Rats nailed to boards, ready for skinning. This picture belongs to the Los Angeles Museum, historical pictures on line. Here we have two auto-organized criticalities: one for the rats community system, the other for the Mexican neighbourhoods in the 1924 plague. Many immigrant houses were completely burnt because of the plague, it was a complete catastrophe for settlements in some blocks in Los Angeles. The L.A. urban morphology changed in consequence.
A fallen tree, maybe there is a Domino´s effect in a storm. Internet download
Picture of the aftemath of an earthquake in Asia. The system´s point of criticality is really evident. Internet download.
Auto-organized criticality is a physical property of dynamical systems which have a critical point as an attractor. The macroscopic system behaviour displays the spatial and/or temporal scale invariance, typical of fractals.
In other words, it refers to the tendency of big disipative systems that leads them to a critical state with a great scale in time and measure. The system evolves without external intervention and without control parameters and this amplification of a small internal fluctuation can precipitate this critical state and provoke a chain reaction leading to a catastrophe. The system becomes critical when all its elements mutually influence each other. This idea gives a unified concept behavior for systems with many grades of freedom. It is typically observed in slowly-driven non equilibrium systems with extended degrees of freedom and a high level of non linearity. It is verified in the structure of an earthquake, in fires, in the biological evolution, in economy and also in the growth of the cities.
Let us take now as example the fall of the trees of the forest. When a tree falls it leaves a clear where the light enters, the conditions change, the vegetation is very affected. Other times, when falling a tree and dragging others with it, a clear of hundreds of square meters is formed. In this case, the chaotic system is destabilized and it could happen that the forest disappears completely, or a community, as some indigenous tribes of hunter-collectors that would no longer have sustenance. This finite size effects could be studied by equally dividing the system into more and more separate subsystems.
When appropriately perturbing a chaotic system, it is forced to take one of the many possible behaviors. But without sincronism, and under different environmental conditions, two virtually identical chaotic systems, will evolve toward different final states. The evolution of urban systems is considered to exhibit some form of self-organized criticality. This concept is important to remember the influence of the contexts (historical, geographical, social, etc) in the comparison of two models of cities or very similar settlements.
A very clear and general explanation could be found athttp://www.google.com/search?q=auto+organized+criticality+cities&hl=en&sa=2