Hi @amiika thanks for the support! Yes, in practise you would use hash maps for an efficient implementation of the Markov matrix, as you suggested. I tried to be close to the notion of a matrix because this is what you’ll find in the literature or in Wikipedia on the subject matter.
In the example Harmonic random walk in major I am using a 2-dimensional hash map and a state space that is not just a scale of 7 notes but a complete selection of chords and tonic keys. But the idea is the same: Whenever you want to combine rules and randomness, Markov chains are a great way of achieving it.
Why would we want to combine rules and randomness? Well, the rules can implement the concept of style, while the randomness is the variation within a style. If we would be able to map Beethoven’s style of composition inta a Markovian matrix and do the same with Schubert’s or Chopin’s style, they would have different Markovian matrices. And when you let the program play, it will produce a random output but sound like the respective styles (ok, in practise this would be a very difficult and complex task, but I just wanted to illustrate the idea of combining rules and randomness).