How does an electronically controlled distributor advance or alter the timing? If I understand correctly, there is no physical change in the rotor position.

 

The ECM has a look-up table where, based on the last 2 cylinders' ignition pulses, it looks up how many milliseconds after the last one to produce the next one. It doesn't "advance" the timing as such; but when it gets a pulse, and it knows that there were for example 4 milliseconds between the one 2 pulses earlier and the last one, it can be fairly certain that another will come along just about 4 milliseconds after that; so if it fires the plug 3 milliseconds after the last one, that's 1 millisecond before the next one (which should be coming along at about 6° BTDC or whatever the spec is for the particular motor), which is 1/4 of the 90° of crank motion between cylinder firings, which would be about 22½° plus the 6° of physical "static" advance, or 28½°, of "total advance". The rotor contact is wide enough to make its correct connection over quite a wide range of timing.