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Fig. 6.10 Scheme of constructing the simplest fractal
progressing with a high degree of fractality, which dramatically increases the
number of leaves and, consequently, the amount of absorbed solar energy.
An example of a fractal structure is the human blood circulatory system where
oxygenated blood passes through a sequence of increasingly branching vessels.
This makes it possible to nurture all body tissues.
Apparently, the first nonlinear phenomena have attracted the attention of spe-
cialists more than 150 years ago. John Scott Russell, a marine engineer and a
lecturer at the Edinburgh University, observed the movement of horse-drawn
barges on the canal. In his report, Scott Russell wrote that he discovered that
upon a sudden halt of the barge, towed by a pair of horses, a part of the water
separated from it: “A mass of water rolled forward with great velocity, assuming the
form of a large solitary elevation, a rounded, smooth and well-defined heap of
water, which continued its course along the channel apparently without change of
form or diminution of speed.” Scott Russell followed it on horseback for a few
miles until he lost the sight of it. Only 50 years later, D. J. Korteweg and G. de
Vries derived nonlinear equations, which had a solution in the form of a solitary
bell-shaped wave moving at a constant speed along the surface of water in a shallow
channel of rectangular cross section.
Interest in nonlinear phenomena resumed in the 50 years in connection with
research on plasma physics. This was greatly facilitated by the emergence of
opportunities to solve nonlinear equations with the help of powerful computers.
The study of nonlinear phenomena during the last decades of the past century has
led to fundamental results. The understanding was achieved of the fact that they not
only have high complexity but, in general, cannot be regarded as a refinement of
linear models.
4. An important consequence of the nonlinearity of dynamic mechanisms in
distributed systems is the manifestation of the so-called emerging properties and
“emerging” mechanisms. They were discussed in detail in Chap.
4
using as an
example chemical reaction-diffusion media. As in these media, in an arbitrary
distributed dynamic system, three levels of dynamics can be distinguished:
The level of interaction between the elements of the medium, i.e., the nature of
their interconnections (microlevel)
The level at which the system can be in some kind of a stationary state
(mesolevel)
