Timothy W. Butcher and I collaborated on a number of diverse projects. One was a personality disorder quiz that he devised while taking an abnormal psychology university course.
What are the note frequencies of music by Bach? That is, "How often does an F follow a C?" etc. What does it sound like if you "reconstruct" playable music from these frequencies?
Yesterday, I decided to plot the bifurcation diagram of the logistic equation. This is a famous plot from the 70s, with which many geeks will be familiar. It shows that simple systems can switch into "chaos mode" and begin to bifurcate wildly.
When I was a kid, my younger brother became a chess master and would regularly thrash me in the game. Invariably this seemed to be because I would do something dumb like leaving my queen threatened and unattended.