complex and beautiful object in mathematics. When software displays the Set in false colors, a viewer can be excused for concluding that the Set is a Set of infinities.

Software displays segments of the Set along its rich, complex edges, under greater and greater degrees of magnification. As each tiny portion is magnified, more detail emerges. Mathematicians insist that the Set holds the entire set of Julia sets in infinitely many places in its infinite numbers of levels of organization. An eternity would not be long enough to explore the Set's many hidden splendors.

Watch as "...its disks grow spikes of prickly thorns, spirals and filaments curl outward and around, bearing bulbous molecules that hang infinitely variegated like grapes on God's personal vine."

This lovely description of the Mandelbrot Set is taken from James Gleick's book, "Chaos," which I commend to anyone interested in a more in-depth exploration of fractals and chaos theory. Explore the Set in detail at this site:

Fractals aren't limited to two dimensions. Fractal geometry explores the dimensions between the traditional geometric concepts of the zero-dimensional point, the one-dimensional line, the two-dimensional plane, and the three-dimensional solid.

The dimensionality of fractal shapes can be calculated: a 2.636-dimension sponge, for example, is quite possible. A fractal sponge is generated by dividing a cube into nine cubes and removing the middle one, then subdividing each cube further, and removing the middle one at each turn. The process continues to infinity.

Fractals also include the nearly dimensionless particles known as fractal dust. They are generated by taking a line, dividing it into thirds, removing the middle third, dividing each remaining segment into thirds, removing in turn their middle thirds, and so on, ad infinitum. What remains is a ghostly faint line of points, virtually there or not there.

And then there is the famous Koch Curve or "fractal snowflake." Take an equilateral triangle, divide each side so that they extend outward, creating a hexagon. Then, divide each side again, so that the form begins to look like a snowflake. Continue dividing the sides of the snowflake forever, creating a boundary that encompasses a finite area but is itself infinite in length. The iterative process of generating a Koch Curve will look very much like the "fractal movie" posted on this site:

Just as Koch Curves can pack infinite length into a comparatively

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