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ELLIOTT WAVE FRACTALS
One of the basic tenets of Elliott Wave theory is that market structure is fractal in character. The non-scientific explanation of this fractal character is that Elliott Wave patterns that show up on long term charts are identical to, and will also show up on short term charts, albeit with sometimes more complex structures. This property of fractals is called "self-similarity" or "self-affinity" and it is what this writer is referring to when he says that the market is fractal in character.
The February, 1999 issue of Scientific American presents a cover article by the well-known scientist Benoit Mandelbrot. In "A Fractal Walk Down Wall Street," Mandelbrot claims to have discovered self-affinity in markets, i.e., the idea that fluctuations at small scales are no different from those at large scales. Robert Prechter took Benoit Mandelbrot to task for taking credit for the work RN Elliott did in the 1930s.
Our use of the word fractal, or Elliott Wave fractal, is not a proper use of the property of self-similarity. When we use the term here we mean a "counting fractal," which is really a description of the relative position of a bar on a high-low bar chart. This may create confusion but we do not want to hijack 'Elliott Wave Fractal' from Dr. Bill Williams, the originator of the expression.
Using so called fractals to count Elliott Waves first appeared, to our knowledge, in Dr. Bill Williams' book "Trading Chaos." Like many other concepts in Dr. Willams' books, the fractal is elegant in its simplicity. The basic definition of an 'up' fractal is a bar high that is both higher than the two bars immediately preceding it, and higher than the two bars immediately following it. The lows of the bars are not considered in determining the up fractal progression.
If two bars in the progression have equal highs followed by two consecutive bars with lower highs, then a total of six bars rather than the usual five bars will make up the progression. The first high becomes the counting fractal. Reverse for 'down' fractals.
A wide range bar can be both an 'up' fractal and a 'down' fractal at the same time.
FRACTAL WAVE COUNTING IS A BREAKTHROUGH
Using fractals to count Elliott Waves is a breakthrough because any particular bar either is a fractal or it is not a fractal. There are no half-pregnant fractals. You will especially appreciate this if you have ever tried counting waves from a close only line chart.
HOW TO DEAL WITH FUGITIVE FRACTALS
In a perfect world every time frame chart would have unambiguous sequences of up and down fractals to mark every Elliott Wave. Unfortunately, that's not the case. Quite often the fractal progression is broken with what we call 'fugitive' fractals', for example, two clearly marked up fractals with no intervening down fractal to unambiguously complete the wave. In these cases you have to use your own judgment and go lower or higher in time frames, or use a close only chart to resolve the relative importance of the fugitive fractal and whether or not it should be "forced" into the wave count.
Fractals always mark the beginning and ending points of individual waves. As Dr. Williams put it, "Whatever happens between fractals is an Elliott Wave."
FRACTALS ARE BEST COMBINED WITH THE ELLIOTT OSCILLATOR
Counting fractals can be combined with the Elliott Wave Oscillator to get as close to unambiguous wave counts as Elliott Wave theory allows. Here's an example of (resizeable pop-up) fractal counting . And yes, you would lose the debate with Robert Prechter on the purity of Momentum Waves as an integral part of Elliott Wave theory.The 5 bar formation works best on Daily or longer time frame charts. For intraday data charts we often use 9 bar, 13 bar and 21 bar formations for fractal counting.
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