Which still-life patterns are noteworthy?

[confocaloid]

Which still-life patterns are considered interesting/useful/noteworthy?
There is some discussion in Chapter 2 in Conway's Game of Life: Mathematics and Construction, and there is also an interesting discussion thread about p2 oscillators here, so might be nice to have a forum thread about what can make a still-life interesting.

Maybe also mention that new still-lives or p2 oscillators etc are not considered notable unless they do something unusual.

I'm interested in good ways to formulate more directly what it means in this case to "do something unusual".

For example, I do understand that catalysts count (although how about useless variants of catalysts, like an eater 1 with a giant blob welded to it?)

What should be mentioned to explain the "do something unusual" part?

I'm not sure it can be formulated in a rigorous way. "Has an unique and useful reaction associated with it" (so the eater 1 with a blob wouldn't count because the actual reacting part is the same as the eater 1).

Defining "useful" is harder but I think common sense can manage.

[LuveelVoom]

There was a discussion on the discord about still lifes that contained all SL-compatible n by m grids. The 2x2 case, where all elements are compatible, was provided (i backed myself into a grammar hole here, oops) with this solution (not by me):

Code: Select all

 x = 9, y = 4, rule = B3/S23
2ob2ob2o$bob2obobo$bo4bobo$2o4b2o!

(18 bits. A smaller solution may exist.)
While this isn’t that interesting on its own, if a search/sat solver was used to find a similar still life for all 3x3 (4x4?!?!?) grids it might warrant a page, a rarity for high-pop still lives, of which the majority that have pages (EDIT) have no fathers besides themselfs.

[KittyTac]

That one is definitely interesting imho.

A good way to define this might be is, what property does the still-life have to distinguish it from other still-lives? It can be a reaction from an engineering perspective or some quality of it from a mathematical perspective.

[confocaloid]

[...] high-pop still lives, of which the majority that have pages are gardens of eden.

Correction: a still life (which always has at least one parent, namely itself) cannot be a Garden of Eden (which has no parents at all).
However, it may be impossible to construct a still life "from scratch" by any means (Unique father problem).
Other wiki pages about kinds of large (or infinite) still-life patterns include Quad pseudo still life, Triple pseudo still life, Block agar, Lake, Category:Stable agars

[LuveelVoom]

[...] high-pop still lives, of which the majority that have pages are gardens of eden.

Correction: a still life (which always has at least one parent, namely itself) cannot be a Garden of Eden (which has no parents at all).
However, it may be impossible to construct a still life "from scratch" by any means (Unique father problem).
Other wiki pages about kinds of large (or infinite) still-life patterns include Quad pseudo still life, Triple pseudo still life, Block agar, Lake, Category:Stable agars

Thanks.
I wouldn't consider an agar a still life though. Has anyone searched for N pseudo still lifes N>4? Obviously minimality is very hard beyond 4, but surely examples exist.

[H. H. P. M. P. Cole]

There was a discussion on the discord about still lifes that contained all SL-compatible n by m grids. The 2x2 case, where all elements are compatible, was provided (i backed myself into a grammar hole here, oops) with this solution (not by me):

Code: Select all

 x = 9, y = 4, rule = B3/S23
2ob2ob2o$bob2obobo$bo4bobo$2o4b2o!

(18 bits. A smaller solution may exist.)
While this isn’t that interesting on its own, if a search/sat solver was used to find a similar still life for all 3x3 (4x4?!?!?) grids it might warrant a page, a rarity for high-pop still lives, of which the majority that have pages (EDIT) have no fathers besides themselfs.

16 bits for the 2x2 case, though not a strict SL:

Code: Select all

x = 10, y = 3, rule = B3/S23
2o3b2ob2o$obobobob2o$b2ob2o!

