ConwayLife.com

Posted: **November 27th, 2023, 2:04 pm**

I made One-dimensional cellular automaton/Wolfram rule, containing a table of conjugacy classes of Wolfram rules, with one row per conjugacy class (up to left/right reflection and black/white reversal), reducing them from 256 to 88. Alike the 2-dimensional analogues, the self-complementary rules may be further reduced by strobing and chequerboard duality, reducing it to 79

in conjugacy classes 0, 8, 32, 40, 128, 136 and 168, all patterns die, so they probably are not interesting enough to warrant pages.
We have pages for the conjugacy classes represented by
- 22, Life on a 1D cylinder,
- 54, conjectured Turing-complete,
- 110, proven Turing-complete,
- 225, page created by me, its evolution from a single cell admits exact descriptions and has Θ(√t) growth, and 225 is of the form (2^2^2 - 1)². In general, rule (2^2^n - 1)² in a width-(n+1) neighbourhood grows with Θ(ⁿ√t).

Of the 68 that this leaves.

Three classes (60/102/153/195, 90/165, 150/105) are distributive with XOR, and as such are expressible in terms of XOR and NOT alone, maybe they could be grouped together (since there is much that can be said about 150, due to yujh's proof of omniperiodicity of bounded regions with opposite-colour edges, in the context of B34kz5e7c8/S23-a4ityz5k).
73 (dual 109) is a somewhat interesting strobing rule, any two adjacent on-cells surrounded by off-cells behave as indestructible walls, which partition random soups into isolated sections, which behave periodically. It is easy to prove inductively that a pattern consisting of odd run-lengths will remain as such forever, and as such the state emerging from a single cell grows semi-chaotically, with various different kinds of agar emerging.
Rules 30 (the most famous chaotic one, resembling a certain type of conch shell) and 184 (the voting/moving-antiparticles one) have pages on Wikipedia but not the LifeWiki.
The set of rules which neither have wiki pages nor are trivial to disprove Turing-completeness in is {18,25,26,30,41,45,73,122,126,146,162}.

Would anyone be interested in increasing the breadth of our collection of Wolfram rules on the wiki to include any of these?

It would also be nice to be able to provide 1D replicators in 2D INT rules emulating some more of those which we have, if anyone has a collection or database of them.

Posted: **December 10th, 2023, 5:55 pm**

Can't you just make a page for W120 because that's W225's dual? It doesn't really matter if there is slow growth from a single cell.

Posted: **February 5th, 2024, 11:30 am**

DroneBetter wrote: November 27th, 2023, 2:04 pm[...] Would anyone be interested in increasing the breadth of our collection of Wolfram rules on the wiki to include any of these? [...]

I think I would like to know what is the intended target audience for those pages. They contain lots of formulas, with little or no explanation as to why all this belongs to LifeWiki. Some parts look like SPAM. Are you writing for other people?

As an example, the edit https://conwaylife.com/w/index.php?diff ... did=144364 added a new section with content collapsed by default. (Collapsing content by default is already a bad enough idea, from the accessibility viewpoint. If you don't want to keep the content visible by default, then it is probably better to avoid putting that content on that page.) The hidden content is basically spam by formulas without explanations why these are in the LifeWiki scope.

I think most of those additions should be removed, as out-of-scope (and hard to read) content added by an overenthusiastic editor.

DroneBetter wrote: January 12th, 2024, 9:35 pm[...] I think it would also benefit from either the Math or MathLaTeX extension, since galoomba recently made me aware of a discussion in the lounge regarding the OCA:Rule 120 page (also my contribution) being difficult to read, it turned out that Moosey had in fact misinterpreted its misrendering (on what I can only assume to be a portrait mobile device with small page width) as its intentional appearance. [...]

I don't believe changing formatting of expressions could automatically make the pages easy to read. There should be much more explanatory text written for readers.
And of course changing the formatting cannot solve the problem with content that simply does not belong on LifeWiki.

