Thread for your unsure discoveries

[Extrementhusiast]

Tim Coe's p8 can apparently be used as a block deleter:

Code: Select all

x = 14, y = 10, rule = B3/S23
b2o3bo$b2ob2o$5bobo$6bo$2o4b3o2b2o$2o9b2o3$12b2o$12b2o!

This means that it can hassle an eater bridge snake in two slightly different ways:

Code: Select all

x = 22, y = 12, rule = B3/S23
6b2o$ob2obobo$2obobo$4b2o$5bo8b2o$14bobob2obo$5b2o9bobob2o$5b2o2b2o5b
2o$10b2o$9bo2bo$12bo2b2o$10bobo2b2o!

[danieldb]

Loaf+spark+glider=loaf

Code: Select all

x = 10, y = 8, rule = B3/S23
9bo$7b2o$3bo4b2o2$b2o$o2bo$obo$bo!

[Tropylium]

Here's a reaction that causes a blinker to change its phase.

Code: Select all

x = 12, y = 4, rule = B3/S23
4bo6bo$4bo6bo$2o2bo6bo$obo!

This "horn" mechanism is very closely related to several previously known p3 oscillators. Compare e.g. jam and pulsar quadrant:

Code: Select all

x = 8, y = 23, rule = B3/S23
5b2o$4bo$7bo$3bo3bo$2bobo2bo$2bo2bo$3b2o3$7bo$7bo$3b2o2bo$3bobo3$3b3o
2$2bo4bo$bobo3bo$bo2bo2bo$2o3bo$2b3o$2bo!

[Tropylium]

How many tiles are there in the Still Life Compatible 3x3 set? And how many if rotations and reflections are allowed?

50 modulo symmetries, or 51 if we count the vacuum tile. (Which happens to be just barely under ½: there are 104 distinct 3×3 tiles altogether.)

[dvgrn]

Now, if we're allowed to just stick 3x3 tiles next to each other, we can still build lots of things that aren't still lifes. For example, one parity of a glider can be divided into two Still-Life Compatible 3x3s. It doesn't do any good to go to N>3, because you could still build a glider with two SLC tiles for any size N. So how do we make sure that we can build all still lifes and nothing but still lifes using this set?

Actually, it's really easy to mess up(i.e. build a non-still-life) with only tiling. If you restrict the tiles so that tiling up makes only still lifes,
i) Obviously you'll need to include the blank tile.
ii) If a tile T is in the set, then tile T surrounded by blank tiles should be stable, so tile T should be stable itself.
iii) If a tile T is in the set, then the plane tiled by T should be stable.
ii) and iii) restricts the tiles a LOT. I don't think most of the still lifes can be covered by these tiles at all. i.e. Can you build a Long^n table with sufficiently big n with NxN tiles that satisfy ii) and iii)?

EDIT: And that means you should restrict the neighbor tiles a tile can have.

I missed this posting a month ago. I was trying to address the "restricting the neighbor tiles" point in my last three paragraphs. Another way of saying it is that every cell in the MxN rectangle containing the still life has to be centered on a 3x3 tile that's in the 51-tile Still Life Compatible set. You have to overlap the tiles as you're choosing which one to place next, so that the center of each new tile is on top of (and consistent with) an edge cell of a previously placed tile.

Offhand I don't see how to simplify the SLC any more. For example, it's clearly not sufficient that every ON cell be centered on a tile from the SLC -- we need to include tiles centered on OFF cells as well, and test OFF cells inside the MxN area as well, at least the inducting ones.

So, does all this allow for an algorithm that enumerates still lifes without going down any blind alleys? I.e., can we recursively take a free choice of tiles from the SLC that match the current set of constraints -- let's say, starting from a central tile and working outward one cell at a time in a spiral pattern until we hit MxM (for M>=N)? Will there always be at least one tile in the set that works, or will we hit contradictions at the corners sometimes and have to backtrack?

Probably this isn't the best way to do still life enumerations, of course. De Bruijn graphs seem to be a common way to attack the problem, but I'd have to do some more reading to find out exactly how past still-life enumeration projects ensured that they came up with exhaustive lists. Have there been any enumerations done for more than 24 bits?

[mniemiec]

So, does all this allow for an algorithm that enumerates still lifes without going down any blind alleys? I.e., can we recursively take a free choice of tiles from the SLC that match the current set of constraints -- let's say, starting from a central tile and working outward one cell at a time in a spiral pattern until we hit MxM (for M>=N)? Will there always be at least one tile in the set that works, or will we hit contradictions at the corners sometimes and have to backtrack?

Suppose one starts with a central tile. The north edge constrains the set of possible sets to the north, and the west edge constrains the set of possible tiles to the west. The northern edge of the west tile and the western edge of the north tile both constrain the tile to the northwest, and it's likely that the intersection of the two possible tiles (west then north, and north then west) will be empty. This situation is unavoidable for most rules, but with luck, it will occur relatively seldom.