Code: Select all

x = 67, y = 18, rule = LifeHistory
7.2D14.2D11.2D$2A3.2ADCA4.2A3.2A.ACD3.2A3.2A.2C4.2A3.2A.2A4.2A3.2ADCA
$A.A.A.A.2A4.A.A.A.A.2A4.A.A.A.A.2A4.A.A.A.ADCA4.A.A.A.ADCA$.2A.2A9.2A
.2A9.2A.2A9.2A.2A.2D6.2A.2A5$2A3.2A.2A4.2A3.2A.2A4.2A3.2A.2A4.2A3.2A.
2A4.2A3.2A.ACD$A.A.ADC.2A4.ADC.A.A.2A4.A.A.A.A.ACD3.CDA.A.A.2A4.A.A.A
.A.ACD$.2A.ACD8.2C.2A9.2A.2A3.2D3.DCA.2A9.2A.2A5$2A3.2A.2A4.2A3.2A.2A
4.2A3.2C.2A4.2C3.2A.2A4.2A3.2A.2C$A.A.CDA.2A4.A.A.A.A.2C4.A.A.ADC.2A4.
CDA.A.A.2A4.A.A.A.A.2C$.2A.2C9.2A.2A2.2D5.2A.2A9.2A.2A9.2A.2A!

[LuveelVoom]

16 bits for the 2x2 case, though not a strict SL:

Code: Select all

x = 10, y = 3, rule = B3/S23
2o3b2ob2o$obobobob2o$b2ob2o!

Code: Select all

x = 67, y = 18, rule = LifeHistory
7.2D14.2D11.2D$2A3.2ADCA4.2A3.2A.ACD3.2A3.2A.2C4.2A3.2A.2A4.2A3.2ADCA
$A.A.A.A.2A4.A.A.A.A.2A4.A.A.A.A.2A4.A.A.A.ADCA4.A.A.A.ADCA$.2A.2A9.2A
.2A9.2A.2A9.2A.2A.2D6.2A.2A5$2A3.2A.2A4.2A3.2A.2A4.2A3.2A.2A4.2A3.2A.
2A4.2A3.2A.ACD$A.A.ADC.2A4.ADC.A.A.2A4.A.A.A.A.ACD3.CDA.A.A.2A4.A.A.A
.A.ACD$.2A.ACD8.2C.2A9.2A.2A3.2D3.DCA.2A9.2A.2A5$2A3.2A.2A4.2A3.2A.2A
4.2A3.2C.2A4.2C3.2A.2A4.2A3.2A.2C$A.A.CDA.2A4.A.A.A.A.2C4.A.A.ADC.2A4.
CDA.A.A.2A4.A.A.A.A.2C$.2A.2C9.2A.2A2.2D5.2A.2A9.2A.2A9.2A.2A!

I was aware of this, but discarded it (because, as you say, it's not strict.)
I guess the 18 bit solution isn't really strict either? Is there a <20 bit solution where no disconnected part can be removed without the still life failing?

[get_Snacked]

Is there a <20 bit solution where no disconnected part can be removed without the still life failing?

no. the block must always be its own island, as adding anything to the edge of it will cause at least one of the cells in the block to die of overpopulation.

[confocaloid]

Is there a <20 bit solution where no disconnected part can be removed without the still life failing?

no. the block must always be its own island, as adding anything to the edge of it will cause at least one of the cells in the block to die of overpopulation.

By itself, that logic does not appear to be sufficient for proving impossibiity of a solution below 20 bits.

If I understand correctly, the following is a 20-bit solution (every 2-by-2 configuration of alive and dead cells appears somewhere; and no single island can be removed while keeping the remainder a still life, although it is possible to remove two or three islands at once):

Code: Select all

x = 5, y = 7, rule = B3/S23
2ob2o$o3bo$bobo$2ob2o2$2ob2o$2ob2o!
#C [[ THEME MCell GRID SHOWGENSTATS ]]

However, it uses two blocks, which seems redundant, suggesting that in principle there could be some way to do with fewer alive cells.

edit:

This was found on Discord nine hours ago.

Code: Select all

x = 5, y = 7, rule = B3/S23
2o$o$bo$2o$bob2o$o2b2o$2o!

The larger island can be removed while keeping the remainder (i.e. the block) a still life. Hence IIUC this one doesn't count as a solution to the above puzzle (despite being a strict still life).

[hotdogPi]

This was found on Discord nine hours ago.

