Evolution patterns in Collatz problem

TL;DR

This paper introduces the concept of evolution patterns in Collatz sequences, demonstrating that every finite pattern can be realized within some Collatz sequence, advancing understanding of their structural properties.

Contribution

It is the first to formalize evolution patterns in Collatz sequences and prove their realizability within specific sequences.

Findings

Any finite evolution pattern is implementable in some Collatz sequence.

The concept of evolution patterns provides new insights into Collatz sequence structure.

The results open avenues for further analysis of Collatz dynamics.

Abstract

The concept of evolution patterns is introduced for Collatz sequences and it is shown that any finite evolution pattern is implemented in some particular Collatz sequence.