Re: Thread for basic questions
Posted: January 4th, 2019, 11:45 am
I assume you're excluding the rules b1357s1357, b1357s02468, b02468s1357 and b02468s02468?danny wrote:Can a universal GoE working in all outer totalistic rules exist?
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I assume you're excluding the rules b1357s1357, b1357s02468, b02468s1357 and b02468s02468?danny wrote:Can a universal GoE working in all outer totalistic rules exist?
No, because those produce 4 copies of each pattern at the least.muzik wrote:danny wrote:I assume you're excluding the rules b1357s1357, b1357s02468, b02468s1357 and b02468s02468?
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 -- likedanny wrote:No, because those produce 4 copies of each pattern at the least.muzik wrote:danny wrote:I assume you're excluding the rules b1357s1357, b1357s02468, b02468s1357 and b02468s02468?
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x = 17, y = 7, rule = B1357/S02468
b3o3b3o2b5o$o3bobo3bobo$o5bo3bobo$ob2o2bo3bob4o$o3bobo3bobo$o3bobo3bob
o$b3o3b3o2b5o!
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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!
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.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.
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.dvgrn wrote:-- Did I say all that right? It's so easy to get tripped up on definitions with these GoEs/orphans...
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.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.
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.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...
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.Macbi wrote: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.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.
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:dvgrn wrote: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.Macbi wrote: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.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 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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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!
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.
Uh-oh. Can of worms was right -- the R-pentomino has now migrated backwards to 1969 on the LifeWiki.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...
I think I've seen one before. However I can't find the link.Saka wrote:Has an SMS or SSS breeder been constructed?
What about it in other rules?
Paul Tooke's pianola breeder experiments include something he labeled as an SSS breeder.Hunting wrote:I think I've seen one before. However I can't find the link.Saka wrote:Has an SMS or SSS breeder been constructed?
What about it in other rules?
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x = 63, y = 40, rule = LifeHistory
4.A.2A$4.2A2.A$7.A2.A$2.5A.2A.A2.A$.A4.A.A2.4A$.A2.A3.3A6.A$2A.A.3A2.
A2.5A38.2A$3.A6.A.A5.2A35.A2.A2.2A$2A.A.3A2.A2.A.2A.A.A34.A.A.A2.A$A
2.A.A2.A.2A.A.A.A2.A31.2A.A.A2.2A$2.2A2.A2.A3.A.A4.A.2A29.A.A.A$4.2A
4.4A.2A2.2A2.A29.A.A2.4A$4.A3.A.A6.A3.A28.2A.A.A5.A$5.4A.A.5A.3A3.A
24.A.A.A2.3A$9.A.A4.A.A2.4A24.A.A.A4.A$7.A3.A2.A3.A.A6.A18.2A.A.A2.4A
$7.2A2.A.A.4A.A2.5A19.A.A.A$10.2A.A6.A.A5.2A3.2A12.A.A2.4A$13.A.4A.A
2.A.2A.A.A.A.A9.2A.A.A5.A$13.A.A2.A.2A.A.A.A2.A.A10.A.A.A2.3A$12.2A2.
A2.A3.A.A4.A.2A9.A.A.A4.A$14.2A4.4A.2A2.2A4.A4.2A.A.A2.4A$14.A3.A.A6.
A3.4A.A4.A.A.A$15.4A.A.5A.3A5.A4.A.A2.4A$19.A.A4.A.A2.6A.2A.A.A5.A$
17.A3.A2.A3.A.A6.A.A.A2.3A$17.2A2.A.A.4A.A2.2A2.A.A.A4.A$20.2A.A6.A.A
2.A.A.A2.4A$23.A.4A.A2.A.A.A.A$23.A.A2.A.2A.A.A.A2.4A$20.A.2A2.A2.A3.
A.A.A5.A$20.2A2.2A4.AC2A.A2.3A$23.A2.4A3.D.A4.A$24.A5.2ACA.C4A$25.3A
2.A2.A$27.A3.A2.6A$28.3A5.A2.A2$28.2A.A$28.A.2A!
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#C A glider hits a still-life, sending a 2c/3 signal along a diagonal.
#C Another glider on the same path causes the pattern to decay.
#C Dean Hickerson, 4/11/97
x = 132, y = 133, rule = LifeHistory
.A$2.A6.A$3A5.A.A$8.A.A$7.2A2.2A$4.2A3.A.A$4.A.4A2.A$10.A.A$4.A.5A.2A
3.A$2.3A.A8.3A$.A4.A.7A$2.3A.A.A6.A$4.A.A.A2.5A$7.2A.A7.A$10.A2.6A$
10.A.A$9.2A.A2.6A$12.A.A6.A$12.A.A2.5A$13.2A.A7.A$16.A2.6A$16.A.A$15.
2A.A2.6A$18.A.A6.A$18.A.A2.5A$19.2A.A7.A$22.A2.6A$22.A.A$21.2A.A2.6A$
24.A.A6.A$24.A.A2.5A$25.2A.A7.A$28.A2.6A$28.A.A$27.2A.A2.6A$30.A.A6.A
$30.A.A2.5A$31.2A.A7.A$34.A2.6A$34.A.A$33.2A.A2.6A$36.A.A6.A$36.A.A2.
5A$37.2A.A7.A$40.A2.6A$40.A.A$39.2A.A2.6A$42.A.A6.A$42.A.A2.5A$43.2A.
