Abstract: Brown dwarfs have exotic clouds made of silicates and molten iron. Uneven distribution of these over a brown dwarf's photosphere will cause the object to exhibit periodic flux variations as it rotates. Several brown dwarfs that vary in this way have been discovered. Others, however, have been found to exhibit non-periodic variations. As recently as two years ago, the reality of these was regarded with skepticism -- quite reasonably, since measurement systematics can mimic non-periodic variations, and theory did not predict the swift, global changes in brown dwarf cloud distributions that the data seemed to imply. However, new evidence shows that aperiodic variability is real: the photometric amplitude and phase of some brown dwarfs do change on a rotational timescale. We present four new brown dwarfs with confirmed aperiodic behavior, and show that there is a wide range in the degree of their departure from perfect periodicity. The extent of this departure should be determined mostly by the rapidity of cloud evolution on the brown dwarf, and therefore aperiodicity constitutes a direct probe of the atmospheric dynamics of these fascinating objects.