As an aside, when you convert Champernowne's number into binary, you get a number that has every possible finite binary string embedded within it somewhere. If you digitized a picture of your grandmother and looked at the sequences of 1's and 0's, it is guaranteed to appear somewhere in the expansion. So does every poem, phone number, and work of Shakespeare.

Before anyone brings up the fact that pi behaves the same way, let me point out that no one has actually proved that yet.