The above animation shows a sequence of avalanche correlated configurations. To make the changes visible, subsequent frames differ by 64 avalanches. We can see the surface configurations are highly correlated.
A stable sandbox surface can be viewed as a space-time configuration of a growing interface. We can say that they share the same ensemble space. However, while the statistical properties of the growing interface are determined from summing over the ensemble with equal weight, a stationary sandbox surface is a running average iterated by the avalanche process. As the subsequent sandbox surfaces differ only by the avalanche area between them, this running average is highly correlated and doesn't produce equal weights for all possible configurations.
Following animated GIF files illustrate these two kinds of averaging processes. The system is the continuous height sandbox model defined on a lattice of 64x64 sites.
The above animation shows a sequence of avalanche correlated configurations.
To make the changes visible, subsequent frames differ by 64 avalanches.
We can see the surface configurations are highly correlated.
The following animation shows a sequence of independent fresh sandbox
configurations. This is the sampling used in measuring the properties of
interface growth dynamics.
These animations are generated with Mesa, an implementation of OpenGL.