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 AwesoMan3000 created this page with the name "Logarithmic replicator rule" despite David Eppstein's page not anywhere describing it as such.

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. Where 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*A000695(n-1)+A000695(⌊n-12⌋)+4 if n>0 else 1) < 9*n²4 and the right edge's by 3*n²8 < (3*A000695(⌊n2⌋+1)+6*A000695(⌊n+2-2^{⌊log₂(n+2)⌋}2⌋)+2*(n%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)

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