One of these days, I should try rewriting my still-life enumerator using this principle to see if it is faster than the current one. I know the order of magnitude can't change (since there are around O(2.4^n) objects, requiring around O(2.4^n) CPU time to search), but if the base search time can be dramatically increased, this would help. It would also eliminate many of the esoteric kludges I had had to make to include certain "problematic" objects show up (plus having to manually add some classes of objects that fall between the cracks).

[Scorbie]

About the SLC:
Maybe yet another alternative is to find out non-contradictory 4x4 tiles and tile them so that each 2x2 at the corner would overlap. Not sure if this is any better, though.
EDIT: Personally this looks a little like hashlife algorithm, if I'm not making another stupid mistake again.

[Extrementhusiast]

About the SLC:
Maybe yet another alternative is to find out non-contradictory 4x4 tiles and tile them so that each 2x2 at the corner would overlap. Not sure if this is any better, though.
EDIT: Personally this looks a little like hashlife algorithm, if I'm not making another stupid mistake again.

Well, you have 1058 tiles to choose from, plus rotations and reflections (assuming I didn't make any programming mistakes):

Code: Select all

x = 4, y = 6346, rule = LifeHistory
4B$4B$4B$4B3$4B$4B$4B$3BA3$4B$4B$4B$2BAB3$4B$4B$4B$2B2A3$4B$4B$4B$BAB
A3$4B$4B$4B$B2AB3$4B$4B$4B$A2BA3$4B$4B$4B$AB2A3$4B$4B$3BA$2BAB3$4B$4B
$3BA$BA2B3$4B$4B$3BA$B3A3$4B$4B$3BA$A3B3$4B$4B$3BA$A2BA3$4B$4B$3BA$AB
AB3$4B$4B$3BA$2A2B3$4B$4B$2BAB$2B2A3$4B$4B$2BAB$BABA3$4B$4B$2BAB$3AB
3$4B$4B$2BAB$4A3$4B$4B$2B2A$2BAB3$4B$4B$2B2A$2B2A3$4B$4B$2B2A$BA2B3$
4B$4B$2B2A$BABA3$4B$4B$2B2A$A2BA3$4B$4B$2B2A$3AB3$4B$4B$BABA$B2AB3$4B
$4B$BABA$AB2A3$4B$4B$BABA$2ABA3$4B$4B$BABA$3AB3$4B$4B$B2AB$2BAB3$4B$
4B$B2AB$2B2A3$4B$4B$B2AB$BABA3$4B$4B$B2AB$B2AB3$4B$4B$B2AB$A2BA3$4B$
4B$B2AB$AB2A3$4B$4B$A2BA$4B3$4B$4B$A2BA$3BA3$4B$4B$A2BA$2BAB3$4B$4B$A
2BA$A2BA3$4B$4B$A2BA$4A3$4B$4B$AB2A$3BA3$4B$4B$AB2A$B2AB3$4B$4B$AB2A$
ABAB3$4B$4B$AB2A$AB2A3$4B$4B$AB2A$2A2B3$4B$4B$AB2A$2ABA3$4B$3BA$4B$BA
2B3$4B$3BA$4B$B3A3$4B$3BA$4B$A3B3$4B$3BA$4B$A2BA3$4B$3BA$4B$ABAB3$4B$
3BA$4B$2A2B3$4B$3BA$3BA$B2AB3$4B$3BA$3BA$B3A3$4B$3BA$3BA$A3B3$4B$3BA$
3BA$AB2A3$4B$3BA$3BA$2ABA3$4B$3BA$2BAB$BA2B3$4B$3BA$2BAB$BABA3$4B$3BA
$2BAB$A2BA3$4B$3BA$2BAB$3AB3$4B$3BA$BA2B$B2AB3$4B$3BA$BA2B$B3A3$4B$3B
