I did a strange experiment once, I implemented a markov predictor like this and used it to predict the next bit of a sequence. Then I extended the sequence with the negation of that bit an increased the length of the markov chain. The result was a very random unpredictable looking sequence, but of course it was completely deterministic. I wonder if this sequence has a name?
I would recommend Lawvere's book Sets for mathematics to anybody who is interested in learning some mathematics. It's a beginner book but it covers interesting category theoretical stuff you wont find in any other beginner book.