Code: Select all

x = 5, y = 7, rule = B3/S23
2o$o$bo$2o$bob2o$o2b2o$2o!

[get_Snacked]

This was found on Discord nine hours ago.

Code: Select all

x = 5, y = 7, rule = B3/S23
2o$o$bo$2o$bob2o$o2b2o$2o!

The larger island can be removed while keeping the remainder (i.e. the block) a still life. Hence IIUC this one doesn't count as a solution to the above puzzle (despite being a strict still life).

i think hotdogPi was referring the original puzzle without the constraint of not being able to contain an induction coil:

There was a discussion on the discord about still lifes that contained all SL-compatible n by m grids. The 2x2 case, where all elements are compatible,

[confocaloid]

i think hotdogPi was referring the original puzzle without the constraint of not being able to contain an induction coil:

I don't understand what you mean by "the constraint of not being able to contain an induction coil". Can you explain?

[hotdogPi]

I was answering the original question: minimum number of cells.

There was a discussion on the discord about still lifes that contained all SL-compatible n by m grids. The 2x2 case, where all elements are compatible, was provided (i backed myself into a grammar hole here, oops) with this solution (not by me):

Code: Select all

 x = 9, y = 4, rule = B3/S23
2ob2ob2o$bob2obobo$bo4bobo$2o4b2o!

(18 bits. A smaller solution may exist.)
While this isn’t that interesting on its own, if a search/sat solver was used to find a similar still life for all 3x3 (4x4?!?!?) grids it might warrant a page, a rarity for high-pop still lives, of which the majority that have pages (EDIT) have no fathers besides themselfs.

[otismo]

