OCA talk:Sqrt replicator rule

Proper wiki article?

Would it be a good idea to make this a proper article? I'm not sure how notable this rule is (I do remember seeing some discussion about it on the forums or elsewhere) but I do want to point out that not only is this page the sole instance of a soft redirect on the wiki, but it's also to an external site and therefore doesn't even work because the template interprets it as an internal link. Ian07 (talk) 20:44, 15 February 2019 (UTC)

Yeah, it's quite an interesting rule (the replicator behaviour seems to be unique), and also outer-totalistic. 77topaz (talk) 09:55, 3 March 2019 (UTC)

The asymptotic growth is matched by that of rule 225, however this one is novel due to its isotropicness. DroneBetter (talk) 15:45, 29 September 2023 (UTC)

Incorrectness of name

Note that Muzik created this page with the name "Logarithmic replicator rule" despite David Eppstein's page not anywhere describing it as such. (Edit 2023-11-27: They clarified that the name in fact stemmed from a 2009 edit by apg)

The width of the pattern in the equivalent INT rule given by AforAmpere is not in fact logarithmic, it grows with Θ(√t). Where ..., .o., o.o and ooo refer to 0, 1, 2 and 3, it is equivalent to the 4-state range-1 one-dimensional cellular automaton with rule integer 0x190e002061040c0b86d0010e5980, here is a demonstration

from functools import reduce;from itertools import starmap,accumulate;redumulate=lambda f,l,i=None: accumulate(l,f,initial=i);print('\n'.join(starmap(lambda i,n: ' '*(l-i<<1)+''.join(map(lambda i: ' 123'[n>>(i<<1)&3],range(n.bit_length()+1>>1))),enumerate(redumulate(lambda n,i: reduce(int.__or__,map(lambda i: (0x190e002061040c0b86d0010e5980>>((n<<4>>(i<<1)&63)<<1)&3)<<(i+1<<1),range(n.bit_length()+4>>1))),range(l:=64),0b110)))))

Anyway, where l(t) is the bit-length of the pattern on the tth iteration, we have the limiting bounds 2 < l(t)√t < 2*√5√3.

As such, I will move the page to OCA:Θ(√t) replicator rule. DroneBetter (talk) 15:45, 29 September 2023 (UTC)

Addendum: For what it's worth, it is more similar to rule 225 than one may expect. I have found explicit forms that may be of interest. Alike OCA:Rule 225, where b₂(n) (A000695(n)) is the number obtained from writing n in binary and reading this result as a base-4 number, in the emulated 4-state Wolfram rule, the left edge's number of generations to grow by n cells is 3*n²4 < (2*b₂(n-1)+b₂(⌊n-12⌋)+4 if n>0 else 1) < 9*n²4 and the right edge's by 3*n²8 < 3*b₂(⌊n2⌋+1)+6*b₂(⌊n+2-2^{⌊log₂(n+2)⌋}2⌋)+(n%2)*2+4 < 3*n²4 (where bounds given are asymptotic). The inverse of their sum is slightly harder, but this should be sufficient justification. DroneBetter (talk) 15:58, 10 October 2023 (UTC)

I am going to move it back. Forum search gives a number of results where people mention this rule by the name "Logarithmic replicator rule". I do not think your proposed alternative is anywhere near common. Confocal (talk) 15:49, 29 September 2023 (UTC)

The commonness matters not, it is correctness that is important. DroneBetter (talk) 15:58, 10 October 2023 (UTC)

Both are important. I cannot find any actual uses of your proposed names by others elsewhere, i.e., it is your newly invented terminology. According to LifeWiki:Notability, "To prevent overenthusiastic edits and conflicts of interest, a commonly accepted rule is that the discoverer of a pattern, inventor of new terminology, writer of a program, etc., etc., should not be the one to document that pattern, term, or program on the LifeWiki."
In contrast, there are multiple places where 'logarithmic replicator' and/or 'logarithmic replicator rule' is used by various people: post78463 post102490 post126381 post129591 post130676 post136832 post151358. Confocal (talk) 00:24, 11 October 2023 (UTC)

It might be best to just use the rulestring then. --Galoomba (talk) 09:26, 11 October 2023 (UTC)

I added a "proposed move" template transclusion for the rulestring suggestion. As I already clarified, personally I prefer to keep the existing name Logarithmic replicator rule, because it is how the rule is commonly referred to (forum, Catagolue and most likely elsewhere). A rulestring would be a valid name as well, but then certain people will complain that the rule is "unnamed" and will want to invent a completely new name and put it on LifeWiki (this already happens). Confocal (talk) 04:12, 12 October 2023 (UTC)

After yet another attempt to move to an invented name, I removed proposed move. Obviously there is no consensus for the proposed move to rulestring-based pagename, and there are no alternative names in sufficiently common use either. Confocal (talk) 07:34, 21 October 2023 (UTC)

Related discussion: LifeWiki:Tiki_bar#"logarithmic"_replicator_rule_and_prospect_of_"OCA:rule_225"_page. Confocal (talk) 12:41, 30 September 2023 (UTC)