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Thread for basic questions

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Re: Thread for basic questions

Postby danny » January 4th, 2019, 11:43 am

Can a universal GoE working in all outer totalistic rules exist?
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Re: Thread for basic questions

Postby muzik » January 4th, 2019, 11:45 am

danny wrote:Can a universal GoE working in all outer totalistic rules exist?


I assume you're excluding the rules b1357s1357, b1357s02468, b02468s1357 and b02468s02468?
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Re: Thread for basic questions

Postby Macbi » January 4th, 2019, 12:11 pm

Every GoE (a pattern that can't appear after generation 0) contains an orphan (a finite region of alive and dead cells such that any pattern containing that region is a GoE). It's possible to make a pattern that contains every finite arrangement of cells (just list all finite arrangements one after another). This pattern is therefore a GoE in every rule with a GoE.

However not all outer totalistic rules have GoEs. For example in B/S012345678 every pattern is its own parent.
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Re: Thread for basic questions

Postby danny » January 4th, 2019, 12:39 pm

muzik wrote:
danny wrote:I assume you're excluding the rules b1357s1357, b1357s02468, b02468s1357 and b02468s02468?

No, because those produce 4 copies of each pattern at the least.

Good point about B/S012345678 though.
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Re: Thread for basic questions

Postby 77topaz » January 4th, 2019, 4:27 pm

Rules like B1357/S1357 and the other three don't have GoEs, because they are reversible; any finite region containing a single small pattern plus a large amount of empty space will have a parent that is very dense in that region, dying off in all places except for where the small pattern is (and what happens outside of the finite region is then irrelevant). If I recall correctly, there was a discussion about this a few months ago, where someone produced an example of this.
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Re: Thread for basic questions

Postby dvgrn » January 4th, 2019, 4:28 pm

danny wrote:
muzik wrote:
danny wrote:I assume you're excluding the rules b1357s1357, b1357s02468, b02468s1357 and b02468s02468?

No, because those produce 4 copies of each pattern at the least.

Not sure why the number of copies would matter to the GoE-ness of a pattern. That just makes it really easy to prove that any given finite region of cells in those rules -- like

x = 17, y = 7, rule = B1357/S02468
b3o3b3o2b5o$o3bobo3bobo$o5bo3bobo$ob2o2bo3bob4o$o3bobo3bobo$o3bobo3bob
o$b3o3b3o2b5o!

-- is not in fact a GoE (in the conventional "can only occur in generation 0" sense). You just have to run it for some length of time proportional to the size of the pattern, and there's your exact pattern appearing again at time T>0, so it must not be a GoE:
x = 39, y = 40, rule = B1357/S02468
ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2o3bo3b2obobo2bob2ob2ob
2ob2o$b2ob2ob2ob3o2b2o5b6ob2ob2ob2obo$ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob
2ob2o$2ob2ob2ob2o3bo3b2obobo2bob2ob2ob2ob2o$b2ob2ob2ob3o2b2o5b6ob2ob2o
b2obo$ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2o3bo3b2obobo2bob
2ob2ob2ob2o$b2ob2ob2ob3o2b2o5b6ob2ob2ob2obo$ob2ob2ob2ob2ob3ob2ob2ob2ob
2ob2ob2ob2o$2ob2ob2ob2o3bo3b2obobo2bob2ob2ob2ob2o$b2ob2ob2ob3o2b2o5b6o
b2ob2ob2obo$ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2o3bo3b2obo
bo2bob2ob2ob2ob2o$b2ob2ob2ob3o2b2o5b6ob2ob2ob2obo$ob2ob2ob2ob2ob3ob2ob
2ob2ob2ob2ob2ob2o$2ob2ob2ob2o3bo3b2obobo2bob2ob2ob2ob2o$b2ob2ob2ob3o2b
2o5b6ob2ob2ob2obo$b2ob2ob2ob2o2bo4bo4bo2bob2ob2ob2obo$b2ob2ob2ob2o7bo
4b2obob2ob2ob2obo$2ob2ob2ob2o3bo3b2obobo2bob2ob2ob2ob2o$2ob2ob2ob2obob
3obo2b2o5b2ob2ob2ob2o$b2ob2ob2ob2o2bo4bo4bo2bob2ob2ob2obo$2ob2ob2ob2o
3bo3b2obobo2bob2ob2ob2ob2o$b2ob2ob2ob3o2b2o5b6ob2ob2ob2obo$ob2ob2ob2ob
2ob3ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2o3bo3b2obobo2bob2ob2ob2ob2o$b2ob
2ob2ob3o2b2o5b6ob2ob2ob2obo$ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2o$2ob
2ob2ob2o3bo3b2obobo2bob2ob2ob2ob2o$b2ob2ob2ob3o2b2o5b6ob2ob2ob2obo$ob
2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2o3bo3b2obobo2bob2ob2ob2o
b2o$b2ob2ob2ob3o2b2o5b6ob2ob2ob2obo$ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2o
b2o$2ob2ob2ob2o3bo3b2obobo2bob2ob2ob2ob2o$b2ob2ob2ob3o2b2o5b6ob2ob2ob
2obo$ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2o3bo3b2obobo2bob
2ob2ob2ob2o$b2ob2ob2ob3o2b2o5b6ob2ob2ob2obo!

