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FRACTAL GEOMETRY AND THE MARKETS
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Wherever chaos, turbulence, living systems, and disorder are found, fractal geometry is at work. As noted above, fractal actually means a fractional dimension. Imagine you are looking at a three-inch ball of twine from 200 yards away. It will look like a dot, and a dot has zero dimension. Now imagine you are walking up toward the ball of twine. You notice that it is, indeed, a ball of twine and thus has three dimensions. As you approach more closely, you see it is in reality made up of one long string that has only one dimension. By using a magnifying glass and looking even closer, you see that the string itself is actually three dimensional. So, depending on your perspec­tive, you have seen zero dimension, then three dimensions, then one, and then back to three. What you see in the market depends just as much on your perspective or your current paradigm. Actually, your current perspective is your paradigm. If you are coming from a linear perspective, you will never see the "real" market and will be at a disadvantage when it comes to trading and making profits.

The fractal is also a measure of irregularity. The more ir­regular and choppy a market is, the larger will be its fractal number. The fractal number of a portion of a move will always peak at the turnaround point. Therefore, all market trend changes are accompanied by a higher fractal number than the bars leading up to the change in trend.

Figure 3-4 shows British scientist Michael Batty's generation of a fractal tree via a computer. Each branch splits into two

Figure 3-4 Computer-generated fractal tree.

to create a fractal canopy. The illustration on the left has six iterations or bifurcations. By the thirteenth iteration (the illustration on the right), the tree begins to look more realistic. Fractal modelers can produce different species of trees by changing the fractal number. Fractal trees illustrate the point that fractal geometry is a measure of change. Each branching of a tree, each bend in a river, each change of direction in a market is a decision point. This notion became a crucial factor in discovering the '''fractal" of the Elliott wave.

CONCLUSION

The science of chaos supplies us with a new and provocative paradigm to view the markets. It provides a more accurate and predictable way to analyze the current and future action of a commodity. It gives us a better map with which to trade. It does not depend on constructing a template from the past and applying it to the future. It concentrates on the current market behavior, which is simply a composite of (and is quite similar to) the individual fractal behavior of the mass of traders. For a more in-depth look at the science of chaos from an academic and research point of view, I suggest the following readings, listed in the Bibliography: Peters (1991a, 1993), Deboeck (1994), and Chorafas (1994). Most of the current research techniques are found in physics and mathematics journals.

The fractal is the underlying structure of both the market and individual traders. In the next chapter, we will examine the two basic types of underlying structures and how they add to our market paradigm.

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