Fractals in markets

Your jaw might have dropped when you heard Professor Langdon wax eloquent in the book, The Da Vinci Code , about the mathematical patterns in nature — how the orbits of planets in solar systems, the structure of the human body and the design of the pine cones have a certain mathematical basis. The Phi, the Fibonacci numbers and the golden ratio mentioned in this lecture are used in stock markets as well.

Another concept that is commonly found in nature, that is useful in understanding the movement of stocks is, fractals. Fractals is a fragmented geometric shape that can be broken into parts which are similar in shape to the whole. Though the study of fractals dates back to 17th or 18th century, the term ‘fractal’ was used by Benoit Mandelbrot who is also known as “father of fractal geometry” in 1975.

Parts make up the whole You can understand fractals better if you open the refrigerator and take out a broccoli or a cauliflower. You will notice that each tiny floret is similar to the whole flower. The tiny floret can also be further broken down in to smaller pieces that again resemble the whole.

This can be observed in trees too — how a twig is similar to a branch, in the formation of clouds, coastline etc. My favourite example of a fractal is in the manner in which our emotions change. Our entire life can be charted in a series of happy, sad and neutral phases and each phase can be further sub-divided into these three phases so that each hour of the day can also be thus divided in similar up and down cycles.

History repeats itself And what does this concept have to do with stock market and traders? Any keen observer of the market would be aware that the patterns seen on the intra-day charts of 1-minute, 5-minute, 10-minute interval, and so on, are very similar to the patterns seen on the daily, weekly, monthly or even quarterly charts.

In other words, stock price movements also are fractal. It is due to this characteristic that one of the tenets of technical analysis, ‘history repeats itself' was born. Since the patterns tend to repeat themselves along all time-frames, it can be surmised, with a reasonable degree of accuracy, how stock prices will react to a given set of conditions.

Why do stock price moves unfold in fractals? This is because stock market movement is a manifestation of the actions of a number of individual traders/men.

Since human thought process also follows fractal patterns, stock market and individual stock price movement also unfolds in similar manner.

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