How do I write a paper on the Collatz Conjecture without fooling or making an ass out of myself? Im not affiliated to any University at the moment (my past Uni was like 20 years ago, but I didnt fullfill my studies). I am afraid I won't be taken seriously if I write my paper in a not so good formal matter even though I have the description in figures and notes and such.
I think I have a nice approach to atleast make a serious attempt on solving the Collatz C. but I can only give a description of the Automaton that generates configurations of any Collatz-sequence. I think someone with a professional or very good knowledge in Graph Theory can turn my description into a rigorous proof, disproof or determine wether it is undecidable or not. I have a feeling that determining wether it is decidable will also solve the conjecture at an instant, because it might turn into a proof right there. It might take a year or more than a year to write my paper, but now when I do have some ideas I am eager to start writing it quite soon. I know there are other threads on this subject, but writing my paper is specific to Collatz Conjecture, Binary numbers, Cellular Automata, Lattices, Graph Theory (I have little knowledge of) and a little bit of Number Theory (and perhaps Set Theory).
Just want some easy directions and hints before I start writing my paper. Thanks
Take a look at Cloney, Goles & Vichniac (1987) and German (2004) as examples of articles that say something interesting about the Collatz Conjecture without claiming to prove or disprove it. The two articles will likely be of interest anyway as they use cellular automata. They are also indicative of the kind of standards that may be expected, even for journals such as Complex Systems or Experimental Mathematics that are receptive to research that is a mixture of proved results and experiments.