• Why makes a system complex? Fundamentally a system is complex, if its behavior cannot be easily described. One way this can arise is if the system consists of many components, with numerous relationships and interactions between these components. The presence, absence, or nature of these relationships may affect the behavior of the aggregate system, so a description of this behavior must take into account each of these relationships. (Notice that if the components of the system are identical and their interconnection is regular, then the aggregate behavior can be quite simple. This is well demonstrated by the behavior of a memory chip, which have the greatest density of transistors of any integrated circuit.
  

• Another way in which a system can be complex, is if the inherent behavior of a component is non-linear. Such systems can exhibit chaotic behavior. Examples of such systems are certain non-linear oscillators, weather systems (at almost all levels of fidelity) and the 3n+1 (Collatz) process. Such systems may possess succinct descriptions, but highly complex behavior. Detailed behavior of non-linear systems will not be the focus of this study, although the difficulties they induce will arise in systems of the type discussed above.