Self assembly is a concept in science and is part of many biological and chemical systems.  This concept  is known as a Turing structure named for Alan Turing, the father of computer science.  In 1952 he published his theoretical study of the development of pattern and form in living organisms.  As one of his examples,  he showed how the leopard developed it spots via this process.  His theory is very elegantly modeled with just a couple of differential equations. Nature abounds with beautiful patterns that can be explained by this theory which is an activator-inhibitor reaction-diffusion system, a mouthful I know.

To explain diffusion I like to use the experiment of putting a drop of ink in a glass of water. The ink ends up invading all the solution. It is the process of diffusion that provides the transport of the ink. A spontaneous transfer appears from the zones of high concentrations to ones of lower concentrations.  This experiment explains diffusion, but diffusion alone is not a Turing structure.  Turing noticed that in natural systems of biology and chemistry, diffusion is often accompanied with additional conditions.  It is those additional conditions that create the patterns we see in nature like spots on a leopard, stripes on zebras, or even the patterns created by slime mold.

These Turing structures combine two elements that diffuse at different rates in a dissipation area while being affected by waves.  All of these elements combine to self initiate and terminate a process.  One of the diffusing elements or mediums is the activator and the other is an inhibitor.  The activator and the inhibitor are both influence by different frequency of waves.  The two elements cause a reaction that forms spatial structures in the form of patterns -- like spirals, stripes or spots. The rates being different, the faster one is the activator and the slower one is the inhibitor. 

These Turing structures explain many natural phenomena including the initiation of life itself as well as the initiation of a supernova.  It may also be the mechanism behind the long life of ball lightning.

References:

http://www.fasebj.org/cgi/content/full/17/1/1