Fractals are a pretty neat mathematical phenomenon that I had the pleasure of exploring through my Chaos Theory class last fall. I ended the class with a comprehensive project studying fractals in nature, a topic I find beautifully interesting both from a visual and mathematical point of view.
Hot take: I love mathematics. I also love music and having a good time, so I am hoping to produce a final project that incorporates all three of these things. My goal is to create a music video of some sort, incorporating fractals and tracks from the European techno scene. I’m sure I’ll explore many different directions in the coming weeks and run into countless challenges, however, here is my jumping off point:
What the hell is a Koch curve?
This is, like, day-one fractals. Pretty easy to draw, but what about write an algorithm? My goal is to write a class in python that returns different iterations of specified fractals. n = 1 returns a triangle, n = 2 returns a star, n = 3 returns a snowflake?
Now what about squares!
The T-Square fractal is a beautiful example of geometric complexity and convergence. Or chaos? Here, n = 1 returns a square, n = 2 returns a square with square corners, n = 3 returns a square with square corners with square corners… you still with me?
Let’s take a step back.
Here is the Sierpiński triangle. This is one of the most basic examples of a self-similar set, officially named after Polish mathematician Wacław Sierpiński in the 1900s. Interestingly enough, this design appeared as a decorative pattern in the 13th-century Cosmatimosaics in the cathedral of Anagni, Italy. Pretty neat, eh? Math is so cool and old and fundamental.
Fractals are a natural phenomenon. Trees, riverbeds, lightning strikes, veins, and even broccoli return self-similar, self-repeating patterns that can be constructed mathematically. My goals for this project are to do just this: construct art mathematically. I’m sure there are a million and one python libraries that would do all of this for me, however I want full artistic control over my outputs. I want to see what I can achieve on my own. This may limit how far I can take video capabilities, but I think I would take great pride in knowing I did it all from scratch. Ha! Famous last words, Emily. We’ll see how it goes.
My musical inspiration stems, as I said, from the European techno scene. I’ll probably include a little house, a little US bass. Let me know if you have any song requests 😉 Or really any suggestions in general. I’m excited to see how this turns out!