CHAOS THEORY
The Who, What, And How
Finding Out About Fractals
by Clem Chambers
How are fractals related to the financial markets?
Fractals hold a powerful mystique, but few truly understand what a fractal is and how it relates to the market. To most, a fractal is a fantastically beautiful graph with curly edges that seems to have a hypnotic grip on the viewer. Expressed as images, fractals have an almost-magical charm, while the word itself, coined and popularized by scientist and mathematician Benoit Mandelbrot, has taken on an almost incantation-like property, as though it were a synonym for "abracadabra."
You don't have to look far to find "fractal" used in ways that have no relation to the original meaning. Buzzword builders have purloined this revolutionary mathematical concept, leaving most of us confused about what it really means.
WHAT IS A FRACTAL DIMENSION?
Dimension is critical to the concept of fractals. Dimension as a concept is wedded to the idea of four dimensions, and considering more than four dimensions appears to many to challenge both physics and existence itself. You can mathematically express things in many more dimensions than four. Fractals take this idea further; it enables geometry to be expressed in fractional dimensions. In classical geometry, a 10'x10' lawn might have an area of 100 feet. However, for an ant climbing up and down every blade of grass, the total area would be very different. Playing with dimensions in this way is what makes fractal theory interesting, and this is particularly true for those of us with stock charts.
Figure 1: Fractals that appear repeatedly. The occurrence of the winged Ws marked here shows the self-affinity of this specific time series.
...Continued in the November 2003 issue of Technical Analysis
of STOCKS & COMMODITIES
Excerpted from an article originally published in the November 2003 issue of Technical Analysis of STOCKS & COMMODITIES magazine. All rights reserved. © Copyright 2003, Technical Analysis, Inc.