If you take the first million digits of pi, and compress it with, say, bzip2, you get a file of about 420KB. This is pretty good in one sense - an 8 bit byte that stores a decimal digit can store 3.3 bits of information, right? As such, you would expect output to be 3.3/8 or about 42%. But obviously that 420KB + a decompressor is nowhere near a minimal program. I've always been fascinated with the Mandelbrot/Julia sets and where that information comes from as well.
