Many a student thinks that the first pic was created by some underlying pattern (because of its points clumping together in some areas while leaving others empty) and that the second one is “more” random. The truth is that technically both are not random (but only pseudo-random) but the first resembles “true” randomness more closely while the second is a low-discrepancy sequence.
While coming to the point of pseudo-randomness in a moment “true” randomness may appear to have a tendency to occur in clusters or clumps (technically called Poisson clumping). This is the effect seen (or shall I say heard) in the iPod shuffling function. Apple changed it to a more regular behaviour (in the spirit of the second picture)… which was then perceived to be more random (as with my students)!
Read the whole thing.