Bonus Fourier video (not a paid post)

Firstly, thanks muchly. Secondly: Is the background music a partilcuar artist you selected, or perhaps simply some canned relaxation music? Either way who is the artist ? (I'm looking for more of the same :)

Chris Jennings

Grant, would there be any chance you could make this available as a downloadable video, and/or a screensaver ? Complete with music of course :-) I find it mesmerising while very relaxing. That I understand the math only makes it even more immersive. I would happily pay for this ! (and I could use it anytime as backrgound mood music while doing my math hobby :-)

Chris Jennings

Yup. It might be a little convoluted to track down what exactly is going on, but these animations come from this file: https://github.com/3b1b/manim/blob/master/active_projects/diffyq/part4/fourier_series_scenes.py

3blue1brown

I love this. Quick question: I noticed that manimlib is available at GitHub. But do you know if the source of this animation is shared in any way?

Well put! I love this video.

Programmable Spacecraft

I like the illusion of a third dimension with the smaller vectors rolling in a plane perpendicular to the plane of the screen!

Gregor Shapiro

Not so much "oddly satisfying" as "rapture-inducing". The full lecture evokes a joy of understanding, but this dance of vectors awakens something at the core. Thanks, Grant!

Hilariously wonderful!

Steven Siddals

At first I guessed he was centering the camera on the tip of one arrow, but soon discovered that's not the case. No particular arrow stays at center. The last hundred arrows whip around too much, too far, and the camera has to track them too. So my next guess would be, take a deep arrow (like #20 or #30) as an "anchor", then add the average location of the rest of the arrows... and use that as the camera's center location. Tell me if I'm right Grant.

Jacob Mirra

Ooh, wanted to see more Hilbert curves. I'd expect to see higher iterations of the fractal the more Fourier terms used. And you could predict the rate of decay of the Fourier coefficients based on the fact it is 1/2-Holder.

Jacob Mirra

No math content? This is the why do math and not just the how to do math.

white beard geek

What is your algorithm for camera placement? The close-up shots have very nice and smooth camera movement following the action, and it doesn't look like a trivial nothing. This alone intrigues me.