What Does a Fractal Look Like?
And What Does It Have to Do with the Stock Market?
May 26, 2011
By Elliott Wave InternationalIf the word 'fractal' comes up at all in conversation, that conversation is probably being held in a mathematics department. However, anyone who is interested in the Wave Principle and how it applies to the stock market may have stumbled across the phrase "robust fractal." If you want to know more about what it means in that context, here's an excerpt from Elliott Wave International's primer on fractals that explains the connection.
by Robert R. Prechter
In the 1930s, Ralph Nelson Elliott discovered that aggregate stock market prices trend and reverse in recognizable patterns. In a series of books and articles published from 1938 to 1946, he described the stock market as a fractal. A fractal is an object that is similarly shaped at different scales.
Although Elliott came to his conclusions fifty years before the new science of fractals blossomed, he took a step that current observers of natural processes have yet to take. He explained not only that the progress of the market was fractal in nature but discovered and described the component patterns. The patterns that Elliott discerned are repetitive in form but not necessarily in time or amplitude. Elliott isolated and defined a number of patterns, or "waves," that recur in market price data. He named and illustrated the patterns. He then described how they link together to form larger versions of themselves, how they in turn link to form the same patterns at the next larger size, and so on, producing a structured progression. He called this phenomenon The Wave Principle….
The Stock Market as a Robust Fractal
A classic example of a self-identical fractal is nested squares. One square is surrounded by eight squares of the same size, which forms a larger square, which is surrounded by eight squares of that larger size, and so on.
A classic example of an indefinite fractal is the line that delineates a seacoast. When viewed from space, a seacoast has a certain irregularity of contour. If we were to drop to ten miles above the earth, we would see only a portion of the seacoast, but the irregularity of contour of that portion would resemble that of the whole. From a hundred feet up in a balloon, the same thing would be true.
Scientists today recognize financial markets' price records as fractals, but they presume them to be of the indefinite variety. Elliott undertook a meticulous investigation of financial market behavior and found something different. He described the record of stock market prices as aspecifically patterned fractal yet with variations in its quantitative expression. I call this type of fractal, which has properties of both self-identical and indefinite fractals, a robust fractal. Robust fractals permeate life forms. Trees, for example, are branching robust fractals, as are animals, circulatory systems, bronchial systems and nervous systems. The stock market record belongs in the category of life forms since it is a product of human social interaction.
How Is the Stock Market Patterned?
Figure 1 shows Elliott's idea of how the stock market is patterned. If you study this depiction, you will see that each component, or "wave," within the overall structure subdivides in a specific way by one simple rule: If the wave is heading in the same direction as the wave of one larger degree, then it subdivides into five waves. If the wave is heading in the opposite direction as the wave of one larger degree, then it subdivides into three waves (or a variation). These are called motive and corrective waves, respectively. Each of these waves adheres to specific traits and tendencies of construction, as described in Elliott Wave Principle (1978).
Waves subdivide this way down to the smallest observable scale, and the entire process continues to develop larger and larger waves as time progresses. Each wave's degree may be identified numerically by relative size on a sort of social Richter scale.