The usual caveat applies about "junk around the edges not counting". It may be true that the above pattern plus dead cells all the way to infinity in all directions has no parent with a finite number of ON cells. But I think if you have an infinite number of cells in the GoE definition, whether ON or OFF, you should be allowed to have an infinite number of cells in the parent.

That might not quite fit with Achim Flammenkamp's definition of a Garden of Eden, but it fits pretty well with common usage. (Achim's term for a finite group of cells with no parent is "orphan", and you embed an orphan in an infinite field of OFF cells to get a GoE.)

It's certainly easy enough to describe the infinite background pattern that would constitute (most of) the parent for any finite pattern you might choose in an XOR rule. It just wouldn't be a finite parent.

-- Did I say all that right? It's so easy to get tripped up on definitions with these GoEs/orphans...
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Re: Thread for basic questions

Postby 77topaz » January 4th, 2019, 4:41 pm

Yeah, that what more or less what I said in my post (which I assume I published while you were already writing yours), plus an example of the sort I was looking for. :)
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Re: Thread for basic questions

Postby Ian07 » January 4th, 2019, 5:05 pm

When exactly was the glider discovered? The Glider article a quote from Genius at Play which says it was found in the fall of 1969 while investigating the R-pentomino, but just before the quote claims 1970. Other articles also support the 1970 date; the wiki pages for block and blinker both say they were found in 1970, and therefore the glider would have to have been discovered afterwards since they were already present in the R-pentomino's evolution.
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Re: Thread for basic questions

Postby Apple Bottom » January 4th, 2019, 5:13 pm

Ian07 wrote:When exactly was the glider discovered? The Glider article a quote from Genius at Play which says it was found in the fall of 1969 while investigating the R-pentomino, but just before the quote claims 1970. Other articles also support the 1970 date; the wiki pages for block and blinker both say they were found in 1970, and therefore the glider would have to have been discovered afterwards since they were already present in the R-pentomino's evolution.


I think most sources (including the article infobox) say 1970 because that's when Life was first written about and made known to the general public (Gardner wrote his first article on Life in 1970). However, Conway and his gang were (of course) investigating Life beforehand. Given that Siobhan Roberts had access to Conway and interviewed him extensively for his biography, I would wager that 1969 is in fact correct. However, it's merely an "internal" figure; nothing was published (in any sense of the word), which is why 1970 is usually quoted.

For much the same reason, other small patterns were discovered by Conway & Co. before 1970, and the 1970 figure again refers to Gardner's article.

As for the wiki, BTW, we never tried to find a consensus as to what dates should be given. I added the quote from Conway's biography since it was interesting, informative and apropos, but I did not want to go against long-established consensus that patterns only known to members of Conway's gang before 1970 would be considered to have been "discovered" with the publication of Gardner's first article.
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Re: Thread for basic questions

Postby Macbi » January 5th, 2019, 6:06 am

dvgrn wrote:-- Did I say all that right? It's so easy to get tripped up on definitions with these GoEs/orphans...
It sounded right to me. But wouldn't it be much easier if the definitions were the other way around? To me "Garden" suggests a bounded region, whereas "orphan" just means "has no parents". Maybe we should just declare that they've swapped, especially since everyone talks about finding GoEs when they mean finding orphans.

It would also be nice to have a term for a finite pattern with a parent but no finite parent, like the "GOE" pattern you posted. It's an open problem whether these exist in Life.

Apple Bottom wrote:I did not want to go against long-established consensus that patterns only known to members of Conway's gang before 1970 would be considered to have been "discovered" with the publication of Gardner's first article.
This makes sense. Since Gardner's article was published in October 1970, we have no way of knowing which patterns (except the glider) were found in 1969.
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Re: Thread for basic questions

Postby calcyman » January 5th, 2019, 7:59 am

dvgrn wrote:It's certainly easy enough to describe the infinite background pattern that would constitute (most of) the parent for any finite pattern you might choose in an XOR rule. It just wouldn't be a finite parent.

-- Did I say all that right? It's so easy to get tripped up on definitions with these GoEs/orphans...


It's also possibly worth saying that by using a 'proof by compactness' you can show (in any CA) that if every finite subset of an infinite universe has a parent (that is allowed to produce junk around the edges), then the entire universe has a (possibly infinite) parent. So the fact that every pattern has a (not necessarily finite) parent is not unique to XOR rules; it applies to every GoE-less rule.
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Re: Thread for basic questions

Postby dvgrn » January 5th, 2019, 9:35 am

Macbi wrote:
Apple Bottom wrote:I did not want to go against long-established consensus that patterns only known to members of Conway's gang before 1970 would be considered to have been "discovered" with the publication of Gardner's first article.

This makes sense. Since Gardner's article was published in October 1970, we have no way of knowing which patterns (except the glider) were found in 1969.

Yeah, I certainly worried a little bit that creating a "1969" category for pattern discoveries was opening an unnecessarily messy can of worms. If anyone wants to change the date back to 1970, it's fine by me.

