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!
Code: Select all
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!
anti B3a(-1,0)
Code: Select all
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!
Code: Select all
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!
Code: Select all
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!
Code: Select all
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!
THEREFORE (1,0)(1,1) are ON
Code: Select all
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!
Code: Select all
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!
IF (-1,2)(-2,2) are ON
Code: Select all
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!
Code: Select all
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!
Code: Select all
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!
Code: Select all
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!
Code: Select all
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!
Code: Select all
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!
Code: Select all
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!
Code: Select all
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!
Code: Select all
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!
Code: Select all
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!
QED
Re: Still life puzzles
Does an eater exist that can eat a glider, a lightweight spaceship, a middleweight spaceship, and a heavyweight spaceship?
Re: Still life puzzles
Interesting question. I don't immediately see how to turn a corner without resorting to an infinite agar, but there are enough possibilities that I can't instantly prove it's impossible:wwei23 wrote:Do still lives exist in B/S4?
Code: Select all
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 ]]
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:Does an eater exist that can eat a glider, a lightweight spaceship, a middleweight spaceship, and a heavyweight spaceship?
Otherwise you can just weld together any glider eater, any LWSS eater, any MWSS eater, and any HWSS eater.
If you want the three *WSSes at least to use the same mechanism, here's a three-bait constellation that would work. Just have to add a factory to each of the signal outputs to rebuild one of the bait objects -- and then simply add a fishhook eater to eat a glider, or change your question to disallow that somehow.
Seems to me something better has been found for a universal *WSS signal converter since 2009, but I'm not finding it offhand, and it doesn't appear to be on the Big Converter List. Anyone have a link?
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Re: Still life puzzles
Could Simon Ekström's still life searcher be adapted to other CAs beyond Conway Life to answer this sort of question? It seems like a good tool for the job -- unfortunately the assumption that the rule worked with is B3/S23 seems to be baked fairly deeply into it, and I can't tell off-hand where.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.
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Re: Still life puzzles
dvgrn wrote:Interesting question... there are enough possibilities that I can't instantly prove it's impossible...wwei23 wrote:Do still lives exist in B/S4?
Code: Select all
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 ]]
Consider the ON cell in a hypothetical still life that's farthest to the left along the top edge of the still life's bounding diamond (let's say). That cell (white) forces four ON cells below and to the right of it (green):
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x = 3, y = 2, rule = B/S4History
.CA$3A!
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x = 3, y = 2, rule = B/S4History
..2A$.CEA$2A!
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- praosylen
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Re: Still life puzzles
I believe so.dvgrn wrote:Q.E.D., right?
It's also interesting to note that this disproves the existence of P1 photons in any 3D outer-totalistic rule in the logical extension of the Moore neighborhood containing B5 and none of B0234678 (B1 is disallowed for obvious reasons). The existence of higher-period photons would depend upon the existence of oscillators in 2D B5/S4. I suspect, but cannot prove at the moment, that they are impossible.
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Re: Still life puzzles
The XWSSes have to be on the same path. The glider must hit the same spot.dvgrn wrote: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:Does an eater exist that can eat a glider, a lightweight spaceship, a middleweight spaceship, and a heavyweight spaceship?
Re: Still life puzzles
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.wwei23 wrote:The XWSSes have to be on the same path. The glider must hit the same spot.
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 glider
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x = 97, y = 24, rule = B3/S23
bo$2bo$3o7$11b2o$10bo2bo$10bo2bo$11b2o!
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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!
Re: Still life puzzles
Basically first interaction must be the same.dvgrn wrote: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.wwei23 wrote:The XWSSes have to be on the same path. The glider must hit the same spot.
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 glider
strike in the "same spot" as these *WSSes?Code: Select all
x = 97, y = 24, rule = B3/S23 bo$2bo$3o7$11b2o$10bo2bo$10bo2bo$11b2o!
Code: Select all
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!
Re: Still life puzzles
Hmm. Okay, that makes it a little tougher. Now I'm fairly sure that no such eater currently exists, and also that the easiest way to find one would be to build something very large that recovers very slowly.wwei23 wrote:Basically first interaction must be the same.dvgrn wrote:One more question: does this glider... strike in the "same spot" as these *WSSes?
If I had to construct one of these, I'd probably look for a small constellation that exploded when struck by any *WSS, as the pond does -- but that also exploded in a different way when struck by a glider (with the same initial interaction).
Then it's "just" a matter of adding catalysts to channel the two explosions, getting a different signal output in each case, and using each signal appropriately to send glider salvos back to clean up any leftover junk and rebuild the initial constellation.
It would certainly be much nicer to find a bait object that explodes the same way no matter what hits it, or even better a true four-way omnivorous eater -- generated by Bellman, let's say. But it seems as if that's likely to be a lot harder to find. Gliders just plain have a lot less "weight" behind them than the weightships do.
Re: Still life puzzles
No. I just did some searches in rule B3/S23 (where all still-lifes must necessarily be of that form), and the counts for various populations are: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.)?
4=1; 6=2; 7=1; 8=2; 20=4; 21=1; 22=34; 23=34; 24=57; 25=25; 26=97; 27=88; 28=165; 29=91; 30=129; 31=121; 32=265.
The reason there is a huge gap between 8 and 20 is that this constraint requires that all still-lifes be formed of one or more loops of living cells. This can be stable loops like beehives and ponds, unstable loops that require external stabilization, or L-trominos which also require stabilization. The smallest island that requires such stabilization is 8 bits (a long beehive) but that would require at least another copy of itself on both sides. A 10-bit long long beehive requires at least two beehives, for 22. A 12-bit long beehive can be supported by 2 tubs, for 20, but at that point, we already have the small lake.
A brute-force search reveals none (other than the block) up to 36 bits. If you try to construct one manually, there are many that work as wicks or agars, but none appear to have finite stabilizations. It may be possible to prove this, although it appears that such a proof would be fairly complicated.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?
Some years ago, I went through a similar process for the rule B34/S34, in which P2 oscillators are plentiful, but the block appears to be the only still-life. I was able to show that other than the block, all still-lifes must necessarily have an exterior that consists of crenelations (straight lines with 1-bit protrusions every 2 or 3 cells), with Life ships or long ships at each corner. No other forms are possible. The smallest such still-life is 36 bits, and an exhaustive search did indeed find that one, plus one at 44; the next ones are two at 50 and one at 51.