Self-organised criticality occurs in a wide range of systems such as growing
sand piles. Quite spontaneously, these systems reach a critical state. If you
drop sand grains one by one onto a sand pile, for instance, they build up and
up into a cone until avalanches start to happen. The slope of the side of the
cone settles down to a critical value, at which it undergoes small avalanches
and big avalanches and all avalanches at all scales in between. This behaviour
is independent of the size and shape of the sand grains, and in general it is
impossible to deduce anything about the building blocks of a self-organised
critical system from its behaviour. In other words, the scale and timing of
avalanches doesn't depend on the size or shape of the sand grains.