New video! Visualizing the Riemann zeta function and analytic continuation

Best video of this kind I have seen. Well done. Given your resent video using asymptotics to talk about box dimension, I think you might be able to tackle (real-variable) analytic continuation using asymptotic expansion as can be see in the post by Terrance Tao. With your animation toolbox, you can give another great explanation of this to the public. <a href="https://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation" rel="nofollow noopener" target="_blank">https://terrytao.wordpress.com/2010/04/10/the-euler-maclaurin-formula-bernoulli-numbers-the-zeta-function-and-real-variable-analytic-continuation</a>

Amazing video! This convinced me to become a supporter.

On that, I plan to do in a little bit is on why 1-1/3+1/5-1/7+1/9-... = pi/4. It's a great excuse to talk about some beautiful number theory, and the ultimate connection is both surprising and (once known) intuitive.

3blue1brown

Yes, please do devote a video to the "why does Pi keep showing up in solutions!" question

Chase Turner

I just came to say how much I love the music here as well (actually all of the videos). When background music is done well it's really easy to under-appreciate it - you only notice when it's done poorly, and tends to get boring or distracting. However, here the music is pleasant to listen to, hits just the right balance between being calm and soothing, and excited about the topic at the same time, and it "gets out of the way" otherwise. Excellent choice! I don't know how much effort you put into selecting the right music for the videos, but I think the results are totally worth it :)

Job van der Zwan

You can see the scripts for videos in the old_projects folder of <a href="https://github.com/3b1b/manim" rel="nofollow noopener" target="_blank">https://github.com/3b1b/manim</a>

3blue1brown

Fantastic video! I'm curious, did you or would you ever do a behind-the-scenes? As someone working on Data Visualization using WebGL and the like I would be really interested in how the sausage is made :)

Magnificent! Really enjoyed this. Its a trivial piece of feedback regarding aesthetics and not critical to the content but I find the hard cut of the edges of the visible portion of the grid (that undergoes transformation) a little distracting. I know you mention this and the importance of the extended grid lines and where they cross zero later on, but I have a suggestion for improving this (potentially in future videos on transformations too): If you alpha blend the values of the grid to 0.0 (transparent) at the edges of the visible part of the grid (linearly or even better with an ease) these hard edges might be less jarring and the eyes can focus on the beautiful spiralling transformation which will seem continuous across space. Just a thought! Cant wait for the next videos. Ps. Loved the music in this one too!

Thanks for letting me know!

3blue1brown

Wonderful video! You have put Mathologer's video link twice in the description (the first time instead of your video), please fix.

Ah, interesting point. I can imagine an implementation where at every given moment the spiral is a perfect reflection of the input point, but those animations tend to take longer to load, so I shy away from them. Thanks for pointing it out, though, I hadn't noticed the discrepency.

3blue1brown

At 7:14 I was very confused for a moment. It seems that you "cosine-interpolate" between the positions of the yellow dot, but do the same between the spiral structure, so you don't calculate the structure at every point, just interpolate between the values. When the yellow dot crosses the x-axis, the i component is zero and the spiral should be straightened out fully, but this never happens. I found this counterintuitive and was very confused for a moment!

Holy crap, that was one ambitious video. Anybody who down votes this is either lazy or a total jerk . . . or both.

Don Sanderson

Even though i was explained this many times, this video was full of "oooh" and "aaah" moments, and brought a tear of joy. Thank you so much for this, it is wonderful