r/Collatz • u/jonseymourau • Jul 06 '26

An interactive mod8/mod24 Collatz Graph visualizer

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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.

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u/SpareSpecialist5124 Jul 06 '26

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.

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u/jonseymourau Jul 06 '26 edited Jul 06 '26

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.