AforAmpere wrote:I have that downloaded, but is there a way to find specific reactions?
There's a pattern that has a parent but no grandparent. So it has a parent but no glider construction. So really you want to ask if there is a pattern which has an infinite chain of ancestors (each with finitely many cells) but no glider synthesis. As far as I know this problem is completely open, and no one knows any ways to approach it.Apple Bottom wrote:There's Gardens of Eden, and there's patterns that (provably) cannot be constructed using gliders. Obviously, the former are a subset of the latter, but are they a strict subset? Put another way, is there a pattern that has a parent, yet is provably inconstructible using gliders?
If yes: is there a known example? If no: can it be proven that "Garden of Eden" and "not glider-constructible" are the same? (And if "we don't know", but also otherwise: is there any published research on this?)
Majestas32 wrote:I suspect that the answer to the unique father problem is in the affirmative.
Majestas32 wrote:I suspect that the answer to the unique father problem is in the affirmative.
x = 26, y = 19, rule = B3/S23
3b2ob2o10b2ob2o$4b2obo10bo3bo$5b2o12b3o2$2o3b2o2b2o4b2o2b3o2b2o$o2bobo
2bobo4bo2bobo2bobo$2b2obob2o8b2o3b2o$obo4bo2bo4bobo2bobo2bo$2o2b2o3b2o
4b2o2b3o2b2o$5bo$2o3b2o2b2o4b2o2b3o2b2o$o2bo4bobo4bo2bobo2bobo$2b2obob
2o8b2o3b2o$obo2bobo2bo4bobo2bobo2bo$2o2b2o3b2o4b2o2b3o2b2o2$4b2o13b3o$
3bob2o11bo3bo$3b2ob2o10b2ob2o!
Macbi wrote:There's a pattern that has a parent but no grandparent. So it has a parent but no glider construction. So really you want to ask if there is a pattern which has an infinite chain of ancestors (each with finitely many cells) but no glider synthesis. As far as I know this problem is completely open, and no one knows any ways to approach it.
You might begin by working on an easier problem: does every still life have a glider synthesis? We can imagine a sort of "still life printer" that builds up any given still life piece by piece, based on a finite number of recipes that cover every possible way it could want to expand the part it has built so far.
dvgrn wrote:Seems like there was some further discussion about these problems, but I can't find it offhand, and probably it was mostly high-level theoretical hand-waving anyway. I don't think there have been many published hard results from actual searches.
This would guarantee that such a still life was unsynthesisable.Is there an assignment of alive or dead to a finite number of cells such that (a)the assignment can be extended to a still life and (b)any predecessor (with a finite number of cells) of any pattern (with a finite number of cells) containing those cells also contains those cells?
Macbi wrote:Maybe a good phrasing would beThis would guarantee that such a still life was unsynthesisable.Is there an assignment of alive or dead to a finite number of cells such that (a)the assignment can be extended to a still life and (b)any predecessor (with a finite number of cells) of any pattern (with a finite number of cells) containing those cells also contains those cells?
Apple Bottom wrote:You might begin by working on an easier problem: does every still life have a glider synthesis? We can imagine a sort of "still life printer" that builds up any given still life piece by piece, based on a finite number of recipes that cover every possible way it could want to expand the part it has built so far.
I'd expect that the answer to this is "yes", but I couldn't really justify it.
...
On the flip side -- re: the possibility of a "still life printer", are all still lifes (finite still lifes of sufficient size, anyway) variants/extensions of earlier still lifes, or is there always, for any n, a still life with of population not below n that is not "based on" smaller still lifes, whatever that means?
Apple Bottom wrote:Speaking of which, are there any known properties that Gardens of Eden must possess? Something that would contradict a (finite) GoE also being a still life, perhaps?
Apple Bottom wrote:Speaking of which, are there any known properties that Gardens of Eden must possess? Something that would contradict a (finite) GoE also being a still life, perhaps?
x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!
Gamedziner wrote:By definition, a GoE has no parents. A still-life is its own parent, and thus always has a parent. These two statements thus show that a still-life GoE is contradictory, and therefore cannot exist.
A still-life with no parents other than itself would answer the unique father problem.
dvgrn wrote:Apple Bottom wrote:Speaking of which, are there any known properties that Gardens of Eden must possess? Something that would contradict a (finite) GoE also being a still life, perhaps?
Can't think of anything besides the obvious stuff -- must be bigger than 6x6, must contain more than ten ON cells (I have no proof, but I think I'm pretty safe on this one). A GoE can't be a still life, oscillator, or spaceship, so I think you must be intending to say "(finite) unique-parent pattern" or something like that?
77topaz wrote:That was already addressed a few posts above yours
x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!
Macbi wrote:Here's something I realised the other day: Agar crawlers can't travel along the stripes of the zebra agar (lightspeed wire) slower than light.
...
... "deconstructing the agar in front of it" is impossible do do in a controlled fashion.
This shows that you can't do arbitrary tweaks to still lives with gliders. But it doesn't necessarily rule out the constructibility of any still life in particular.
x = 54, y = 53, rule = B3/S23
bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo$b52o2$b52o$o52bo
$b52o2$b52o$o52bo$b52o2$b52o$o52bo$b52o2$b52o$o52bo$b52o2$b52o$o52bo$b
52o2$b52o$o52bo$b52o2$b52o$o52bo$b52o2$b52o$o52bo$b52o2$b52o$o52bo$b
52o2$b52o$o52bo$b52o2$b52o$o52bo$b52o2$b52o$o52bo$b52o2$b52o$bo2bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo!
x = 29, y = 54, rule = B3/S23
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob
2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o$2ob2ob2ob2obo3bob2ob2ob2ob2o$12bo3bo$2ob2ob2ob3o3b2o$2ob2ob2obo7$2o
b2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2o
b2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2o
b2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
$2ob2ob2ob2obo3bobo3bob2ob2o$12bo3bobo3bo$2ob2ob2ob3o5bo3b2o$2ob2ob2ob
o7$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o$2ob2ob2ob2ob2ob2obo3bob2ob2o$18bo3bo$2ob2ob2ob2ob2ob3o3b2o$2ob2o
b2ob2ob2obo!
./knightt -e -p 7 -x 2 -w 9
danny wrote:What's the biggest notable pattern that has ever been constructed in an OCA?
wildmyron wrote:danny wrote:What's the biggest notable pattern that has ever been constructed in an OCA?
"Biggest" and "notable" are rather vague in this context, however, one pattern which might qualify is calcyman's c/24 backward glider rake in HighLife which has a population of >10^6 cells.
AforAmpere wrote:What speed waves have been found? I know of C, the 12c/28 wave, but that is all I know for orthogonal waves. Is a 2c/3 wave possible?
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