Collatz‑5: Python Implementation and Pentadica Orbit 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‑5 dynamical system, also known as the Pentadica map.The Collatz‑5 map is defined by modular rules based on n mod 5, including four Outer‑Circuit update rules and a division rule when n is divisible by 5.Although the system always converges to the stable core {1, 2, 3}, many numbers exhibit glider‑like behavior, remaining in the Outer Circuit (mod 5 = 1, 2, 3, 4) for long periods before eventually falling into deeper layers.Some numbers show dramatic oscillations, high maximum values, and long “laps,” forming Endurance Gliders, High‑Altitude Jumpers, or even Legendary Gliders.This archive supports numerical exploration of such behavior.Included in this dataset:- A Python implementation (collatz5.py)- Documentation files (overview, how‑to)- A plain‑text README for long‑term preservation- A CC BY 4.0 licenseThe purpose of this dataset is to support reproducible research, numerical experiments, and exploration of dynamical behavior in the Collatz‑5 system.

Fields of Study & Subjects

Mathematical Dynamics and Fractals Advanced Mathematical Theories Mathematical and Computational Methods

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
8 February 2026
Language
EN