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 also utilizes the playgrounds format of the submission to also explain how the math relates to the code and so that the reader would be able to
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.