Collatz‑3: Python Implementation and Documentation

Overview

This archive provides a clean and minimal Python implementation of the Collatz‑3 dynamical system. The Collatz‑3 map is defined by repeated division by 3 when possible, and by a 4n ± 1 transformation when n is not divisible by 3.

The system behaves similarly to the classical Collatz map but uses 3-adic valuation instead of 2-adic valuation. All tested values eventually converge to 1, although some numbers exhibit long transient behavior before reaching the fixed point.

Definition of the Collatz‑3 Map

For a positive integer n:

1. If n is divisible by 3: n := n / 3

2. If n ≡ 1 (mod 3): n := (4n - 1) / 3

3. If n ≡ 2 (mod 3): n := (4n + 1) / 3

The process repeats until n reaches 1.

Included Files

• collatz3.py
  Python implementation of the Collatz‑3 map, including:

  • trajectory generation
  • step counting ("3‑Resistance")
  • interactive command-line interface

• overview.pdf
  Mathematical background and explanation of the Collatz‑3 system.

• howto.pdf
  Instructions for running the code and performing numerical experiments.

• LICENSE
  CC BY 4.0 license with copyright notice.

Usage

Run the script from the command line:

python collatz3.py

Enter a positive integer when prompted.
The program will output:

• the full trajectory
• the number of steps required to reach 1

Example

Input: 7

Output: Path: 7 → 9 → 3 → 1 Steps (3‑Resistance): 3

Requirements

• Python 3.x
  No external libraries are required.

License

Copyright (c) 2026 Hiroshi Harada
This work (Collatz‑3 Python Implementation and Documentation) is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
You are free to use, modify, and share this work with attribution.

The full text of the CC BY 4.0 license is available at: https://creativecommons.org/licenses/by/4.0/legalcode

Citation

If you use this code or dataset in academic work, please cite the Zenodo DOI associated with this archive.

Author

Hiroshi Harada