In 2-D, sandpiles shed to square cells with adjacent edges. The 3-D equivalent is sandpiles shedding to cubic cells with adjacent faces. There are six of these for every cubic cell, as compared to four in the 2-D case. Hence the instability threshold has to be raised to 6 as compared to 4 in 2-D. The behaviour is now very similar. If a cell has 6 or more sand grains on iteration N, it loses 6 grains on iteration, N + 1. The six cells with adjacent faces all gain 1 grain each on iteration N + 1, thus the total number of sand grains is conserved, as in the 2-D case. 

Colour scheme: 

Black = 1 sand grain 

Red = 2 sand grains 

Orange = 3 sand grains 

Yellow = 4 sand grains 

White = 5 or more sand grains (always exactly 5 once the automaton reaches its end state) 

This example grows from the outline ("skeleton") of a square with overloaded cells. 

The video is in three parts: 

1. Growth 0.00 

2. Rotation of the end state 0.32 

3. Successive cross-sections through the end state in the XY, XZ and YZ planes 1.16 

The cross-sections demonstrate that most of the complexity is hidden under the surface, which looks comparatively simple.