ART MATRIX  PO 880  Ithaca, NY  14851-0880  USA
                   (607) 277-0959, Fax (607) 277-8913
 
            'The Paths of Lovers Cross in the Line of Duty.'
 
                             THE LAST LAUGH
 
                Copyright (C) 1990 by Homer Wilson Smith
 
     A Mandelbrot fractal is a statement of how well something
survives in a given environment.  If it does NOT survive well you give
the environment some color of the rainbow specifying how quickly the
thing died.  If the item in question DOES survive well or lives
forever you color that environment black.
 
     Mathematically speaking infinity does not mean infinite survival.
Infinity means infinite change, which means death.  Thus in the
Mandelbrot plane (C) if the iterated variable Z goes off to infinity
that means it died and you give the environment (C) some color
representing that fact, and how long it took to go out of bounds.
 
     What the Z variable does in most of the black area of the
Mandelbrot set is not much better as far as survival is concerned.  In
much of the black area the iterated variable attains a steady state of
no change at all, or a periodic change from one state to another and
back again.  This too is not life.
 
     Life is not a rock or a statue.  It is a constantly changing
system.  You grow, you change, you shed your entire skin every so
often, you replace broken parts, you age, you split in half, or you
procreate and then die.
 
     This is very unlike the behavior of the variable going off to
infinity and it is very unlike the variable hanging out at a fixed
point or fixed period cycle.  Life much more resembles the iterated
variable involved in a chaotic attractor, those areas of constant
change within reasonable boundaries.
 
     These areas of constant change, of chaotic attraction, happen for
environments (C) that are on the boundary of the Mandelbrot Set.  But
they also happen if the environment (C) is constantly changing from
iteration to iteration.  A fixed point for one value of (C) will not
be a fixed point for another value of (C).  So if Z is zooming in on a
fixed point or dull periodic cycle for a particular value of (C) and
you keep changing (C), you will change the value of the fixed point
out from under the variable that is homing in, and it will attain a
state of constant change within reasonable bounds never settling down
to a dull or rigid cycle.  This is life.
 
     One last point should be made here.  Once the iterated variable
(Z) reaches a fixed point or cycle, it stays there BECAUSE the
environment (C) is NOT changing.  But in real life the environment is
always changing and in fact it is often changed by the very production
output of the iterated item in question.  The cell that splits in two
while iterating CREATES a new environment for itself consisting of its
newly formed sister cell.  Thus what may be a fixed point during one
iteration may no longer be a fixed point during the next iteration
because the environment variable (C) has changed.  Thus the iterated
variable Z, the inside trying to survive in an outside, may constantly
skit around looking for stability to find it always eluding its grasp.
This keeps you from becoming a rock or a statue.  This is the constant
ebb and flow of biological life, and keeps the wheels of progress,
production and consumption, always turning.
 
     This can have a negative side too.  People trying to find health
and happiness by DRIVING to work everyday may be foiled by the
productive output of their automobile engines.
 
     A lot of people laugh at 'The Cell and the Womb' or the idea that
fractals have anything to do with insides surviving in outsides.
However the equation Z = Z*Z + C directly says that what happens to Z is
a function of what Z was just a moment before and EVERYTHING ELSE IN THE
WORLD THAT IS NOT Z.  If that is not something 'surviving by changing'
in an environment not itself, then I don't know what is.
 
     You got to remember something about fractals.  A long time ago
Ben Franklin was playing around with electricity and he came up with
some interesting theories to explain some very interesting phenomenon.
They really knew how to zap people in those days, what with Leyden
jars and kites on strings and all.  Everyone had to 'feel the spark',
that was part of their initiation into the inner conclave of
Electricians.  If you failed the initiation, either by accident or
otherwise, they buried you and found someone else.
 
     No joking, Leyden jars ganged in parallel could store millions of
volts and throw sparks 2 feet long.  But they still thought
electricity was a liquid that you could dissolve in water.  That's HOW
they discovered the Leyden jar.  ZAP!
 
     This was all very impressive to everyone involved, but does this
mean that Ben was right?  No of course not, Ben's ideas of electricity
were near ridiculous.  It took a guy by the name of Faraday to make
any real sense out of the matter, but to hear HIM talk of it Ben was a
pioneering genius.
 
     That's because before Ben's time people were pretty much passing
banana's back and forth in the trees as far as electricity was
concerned.  Ben made the first bold steps towards making electricty a
respected and controllable subject of knowledge.
 
     Just so today with fractals.  Chaotic dynamical systems is a VERY
VERY NEW field of math and it is VERY DIFFERENT from anything that has
gone before.  People have no idea what is to be found there, and
people have no idea what it could be used for.  They might as well be
passing bananas back and forth in the trees when it comes to fractals.
 
     So you could say that these ideas about the 'Cell and the Womb'
and so forth are in the Ben Franklin stage of discovery.  No one has
even proven them wrong yet.  They are still LAUGHING at them, don't
you see?  The Faraday stage of development, where they get ripped
apart and put back together again correctly, is still way down the
road.  But in 200 years people will know what this was all about and
not only will they be able to prove that their understanding is
correct they will be able to use it to incredible ends.
 
     Of course we may not be able to recognize these original ideas in
the final workable version, just as Ben's original ideas have been
lost in the upgrades.  But the people who LAUGHED at Ben were not the
ones to make the upgrades, and Ben himself would have been the first
to embrace the improvements even if it had meant leaving his own name
in the dust.
 
     And with that attitude you can be sure his name will live
forever.

     Homer