I think these still-life patterns are noteworthy because they are common

Code: Select all

x = 69, y = 74, rule = B3/S23
5b2obo4b2obo4b2o6b2o2b2o6b2o4b2obo4b2o6b2o$5bob2o4bob2o5bo6bo4bo6bo5bo
b2o5bo6bo$3b2o6b2o4b2o3bobo2bobo4bobo2bobo3b2o4b2o2bo8bo$3bo7bo5bo3b2o
b4ob2o2b2ob4ob2o2bo5bo3b2o6b2o$4bo7bo5bo27bo5bo5b2o$3b2o6b2o4b2o2b10o
2b10o2b2o4b2o2b2obo4b2o$3bo7bo5bo3bo8bo2bo8bo2bo5bo4bobobo2bo$4bo7bo5b
o3bo2b2o2bo4bo2b2o2bo4bo5bo3bo2bobobo$3b2o6b2o4b2o2b2o2b2o2b2o2b2o2b2o
2b2o2b2o4b2o2b2o4bob2o$3bo7bo5bo27bo5bo8b2o$4bo7bo5bo2b2o6b2o2b2o6b2o
3bo5bo2b2o6b2o$3b2o6b2o4b2o2bo7bo3bo7bo3b2o4b2o2bo8bo$5b2obo4b2obo5bo
7bo3bo7bo4b2obo5bo6bo$5bob2o4bob2o4b2o6b2o2b2o6b2o4bob2o4b2o6b2o3$26bo
15bo$16bo3bo4bobo4bo3bo4bobo4bo3bo$16b5o4bobo4b5o4bobo4b5o$16bo3bo3b2o
b2o3bo3bo3b2ob2o3bo3bo$12b2o2b2ob2o3bo3bo3b2ob2o3bo3bo3b2ob2o2b2o$11bo
bo3bobo4b5o4bobo4b5o4bobo3bobo$5bo5bo5bobo4bo3bo4bobo4bo3bo4bobo5bo5bo
$4bobo3b2o6bo15bo15bo6b2o3bobo$3bobobo53bobobo$3bo3bo53bobobo$2obo3bob
2o47b2ob2ob2ob2o$2obo3bob2o9b2o6bo5b2o4bo5b2o5b2o3b2obobobob2o$3bobobo
6b2o3bo2bo4bobo3bobo3bobo3bo2bo3bobo6bo3bo$3b2ob2o6b2o4b2o4bo2bo4bo5bo
4bo2bo3b2o7bo3bo$2obobobob2o16b2o17b2o10b2obo3bob2o$2obo3bob2o47b2obob
obob2o$3bo3bo53b2ob2o$3bo3bo53bobobo$2obobobob2o4b2o14bo6b2o6bo6b2o3b
2obo3bob2o$2ob2ob2ob2o3bo2bo5bo5bo2bo6bo4b2o6bobo3b2obo3bob2o$3bobobo
7bo2bo4bo5bo2bo3bo9b2o4bo8bo3bo$3bo3bo8b2o5bo6bo5b2o7bo5b2o8bobobo$2ob
o3bob2o47b2ob2ob2ob2o$2obo3bob2o47b2obobobob2o$3bobobo53bo3bo$3b2ob2o
14b2o28b2o7bo3bo$2obobobob2o10bo2bo4b2o4b2o6b2o6bo2bo3b2obo3bob2o$2obo
3bob2o5b2o3b2obo5bo4bo7bo7bob2o3b2obobobob2o$3bo3bo6bo2bo4bob2o3bo6b3o
5bo3b2obo9b2ob2o$3bo3bo6b2o6bo2bo3bobo7bo3b2o3bo2bo9bobobo$2obobobob2o
12b2o5b2o6b2o9b2o7b2obo3bob2o$2ob2ob2ob2o47b2obo3bob2o$3bobobo53bo3bo$
3bobobo53bobobo$4bobo3b2o6bo15bo15bo6b2o3bobo$5bo5bo5bobo4bo3bo4bobo4b
o3bo4bobo5bo5bo$11bobo3bobo4b5o4bobo4b5o4bobo3bobo$12b2o2b2ob2o3bo3bo
3b2ob2o3bo3bo3b2ob2o2b2o$16bo3bo3b2ob2o3bo3bo3b2ob2o3bo3bo$16b5o4bobo
4b5o4bobo4b5o$16bo3bo4bobo4bo3bo4bobo4bo3bo$26bo15bo3$5b2obo6b2obo10b
2o4b2obo4b2obo2b2ob2ob2o4b2obo$5bob2o5bo2b2o10bo5bob2o4bob2o2b2obo3bo
4bob2o$3b2o4b2o2bobo3b2o9bo2b2o6b2o9bob2o3b2o$3bo5bo4bo4bo9b2o2bo7bo
10bobo4bo$4bo5bo9bo13bo7bo8b2obo5bo$3b2o4b2o4bo3b2o8b2o2b2o6b2o11b2o3b
2o$3bo5bo4bobobo11bo4b2obo2bo9b2obo6b2obo$4bo5bo2bobob2o10bo5bob2o3bo
9bobobo4bob2o$3b2o4b2o2bobo3b2o8b2o2b2o6b2o9bo2b2o8b2o$3bo5bo4b2o3bo
10bo2bo7bo9b2o12bo$4bo5bo9bo3bo4bo4bo7bo8bo14bo$3b2o4b2o3b2o3b2o2bobo
3b2o2b2o6b2o9bo12b2o$5b2obo4bo2bobo5bo2b2o6b2obo4b2obo6bo7b2obo$5bob2o
4b2o2b2o6b2obo6bob2o4bob2o5b2o7bob2o!

the seven most common and the eight less common...

( non-derivative )

[LuveelVoom]

There was a discussion on the discord about still lifes that contained all SL-compatible n by m grids. The 2x2 case, where all elements are compatible, was provided (i backed myself into a grammar hole here, oops) with this solution (not by me):

Code: Select all

 x = 9, y = 4, rule = B3/S23
2ob2ob2o$bob2obobo$bo4bobo$2o4b2o!

(18 bits. A smaller solution may exist.)
While this isn’t that interesting on its own, if a search/sat solver was used to find a similar still life for all 3x3 (4x4?!?!?) grids it might warrant a page, a rarity for high-pop still lives, of which the majority that have pages (EDIT) have no fathers besides themselfs.

I'd like to bring this question up again as I feel like this could be solved quickly with a couple dozen lines of python code and would be an interesting object.