Find repeating patterns in data
I think this problem could be represented as a Markov Chain.
Maybe a Markov model (or Markov Random Fields) could be used to estimate the probabilities. Normally it's easier than with the more standard Hidden Markov Model since there is no hidden state.
My suggestion would be to estimate the probabilities of the model (parameters) from the data, then it should be easier to discover the patterns based on these probabilities.