A$BA2B$AB2A3$4B$3BA$BA2B$2ABA3$4B$3BA$BA2B$3AB3$4B$3BA$BA2B$4A3$4B$3B
A$B3A$A3B3$4B$3BA$A3B$4B3$4B$3BA$A3B$3BA3$4B$3BA$A3B$2BAB3$4B$3BA$A3B
$BA2B3$4B$3BA$A3B$A3B3$4B$3BA$A3B$A2BA3$4B$3BA$A3B$4A3$4B$3BA$A2BA$4B
3$4B$3BA$A2BA$2B2A3$4B$3BA$A2BA$BABA3$4B$3BA$A2BA$A3B3$4B$3BA$A2BA$3A
B3$4B$3BA$A2BA$4A3$4B$3BA$ABAB$3BA3$4B$3BA$ABAB$B2AB3$4B$3BA$ABAB$ABA
B3$4B$3BA$ABAB$AB2A3$4B$3BA$ABAB$2A2B3$4B$3BA$ABAB$2ABA3$4B$3BA$2A2B$
2B2A3$4B$3BA$2A2B$BABA3$4B$3BA$2A2B$B2AB3$4B$3BA$2A2B$B3A3$4B$3BA$2A
2B$A3B3$4B$3BA$2A2B$AB2A3$4B$3BA$2A2B$2ABA3$4B$2BAB$2B2A$ABAB3$4B$2BA
B$2B2A$2A2B3$4B$2BAB$BABA$2BAB3$4B$2BAB$BABA$2B2A3$4B$2BAB$BABA$BA2B
3$4B$2BAB$BABA$BABA3$4B$2BAB$BABA$B2AB3$4B$2BAB$BABA$A2BA3$4B$2BAB$BA
BA$ABAB3$4B$2BAB$BABA$AB2A3$4B$2BAB$BABA$2A2B3$4B$2BAB$BABA$2ABA3$4B$
2BAB$3AB$4B3$4B$2BAB$3AB$3BA3$4B$2BAB$4A$4B3$4B$2B2A$3BA$A2BA3$4B$2B
2A$3BA$3AB3$4B$2B2A$2BAB$ABAB3$4B$2B2A$2BAB$2A2B3$4B$2B2A$BA2B$BA2B3$
4B$2B2A$BA2B$BABA3$4B$2B2A$BA2B$B2AB3$4B$2B2A$BA2B$B3A3$4B$2B2A$BA2B$
A2BA3$4B$2B2A$BA2B$ABAB3$4B$2B2A$BA2B$AB2A3$4B$2B2A$BA2B$2A2B3$4B$2B
2A$BA2B$2ABA3$4B$2B2A$BABA$B2AB3$4B$2B2A$BABA$A3B3$4B$2B2A$BABA$A2BA
3$4B$2B2A$BABA$ABAB3$4B$2B2A$BABA$2A2B3$4B$2B2A$BABA$2ABA3$4B$2B2A$A
2BA$3BA3$4B$2B2A$A2BA$B2AB3$4B$2B2A$A2BA$ABAB3$4B$2B2A$A2BA$2A2B3$4B$
2B2A$A2BA$2ABA3$4B$2B2A$A2BA$3AB3$4B$2B2A$3AB$4B3$4B$BABA$B2AB$4B3$4B
$BABA$B2AB$A3B3$4B$BABA$AB2A$A3B3$4B$BABA$2ABA$4B3$4B$BABA$2ABA$3BA3$
4B$BABA$2ABA$2BAB3$4B$BABA$2ABA$2B2A3$4B$BABA$2ABA$BA2B3$4B$BABA$2ABA
$BABA3$4B$BABA$2ABA$A3B3$4B$BABA$2ABA$A2BA3$4B$BABA$3AB$4B3$4B$B2AB$
2BAB$A3B3$4B$B2AB$2BAB$A2BA3$4B$B2AB$2BAB$ABAB3$4B$B2AB$2BAB$2A2B3$4B
$B2AB$2B2A$A3B3$4B$B2AB$BABA$2BAB3$4B$B2AB$BABA$2B2A3$4B$B2AB$BABA$BA
2B3$4B$B2AB$BABA$BABA3$4B$B2AB$BABA$A3B3$4B$B2AB$BABA$A2BA3$4B$B2AB$B
2AB$4B3$4B$B2AB$A2BA$2BAB3$4B$B2AB$A2BA$2B2A3$4B$B2AB$A2BA$BABA3$4B$B
2AB$A2BA$B2AB3$4B$B2AB$A2BA$B3A3$4B$B2AB$A2BA$A2BA3$4B$B2AB$A2BA$AB2A
3$4B$B2AB$A2BA$4A3$4B$B2AB$AB2A$4B3$4B$B2AB$AB2A$A3B3$4B$B3A$2BAB$A3B
3$4B$B3A$BA2B$BA2B3$4B$B3A$BA2B$BABA3$4B$B3A$BA2B$A3B3$4B$B3A$BA2B$A
2BA3$4B$B3A$A3B$2BAB3$4B$B3A$A3B$2B2A3$4B$B3A$A3B$BA2B3$4B$B3A$A3B$BA
BA3$4B$B3A$A3B$B2AB3$4B$B3A$A3B$B3A3$4B$B3A$A3B$A2BA3$4B$B3A$A3B$ABAB
3$4B$B3A$A3B$AB2A3$4B$B3A$A3B$2A2B3$4B$B3A$A3B$2ABA3$4B$B3A$A3B$3AB3$
4B$B3A$A3B$4A3$4B$B3A$A2BA$2BAB3$4B$B3A$A2BA$BA2B3$4B$B3A$A2BA$BABA3$
4B$B3A$A2BA$B2AB3$4B$B3A$A2BA$A3B3$4B$B3A$A2BA$A2BA3$4B$B3A$A2BA$ABAB
3$4B$B3A$A2BA$2A2B3$4B$B3A$A2BA$2ABA3$4B$B3A$A2BA$3AB3$4B$B3A$ABAB$A
