This page illustrates the contents of my paper with Chao Tang and Yi-Cheng Zhang. In this paper we studied sandpile models defined on narrow (Lx >> Ly) stripes with periodic (or closed) boundary conditions in y-direction and driven by random addition of sand to a unique column.   Our main observation was that these models exibit extremely long configuration memory.  The height of sand columns that are far from the driving point is changed extremely rarely (the frequency of updates falls of with distance exponentially). This is somewhat surprising since system-wide avalanches occur all the time, and sand is constantly transported from the driving site to open boundaries through every cross-section of the pile. As a result of the long configuration memory and broad distribution of time scales, Z(t) -- the total amount of sand in the sandpile -- has 1/f power spectrum.

To get some feeling about how avalanches change configuration check out applets simulating the dynamics in directed  (1, 1A) and isotropic (2, 2A) models.