Here’s a really fun paper on Bernoulli numbers by S. C. Woon from 1997.  Woon generates the Bernoulli numbers by…

Here’s a really fun paper on Bernoulli numbers by S. C. Woon from 1997.  Woon generates the Bernoulli numbers by some operators that he then analytically continues.  He does the same for Bernoulli polynomials and Euler polynomials, plays with the relation of Bernoulli numbers to the Riemann zeta function, and then gives us these fun graphs of the behavior of the zeros.

Quoting from the end of the paper:

As s approaches every integer > 5, an interesting phenomenon occurs: A pair of real zeros may meet and become a doubly degenerate real zero at a point, and then bifurcate into a pair of complex zeros conjugate to each other. Thus, the pair of real zeros appears to “collide head-on and scatter perpendicularly” into a pair of complex zeros.

3 fundamental kinds of scattering can be observed:

• Point scattering:
A pair of real zeros scatter at a point into a pair of complex zeros which head away from each other indefinitely.
• Loop scattering:
The same as point scattering but the pair of complex zeros loops back to recombine into degenerate real zeros within unit interval in s and then scatter back into a pair of real zeros, much like the picture of pair production and annihilation of virtual particles.
• Long-range sideways scattering:
The additional zero that flies in appears as if “it is carrying with it a line
front of shockwave” that stretches parallelly to the Im(w) axis. When the “shockwave” meets a pair of complex zeros that are looping back, the pair gets deflected away from each other momentarily before looping back again, while the additional zero gets perturbed and slows down discontinuously.

http://arxiv.org/pdf/physics/9705021v2.pdf