Even the ordered structural complexity of Elliott wave forms reflects the Fibonacci sequence. There is 1 basic form: the five-wave sequence. There are 2 modes of waves: motive (which subdivides into the cardinal class of waves, numbered) and corrective (which subdivide into the consonant class of waves, lettered). There are 3 orders of simple patterns of waves: fives, threes and triangles (which have characteristics of both fives and threes). There are 5 families of simple patterns: impulse, diagonal, zigzag, flat and triangle. There are 13 variations of simple patterns: impulse, ending diagonal, leading diagonal, zigzag, double zigzag, triple zigzag, regular flat, expanded flat, running flat, contracting triangle, barrier triangle, expanding triangle and running triangle.
The corrective mode has two groups, simple and combined, bringing the total number of groups to 3. There are 2 orders of corrective combinations (double correction and triple correction), bringing the total number of orders to 5. Allowing only one triangle per combination and one zigzag per combination (as required), there are 8 families of corrective combinations in all: zig/flat, zig/tri, flat/flat, flat/tri, zig/flat/flat, zig/flat/tri, flat/flat/flat and flat/flat/tri, which brings the total number of families to 13. The total number of simple patterns and combination families is 21.
Figure 3-14 is a depiction of this developing tree of complexity. Listing permutations of those combinations, or further variations of lesser importance within waves, such as which wave, if any, is extended, which ways alternation is satisfied, whether an impulse does or does not contain a diagonal, which types of triangles are in each of the combinations, etc., may serve to keep this progression going.
There may be an element of contrivance in this ordering process, as one can conceive of some possible variations in acceptable categorization. Still, that a principle about Fibonacci appears to reflect Fibonacci is worth some reflection.
Phi and the Additive Growth
As we will show in subsequent chapters, market action is governed by the Golden Ratio. Even Fibonacci numbers appear in market statistics more often than mere chance would allow. However, it is crucial to understand that while the numbers themselves do have theoretic weight in the grand concept of the Wave Principle, it is the ratio that is the fundamental key to growth patterns of this type. Although it is rarely pointed out in the literature, the Fibonacci ratio results from this type of additive sequence no matter what two numbers start the sequence. The Fibonacci sequence is the basic additive sequence of its type since it begins with the number 1 (see Figure 3-15), which is the starting point of mathematical growth. However, we may also take any two randomly selected numbers, such as 17 and 352, and add them to produce a third, continuing in that manner to produce additional numbers. As this sequence progresses, the ratio between adjacent terms always approaches the limit phi very quickly. This relationship becomes obvious by the time the eighth term is produced (see Figure 3-16). Thus, while the specific numbers making up the Fibonacci sequence reflect the ideal progression of waves in markets, the Fibonacci ratio is a fundamental law of geometric progression in which two preceding units are summed to create the next. That is why this ratio governs so many relationships in data series relating to natural phenomena of growth and decay, expansion and contraction, and advancement and retreat.
Figure 3-15
Figure 3-16
In its broadest sense, the Wave Principle suggests the idea that the same law that shapes living creatures and galaxies is inherent in the spirit and activities of men en masse. Because the stock market is the most meticulously tabulated reflector of mass psychology in the world, its data produce an excellent recording of man’s social psychological states and trends. This record of the fluctuating self-evaluation of social man’s own productive enterprise makes manifest specific patterns of progress and regress. What the Wave Principle says is that mankind’s progress (of which the stock market is a popularly determined valuation) does not occur in a straight line, does not occur randomly, and does not occur cyclically. Rather, progress takes place in a "three steps forward, two steps back" fashion, a form that nature prefers. More grandly, as the activity of social man is linked to the Fibonacci sequence and the spiral pattern of progression, it is apparently no exception to the general law of ordered growth in the universe. In our opinion, the parallels between the Wave Principle and other natural phenomena are too great to be dismissed as just so much nonsense. On the balance of probabilities, we have come to the conclusion that there is a principle, everywhere present, giving shape to social affairs, and that Einstein knew what he was talking about when he said, "God does not play dice with the universe." The stock market is no exception, as mass behaviour is undeniably linked to a law that can be studied and defined. The briefest way to express this principle is a simple mathematical statement: the 1.618 ratio.
The Desiderata, by poet Max Ehrmann, reads, "You are a child of the Universe, no less than the trees and the stars; you have a right to be here. And whether or not it is clear to you, no doubt the Universe is unfolding as it should." Order in life? Yes. Order in the stock market? Apparently.
