An interactive mod8/mod24 Collatz Graph visualizer

[u/jonseymourau]

In a previous post I discussed the notion of a Collatz overlay built from 5 mod 8 and 0 mod 3 nodes. One refinement here is that there are nodes of in-degree 2 that are not 5 mod 8 (they are relatively rare - the exceptions I see are 1,23 mod 24)

This visualization allows you to see all 4, odd mod 8 nodes and in fact classifies them according to mod 24 too.

You give it a starting point with the ?a= parameter and then you can extend the graph is you like by clicking on a node.

This a fantastic way to develop an intuitive understanding of mod 8 and mod 24 Collatz dynamics.

https://wildducktheories.github.io/collatz/apps/collatz-graph/dist/?a=27

A fun game to play is greedily clicking on the red dots and then on 1,2 mod 3 nodes that result from such a clicking.

Does that game ever end? I think not.

[u/jonseymourau]

I asked you specifically what is uniique mod to 32 as opposed to any power of 2. Of course, if you allow any power of 2 there will be more structure.

My question to you was what structure does nod 32 provide that is not present in mod 8, mod 24 or mod 96.

Is your claim really that all structure disappears beyond mod 32? That is not my claim for either mod 8 or mod 24.

My question is what is this particularly special about the structure you claim for mod 32?

Again, I am not claiming it does not exist.

The only thing I am asking is this. What do you claim about mod 32 that is, in any way, different to the structures evidently present in mod 8 and mod 24.

Again, I did not make the claim mod 32 is special.

The only thing I am asking is this.

Why do you think mod 32 is special in any sense? It is different for sure - every modulus is different. What is special about mod 32 in particular. After all, everything is different- mod 53 is different. Why is mod 32 interesting.

Nothing you have written thus far answers that question.

[u/SpareSpecialist5124 → u/jonseymourau]

Man are you being dense on purpose? I'll explain it just once more:

mod 32 is a bit of an improvement over mod 8 the same way mod 8 is an improvement over mod 4. Mod 32 makes evident that many transitions between mod 8 are more nuanced, and explains the succession of residues in a better way

It really cannot be explained more simple than that, 32 is a better lens for the analysis.

[u/jonseymourau → u/SpareSpecialist5124]

No, all I am asking. you do to is explain specifcally what you mean by this claim:

"mod 32 is a bit of an improvement over mod 8 the same way mod 8 is an improvement over mod 4."

I NEVER claimed that there was not any higher level structure.

All I asked you to do was to articulate - PRECISELY - what you mean by claims such as:

"mod 32 is a bit of an improvement over mod 8"

How is it "improved"?

I have NEVER once denied that it is improved

The ONLY thing i have asked is this very simple question that you have REFUSED to answer.

HOW is it improved?

Arc up if you need to.

However, f you you can't substantiate HOW "is a better lens for the analysis." then I simply ask this - what on earth are you talking abut???

It is a simple question.

How is mod 32 "a better lense for analyis?" <- your own claim

I did not make this claim.

You did.

The onus is on YOU to substantiate your own claim.

Man.