Multiscale Representations

Complex systems have structure and behavior on multiple scales of space and time. In a multiscale approach, the behavior of a system is described at a specific scale of precision or accuracy, then this behavior is related to behaviors at finer or coarser scales. In a sense this is like using a zoom lens on a camera, being able to see greater detail when it is needed, and less detail when the detail is not needed. However, unlike a zoom lens, the idea is always to look at the entire system no matter how much detail one is looking at.

The key to developing multiscale representations is to obtain the relevant parameters for a particular scale of description. In addressing specific questions about a system, describing the system only at the scales that are of interest can make practical answers possible. By contrast, describing the system at all scales is generally impractical. Thus, identifying the relevant parameters at a particular scale of description is both a practical and fundamental approach to the study of complex systems.

 

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