This repository contains the Python source code for generating and analyzing Collatz-Matthews Sequence Networks (CMSNs), a multidimensional extension of the Collatz conjecture introduced in the paper "Collatz-Matthews Sequence Networks: A Multidimensional Extension of the 3n + 1 Problem" by Daniel Scott Matthews (March 2025). CMSNs augment the traditional Collatz sequence with metrics ( b_x ) (total steps), ( b_y ) (odd-step logarithmic sums), ( b_z ) (odd-step counts), and ( G ) (odd-step growth), providing insights into convergence dynamics.
The Collatz conjecture posits that for any positive integer ( n ), iterating ( n \to n/2 ) if even and ( n \to 3n + 1 ) if odd leads to 1. This code computes CMSNs for ( n = 1 ) to 30,000,000, revealing a key finding: ( b_z / b_x < 0.388 ) (max 0.374), with ( b_x - b_z > G ) universally across 30 million sequences. This supports the conjecture empirically and suggests a heuristic proof, detailed in the associated paper.
CMSN Analysis Script 4.0.py: The main Python script that generates CMSN sequences, analyzes metrics, and produces output files (CSV, PNG figures). It uses multi-threading for efficiency, processing 30M sequences in ~2-4 minutes with 16 processes.
- Python: Version 3.6+ (tested with 3.9).
- Dependencies:
pandas: For data handling and CSV output.numpy: For numerical computations (e.g., ( \log_2 )).matplotlib: For plotting distributions and scatters.seaborn: For enhanced visualization.scipy: For statistical analysis (e.g., regression).- Install via:
pip install pandas numpy matplotlib seaborn scipy
- Clone the Repository:
git clone https://github.com/yourusername/cmsn-analysis.git cd cmsn-analysis