Collatz Conjecture
An immersive exhibit and exploration of the Collatz Conjecture—a simple mathematical sequence that is unsolvable.
Overview
The Collatz conjecture is a mathematical speculation that is said to be unsolvable. Introduced by Lothar Collatz in 1937, it is also known as the “3n + 1 problem.”
The conjecture states:
- Start from any positive integer, n.
- If n is even, divide by 2; if n is odd, multiply by 3 and add 1.
- Continuing this sequence will always end in 1, regardless of which positive integer is chosen initially.
The conjecture is considered “dangerous,” because it is notorious for absorbing massive amounts of time from both amateur and professional mathematicians alike seeking to find a proof. Although it has not been proven, it has been confirmed by computer for all starting values up to 268 ≈ 2.95×1020.
In this immersive audio-visual exhibit in the Visualization Studio at the Hill Library, Trevor Thornton explores this simple, yet seemingly infinite sequence. The sequence begins with a number represented in a large circle and a simple musical tone. The circle is red if the number is odd and green if the number is even. Each subsequent number in the sequence follows this pattern, and the tone goes up or down depending on the progression of the sequence. What results is a meditative and soothing experience, wherein the pattern of the sequence is heard, seen, and felt.
How We Did It
The project was built using Javascript, CSS, and HTML. It plays from a local directory in the Google Chrome browser.
This project utilized the immersive display technology in the Libraries and was facilitated and supported by the Libraries staff.
NC State students, faculty, and staff can request a consultation in this space through this form or by emailing library_hightechspaces@ncsu.edu.
