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The definition of complexity through Statistical Complexity Measures (SCM)has recently seen major improvements. Mostly, effort is concentrated inmeasures on time series. We propose a SCM definition for spatial dynamicalsystems. Our definition is in line with the trend to combine entropy withmeasures of structure (such as disequilibrium). We study the behaviour of ourdefinition against the vectorial noise model of Collective Motion. From aglobal perspective, we show how our SCM is minimal at both the microscale andmacroscale, while it reaches a maximum at the ranges that define the mesoscalein this model. From a local perspective, the SCM is minimum both in highlyordered and chaotic areas, while it reaches a maximum at the edges between suchareas. These characteristics suggest this is a good candidate for detecting themesoscale of arbitrary dynamical systems as well as regions where thecomplexity is maximal in such systems.

Statistical complexity measures as telltale of relevant scales in emergent dynamics of spatial systems