Active-Site Motion and Pattern Formation in Self-Organized Interface Depinning

We study a dynamically generated pattern in height gradients, centered around the active growth site, in the steady state of a self-organized interface depinning model. The pattern has a power-law tail and depends on the interface slope. An approximate integral equation relates the profile to local interface readjustments and long-ranged jumps of the active site. The pattern results in a two-point correlation function saturating to a finite value which depends on system size. Pattern formation is generic to systems in which the dynamics leads to correlated motion of the active site.