Talk:Isotropic non-totalistic rule

There are 2^102 isotropic Life-Like rules

OEIS sequences

A000616(n) is the number of isotropic 2-cell-wide block neighbourhood rules in n dimensions, and of course A054247(2*n+1) is the number of range-n 2D Moore rules. We have a link to the sequence of doubly-triangular numbers pertaining to generalisations to arbitrary numbers of states, should we try to find and list more? DroneBetter (talk) 13:44, 31 December 2022 (UTC)

a section on Integer sequences may be in order

wildmyron has explained the reason for the original footnote on the 3D Moore INT transitions to me

The footnote on this cell in the table had initially said "Upper bound; calculations by Milo Jacquet returned this number of transitions, however calculations by wildmyron returned 1426132". This seemed odd to me, for surely such a number was calculable, which was the motivation for my program, which I told wildmyron about over a forum messaging thread. They replied to me on 22-12-24.

It's been quite some time since the post in question and you may have noticed that I haven't been active on these forums. I don't have much time for this hobby these days and don't have any time for snide remarks, hence my curt response before. I'll come back to answer your questions in full after the holiday season, but I can say I wrote the code which I used to calculate the number I came up with because it was unclear to me how to correctly apply Burnside's lemma to this problem and I wanted to enumerate all the possibilities. I remember initially having an error in my code which caused a discrepancy with dvgrn's result but AFAICR we reconciled the difference. As I said, it's been a while and I don't have any more time to look back at this problem right now.

(the 'snide remarks' referring to my initial message's title having been "Your maths is bad and you should feel bad" before I messaged again to inquire about their program's workings.) I then sent them another message briefly explaining that I was also unable to apply Burnside's lemma but made my program do so instead (then referring to the polynomial fitter, as it's explained in that article)

After some investigation I think I understand what happened here. In short, the wiki history is a poor reflection of real history (and or my memory of events is inaccurate - probably some combination of both).

My contribution to this question came in response to this post on 2019-09-18 viewtopic.php?p=82883#p82883

My initial response to the query was embarrassingly wrong, but I made that clear fairy soon after. Somewhere between then and 2019-09-28 I considered the problem further, did some reading about Burnside's Lemma, looked at some examples of its use and decided there was no way I'd get the right answer using it. So I wrote the program I mentioned earlier which used matrix multiplication to calculate the number of unique configurations after symmetry for each number of neighbours. This program was woefully inefficient but I have run it again and it produces the correct value. Somewhere there's some discussion where I posted about my progress on this calculation and I'd made an error in calculation of the number of configurations for one of the neighbour counts. This is where the erroneous value which ended up on the wiki (attributed to me) came from. I'm sure dvgrn reproduced my work and identified that there was a discrepancy between his values and mine. I fixed my code and reproduced the same (correct) value as he found. Where this discussion occurred I can't tell you, possibly on the Discord server. Although I'm sure it should have happened on the thread where the original question was posted. If it did happen there I can't explain how or why it's disappeared. Somewhere along the line, Milo Jacquet posted the result of a calculation which also gave the correct answer (I believe based on application of Burnside's Lemma) but again I can't find the discussion or explain why the wiki noted it as being an upper bound. I published my code to Github on 2019-09-28 and refined it a little the next day. I also applied the same technique to the question of the number of isotropic configurations on the range-2 Moore neighbourhood. Both programs were published here. As I mentioned I confirmed that my 3DCA_iso_neighbourhoods.py program produces the correct result. Despite your implementation of Pólya's enumeration theorem in your published program I rewrote my program to use permutations in place of matrix multiplications which gave an order of magnitude improvement in performance. Obviously it is not ever going to compete with the other method.

I hope that clears a few things up, though I'm a bit annoyed I wasn't able to find the previous public discussion about this topic. And yes, I did have a look at your program and I'm impressed with the results it gives. I can't say I understand what it does very well, but I'm not inclined to spend much time figuring it out because I've been dealing with some code at work which has far too many layers of abstraction and has been giving me a big headache.

I will send them a link to the explanation in my new article (which I hope will provide general programming insight as well as only concerning the problem itself) and see what they have to say, but I'm sharing this here because I think it answers some questions and explains history (and I wouldn't like such a thoughtfully-written message to be left in my inbox, to be deleted when it reaches the limit). I would like to see the original discussion myself one day, if anyone can find it, so it can be linked to from this article for completeness's sake. DroneBetter (talk) 19:20, 13 January 2023 (UTC)