My latest article has been posted at Helium.com. Check it out at this link.

Here's a sample:

Consider the most striking form of fractal: the Mandelbrot Set. Mandelbrot generated a collection of points on a graph by taking a series of complex numbers, squaring each of them, adding the original number to each, and squaring them again and again. If the number remains finite after many such iterations, it remains in the Set and is plotted on the graph.

The resulting shape is composed of successful solutions to what is truly an extraordinarily simple equation. Paradoxically or not, it’s the most 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.

Wouldn't it be WAY COOL if our highly advanced future avatars could play in a version of Second Life loaded with n-dimensional fractals. Wheeeeee!