Exploring Number Theory with Divisor Patterns

This video describes a pattern I discovered when I was young. I was exploring polyrhythms. I plotted rows of numbers and spaced them out in a way that also visualizes integer divisibility.
Of course I'm not the only one to come across this pattern. A handful of mathematicians have written about it as well, with some mathematical analysis (see divisorplot.com).
This is an endless pattern that can be investigated in a purely-visual way...and though this visual analysis, many concepts from number theory can be discovered.
I was a poor math student; I never got past algebra in High School, and I failed Math 001 in college. Math notation and I never got along. But as an artist with a love of geometry and music, I was able to find a new way to appreciate math, after learning how to write code and starting my career in computer graphics, in the late 1980's.
This video was submitted to the 3Blue1Brown Summer of Mathematical Exposition in August of 2022.
I'd like to thank Dan Bach, Canton Becker, Michael Dunworth, and others who have shared ideas and motivations, and given me support and feedback over the course of developing this material.
I hope you enjoy this video.
Visit divisorplot.com for more info.

[@NonTwinBrothers]

I'm so glad they finally announced Pascal's triangle 2

[@whatelseison8970]

This was a lot of fun! Over my time stumbling and bumbling around playing with math visualization and music I've noted a number of these sorts of cool patterns. Another method the brain has for hearing patterns that's even faster is in its ability to distinguish the harmonic and fundamental content of tones through their pitch, and timbre. For example, if those monkeys were sped up about 100 fold the musical intervals between any 2 of them would be immediately recognizable to the ear.
Math terminology is littered with great band and album names too like "The Roots of Unity", "The Quadrilateral Hierarchy", "Asymptote", or "Analytic Continuation" (That last one would be a B-side record).

[@abdusshaikh2842]

This is one of the most fascinating math videos I’ve seen in a while.
Thank you for putting this out. Excellent work

[@craigtuggy7051]

Thank you so much for sharing this! I really enjoyed it and plan on watching it again as well as making my own divisor pattern explorations.

[@rcfadli8762]

your channel is underrated sir

[@sizur]

A masterpiece!

[@seanoneill2098]

Way to go, congratulations on bringing this together

[@dgusev]

Mind blowing 😀

[@f.j.9094]

thanks to be inspired

Excellent, you should try sometime to represent the prime numbers on circles or spheres too !

[@S.G.Wallner]

Inspiring.

[@benfletcher8469]

wow

[@nycoshouse]

only in base 10 ?