A7.A$46.A2.6A$46.A.A$45.2A.A2.6A$48.A.A6.A$48.A.A2.5A$49.2A.A7.A$52.A
2.6A$52.A.A$51.2A.A2.6A$54.A.A6.A$54.A.A2.5A$55.2A.A7.A$58.A2.6A$58.A
.A$57.2A.A2.6A$60.A.A6.A$60.A.A2.5A$61.2A.A7.A$64.A2.6A$64.A.A$63.2A.
A2.6A$66.A.A6.A$66.A.A2.5A$67.2A.A7.A$70.A2.6A$70.A.A$69.2A.A2.6A$72.
A.A6.A$72.A.A2.5A$73.2A.A7.A$76.A2.6A$76.A.A$75.2A.A2.6A$78.A.A6.A$
78.A.A2.5A$79.2A.A7.A$82.A2.6A$82.A.A$81.2A.A2.6A$84.A.A6.A$84.A.A2.
5A$85.2A.A7.A$88.A2.6A$88.A.A$87.2A.A2.6A$90.A.A6.A$90.A.A2.5A$91.2A.
A7.A$94.A2.6A$94.A.A$93.2A.A2.6A$96.A.A6.A$96.A.A2.5A$97.2A.A7.A$100.
A2.6A$100.A.A$99.2A.A2.6A$102.A.A6.A$102.A.A2.5A$103.2A.A7.A$106.A2.
6A$106.A.A$105.2A.A2.6A$108.A.A6.A$108.A.A2.5A$109.2A.A7.A$112.A2.6A$
112.A.A$111.2A.A2.6A$114.A.A6.A$114.A.A2.5A$115.2A.A7.A$118.A2.6A$
118.A.A8.A$117.2A.A2.7A$120.A.A$120.A.A2.5A$121.2A.A4.A$124.A2.A$124.
A.A.4A$123.2A.A4.A$127.3A$129.2A!
No Blockic glider eaters or glider-to-anything converters are known, given your restriction #4.Moosey wrote:Are there any glider eaters consisting entirely of blocks that meet these conditions?...
4) Having a universal constructor rebuilding the blocks is not a valid solution, for the sake of the argument, unless they are unusually fast (no more than 1000 gens recovery time)
Code: Select all
x = 55, y = 66, rule = LifeHistory
21.2A$21.2A3$19.2A$19.2A3$8.2C$8.2C$4.2A$4.2A7$17.2A$17.2A29.2A$48.2A
3$35.2C$35.2C2$45.2C$45.2C3$.A8.2A$.2A7.2A$A.A28$48.2C$48.2C3$53.2C$
53.2C!
What about one where restriction 2 is removed?dvgrn wrote:No Blockic glider eaters or glider-to-anything converters are known, given your restriction #4.Moosey wrote:Are there any glider eaters consisting entirely of blocks that meet these conditions?...
4) Having a universal constructor rebuilding the blocks is not a valid solution, for the sake of the argument, unless they are unusually fast (no more than 1000 gens recovery time)
Even without restriction #4, nobody has actually built anything that fills the bill, and I don't think anybody knows a way to do it that wouldn't also violate your restriction #2.
The problem is that we don't have enough blocks-only Herschel conduits to make a universal set. We have R64 and B60 and whatever-that-other-elementary-conduit-is, but they don't connect to each other at all, let alone in a way that would allow for splitting off signals and repairing circuits that only work once.
Works-once Blockic conduits are actually pretty common. For example, here's a glider-to-Herschel converter based on Paul Callahan's receiver:
If we had enough Blockic conduits to make a universal set (including a signal splitter) then we could use this to get a Herschel, and then produce gliders to rebuild the five blocks that go missing when the glider comes in -- and then we'd have a Blockic glider eater.Code: Select all
x = 55, y = 66, rule = LifeHistory partial blockic conduit
Really we wouldn't do it that way, though. It would probably be better to hunt for a Blockic constellation that produced a clean output Herschel or two, and then use hypothetical Blockic splitters to rebuild that constellation directly. But none of this can work until someone finds more Blockic conduits.
Makes no difference. You have to either lift restriction #4 or also allow boats (don't need beehives so much). The first option lets you theoretically design some UC-based system with a stage where all the required data is encoded into blocks. Don't go there; it wouldn't be much fun at all to try to build such a ridiculous thing in practice, without some new technological breakthroughs anyway.Moosey wrote:What about one where restriction 2 is removed?
Or what if, instead, beehives, and loaves were also allowed?
Okay, so if restrictions 2 and 4 are removed... What's the smallest universal constructor that would do that?dvgrn wrote:Makes no difference. You have to either lift restriction #4 or also allow boats (instead of beehives) -- that gives you access to the sidesnagger, so you have a glider eater that answers your original question.Moosey wrote:What about one where restriction 2 is removed?
Or what if, instead, beehives, and loaves were also allowed?
To get a universal set of Herschel conduits, even blocks, boats, beehives and loaves aren't enough -- you really need fishhook eaters to get anywhere. But of course that would trivially answer your eater question with no need for any crazy complicated bait or staged recovery mechanisms.
It's fairly painful. There's a description by calcyman "(where x = (0,0))" that probably comes pretty close. You can get a vague sense of how big something like this would be, by looking at half of the Caterloopillar.Moosey wrote:Okay, so if restrictions 2 and 4 are removed... What's the smallest universal constructor that would do that?