Collatz‑6: Python Implementation and Numerical Exploration Tools

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Authors: Hiroshi Harada
Cited by: 0

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