Based in Honolulu, HI, 3leet5u is the software sketchbook of Tristan Madden.

Collatz Conjecture + Unit Circle

Collatz Conjecture + Unit Circle

The Collatz conjecture is a conjecture in mathematics that concerns a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1.
— https://en.wikipedia.org/wiki/Collatz_conjecture

I was inspired by this page to write my own Collatz Conjecture visualizer. My first build yielded something very close to what I saw in the Numberphile video, which I was happy with, but somewhat underwhelmed. I tried something different by keeping the rules used to create the original visualization, but wrapping everything around a unit circle. There are 360 "branches", each branch representing a 1-degree turn. I don’t suspect this reveals any new insights into the Collatz Conjecture, but I had fun generating some pretty organic looking motion and flocking behavior using a simple number sequence. The number 327 has a particularly long and interesting life here.

Recamán's Sequence

Recamán's Sequence

Barnsley Fern

Barnsley Fern