Self-Organising Systems 

by William Silvert 

Abstract

The concept of self-organisation is key to our understanding of many apparently complex phenomena, and many systems which seem to be very complicated can easily and simply be understood in terms of instability leading to self-organisation.

Instability

Many systems are inherently unstable. Although it is common to think that the normal state of the universe is marked by constancy and symmetry, instability gives rise to variability and asymmetric behaviour, referred to as broken symmetry. For example, if we balance a pencil on its tip it exhibits radial symmetry, but soon it falls down and since it points in some definite direction, the radial symmetry is broken.

Self-Organisation

Often the instability leads to a pattern of lower symmetry. A current flowing over a flat surface can generate a ripple pattern. This is seen in the fluttering of a flag or sail in the wind, and in the sand ripples formed on a beach. The uneven surface of a dirt road after it has been passed over by many cars is due to a similar effect. This spontaneous appearance of pattern is called self-organisation and is believed to be an important part of the processes that led to the emergence of living creatures.

Self-organisation is often seen in water flow. Turbulence is one example. Another example is the appearance of cellular circulation when wind blows over a body of water or when a layer of fluid is in a thermal gradient, as shown here.

Conclusion

Self-organisation is a very common phenomenon and offers a simple explanation of how structure and asymmetry can arise in uniform symmetric systems. There is often no further need to invoke complicated mechanisms to explain apparently complex systems.

Address all correspondence to the editor, william@silvert.org. As for copyright, who would steal a simple idea? Just be sure to acknowledge the source.