You can use a decision tree as a predictor to choose the next item in a sequence.
In particular you can arrange things that so that it is context sensitive and will read back a variable number of symbols into the past to make a prediction.
I guess it becomes an automata when you do that.
I did some text prediction with that (Linux AMD64):
https://drive.google.com/file/d/0BwsgMLjV0BnhdlBsTElBekg1WFE/view
I suppose you can use such trees as fractal rules.
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