3B3$4B$B3A$2A2B$3BA3$4B$A2BA$4B$3BA3$4B$A2BA$4B$2BAB3$4B$A2BA$4B$A2BA
3$4B$A2BA$4B$4A3$4B$A2BA$3BA$2B2A3$4B$A2BA$3BA$BABA3$4B$A2BA$3BA$A3B
3$4B$A2BA$3BA$3AB3$4B$A2BA$3BA$4A3$4B$A2BA$2BAB$3BA3$4B$A2BA$2BAB$B2A
B3$4B$A2BA$2BAB$ABAB3$4B$A2BA$2BAB$AB2A3$4B$A2BA$2BAB$2A2B3$4B$A2BA$
2BAB$2ABA3$4B$A2BA$2BAB$3AB3$4B$A2BA$A2BA$4B3$4B$A2BA$A2BA$B2AB3$4B$A
2BA$A2BA$B3A3$4B$A2BA$A2BA$AB2A3$4B$A2BA$A2BA$4A3$4B$A2BA$4A$4B3$4B$A
B2A$3BA$3BA3$4B$AB2A$3BA$B2AB3$4B$AB2A$3BA$ABAB3$4B$AB2A$3BA$2A2B3$4B
$AB2A$3BA$2ABA3$4B$AB2A$3BA$3AB3$4B$AB2A$ABAB$3BA3$4B$AB2A$ABAB$2BAB
3$4B$AB2A$ABAB$BA2B3$4B$AB2A$ABAB$A3B3$4B$AB2A$ABAB$A2BA3$4B$AB2A$ABA
B$ABAB3$4B$AB2A$ABAB$2A2B3$4B$AB2A$AB2A$4B3$4B$AB2A$AB2A$A3B3$4B$AB2A
$2A2B$3BA3$4B$AB2A$2ABA$4B3$4B$AB2A$2ABA$3BA3$4B$4A$4B$2BAB3$4B$4A$4B
$2B2A3$4B$4A$4B$BABA3$4B$4A$4B$B2AB3$4B$4A$4B$B3A3$4B$4A$4B$A2BA3$4B$
4A$4B$AB2A3$4B$4A$4B$4A3$4B$4A$3BA$2BAB3$4B$4A$3BA$BA2B3$4B$4A$3BA$BA
BA3$4B$4A$3BA$B2AB3$4B$4A$3BA$A3B3$4B$4A$3BA$A2BA3$4B$4A$3BA$ABAB3$4B
$4A$3BA$2A2B3$4B$4A$3BA$2ABA3$4B$4A$3BA$3AB3$4B$4A$2BAB$A3B3$4B$4A$A
2BA$3BA3$4B$4A$A2BA$2BAB3$4B$4A$A2BA$BABA3$4B$4A$A2BA$B2AB3$4B$4A$A2B
A$A2BA3$3BA$4B$4B$A3B3$3BA$4B$4B$A2BA3$3BA$4B$4B$ABAB3$3BA$4B$4B$AB2A
3$3BA$4B$4B$2A2B3$3BA$4B$4B$2ABA3$3BA$4B$3BA$ABAB3$3BA$4B$3BA$2A2B3$
3BA$4B$2BAB$3AB3$3BA$4B$2BAB$4A3$3BA$4B$BA2B$ABAB3$3BA$4B$BA2B$2A2B3$
3BA$4B$BA2B$4A3$3BA$4B$B3A$A3B3$3BA$4B$B3A$A2BA3$3BA$4B$B3A$ABAB3$3BA
$4B$B3A$2A2B3$3BA$4B$A3B$3BA3$3BA$4B$A3B$2BAB3$3BA$4B$A3B$2B2A3$3BA$
4B$A3B$BA2B3$3BA$4B$A3B$BABA3$3BA$4B$A3B$A2BA3$3BA$4B$A3B$3AB3$3BA$4B
$A2BA$3BA3$3BA$4B$A2BA$2BAB3$3BA$4B$A2BA$BA2B3$3BA$4B$A2BA$A3B3$3BA$
4B$A2BA$A2BA3$3BA$4B$A2BA$4A3$3BA$4B$ABAB$B2AB3$3BA$4B$ABAB$B3A3$3BA$
4B$ABAB$AB2A3$3BA$4B$ABAB$2ABA3$3BA$4B$2A2B$2BAB3$3BA$4B$2A2B$BA2B3$
3BA$4B$2A2B$B3A3$3BA$4B$2A2B$A2BA3$3BA$4B$2A2B$ABAB3$3BA$4B$2A2B$2A2B
3$3BA$3BA$4B$2A2B3$3BA$3BA$BABA$ABAB3$3BA$3BA$BABA$AB2A3$3BA$3BA$BABA
$2A2B3$3BA$3BA$BABA$2ABA3$3BA$3BA$BABA$3AB3$3BA$3BA$B2AB$A3B3$3BA$3BA
$B2AB$A2BA3$3BA$3BA$B2AB$ABAB3$3BA$3BA$B2AB$2A2B3$3BA$3BA$B3A$A3B3$3B
A$3BA$A3B$3BA3$3BA$3BA$A3B$2BAB3$3BA$3BA$A3B$BA2B3$3BA$3BA$A3B$A3B3$
3BA$3BA$A3B$A2BA3$3BA$3BA$A3B$4A3$3BA$3BA$AB2A$3BA3$3BA$3BA$AB2A$ABAB
3$3BA$3BA$AB2A$2A2B3$3BA$3BA$2ABA$2BAB3$3BA$3BA$2ABA$2B2A3$3BA$3BA$2A
BA$BA2B3$3BA$3BA$2ABA$BABA3$3BA$3BA$2ABA$B2AB3$3BA$3BA$2ABA$A2BA3$3BA
$3BA$2ABA$ABAB3$3BA$3BA$2ABA$AB2A3$3BA$3BA$2ABA$2A2B3$3BA$3BA$2ABA$2A
