small area, fractal-like biological systems can pack an enormous amount of area into relatively small volumes.

Consider the circulatory system with its miles of veins and arteries, or the nervous system with its enormous arrays of nerve cells in the body and brain. Acres of bronchial tissue layer themselves in the lungs. Muscles cells, too, show signs of fractal organization.

With the enormous numbers of fractal patterns found in nature and in the human body, it's apparent that this is one of the most efficient patterns in which matter may arrange itself.

But, fractal organization isn't limited to nature. Software based on fractal geometry can be used to model complex patterns and events in the human world as well.

Mandelbrot realized that when he discovered that the same equations he used to derive the scalar organization of changes in stock market prices could also be used to model weather patterns, he knew he had stumbled onto an important insight. Similar equations can be used to analyze election returns, traffic patterns, population densities and distribution patterns, migration patterns, rates of information production and distribution, and the patterns in which job specializations and sub-specializations fall.

The clumpiness of buildings in a modern city's downtown skyline strongly resembles fractal formations such as fractal sponges. So do the networks within networks within networks that build upon one another to form computer chips, computer motherboards, computer networks, and the Internet.

Perhaps all of evolution - physical, biological, and cultural - is in some sense a fractal. If so, fractal geometry would have much to say about the spontaneous order of the universe and how it expresses itself in countless ways in our lives.

Stuart Kauffman reminds us: "As the scale of our activities in space and time has increased, we are being driven to understand the limited scope of our understanding and even our potential understanding."

As we learn how truly complex apparently simple things really are and as we learn what "complexity" really means, we are beginning to learn to accept our own human limits. We will never achieve the consciousness described earlier that can see all things and know all things in the universe. And now we know why.

Puncturing mortal hubris is not the least of the good insights we've received by studying fractals. We are all part of the process of fractal formation, created by it, creating it. We participate. We don't command. Perhaps this is as good a definition of evolutionary processes as any.

In the beginning was the Word - the Law. Fractal. The rest follows and we participate.

Learn more about this author, Sally Morem.
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