Towards a Definition of Complexity

We all have an intuitive feel for complexity. An oil painting by Picasso is obviously more complex than the random finger-paint doodles of a three-year-old. The works of Shakespeare are more complex than the rambling prose banged out on a typewriter by the proverbial band of monkeys. Our intuition tells us that complexity is usually greatest in systems whose components are arranged in some intricate difficult-to-understand pattern or, in the case of a dynamical system, when the outcome of some process is difficult to predict from its initial state. 

The problem is to articulate this intuition formally to define a measure that not only captures our intuitive feel for what distinguishes the complex from the simple but also provides an objective basis for formulating conjectures and theories about complexity. While a universally accepted measure has yet to be defined, a number of interesting proposals have been made in recent years. All such measures of complexity fall into two general classes  

Static Complexity - which addresses the question of how an object or system is put together (i.e. only purely structural informational aspects of an object, or the patterns and/or strengths of interactions among its constituent parts), and is independent of the proces.ses by which information is encoded and decoded. 

Dynamic complexity - which addresses the question of how much dynamical or 

Note that while a system s static complexity certainly influences its dynamical complexity, the two measures are clearly not equivalent. A system may be structurally rather simple (i.e. have a low static complexity), but have a complex dynamical behavior. (Think of the chaotic behavior of Feigenbaum s logistic equation, for example). 

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