Focus on Fractals is 25 minutes long, and contains 8 segments.
The first is a brief review of Mandelbrot Sets and Julia Sets which
are the fundamental building blocks of fractal mathematics.

 

     The next 4 scenes are zooms deep into the boundary of the
Mandelbrot Set, which is named after the mathematician Benoit
Mandelbrot.

     The purpose of these zooms is to show you how much there is to
see in the Mandelbrot Set and to give you a taste of the awesome
beauty to be found in pure mathematics.

 

     The next two scenes are Julia Promenades.  Every point on the
Mandelbrot Set gives rise to a unique Julia Set.  A Julia Promenade
results from linking together the many Julia Sets that arise from
taking a predetermined route around the Mandelbrot Set.  Julia Sets
are named after the early 20th century french mathematician, Gaston
Julia.




     The last scene shows the path of a point as it traces out the
Lorenz attractor, named after Edward Lorenz who is credited with the
discovery of sensitivity to initial conditions, commonly known as the
Butterfly Effect.




     This is the Mandelbrot Set.




     It was created from the equation X equals X squared plus C using
simple iteration where X and C are both complex numbers.  Therefore
the Mandelbrot Set lies in the complex number plane which in this case
is the plane of all possible C's.




     Iteration is the process by which the output of an equation
becomes the next input of the same equation in a repeated cycle that
ends when X either goes off to infinity or converges to one or more
finite values.  X always starts at 0 and C is chosen from any place on
the Mandelbrot Set.  During the process of iteration C does not
change.  C acts as a constant that affects the final outcome of X.




     C is colored according to how fast X escapes and results in the
picture called the Mandelbrot Set.  Where X does not escape the
picture is colored black.




     The Mandelbrot Set contains a wealth of beauty and detail in the
border where the areas of black and color intermix in an infinite
frenzy of order and chaos.


FOCUS ON FRACTALS, 30 minute Video