I wanted to build this for a while, and finally had the time to do it. It's almost 100% vibe coded, but for a simple app with a simple functionality, I think that's ok.
The app lets you draw by free hand a line on the input plane, and it shows you how that transforms into a line on the output plane when fed through the Riemann Zeta Function.
In other words, the app visualizes the function:
where are coordinates in the output plane and are coordinates in the input plane.
A couple of animation tools let you visualize the critical line, as well as build some pretty funky images from sets of vertical lines:
You can also just draw pictures by free hand:
Anyway, though I'd share for all ye math nerds out there
Still trying to wrap my head around what this is basically... Have you tried circling the square or squaring the circle, or whatever that's called? Pretty interesting result...
The function is formally defined as:
where s is a complex number, and the function also returns a complex number.
A complex number is really just two coordinates in the complex plane: s=x+iy. So you can plot a complex number on a two-dimensional axis, as in the app.
So the app just shows, for whatever set of complex coordinates you draw on the input plane, what the Riemann Zeta function's output coordinates are in the output plane.
In other words, it transforms your drawing (a set of input points) into another drawing (a set of output points)
It just has a really weird, circular and stretched transformation.
It also has deep connections to number theory and prime numbers, which is why mathematicians obsess over this function. A lot of mathematical theorems rely on the Riemann hypotheis being true, but no one has proved it.
This is really cool! I love the idea of turning the Riemann zeta function into something you can actually explore visually rather than just looking at equations. The freehand drawing and critical-line animation make it especially interesting. Definitely a fun project for math nerds 😄
Also, now I'm wondering if @jasonb can turn this to music, haha
What in the world!? I have no clue what I’m looking at and I love it! I’ve never even seen the first character on the right half of the equation before, the one before the parenthesis. Is that a Greek letter or something else? I can’t wait to dive into this at some point.
It's the greek letter zeta (hence the name Riemann Zeta Function). Haha look up some youtube videos... the zeros of the Riemann Zeta function is considered the number 1 unsolved problem in math
This may be the death of me…