What Does a Fractal Look Like?

[MadMarketScientist 11]

If 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.

 

Excerpted from The Human Social Experience Forms a Fractal

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 a specifically 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.

 

Want to Know More About Fractals and the Stock Market? Then read the whole special report, called "The Human Social Experience Forms a Fractal." It's free of charge, so long as you are a member of Club EWI, which gives you access to many free reports that explain Elliott wave analysis and the Wave Principle.

 

This article was syndicated by Elliott Wave International and was originally published under the headline What Does a Fractal Look Like?. EWI is the world's largest market forecasting firm. Its staff of full-time analysts led by Chartered Market Technician Robert Prechter provides 24-hour-a-day market analysis to institutional and private investors around the world.

[BlowFish 10]

Odd thing. I didn't thing term fractal was coined until until the mid 70's (1975) in Les objets fractals, forme, hasard et dimension? by Benoît Mandelbrot. Pretcher re-writing history per chance?

 

To answer pretchers question want to know about fractals and the stock market? read Mandelbrot. If you want to learn about EW then maybe Pretcher is your man though one has to wonder, he is either pretty poorly researched (you would have thought an EW expert would know what Ralph wrote) or maybe he has an agenda to further his career as market clairvoyant? (He does seem to subscribe to the principle if you make enough predictions some are bound to come true). My hunch it's the latter, associate EW theory with the work of an outstanding mathematician and researcher to add 'scientific credibility'.

 

Edit: I am really not that big a sceptic, honest

[zdo 20]

Elliott Wave Principle - Wikipedia, the free encyclopedia

 

state of the f art

Elliott Wave Fractals

 

Since I personally have not found the 'markets' to be "as above so below" I get suspicious anytime I hear the term used by traders, etc.

It is a mathematical term - and its application to markets and analysis is as limited as the application of some other mathematical stuff like parametric distributions etc... ie I don't think you'll really find what a fractal looks like by looking at charts and other representations of markets

[zdo 20]

More non - ‘lab’ reading

Socionomics Institute

 

“robust fractal” = ~ “anything goes fractal” ?

//

 

Lab work

 

Whispers from the Edge of the Rainforest: Prechter Vs Schiff (Deflation vs Inflation)

 

Chart Of The Day: Currency Devaluation, Old School Style | zero hedge

 

Charting The Non-Linearity Of Hyperinflation, And Predicting America's Future Courtesy Of Ancient History | zero hedge

 

Exercise: Did you find the fractals?

[zdo 20]

... and now to real time "trade" / commerce

 

A Minsk Moment Update: Belarus Hyperinflation Prompts Government To Freeze Food Prices | zero hedge

 

"Show Me the Fractal!"

 

Me 2 Edit "I am really not that big a sceptic, honest "

[KeyToTheCastle 10]

The KISS way I think about fractals is that essentially the market is fractal in nature, made up of waves within waves within waves. Whichever patterns or organizing principles you use to make sense of the market....they're occurring on every time frame or chart periodicity possible. The reason why the smaller timeframes can look chaotic at times is that these occurrences are obviously happening a lot more frequently on say a 1 minute then they are on a weekly chart.

 

DBphoenix posted this quote a few years ago.....it describes the fractal nature of the markets perfectly:

 

"Every upward or downward swing in the market, whether it amounts to

many points, only a few points, or fractions of a point, consists of numerous buying

and selling waves. These have a certain duration; they run just so long as they

can attract a following. When the stops get exhausted and all the losing traders have bailed, the move is exhausted for the time being, that wave comes to an end and a contrary wave sets in."

[Tradewinds 12]

On another side note, here is an interesting show about fractals:

 

NOVA | Hunting the Hidden Dimension | PBS

 

or

 

NOVA | Hunting the Hidden Dimension

[Kojak 10]

Are there fractals that are not derived from the Fibonacci series ?

 

Jose