Visualizing Riemann's zeta function
Added 2016-11-30 22:33:21 +0000 UTCHey folks,
Usually I just share sneak-peak animations with >$4 patrons, but I thought I'd share these with everyone. I was playing around with visualizing various complex functions as transformations, and when I tried it out with the Riemann zeta function, the result was so beautiful I decided that must be the next video I do.
In particular, I think there's a really nice visual intuition behind the idea of analytic continuation to be had here, which, given a proper explanation, could make for a compelling video. Once I finish it, I'll jump back to where I was on the "Essence of calculus" front.
What I've linked to in this video is what the zeta function looks like on half the plane, and here's what it looks like on the full plane: https://youtu.be/PBrUVF2fr5Q
This sneak peak is just for you folks, so kindly refrain from sharing until there's a full video surrounding these. At which point, share like crazy :)
-Grant
Comments
Gorgeous. Now you've got to figure out how to animate the analytic continuation to Re(z) [edit: whoops, you did it already, nice job!] [edit: did you get any insights into the Riemann Hypothesis... ? Present a proof on your channel, you'll get funded for life - organizations will shoot funding at your project like a fire hose]
Jacob Mirra
2016-12-01 14:44:00 +0000 UTC
