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. Of course, Mandelbrot's "discovery" was only a cleverly worded twist of R.N. Elliott's original research done more than 60 years earlier. Robert Prechter took Benoit Mandelbrot to task for taking credit for the work of RN Elliott.


Our use of the word fractal, or Elliott Wave fractal, is not a technically 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 the term 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 'down' fractal then is bar low that is lower than both the two bars preceding it and the two bars following it. A wide range bar can be both an 'up' fractal and a 'down' fractal at the same time.


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 complex Elliott Waves waves from a close only line chart. Fractal counting can be applied in any time frame with the same expectation that the Elliott Wave pattern that shows in the longer time frame will resolve in several lesser degree waves in shorter time frames.


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."


Elliott Wave experts will say that these fractal counts are more momentum waves than pure Elliott Waves. Even so these counting fractals can be combined with the Elliott Wave Oscillator to get as close to unambiguous wave counts as the Elliott Wave theory allows. Here's an example.

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 you can use 9 bar, 13 bar, or even 21 bar formations for fractal counting depending on the periodicity of the bars and the granularity of the wave count your are trading with.

Peter Amaral is a stock market researcher, trader, and trading book author with 25+ years experience in the trenches. He contributes frequently about W.D. Gann, Elliott Wave, Fibonacci and J.M. Hurst and other other legendary traders and their exotic techniques at the www.tradingfives.com website.