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Report . 2026
License: CC BY
Data sources: Datacite
ZENODO
Report . 2026
License: CC BY
Data sources: Datacite
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Collatz‑12: Python Implementation and Sanctuary Dynamics Exploration Tools

Authors: Harada, HIroshi;

Collatz‑12: Python Implementation and Sanctuary Dynamics Exploration Tools

Abstract

This archive provides a minimal and clean Python implementation of the Collatz‑12 (Duodecadia) dynamical system.The Collatz‑12 map is defined by twelve modular rules based on n mod 12, combining division operations (÷12, ÷6, ÷4, ÷3, ÷2) with acceleration operations of the form 13n ± c. A distinctive feature of the system is the Outer Rim, consisting of the residue classes{1, 5, 7, 11} mod 12, where all ×13 accelerations occur.Among them, Class 7 acts as the strongest accelerator and is known as the Sanctuary. Although all orbits eventually converge to 1, many numbers exhibit long, glider‑like behavior by repeatedly returning to the Rim and producing large peak values before collapsing.This archive includes tools for analyzing such Sanctuary‑driven dynamics, identifying “Sanctuary Children,” and exploring near‑escape behavior. This archive includes: A Python implementation (collatz12.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‑12 system.

Keywords

Collatz, computational mathematics, Collatz conjecture, discrete mathematics, playable mathematics, modular dynamics, numerical exploration, dynamical systems, glider, Chaos Rim, 12-adic, Collatz-12, Python

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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