Combinatorics and Graph Theory

    

Revised Collatz Graph Explains Predictability

Authors: Steven M. Tylock

The Collatz Conjecture remains an intriguing problem. Expanding on an altered formula first presented in “Bits of Complexity”, this paper explores the concept that “3N + Least-Significant-Bit” of a number allows the complete separation of the step of “dividing by two on an even number” within the Collatz Conjecture. This alternate formula replaces the original Collatz on a one-for-one basis. The breadth and depth of graphs of the resulting path of numbers resolving with this new formula illustrate its fractal nature. Lastly, we explore the predictability of this data, and how the ultimate goal of reaching one prevented previous work from finding the key to understanding 3N+1.

Comments: 11 Pages.

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Submission history

[v1] 2021-09-09 22:01:08

Unique-IP document downloads: 413 times

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