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Per Bak and the Sandpile How the concept of Self Organised Criticality came into being. Per Bak and his co-workers used a computer model to simulate the sand pile "experiment" in 1987. Their computer simulation showed the sand pile organising itself until the sides of the pile achieved a certain critical slope. Following that critical point, slides of different magnitude occurred and broadly this allowed the sand pile to maintain itself at that critical slope. The distribution of slides measured by the number of "grains" in each fall followed a power law. As the sand pile organised itself until it achieved the critical slope they coined the term "self-organised criticality". Power laws had already been observed by workers in mathematics and other fields. If you get a straight line when you plot the frequency of a given value occurring against the log of the value itself then you have a power law. Ironically, slides on a real sand pile do not truly follow a power law but this was just a metaphor in any case. Computer simulation has been used extensively to study many phenomena that follow fixed local rules such as earthquakes, pulsars and solar flares. Many of these can be shown to exhibit complex behaviour that follows a power law. Per Bak and his team have pushed their ideas on self organised criticality into the study of the brain, market economics and even traffic jams. They have modelled the interdependence of species in an eco-system and shown that if species are dependent upon one another then the extinction of one species can lead to a mass extinction (a large slip on the sand pile) without the intervention of asteroids from space or major climatic change. Self-organising systems and power laws have been found everywhere and they appear to be one of the fundamental structures of the universe
To find out more you could get hold of a copy of
An excellent sand pile simulation can be found at
http://zinc.hpac.tudelft.nl/home/thijssen/sand/sandpile.html
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