In the example given above, the molecular components of a cell can be considered a CAS, as state of cell is subject to change through various feedback processes, such as gene expression. I'd like to make a figure to illustrate the classes. As a paradigm, simple local rules can yield interesting global behavior. As an operational concept, however, complexity must be something quantifiable. This leads us to consider measures of complexity.
CC is related to the time or memory storage requirements for computing some function.
AIC is defined as the length of a computer program required to generate the data. For instance, consider various timeseries of 1's, 0's. However, this definition of complexity is unsatisfactory. This is because a page of gibberish randomly generated by a monkey at a keyboard would have higher AIC than a Shakespearean sonnet. An example is the process of formulating and revising hypotheses about real world data by scientists.