For example:

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            'The Paths of Lovers Cross in the Line of Duty.'
                          THE BEAUTY PRINCIPLE
                Copyright (C) 1990 by Homer Wilson Smith
                          All rights reserved.
     'This love affair with fractals is disturbing to mathematicians
like myself who see too many people believing that this stuff is
serious mathematics.  Fractal geometry has not solved any problems.
It is not even clear that it has created any new ones.' Steven Krantz,
Research News, 27 July 1990.
     The Beauty Principle states that if a theory or idea is beautiful
chances are it is useful.  It also says in reverse that if something
is useful, chances are beauty will be found in it.
     Beauty is surely in the eye of the beholder, and as such, beauty
is surely connected to the fundamental nature of that beholder.
     Life consists basically of survival, of winning, of besting the
elements, even of dying in such a way as to live better as a species.
     Thus the deer is beautiful because it can run, and the tiger is
beautiful because it can chase.  Those that could not run and those
that could not chase long ago passed away, and what is left are those
that won the game of survival.
     As for dying, grass is edible because manure helps it grow.
Being eaten (dying) helps grass grow better.  Thus the deliciousness
of grass is not an evolutionary failure of grass to out survive its
enemies.  If grass had wanted to be poisonous it could have done so,
easily.  The tasty stuff survived better BECAUSE it was tasty.  Get
     Everything in nature, with few exceptions, whose form has been
molded by success in its own element, has beauty in it for the eye of
the human beholder.  From the wing of the bird hovering in the halcyon
winds of summer, to the flight of the Challenger as it lands on the
run way, there is beauty in the form BECAUSE THE FORM WORKS, form that
has been developed over millions of years of evolution when all the
non working ones were left behind as rubble and dust in the wind.
     That the form of a bird's wing could be turned into the wing of
an aeroplane, does not diminish the wisdom contained therein, and the
beauty that results either in the wing or the plane, is directly
proportional to its rightness in the game of survival in a given
     The human body itself (although maybe not the conscious unit
within) is also built on the same principles, and its internal
structure, from its bones to its brain, it based on the simple
mathematics of survival that everything in this physical universe is.
     It is not unreasonable to assume that when the body is placed
near or in communication with another entity built on similar
principles also having withstood the tests of time, that a certain
resonance would take place resulting in an awareness of the beauty,
functionality and inherent rightness in the design of the other thing.
     It is also reasonable to assume that such a human body, put into
direct communication with the basic mathematics of its own internal
structure, would elicit a similar reaction of aesthetic appreciation.
     Being able to appreciate the wing of a bird, or your own body is
no different, each is the workmanship of ages of survival, and one
would assume that, given enough intelligence, each would be able to
appreciate the ideas and mathematics and design principles that went
into each other and their present state of success with existence.
     In other words for those to whom survival is beautiful, one would
expect them to find their own design principles beautiful too.
     Thus one imagines a direct harmonic resonance between the human
central nervous system and fractal images.  The communication line
between the two could not get more direct, as the optic nerve and the
brain are MADE of the very mathematics that are displayed in the
fractal image.
     If you like fractals, it is because you are made of them.
     If you can't stand fractals, its because you can't stand
     It happens.
     This is not a matter of some artistic, philosophical or religious
mumbo jumbo.  We are talking physics at the level of tuning forks on a
sounding board.  Absolutely ground level.
     Such a statement will surely be held against me all the rest of
my days, but it will be well worth it as our future history books will
record who was the fool and who wasn't.
     If it IS true that fractal mathematics has produced no new
problems or solutions it is only because the people who work with
fractals are as yet too dense to figure them out, which is very too
bad, because much of world is still out of control and there is a
crying need for increased understanding, especially in the field of
how things do and do not survive in their environments.
     It is unlikely that the underlying mathematics of this universe
is utterly complex in nature.  In fact one finds the simplest non
linear equations abounding in everything you study in classical
physics, such as planetary motion.
     Fractals are not something special, anymore than the parabola is
something special.  The parabola is a visual representation of the
EVALUATION of the simplest non linear equation Y = X*X + C, and the
Mandelbrot Set is a visual representation of the ITERATION (repeated
evaluation) of the SAME SIMPLEST POSSIBLE non linear equation.
     It is also unlikely that iteration is any less important than
simple evaluation, especially for systems that are a function of
themselves a moment before plus their environment, and so it is
unlikely that the Mandelbrot Set is any less important than the
     And to claim that the parabola is unimportant would be unwise at
this time.