Canter Sets

Anyone have any experience with Canter Sets? I studied them as an undergrad project. Really interesting, but I wish I'd gone further. I have come across them so many times since then. It really seems like there is so much I am missing. They are like pi or e, complex and interesting in their own right, and they keep showing up in strange and diverse places.

I started out studying the Cantor Middle-Thirds Set, and the Devil's Staircase function on that set. It seemed to be going somewhere, but I had to go on to other projects. I don't really know of any books or sources to read more, other than the thousands of sites describing the basic set.

Any thoughts?

"Noone shall expel us from this paradise which Cantor has created." Albert Einstein

I was on bed rest for 6 months when I was 19. I read a good number of math and science texts - their history and philosophy.
Men of Mathematics by E. T. Bell and World of Mathematics by James R. Newman are two I particularly remember.

Bell had a chapter on Cantor, then when I took Real Analysis Cantor sets came up again. Countable, uncountable, and all that was interesting, but something that was a mathematical artifact rather than an attribute of physical reality - at least that's my working hypothesis.