Posted: **February 7th, 2024, 3:08 pm**

confocaloid wrote: February 5th, 2024, 11:30 amI think I would like to know what is the intended target audience for those pages. They contain lots of formulas, with little or no explanation as to why all this belongs to LifeWiki. Some parts look like SPAM. Are you writing for other people?

As an example, the edit https://conwaylife.com/w/index.php?diff ... did=144364 added a new section with content collapsed by default. (Collapsing content by default is already a bad enough idea, from the accessibility viewpoint. If you don't want to keep the content visible by default, then it is probably better to avoid putting that content on that page.) The hidden content is basically spam by formulas without explanations why these are in the LifeWiki scope.

I think most of those additions should be removed, as out-of-scope (and hard to read) content added by an overenthusiastic editor.

I don't believe changing formatting of expressions could automatically make the pages easy to read. There should be much more explanatory text written for readers.
And of course changing the formatting cannot solve the problem with content that simply does not belong on LifeWiki.

I have mainly been adding the results I find without much in the way of explanation, I confess, however I intend to revise it into a more useful explanatory page eventually (after finishing my current addiion, I will write up a proof of the main claim (the bitwise recurrence relations) that will be more plain English than the existing proof of its solution). The new part containing generating functions is there because the sequences l(t) and v(t) are given by quite complicated forms, but become simpler when expressed through their g.f.'s (since forms involving infinite products of rational functions correspond with recursive forms for their series expansions), and I wanted to include those of all of the others for completeness, for all that it was worth.

Also, finding generating functions for sequences of on-cell-counts in cellular automata is not actually a very esoteric idea! The Sierpinski triangle is well-studied and the simplest case, another is rule 150, and a few 2D rules have been studied also

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, 2015
Shalosh B. Ekhad, N. J. A. Sloane, Doron Zeilberger, A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata, 2015 (note that odd rules here do not refer to their rule integers being odd, but to those which (alike 150) are distributive with XOR, since they can be considered to enumerate odd terms of expansions of powers of polynomials)
Alan J. Macfarlane, On generating functions of some sequences of integers defined in the evolution of the cellular automaton Rule 150, 2016 (this one doesn't seem especially well-written to me, and is somewhat convoluted)

It seems rule 120/225 was overlooked by many people for the 42 years since its discovery (I suspect because Stephen Wolfram had already found the main result result regarding the domino's growth rate, and one would either have to consider the odd member of its equivalence class or the even member from two cells to even see the nontrivial behaviour), even though it is the only range-1 rule that produces this fractal.
I asked dvgrn about it over forum mail, and he said it was okay and he in fact welcomes the creation of pages in the OCAspace that are more specific in nature compared to the more introductory pages on the LifeWiki.

No objections from me! The OCA namespace is definitely allowed to be more experimental. It's much more likely to contain documentation of users' own discoveries, mostly just because there are so many OCA rules that each one might only have one person who has done a "deep dive" into exploring it.

and then over Discord,

Heh, I was a math major in college, so I could technically read all of that -- but I have to say, I'm honestly not likely to take the time. The audience for that level of attention to mathematical detail in the community is ... very small, I would think, especially if there might be other non-LaTeX-equation-heavy ways to say the same things.
apgoucher could no doubt read though that and get something out of it quite easily -- but I'm basically just a "recovering math major".

Some parts of the article are of the kind that would belong in the FORMULA section in relevant OEIS sequences, though often they are too general (I think I am the first to consider the extension that is the basis of the generalisations section, as well), and I want to eventually write it all up into a LaTeX paper.

There are other questions that lead to sequences that can be used to characterise 1D rules, ie. "the number of length-n substrings that have finite predecessors in the rule" and "the maximum period of a length-n oscillatory agar with [cylindrical scrolling/fixed end states]," yujh proved that the union (over all n) of the sets of periods of oscillators in length-n finite tapes with opposite-state ends in rule 150 is the positive integers, as the proof of omniperiodicity of B34kz5e7c8/S23-a4ityz5k. I would like for other people to add their findings so it is not all my particular domain of knowledge, though it seems there are not especially many interested.