BA3$3BA$2BAB$BA2B$A3B3$3BA$2BAB$BA2B$AB2A3$3BA$2BAB$BA2B$2ABA3$3BA$2B
AB$BABA$ABAB3$3BA$2BAB$BABA$AB2A3$3BA$2BAB$BABA$2A2B3$3BA$2BAB$BABA$
2ABA3$3BA$2BAB$A2BA$B2AB3$3BA$2BAB$A2BA$B3A3$3BA$2BAB$A2BA$AB2A3$3BA$
2BAB$A2BA$2ABA3$3BA$2BAB$A2BA$3AB3$3BA$2BAB$A2BA$4A3$3BA$2BAB$3AB$3BA
3$3BA$2B2A$BA2B$2A2B3$3BA$2B2A$BA2B$2ABA3$3BA$2B2A$A3B$B2AB3$3BA$2B2A
$A3B$B3A3$3BA$2B2A$A3B$AB2A3$3BA$2B2A$A3B$2ABA3$3BA$2B2A$A3B$3AB3$3BA
$2B2A$A3B$4A3$3BA$2B2A$A2BA$3BA3$3BA$2B2A$A2BA$B2AB3$3BA$2B2A$A2BA$AB
AB3$3BA$2B2A$A2BA$2A2B3$3BA$2B2A$A2BA$2ABA3$3BA$2B2A$A2BA$3AB3$3BA$BA
2B$B2AB$A3B3$3BA$BA2B$B2AB$A2BA3$3BA$BA2B$B3A$A3B3$3BA$BA2B$AB2A$2BAB
3$3BA$BA2B$AB2A$BA2B3$3BA$BA2B$AB2A$A3B3$3BA$BA2B$AB2A$A2BA3$3BA$BA2B
$AB2A$ABAB3$3BA$BA2B$AB2A$2A2B3$3BA$BA2B$2ABA$3BA3$3BA$BA2B$2ABA$2BAB
3$3BA$BA2B$2ABA$2B2A3$3BA$BA2B$2ABA$BA2B3$3BA$BA2B$2ABA$BABA3$3BA$BA
2B$2ABA$A2BA3$3BA$BA2B$3AB$3BA3$3BA$BABA$B2AB$A3B3$3BA$BABA$ABAB$2BAB
3$3BA$BABA$ABAB$BA2B3$3BA$BABA$ABAB$A3B3$3BA$BABA$ABAB$A2BA3$3BA$BABA
$ABAB$ABAB3$3BA$BABA$ABAB$2A2B3$3BA$BABA$AB2A$A3B3$3BA$BABA$2A2B$3BA
3$3BA$BABA$2A2B$2BAB3$3BA$BABA$2A2B$2B2A3$3BA$BABA$2A2B$BA2B3$3BA$BAB
A$2A2B$BABA3$3BA$BABA$2A2B$A2BA3$3BA$BABA$2ABA$3BA3$3BA$BABA$2ABA$2BA
B3$3BA$BABA$2ABA$2B2A3$3BA$BABA$2ABA$BA2B3$3BA$BABA$2ABA$BABA3$3BA$BA
BA$2ABA$A3B3$3BA$BABA$2ABA$A2BA3$3BA$B2AB$BA2B$A2BA3$3BA$B2AB$A3B$2B
2A3$3BA$B2AB$A3B$BABA3$3BA$B2AB$A3B$B2AB3$3BA$B2AB$A3B$B3A3$3BA$B2AB$
A3B$AB2A3$3BA$B2AB$A3B$2ABA3$3BA$B2AB$A3B$3AB3$3BA$B2AB$A3B$4A3$3BA$B
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AB3$2B2A$2ABA$3BA$AB2A3$2B2A$2ABA$3BA$2ABA3$2B2A$2ABA$3BA$3AB3$2B2A$
2ABA$3BA$4A3$2B2A$2ABA$2BAB$A2BA3$2B2A$2ABA$2BAB$ABAB3$2B2A$2ABA$BA2B
$A2BA3$2B2A$2ABA$BABA$A2BA3$2B2A$2ABA$A3B$BABA3$2B2A$2ABA$A3B$B3A3$2B
2A$2ABA$A3B$AB2A3$2B2A$2ABA$A2BA$BABA3$2B2A$2ABA$A2BA$B2AB3$2B2A$2ABA
$A2BA$B3A3$2B2A$2ABA$A2BA$A2BA3$2B2A$2ABA$A2BA$ABAB3$2B2A$2ABA$A2BA$A
B2A3$2B2A$3AB$4B$AB2A3$2B2A$3AB$4B$2ABA3$2B2A$3AB$4B$4A3$BABA$A3B$4B$
A2BA3$BABA$A3B$B2AB$A2BA3$BABA$A3B$B3A$A2BA3$BABA$A3B$AB2A$BABA3$BABA
$A3B$AB2A$B2AB3$BABA$A3B$AB2A$A2BA3$BABA$A3B$AB2A$ABAB3$BABA$A3B$AB2A
$AB2A3$BABA$A3B$AB2A$2ABA3$BABA$A3B$2ABA$BABA3$BABA$A2BA$3BA$3AB3$BAB
A$A2BA$3BA$4A3$BABA$A2BA$B2AB$A2BA3$BABA$A2BA$ABAB$BABA3$BABA$A2BA$AB
AB$A2BA3$BABA$A2BA$ABAB$AB2A3$BABA$A2BA$ABAB$2ABA3$BABA$A2BA$AB2A$A2B
A3$BABA$A2BA$AB2A$ABAB3$BABA$A2BA$2A2B$BABA3$BABA$A2BA$2ABA$BABA3$BAB
A$A2BA$2ABA$A2BA3$BABA$ABAB$A3B$B3A3$BABA$ABAB$A3B$A2BA3$BABA$ABAB$A
