A Markov Chain is a mathematical system that represents statistical properties of a given sequence of distinct states – texts or music as sequences of letters or midi-events for example. It can be used to re-synthesize sequences that will have the same properties as the given sequence.
The order of a Markov Chain determinates how many preceding states will be considered to decide which will be the next one.
To give an example: If there is a sequence like "ABACAD" given, the first order Markov Chain looks like this:
|current letter||next letter (probability)|
|A||B (0.33) C (0.33) D (0.33)|
This means, if the current letter is an 'A', there is a probability of 0.33 that the next letter will be a 'B'. The probability of 'C' is also 0.33 and so on. (Probabilities are written as a value between 0 and 1. 0 means never, 1 means always. The total amount of the probabilities of all possible events is always 1.)
A second order Markov Chain will consider the current and the last letter to evaluate probabilities.
Output of a Markov Chain – based on a text by John Locke
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Output of a word-based Markov Chain, based on first paragraphs of wikipedia-articles
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