Pi and Mandelbrot set
Dave Boll discovered that Pi pops up in the Mandelbrot set. He posted his results to sci.math in 1991, and they were later proven in a journal.
Fernando J. Pereda, a Gentoo developer, recently posted a program for calculating Pi using this algorithm.
Dave Boll’s writeup is atPi and Mandelbrot set.
Fernando J. Pereda’s example is at Hidden Pi.