3B$4A3$BABA$ABAB$A2BA$B2AB3$BABA$ABAB$A2BA$B3A3$BABA$ABAB$A2BA$AB2A3$
BABA$ABAB$A2BA$2ABA3$BABA$ABAB$A2BA$3AB3$BABA$ABAB$A2BA$4A3$BABA$ABAB
$ABAB$BABA3$BABA$ABAB$ABAB$A2BA3$BABA$ABAB$ABAB$AB2A3$BABA$ABAB$ABAB$
2ABA3$BABA$AB2A$A3B$B3A3$BABA$AB2A$A3B$AB2A3$BABA$AB2A$A3B$2ABA3$BABA
$AB2A$A3B$4A3$BABA$2A2B$3BA$AB2A3$BABA$2A2B$3BA$2ABA3$BABA$2A2B$3BA$
4A3$BABA$2A2B$2BAB$A2BA3$BABA$2A2B$2BAB$AB2A3$BABA$2A2B$2BAB$2ABA3$BA
BA$2A2B$2B2A$ABAB3$BABA$2A2B$BABA$A2BA3$BABA$2A2B$A2BA$B3A3$BABA$2A2B
$A2BA$AB2A3$BABA$2ABA$4B$2ABA3$BABA$2ABA$4B$4A3$BABA$2ABA$3BA$3AB3$BA
BA$2ABA$3BA$4A3$BABA$2ABA$BA2B$A2BA3$BABA$2ABA$BABA$A2BA3$BABA$2ABA$A
3B$B3A3$BABA$2ABA$A3B$AB2A3$BABA$2ABA$A2BA$B2AB3$BABA$2ABA$A2BA$B3A3$
BABA$2ABA$A2BA$A2BA3$BABA$2ABA$A2BA$AB2A3$B2AB$A2BA$A2BA$B2AB3$B2AB$A
2BA$A2BA$B3A3$B2AB$A2BA$A2BA$AB2A3$B2AB$A2BA$A2BA$4A3$B2AB$A2BA$AB2A$
A2BA3$B3A$A3B$A2BA$4A3$B3A$A3B$ABAB$AB2A3$B3A$A3B$ABAB$2ABA3$B3A$A3B$
AB2A$AB2A3$B3A$A3B$AB2A$2ABA3$B3A$A3B$2A2B$A2BA3$B3A$A2BA$A3B$4A3$B3A
$A2BA$A2BA$3AB3$B3A$A2BA$A2BA$4A3$B3A$A2BA$ABAB$2ABA3$B3A$A2BA$2ABA$A
2BA3$A2BA$4B$4B$A2BA3$A2BA$4B$4B$AB2A3$A2BA$4B$2BAB$4A3$A2BA$4B$A2BA$
A2BA3$A2BA$4B$A2BA$4A3$A2BA$4B$4A$A2BA3$A2BA$3BA$BABA$AB2A3$A2BA$3BA$
BABA$2ABA3$A2BA$3BA$A3B$A2BA3$A2BA$3BA$A3B$4A3$A2BA$3BA$3AB$A2BA3$A2B
A$2BAB$B2AB$A2BA3$A2BA$2BAB$ABAB$A2BA3$A2BA$2BAB$ABAB$AB2A3$A2BA$2BAB
$ABAB$2ABA3$A2BA$2BAB$AB2A$A2BA3$A2BA$2BAB$2ABA$A2BA3$A2BA$2B2A$ABAB$
A2BA3$A2BA$2B2A$2A2B$A2BA3$A2BA$BABA$BA2B$AB2A3$A2BA$BABA$BA2B$2ABA3$
A2BA$BABA$BABA$A2BA3$A2BA$BABA$BABA$AB2A3$A2BA$BABA$BABA$2ABA3$A2BA$B
ABA$A2BA$AB2A3$A2BA$BABA$A2BA$2ABA3$A2BA$BABA$A2BA$4A3$A2BA$BABA$ABAB
$A2BA3$A2BA$BABA$2ABA$A2BA3$A2BA$B2AB$A2BA$A2BA3$A2BA$B2AB$A2BA$AB2A
3$A2BA$B2AB$A2BA$4A3$A2BA$B3A$A3B$AB2A3$A2BA$B3A$A3B$2ABA3$A2BA$B3A$A
3B$4A3$A2BA$A2BA$4B$4A3$A2BA$A2BA$AB2A$A2BA3$A2BA$AB2A$A3B$AB2A3$A2BA
$AB2A$A3B$2ABA3$A2BA$AB2A$A3B$4A3$A2BA$AB2A$A2BA$2ABA3$A2BA$4A$4B$AB
2A3$A2BA$4A$4B$4A3$AB2A$4B$AB2A$AB2A3$AB2A$4B$AB2A$2ABA3$AB2A$4B$2ABA
$AB2A3$AB2A$4B$2ABA$2ABA3$AB2A$3BA$ABAB$2ABA3$AB2A$3BA$2A2B$AB2A3$AB
2A$3BA$2A2B$2ABA3$AB2A$3BA$2ABA$AB2A3$AB2A$3BA$2ABA$2ABA3$AB2A$BA2B$A
2BA$AB2A3$AB2A$BA2B$A2BA$2ABA3$AB2A$BA2B$A2BA$4A3$AB2A$BABA$A3B$4A3$A
B2A$BABA$A2BA$4A3$AB2A$A3B$2B2A$2ABA3$AB2A$A3B$AB2A$AB2A3$AB2A$A3B$AB
2A$2ABA3$AB2A$A2BA$BABA$2ABA3$AB2A$A2BA$A2BA$AB2A3$AB2A$A2BA$A2BA$2AB
A3$AB2A$A2BA$A2BA$4A3$AB2A$A2BA$ABAB$AB2A3$AB2A$ABAB$A2BA$4A3$AB2A$AB
2A$A3B$4A3$4A$A2BA$A2BA$4A!

