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Examples of Complex Systems and TheirSpace-Time Structure

 

In the previous section, we showed how the process of computation could be viewed as mappings between complex systems. As the book progresses, we will quantify this by providing examples that cover a range of problem architectures. In the next three sections, we will set up the general framework and define terms which will be made clearer later on as we see the explicit problems with their different architectures. The concept of complex systems may have very general applicability to a wide range of fields but here we will focus solely on their application to computation. Thus, our discussion of their properties will only cover what we have found useful for the task at hand. These properties are surely more generally applicable, and one can expect that other ideas will be needed in a general discussion. Section 3.3 gives examples and a basic definition of a complex system and its associated space-time structure. Section 3.4 defines temporal properties and, finally, Section 3.5 spatial structures. 

We wish to understand the interesting characteristics or structure of a complex system. We first introduce the concept of space-time into a general complex system. As shown in Figure 3.7, we consider a general complex system as a space, or data domain, that evolves deterministically or probabilistically with time. Often, the space-time associated with a given complex system is identical with physical space-time but sometimes it is not. Let us give some examples.

  
Figure 3.7: (a) Synchronous, Loosely Synchronous (Static), and (b) Asynchronous (Dynamic) Complex Systems with their Space-Time Structure



next up previous contents index
Next: 3.4 The Temporal Properties Up: 3 A Methodology for Previous: The Process of



Guy Robinson
Wed Mar 1 10:19:35 EST 1995