Systematic Onset of Periodic Patterns in Random Disk Packings.

We report evidence of a surprising systematic onset of periodic patterns in very tall piles of disks deposited randomly between rigid walls. Independently of the pile width, periodic structures are always observed in monodisperse deposits containing up to 10^{7} disks. The probability density function of the lengths of disordered transient phases that precede the onset of periodicity displays an approximately exponential tail. These disordered transients may become very large when the channel width grows without bound. For narrow channels, the probability density of finding periodic patterns of a given period displays a series of discrete peaks, which, however, are washed out completely when the channel width grows.