[Bullet51]

Two oscillators marked "UNKNOWN":

Code: Select all

x = 50, y = 20, rule = B3/S23
bo39b2o$2bo7b2o29b2o$3o8bo3b2o$4b2o5bobo2bo22b4o$3bo2bo3b2ob2o2b2o20bo
3bo$3bobo3bo5b2o2bo21b2obob2o$4bo3bobob2o3b2o21bobobobo2bo$9b2obob2o
26bobo3b2o$6bo5bo3b3o19bo3bo2bo$5bobo4bob2o3bo13b2o8b3o$bo2bob2o5bo2b
3o14bo2bo3b3o$b4o9bobo13b2obobo4bo2bo$6b4o3b2o15b2obob4obo2bo$3b2obo3b
obo2bo18bo4bob2o$4bo2bobob2o2bo19b3obo$2bo2bobobo3b2o23b2o$2b2obo2bob
2o23b2o$4bobobobo24bo$4bobobobo26bo$5bo3bo26b2o!

[BlinkerSpawn]

Stator reduction of the first one.

Code: Select all

x = 18, y = 18, rule = B3/S23
13b2o$13bo$14bo$13b2o$7b2ob2o3b2o$6bobobob2o2bo$5bo2bobo3b2o$4bo3bo3bo
$4b4o2bo3b2o$12bobo2bo$4b3obo2b2o3b2o$4bo5bo2bo$5bobob2o2bo$2obobo5b2o
$ob2o2bob2o$4bobobo$4b2o4bo$9b2o!

I'm sure the other is minimal.

[Sokwe]

Two oscillators marked "UNKNOWN"

Stator minimization:

Code: Select all

x = 47, y = 17, rule = B3/S23
41b2o$10b2o29bo$6b2obo2bo29bo$2b2obobob2obo26b4o2bo$2b2obo6b2o25bo3b3o
$5bo2bob2o28b3o$2b3o3bo2bo30bob2o$bo7bobob2o27bobobo$b2o5b2o2bobo27bo
3bo$4b2obo2bobo20b2o8b3o$b2o3b2o2bob2o19bobo4b3o$obobo3b2o20b2obobo4bo
2bo$o3b3o23bob2ob4obo2bo$b3o3b3o24bo4bob2o$3bo2bo2bo24bob2obo$6b2o25b
2obo2bo$37b2o!

[towerator]

Also, is the mango the smallest still life that can be converted to a glider by a single dot spark?

Code: Select all

x = 5, y = 6, rule = B3/S23
bo2$2b2o$bo2bo$o2bo$b2o!

Equaled by the long ship:

Code: Select all

x = 6, y = 4, rule = B3/S23
2b2o$bobobo$obo$2o!

If you're not too regardant, a ship can create a B&G with the same spark:

Code: Select all

x = 5, y = 3, rule = B3/S23
b2obo$obo$2o!

Edit: whoops, I should have refreshed the page earlier...

[praosylen]

A transparent pond that may or may not be useful:

Code: Select all

x = 11, y = 6, rule = B3/S23
8b2o$7bo2bo$2b2o3bo2bo$obo5b2o$obo$2o!

