The Zhang model of Self-Organized Criticality

(http://arxiv.org/abs/math/0411590)
Though it really shouldn't, the phrase "Self-Organized Criticality" seems to mean "avalanches".

I presume that you, dear reader, are familiar with the sandpile cellular automaton. If not, visit:
http://www.cmth.bnl.gov/~maslov/soc.htm

The Zhang model is a slight variant, where the height/energy at each site is a smooth number (I hate to say "real number", they could be rationals), rather than a small integer.

This paper is the first I've seen that use IFSs (iterated function system - a method for producing fractals) for a real purpose- I thought that people only used them to make pictures of ferns and unrealistic claims of image compression.

It seems like they spend a lot of time analyzing avalanches in a two-site lattice, (sortof like saying you're studying chains of dominoes falling with two dominoes) but I suppose that's where one can draw pictures of the state space. Overall, I recommend this paper.