Is there a more "popular science" description of what is being said here. I would like to understand what is meant by "Collatz-like". Is it a function like:
f(n) = {n/2 : for even n,
3n+1 : for odd n}
What does
M(n) = 0^inf < A 1^n 0^inf.
I have really enjoyed the Busy Beaver stuff and play with simple code to try and learn what I can but when I read about it I run into the brick wall of math reading comprehension. Numberphile on youtube is pretty good sometimes with explanations but is not a reference. I do not know where to turn (I might ask chatGPT just to see what happens).
The definition used on https://wiki.bbchallenge.org/wiki/Collatz-like for a Collatz-like function is:
> a partial function defined piecewise depending on the remainder of an input modulo some number
(for the best known Collatz conjecture specifically: 2)
and
> A Collatz-like problem is a question about the behavior of iterating a Collatz-like function.
(Regarding the first part, there are other functions that do not use modulo to decide on which "path" to take but some other property of the input number (e.g. its primality: https://mathoverflow.net/questions/205911/a-collatz-like-fun...) that may perhaps also be described as Collatz-like.)
The notation for tape states is documented here: https://wiki.bbchallenge.org/wiki/Directed_head_notation
I think part of the reason why it's so difficult to learn more about this kind of problem is that humanity has simply not found the right language for it yet. And in the case of not only describing, but solving them, a terminology/classification for the "shapes" of halting or non-halting behavior of such systems is also still largely missing.
Thank you. I have been looking a little at your github Busy_Beaver repository. I think I will stick with my on code writing for a little while (amateurish but I am learning a little bit writing it).
OK, you were not fast enough. I asked chatGPT. I think it helped but there is still a lot I do not understand.
M(n) = 0^inf <A 1^n 0^inf.
An infinite list of zeros up to the position of the machine pointer followed by some number of ones (maybe zero ones?) followed by another infinite list of zeros.