This morning I added a "historical note" to the Glider article, which should explain the 1969/1970 ambiguity, whichever date is given in the infobox.
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Re: Thread for basic questions

Postby calcyman » January 5th, 2019, 10:47 am

dvgrn wrote:
Macbi wrote:
Apple Bottom wrote:I did not want to go against long-established consensus that patterns only known to members of Conway's gang before 1970 would be considered to have been "discovered" with the publication of Gardner's first article.

This makes sense. Since Gardner's article was published in October 1970, we have no way of knowing which patterns (except the glider) were found in 1969.

Yeah, I certainly worried a little bit that creating a "1969" category for pattern discoveries was opening an unnecessarily messy can of worms. If anyone wants to change the date back to 1970, it's fine by me.

This morning I added a "historical note" to the Glider article, which should explain the 1969/1970 ambiguity, whichever date is given in the infobox.


We know that the R-pentomino dates from before the glider (because the latter was discovered by simulating the R-pentomino). Also, I recall that the polyominoes were investigated in increasing order of size, and that the R was the last pentomino to be resolved. This implies that the block, blinker, beehive, traffic lights, and loaf were known by 1969:

x = 108, y = 44, rule = B3/S23
81b3o$82bo2$41bobo$41b3o29b2o$73b2o$5o3$20b4o$21bo51b2o6b2o15bo$51b2o
20bo8b2o14bo7bo$52b2o19bo24bo7b2o$53bo5$77b4o2$29bo$29b2o72b2o$30bo$
30bo2$5b4o$5bo$104bo$44b2o$44bo$43b2o5$24bo$23b3o32b2o$24bo33b2o$58bo
3$11b3o26bo$12bo27bo$12bo27b3o!


I say 'by' rather than 'in' because no-one knows exactly what year he invented GoL:

Bill sent me an e-mail from Dick Esterle saying that Siobhan Roberts wrote:I'm afraid I tried to pin down Life dates and Conway was wary of doing so, and indeed could not himself, hence I told it like it was in the book. I'd say circa 1967/68. RKG might be able to provide something more specific.
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Re: Thread for basic questions

Postby dvgrn » January 5th, 2019, 3:27 pm

calcyman wrote:We know that the R-pentomino dates from before the glider (because the latter was discovered by simulating the R-pentomino). Also, I recall that the polyominoes were investigated in increasing order of size, and that the R was the last pentomino to be resolved. This implies that the block, blinker, beehive, traffic lights, and loaf were known by 1969...

Uh-oh. Can of worms was right -- the R-pentomino has now migrated backwards to 1969 on the LifeWiki.

I'd like to suggest limiting the migration to calcyman's list... but there are a few other named objects that also must have been seen during that first R-pentomino evolution: certainly R-bee/bun, tub, Herschel, Herschel great-grandparent, and Herschel descendant... and maybe ship and boat if the group made it a little closer to the end of the R's evolution at 1103 ticks, but I'm not sure when that simulation job was completed. When the first glider came out, they had a long way to go.

Also the B-heptomino, of course, but it was the not-really-named B-heptaplet form of the B, so maybe that doesn't count. Then again, quite possibly very few of these things besides the glider were named in 1969.

-- I guess that still seems like a reasonably small collection of objects that can be definitively moved to http://conwaylife.com/wiki/Category:Patterns_found_in_1969. Maybe we can just decide to do these, or some subset of them, and leave all the long canoes and snakes and barges and other probably-early-discovered things in 1970.
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Re: Thread for basic questions

Postby danny » January 6th, 2019, 7:01 am

Another piece of evidence to support that is that R pentomino forms 3 blocks and a blinker before the first glider...
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Re: Thread for basic questions

Postby Saka » January 12th, 2019, 4:46 am

Has an SMS or SSS breeder been constructed?
What about it in other rules?
If you're the person that uploaded to Sakagolue illegally, please PM me.
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

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Re: Thread for basic questions

Postby Hunting » January 12th, 2019, 7:59 am

Saka wrote:Has an SMS or SSS breeder been constructed?
What about it in other rules?

I think I've seen one before. However I can't find the link.
Almost c/2:
x = 19, y = 10, rule = LifeHistory
7.D3.D$6.DCD.DCD$5.DC2AD2ACD$3.2DAC2.A2.CA2D$3.AC.C2.D2.C.CA$.2D.C.AD
.A.DA.C.2D$.2C.A2.A3.A2.A.2C$.CA.2D7.2D.AC$DC2.2A7.2A2.CD$2A15.2A!
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Re: Thread for basic questions

Postby dvgrn » January 12th, 2019, 8:29 am

Hunting wrote:
Saka wrote:Has an SMS or SSS breeder been constructed?
What about it in other rules?

I think I've seen one before. However I can't find the link.

Paul Tooke's pianola breeder experiments include something he labeled as an SSS breeder.

The "super breeders?" topic talks about MSS, and here's an SMS breeder also by Paul Tooke.

Anyone want to decide where to put these links in the LifeWiki so that they don't get lost again?
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