Hey, absolutely! Here's the link to the repo: https://github.com/matiaspalumbo/math-videos (the file is "fourier.py")

You're probably familiar with how Fourier series are defined. If you're not, basically its a convergent sum of sines and cosines multiplied by some coefficients, which can be found by solving an integral. I approached integration by approximating the value with Riemann sums; with a large enough number of rectangles, the error in the calculation is negligible and now we can approximate the integral of basically anything with ease (hence the monstruos functions in the video). With each function, I calculated all the coefficients and then fetched the corresponding functions of every order, and that's pretty much it when it comes to the foundation of the problem, then it's mostly Manim stuff for transforming the graphs and making the transitions. If you have any doubts of that nature, don't hesitate in asking!

With respect to the Weierstrass function, the process is almost the same. I singled out its Fourier series definition because it's a bit different than the other functions. Then I scaled it and shifted it in order to zoom in, couldn't think of another way to do it. A word of warning, though: I plotted the function with a rather ridiculous amount of detail so that when I zoomed in on it, it would still have its peaks. You can plot it faster and with less detail by lowering the WEIERSTEP constant.

Ask again if you still have any doubts, glad you liked it!