FRACTALS -- THE REALLY NEW MATH 

If you had trouble with calculus, you're really going to have to work to understand this. But, if you want to stay in front you better learn what it's all about. It will affect your life.

Calculus, as your teacher tried to tell you, deals with formulas for ratios angles, curves, etc. that relate to physical phenomenon. The new branch of mathematics -- fractal geometry -- also deals with equations and physical phenomenon, but in relation to insides and outsides.

For more than a year now I have been playing on my computer tossing in angles of varying degrees in fractal formulas. The outcome is not rows of figures, columns of debits and credits or even pie, line or bar graphs. The result is pictures of incredible beauty, designs and creations that to some, resemble ancient stained-glass windows from European cathedrals.

This is not some new math fad or passing academic fancy. Fractals will lead us into the 21st Century and provide a tool to handle the much more complicated problems that will arise as the new age gets underway.

Fractal geometry can represent irregularity, randomness with the same sophistication that Euclidian geometry describes rectngles, regular, curved, or straight lines. Fractals can, mathamatically, describe the randomness of anything. A cloud, the shape of a river or a coastline. How a child exists within a family, a bacteria within a culture, a city within a state, a state within a country, a country within a planet. Even a star within a galaxy.

According to geologist Stephen R. Brown of Sandia National Laboratories (the largest in the U.S.) the application of fractals to geology can be valuable "It can relate laboratory-scale work to realworld studies, it can improve predictions of mechanical rock properties and allow more accurate calculations of fluid flows". This is of extreme value to mining, petroleum extraction, construction and other industries.

With fractals as with holograms, any bit of the picture is a microcosm of the entire picture. One foot of a riverbank relates to the banks along the entire river. A micro segment of a coastline will be much like the entire coastline. From his earlier work with Prof. Christopher Scholz and others at Columbia University, Brown now has confirmed that similarity on scales from 10 millionths of a metre to features the size of the San Andreas fault can be shown visually. In fluid flow calculations Brown has compared fractals with highly idealized calculations. As the walls moved together fractals became significantly more accurate. Properties determined in a laboratory can be applied to the evaluation of large-scale problems in the field. The opportunities are unlimited.

Are your kids being taught fractal geometry in their school? More information: Dan Arvizu, Technology Transfer Department, Sandia National Laboratories, Albuquerque, NM 87185-5800. Phone: 505/846-0387.

Other sources for pictures, video (free information pack or US$7 for 38 color postcards. Excellent value):

Art Matrix, P.O. Box 880, Ithaca, New York 14851

* * *

< previous | chapter index | next >
back to Main Chapter Listing
back to Home Page