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Figure 2.8.
Stream segments for the Mississippi River. The spherical coordinates of latitude and longitude
are used and the scale corresponds to approximately 2,000 km along each axis. Top [
18
]and
bottom [
62
] reproduced with permission.
do not want to restrict the discussion to the above geophysical context, so we consider
an argument first exploited by Montroll and Shlesinger [
50
] in an economic context
to determine how introducing increasing complexity into business webs can generate
Pareto's law for the distribution of income.
Consider a complex phenomenon that for most of its range of values is described by
g
, the basic distribution, which asymptotically falls to zero and has no long-range
tail. We consider the normalized variable
(
x
)
the average value of the
observed dynamic quantity
X
if the empirical tail of the distribution is neglected. Now
we consider an iterated amplification process that induces a transition from familiar
ΞΎ
=
x
/
x
with
x
