"For example, the visualization could slowly gray out states that are not visited. In that way, the student could get a feeling for concepts like recurrence etc

"For example, the visualization could slowly gray out states that are not visited. In that way, the student could get a feeling for concepts like recurrence etc." You know, this is actually a good idea. As long as you didn't set any transition matrix elements to zero, the chain will have a stationary distribution that is given by the lead eigenvector of the transition matrix. If you gave each node a score when the chain passed through it, that eigenvector would manifest as the "score" accumulated by each node over a long period of time. This is one of the cool, deep properties of the chain - and it's not "insight-free" in the same way you describe. One of my favorite examples of this is the plinko game at the Museum of Math in NYC: https://www.youtube.com/watch?v=GBu0sfzrGTY https://www.youtube.com/watch?v=GBu0sfzrGTY It's a physical manifestation of the central limit theorem, realized by a series of balls that can go either right or left in a random walk downwards. You can even adjust the bias on the left/right choice to supply drift to the random walk. The mass of balls that accumulates in the bottom is a histogram representation of the associated limiting Gaussian curve. Very cool.