We demonstrate the enhanced capacities of our analysis toolset for three-dimensional data. In particular, we provide supporting evidence for some of the conclusions reached in our previous studies of two-dimensional avalanching heaps. Segregation by self-diffusion is shown to take place in three-dimensional assemblies and self-diffusion velocities are shown to be of a comparable order of magnitude to those found in plane-strain situations. The effect on assembly evolution by discrete avalanching of the availability of a third dimension for translation is investigated. The discrete wavelet transform is again shown to be a useful component of the toolset in coupling process variables in the context of the discrete defining events associated with assembly evolution. In particular, we move towards the determination of time constants by correlating wavelet coefficients with a time shift. (C) 2004 Elsevier Ltd. All rights reserved.