[gmc_nxtman]

Another, less useful reaction that creates a B60:

Code: Select all

x = 16, y = 20, rule = LifeHistory
5.B$4.BDB$2.2BDBD$.3BDBDB$.4BD2B$.8B$.B2D5B$2.2D6B$2.8B$11BDB$5BCD3BD
BD$5B2C4BDE2B$.5B2E4BE3B$2.2D2BE5BE2B$2.2DBE7B$2.6B2E3B$2.6B2E2B$2.6B
$3.B2DB$4.2D!

Also, this:

Code: Select all

x = 3, y = 12, rule = LifeHistory
A.A$2A$.A2$2A$A$2.A$.2A2$.A$.2A$A.A!

[mniemiec]

Also, this: ...

This has long been known. Glider plus pre-pre-block is the classic way to make a LWSS. Frequently, hitting a still-life that has a pre-block on a corner will make a LWSS escaping from whatever is left.

[SuperJedi224]

Is this pentadecomino new? I found it about an hour ago.

-Stabilizes on generation 888
-Produces 3 gliders, 9 blocks, 14 blinkers, 3 boats, a loaf and a ship (a final population of 145 cells)
-Peak population 373 cells (gen 764)

N92y1.png (1.09 KiB) Viewed 414 times

Code: Select all

#15-cell potential methuselah
#Lifespan 888

x = 6, y = 7, rule = B3/S23
bo$3o$2b2o$3bobo$2b4o$4bo$3b2o!

[gameoflifeboy]

Is this pentadecomino new? I found it about an hour ago.

Hey, I know you from Googology Wiki!
There are 3426576 distinct pentadecominoes, so this one was definitely enumerated before. It might not have been run as a pattern, though.
However, it's not notable as a methuselah, because there are patterns lasting 20 times longer with only 10 cells, for instance Bunnies 10. Even the R-pentomino, with only five cells, lasts 1103 generations.
People say methuselahs aren't notable any more, but if you could find a 15-cell pattern with a small bounding box lasting over 30000 generations, it might be notable. It would be very hard without a search script, though.

[SuperJedi224]

However, it's not notable as a methuselah, because there are patterns lasting 20 times longer with only 10 cells, for instance Bunnies 10. Even the R-pentomino, with only five cells, lasts 1103 generations.

Yeah, I know.

[Bullet51]

P9 and P15 from dr2:

Code: Select all

x = 42, y = 19, rule = B3/S23
36bo$12b2o22b3o$12bo26bo$13bo20b4o2bo$12b2o2bo17bo3b2obo$14b3o19b2o3bo
$12b2o16bo6bob2o$11bo2bo14bo5bobobo$9bob2obo16b2obobo2bo$9bo4bob2o13b
2obobobo$7b2o2b2obo2bo16bobobobo$12bobobo9b2o3b3o2bo2bobo$6b2obo2bob2o
10bo3bo5bo4bo$2obobobob3o11b2obobo2b5o4bo$ob2obo18bobob3o9b2o$4bob6o
12bo2bo4b2o$4bo6bo13bobob3o2bo$3b2o3bobo15bo2bo3bo2b2o$8b2o17b2o5b2obo!

[BlinkerSpawn]

Reduction to the p15:

Code: Select all

x = 18, y = 18, rule = B3/S23
13b2o$13bo$14bo$11b4o$11bo3b2o$13b2o2bo$7bo6bob2o$6bo5bobobo$8b2obobo
2bo$8b2obobobo$11bobobobo$3b2o3b3o2bo2b2o$3bo3bo5bo$2obobo2b5o$ob2ob3o
$4bo4b2o$4bob3o2bo$5b2o3b2o!

[gmc_nxtman]

I'm sure this is useless, but is it known? It seems very strange, yet too simple to be new...

Code: Select all

x = 10, y = 5, rule = B3/S23
6bo$bo3bobo$3o2b2obo$8bo$8b2o!

[Linicks]

I just done a small variation on that...

Boom and Bust:

Code: Select all

#CXRLE Pos=0,1
x = 7, y = 2, rule = B3/S23
bo3bo$3ob3o!

Nick

[praosylen]

I'm sure this is useless, but is it known? It seems very strange, yet too simple to be new...

Code: Select all

x = 10, y = 5, rule = B3/S23
6bo$bo3bobo$3o2b2obo$8bo$8b2o!

A simplification:

Code: Select all

x = 14, y = 7, rule = B3/S23
6bo$bo3bobo$3o2b2o2$11b2o$11bobo$11bo!

[praosylen]

Any chance of restoring this block?

Code: Select all

x = 8, y = 12, rule = B3/S23
2o$2o7$5b3o$4bo2bo$3bo2bo$4b2o!

[gmc_nxtman]

Small G to block + boat:

Code: Select all

x = 11, y = 21, rule = B3/S23
o$3o$3bo$2b2o3$7bo$2bo2b2o$bobo2b2o$2b2o7$7b2o$b2o4bo$bo6b3o$2b3o5bo$
4bo!