Posted: **February 7th, 2024, 10:02 pm**

DroneBetter wrote: February 7th, 2024, 3:08 pmAlso, finding generating functions for sequences of on-cell-counts in cellular automata is not actually a very esoteric idea!

Actually, I'm not against esoteric ideas, and of course not against mathematical ideas. This is a mathematical hobby.
Still, this is (mostly) a hobby, a game. And I think pages densely filled with equations are a bad way to present this game to LifeWiki readers. In my view, that's a misrepresentation of what Life/CA actially is (and maybe a misrepresentation of what mathematics really is).
Plain text explanations are needed. Probably you could add an esoteric pattern or two, or maybe an esoteric picture. It does not have to be formulas.

Quoting from LifeWiki:Style guide:

LifeWiki:Style guide wrote:The purpose of LifeWiki is to provide encyclopedia-style content describing Conway's Game of Life and similar cellular automata. All articles should be informative and targeted at the site's audience. Information that is only of interest to the writer or to other editors should not be included in articles. Articles should not assume knowledge that someone with a basic understanding of the Game of Life would not possess; relevant terminology should be explained or linked to.

I think the quote is directly relevant here.

Edit (2024-02-11): unfortunately more nearly-SPAM edits and edit summaries from the same account:
https://conwaylife.com/w/index.php?diff ... did=145142
https://conwaylife.com/w/index.php?diff ... did=131196

Posted: **February 11th, 2024, 9:02 pm**

confocaloid wrote: February 7th, 2024, 10:02 pm Edit (2024-02-11): unfortunately more nearly-SPAM edits and edit summaries from the same account:
https://conwaylife.com/w/index.php?diff ... did=145142

You don't need to say "from the same account," we are talking to each other here, you can refer to me as DroneBetter (or less formally, 'Drone,' as people seem to do :-).

Anyway, sorry for that edit only adding more explicit forms and g.f.'s for functions, I had finished the addition after a computer crash erased some of my previous work and wanted to put it there, I know that the forms are somewhat unwieldy.

I am thinking about including a diagram in a LifeViewer in it, here is what I have thought of (showing the n=1 case (Sierpinski triangle) and n=2 (rule 120) of the series, with the binary representation of o(k) (the index of the first generation at which the k'th cell turns on, and equivalently the constant such that the k'th cell is on iff o(k)&~t = 0 (ie. t contains a superset of the bits of o(k))) on the x axis, and of v(t) (the number of cells on in the t'th generation) on the y). (I tried adding other functions, but they didn't appear so interesting (they encode values that can be seen trivially from the shapes, or have no such apparent order to them when viewed in binary), I kept v(t) because I like that it is 2 to the power of the Hamming weight of t in the Sierpinski triangle, but apparently chaotic when viewed by the same method for all others.)

Code: Select all

x = 173, y = 137, rule = B3/S23
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Does this look suitable, and do you recommend anything more? Should the evolutions run for longer? Should more cases (for higher n, and slower-growing evolutions still) be added?

Posted: **February 13th, 2024, 1:31 pm**

DroneBetter wrote: February 11th, 2024, 9:02 pmDoes this look suitable, and do you recommend anything more? Should the evolutions run for longer? Should more cases (for higher n, and slower-growing evolutions still) be added?

Please review and cleanup your existing edits in wiki pages, instead of adding even more similar content (that will most likely have to be removed/reverted).
See also viewtopic.php?p=177975#p177975

confocaloid wrote: February 5th, 2024, 11:30 amI think I would like to know what is the intended target audience for those pages. They contain lots of formulas, with little or no explanation as to why all this belongs to LifeWiki. Some parts look like SPAM. Are you writing for other people?
[...]
I think most of those additions should be removed, as out-of-scope (and hard to read) content added by an overenthusiastic editor.

ConwayLife.com

More pages for Wolfram rules?

More pages for Wolfram rules?

Re: More pages for Wolfram rules?

Re: More pages for Wolfram rules?

Re: More pages for Wolfram rules?

Re: More pages for Wolfram rules?

Re: "OCA:Rule 120" improvement discussion

Re: More pages for Wolfram rules?