A shower thought turned into a beautiful Collatz visualization
Note
in my reading about human thinking discoveries, there are also walking thoughts and hiking thoughts!
conjectures can be quite the rabbit hole if you have enough tools in your back pocket to reach for when throwing abstract spaghetti at the wall.
i appreciate this authors inclusion of code as well as research, discovering other papers that have reached the same conclusion they have.
Published
2025
Summary
The author details a personal project that began as a 'shower thought' to visualize the Collatz Conjecture. The method involves converting the sequence of operations for any given number into binary digits, which are then treated as a binary fraction. Plotting these fractions reveals intricate, self-similar fractal patterns. The author later discovered this visualization had been previously explored by mathematicians Olivier Rozier and Yukihiro Hashimoto using 2-adic numbers.