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Riemann Zeta function visualizations with Python (christianperone.com)
91 points by rbanffy 11 months ago | hide | past | web | favorite | 7 comments

This is the most intuitive visualization of the Riemann Zeta function I've come across: https://youtu.be/sD0NjbwqlYw.

Wow, thanks for sharing that. Very well done!

I've always wondered what a Riemann Zeta plot would like where you plot two planes and draw the mappings as lines/vectors between them.

i.e., a 3d plot, one plane above the other, the bottom one x,i and the top one f(x,i) and a line from each x,i originating from one plane ending at the plane above.

You'd have to skip some values and have some amount of transparency ... but I think it might be interesting to see how the values map from one domain into the other.

Does something like this already exist?

Good question. I wrote some Javascript to plot complex functions as 2-d vector fields, which is not really what you're asking for, but helped my intuition about simpler functions. I haven't tried it on zeta.

You can plot magnitude and phase as a colored surface, as you probably know.

Last week I found out that the Basel problem was actually the inspiration for the Riemann Zeta function: http://www.fermatslibrary.com/s/a-proof-that-euler-missed#em...

Definitely created with Matplotlib. Interesting graphs!

>first paragraph

What is this, an equation for ants?

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