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Description

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.

Description

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.