Vuza Canons

One of my side projects recenty has been to explore the theory behind Vuza Canons, which are defined as aperiodic rhythmic tilings. These are exceptionally rare mathematical structures that have a natural musical interpretation. They play an unexpected, profound role in the algebraic structure underlying rhythm.

Mathematically, a Vuza Canon is a pair of rhythms, $(A, B)$, that precisely tile a cyclic group $\mathbb{Z}_n$ without any gaps or overlaps, where both the inner rhythm $A$ and outer rhythm $B$ are nonperiodic.

If you are interested in learning more about this work, click here.

That Prime Number Spiral Thing

While at Pasadena City College, as I was developing my interest in mathematics, I noticed an intriguing pattern while experimenting on my computer. I posted about it on Math StackExchange, specifically asking why prime numbers seem to form spirals when plotted in polar coordinates. I've licensed the polar plots I created under CC-BY 4.0.

I was pleasantly surprised one day to discover that 3Blue1Brown had featured my question in one of his videos. Grant Sanderson does a great job of explaining the deep mathematics that I stumbled upon in this video. In the process, he immortalized my afternoon of procrastinating. Thanks 3b1b!