Name: courtney m butler
Date: Around 1995
I have recently read about the reference to the chaos theory. What exactly
is this theory, and where is it being applied?
Chaos Theory is an interdisciplinary branch of research being pursued by
mathematicians, physicists, chemists, engineers, biologists, etc. (the list
goes on and on).
The basic line of research was begun at the turn of the century by a
mathematical physicist named Henri Poincare (France), who was trying to
solve the 3-body problem of planetary motion.
Very grossly, chaos theory says that under certain conditions even very
simple equations can, when solved numerically (perhaps on a computer), give
rise to solutions which diverge from one another at a very fast (exponen-
tial) rate. In the "chaotic regime" the rate of divergence can be so rapid
that it is impossible to follow any one solution with any degree of accura-
cy. So, what workers in the field often do is try to understand how
FAMILIES of solutions behave. The behavior of these families can often be
organized for fairly long times. People say that there is "order in chaos"
when they discover such structures. Now, the thing about these structures
is that certain ones seem to exist on a huge range of length scales, in
principle, an infinite range.
And the manner in which the structures are repeated seems to be as if they
are "moved through" a fractional-dimensional space, thus Mandelbrot called
them "fractals." Have a look at James Gleick's book "Chaos:Making a New
Science" for a better description.
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Update: June 2012