From Eve Andersson's Pi land, we have these histograms of the frequency of (base 10) digits.
The first 100 digits of pi:
Things even out pretty nicely by about 1 million digits:
The digits are just white noise, there might be an interesting pattern now and then, but that is to be expected statistically. Besides, these are base 10 digits, which are an arbitrary representation based on the fact that we have two hands with five fingers apiece…
I could share some more interesting facts and formulae, but printing the greek character pi on a blog is, as they say, a pain in the butt. And I am not in the mood for that tonight.