A recent birthday present (my 36th) was Elias Wegert's Visual complex
functions. On the sides of the pages are strips -- excerpts from
the critical strip of the Riemann zeta function with nontrivial roots.
He wrote a paper about the stochastic period of 2$\pi$, which is easily
observable in the below image as the yellow diagonals:

He's got the images of the functions up on a functions gallery on
the website associated with the book. I thought I couldn't see what
was going on so I used the gimp to prune the white regions from the images
and to glue the remainders together.
So, this led to a mathoverflow question after I asked Matt McIrvin to
take a Fourier transform -- which he did with a set discretely supported
on the roots of the Riemann zeta function, and a post on the n-category
cafe concerning Freeman Dyson's speculation that the roots might form
a quasicrystal.
There are some obvious questions:

- What about other L-functions? The best way of performing such calculations is to use sage and its implementation of the Dokhitser L functions calculator.
- What is the local phase at each root (how much is each root rotated?) -- and this lives on U(1).

Bounty: I am offering a bottle of whisky to anyone who can successfully translate Jacob Lurie's Higher Topos Theory (and/or the stacks project) into the analytic combinatorical language of the manner of Flajolet's Analytic Combinatorics.