Think of the dials on a combination safe

 Remember how they said, turn counter clockwise one urn?

If Markov were a combination dial, like a safe, it is a color operator of M rings, and they have to find the combinations which is a minimum alignment of the notches.  The Markov conditions says turn counter clockwise once for each starting condition of the residual. The round off errors are cyclic. So you align spin, then take it all the way back to start, then align charge, and etc.  

The Markov system is a adjustable combinatorial system. The structured queues are embedded in those adapting binomials.

But the dial system is not flat, it has curvature, and is geodesic in 3D, or mD, as it is relatively prime set of binomials and they will have a change in slope of the geodesic. You never get the exact combination, you get the closest approximation, but the door never opens. It is not exactly cyclic because log(N) is the random variable, and it is never exact. So the miss, the error by which you can never open the safe is uniform density, I would presume.

If you can never open the safe, then the dials continue random errors forever, it is closed. If you try t make a more accurate dial by increasing the notch density, you just get more random noise, variation on log(N) increases.