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RE: Fractal Geometry

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From: Lawrence A. Parker (occti_at_TeacherArtExchange)
Date: Wed Feb 04 2004 - 05:42:18 PST

Ok, the trick of fractals is partly in the mathematical equations which create
them.

A standard fractal equation, and just think of a normal algebraic equation of
the form

        f(x) = 3x(2) + 5x + 7 ; ok? Where (2) indicates 'squared'

You plug in values of x and get values of f(x) {or y}.

But a fractal equation takes the form of using f(x) AS the value of (x) in the
equation, somewhat like

        f(x) = 3f(x)(2) + 5f(x) + 7

See? So that every following f(x) is based on the previous value of f(x).
Where does it all start? A fractal equation has what is referred to as a 'seed
value', like a seed for a crystal solution. This is the initial value of (x)
that is used to generate the first f(x). There are cheaply available software
programs that generate a wide array of fractals and you don't need that much pc
boost to get them going. I have one or two here at home.

As has been mentioned, fractals have been found to be able to represent
occurrences in nature, such as the flight of birds in a flock, of animals in a
herd, or the growth of a trees branches and leaves, which are not random but
follow complex patterns.

Lawrence A. Parker
Philosopher and Educational Consultant 

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