u/tidy-acuty75

I’ve been exploring a custom Collatz-type dynamical system for the past couple months and wanted feedback from people interested in number theory / dynamical systems.

Instead of using a fixed odd rule like (3n+1), my variant uses increasing odd multipliers:

(1,3,5,7,\dots)

Definition:

• If (x) is even: [ x \to x/2 ]
• If (x) is odd: [ x \to mx+1 ] and then the multiplier updates: [ m \to m+2 ]

starting from (m=1).

So the odd multipliers used successively are:
[
1,3,5,7,\dots
]

I ran computational tests for starting values up to 10,000 with a 200,000-step cutoff.

Observations:

• A small minority quickly reach small numbers like ({1,2,3,4,5})
• Most trajectories instead grow extremely large and never returned within the computational limit
• I also proved there are no cycles in the full ((x,m)) state space because the multiplier strictly increases after odd steps

I wrote a short experimental paper about the system and I’d appreciate feedback, criticism, or suggestions for further directions.

I’m not claiming a breakthrough — just sharing an interesting dynamical-system experiment inspired by Collatz.