My accepted WWDC19 Scholarship Application. It takes in a path and then uses the Discrete Fourier Transform to animate it as a series of orbiting epicycles. It utilizes the playgrounds format of the submission to also explain how the math relates to the code.
This was such a fun project to work on because it involved learning a lot of new and fascinating math and resulted in an extremely visually satisfying final product.
Inspiration for the project came when I came across 3Blue1Brown’s video explaining the Fourier Transform. I was immediately fascinated by the math behind it and did a lot more research into the math behind it. During that research, I found that you can also pass in 2D coordinates as complex numbers to break down paths as if they are periodic function. With that, I set off on the project.
At this point I was still a sophomore in pre-calc. Exploring concepts in math way beyond what I was taught in school was a really fascinating and rewarding experience and really grew my appreciation for math. It’s something that I have repeated many times in projects since then. I feel like going down rabbit holes (and learning the necessary fundamentals along the way) is a really fun way to learn.