There are two sets of statistical footprints of a self- organized system. One
set is the inverse power law relationship between the values of a variable X
and the frequency distribution of X.
Freq () = XaX
b
(3.5)
Equation 3.5 is saying that X has a power law distribution. If b < 0 and a
noninteger (which it will be 99% of the time if we confine ourselves to two
decimal places), then b is the fractal dimension of X, which in turn denotes
that a self- organizing process is taking place (Bak, 1996). An example of an
inverse (i.e., b < 0) power law distribution appears in Figure 3.8. Beware,
however ...
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