https://github.com/ratwolfzero/collatz

Collatz Sequence Visualization
https://github.com/ratwolfzero/collatz

3nplus1 collatz collatz-algorithm collatz-conjecture collatz-problem collatz-sequences hailstone-numbers syracuse-problem

Last synced: 7 months ago
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Collatz Sequence Visualization

• Host: GitHub
• URL: https://github.com/ratwolfzero/collatz
• Owner: ratwolfzero
• License: mit
• Created: 2025-02-22T14:54:22.000Z (12 months ago)
• Default Branch: main
• Last Pushed: 2025-07-20T00:17:28.000Z (7 months ago)
• Last Synced: 2025-07-20T02:51:53.313Z (7 months ago)
• Topics: 3nplus1, collatz, collatz-algorithm, collatz-conjecture, collatz-problem, collatz-sequences, hailstone-numbers, syracuse-problem
• Language: Python
• Homepage: https://github.com/ratwolfzero/Collatz
• Size: 469 KB
• Stars: 0
• Watchers: 1
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# Collatz Sequence Visualization

![DLA](collatz.png)

## Overview

The Collatz sequence, also known as the 3n + 1 problem, is named after the German mathematician Lothar Collatz, who first introduced it in 1937. This process leads to what is known as the Collatz Conjecture, one of the most intriguing unsolved problems in mathematics. Despite its straightforward formulation, the sequence's complexity and the absence of a general proof for all positive integers have kept mathematicians engaged for decades.  

**The Collatz sequence is defined by the following simple rules:**

- Let $$a_0 = n$$ be any positive integer. Define the Collatz sequence {ak} recursively by:

$$

\large

a_{k+1} = \begin{cases}

\frac{a_k}{2} & \text{if } a_k \text{ is even} \\

3a_k + 1 & \text{if } a_k \text{ is odd}

\end{cases}

\large

$$

- The Collatz Conjecture asserts that for all starting values n∈N+, the sequence eventually reaches 1. Once the sequence reaches 1, it enters the cycle 1→4→2→1.

In most computational implementations and visualisations, the sequence is conventionally considered to stop at the first occurrence of 1.

Despite its simple rules, the Collatz conjecture remains an unsolved problem in mathematics. The conjecture posits that no matter what positive integer you start with, the sequence will always eventually reach 1. Although no counterexample has been found, a general proof or disproof has yet to be discovered.