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The $qn+r$ Research Lab

This repository serves as the Engine Room for the Collatz Multiverse and Collatz Standard projects. While the main applications focus on visualization, this lab is dedicated to stress-testing conjectures, identifying loops, and mapping the limits of numerical consistency.

Inspired by: The Collatz Multiverse by carykh on YouTube

Included Tools:

1: Deep Search Python Engine:

A high-performance terminal tool designed for massive integers that:

  • Utilizes Python's arbitrary-precision integers with a 1,000,000 digit string limit.

  • Implemented loop detection through using Floyd's algorithm.

  • Uses Safety Guards for automatic divergence detection to prevent exponential memory consumption.

2: Range Computation Python Engine:

A fast terminal tool that allows users to enter custom number ranges to test user-entered conjectures, it does the following:

  • Utilizes Python's multiprocessing library to perform internal math quickly when numbers are huge

  • Utilizes Python's csv library to convert results into a .csv file to be saved on your computer

3: Titan Hunter Python Engine:

An efficient terminal tool designed to test random 1,000 digit numbers (positive and negative, based on user-input) on user-entered conjectures to discover if there is any divergence, loop, or even just to test the strength of known attractors

  • Utilizes Python's random library to randomize 1,000 digit numbers to be used as the value n within the $qn+r$ conjecture

  • Converts loops to text files if any number in them is above one million as displaying them on the CLI could cause unwanted and laggy behaviour (Safety fallback).

4: The Number to Bit Converter:

A side terminal tool that converts numbers to bits for user input in the main engines.

Research Documentation:

Core Findings are in the Research File

Key Discoveries:

  • $3n+1$ & $3n+1$ Mirroring: Proof of the symmetry between $3n-1$ (positive numbers testing) and $3n+1$ (negative numbers testing)
  • $4n+8$ Shared Trajectories: The discovery of mathematical highways in the $4n+8$ system where all paths of negative numbers eventually merge at the commencement 1.
  • $-3n+81$ Loops: Discovered 3 loops while testing -3n+81 that are reached by both positive and negative numbers.

How to Run:

Follow these steps to run the project locally:

1: Clone the repository and enter:

git clone https://github.com/Skayyali3/Collatz_Research.git
cd Collatz_Research

2: To:

I: Run the Deep Search Python Engine:

python Deep-Search.py

II: Run the Custom Range Computation Python Engine:

python Range-Computation.py

III: Run the Titan Hunter Python Engine:

python Titan-Hunter.py

IV: Run the Number to Bits Converter:

python Bits.py

License

This project is licensed under the MIT License – see the license file for details.

Author

Saif Kayyali