Collatz‑6: Python Implementation and Numerical Exploration Tools
Abstract
This archive provides a minimal and clean Python implementation of the Collatz‑6 dynamical system, including 6‑adic valuation, orbit generation, Chaos Rim analysis, and detection of glider‑like behavior. The Collatz‑6 map is a modular dynamical system defined by divisions by 6, 3, and 2, combined with 7n±1 jump operations reduced by 6‑adic valuation. Although the system is strongly convergent, some numbers exhibit temporary escape‑like or glider‑like behavior by remaining in the Chaos Rim (numbers congruent to 1 or 5 mod 6) for many steps before eventually falling to the fixed point 1. This archive includes:- A Python implementation (collatz6.py)- Documentation files (overview, how‑to)- A plain‑text README for long‑term preservation- A CC BY 4.0 license The purpose of this dataset is to support reproducible research, numerical experiments, and exploration of dynamical behavior in the Collatz‑6 system.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
advanced mathematical theories
Advanced Mathematical Theories
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 7 February 2026
- Language
- EN