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## Mandelbrot’s Generator

The Growth Curve Of Money

When it comes to markets, relationships change. But does the behavior that creates price patterns change?

When I first read a book titled The (Mis)Behavior Of Markets, I was not sure if I had wasted my time. I did dog-ear a page and wrote a single note on another. I reread the book several years later, which was fortunate, because I got another, new impression of what author Benoit Mandelbrot called a “generator,” which defines the base component, or characteristic, of price movement.

The generator was such a completely simplified tool that Mandelbrot gave himself a professional caveat before introducing it, saying it was so uncomplicated that he hesitated to call it a “model,” instead calling it a “cartoon.”

The generator is a straight line with a zigzag placed over it (Figure 1). The straight line represents the trajectory of price over time, while the zigzag provides a model for price pattern. The pattern created by the generator is scalable, and fractal in nature in that it both reproduces itself in like form based on the larger time frame pattern and it creates or “generates” smaller patterns of itself on the lower time frames (Figure 2). A fractal is a pattern or shape whose parts echo the whole; and the smaller that part or pattern, the more complex the construction.

FIGURE 1: MANDELBROT’S GENERATOR. This is a simplified tool of the price movement. It is a straight line with a zigzag placed over it. The straight line represents the trajectory of price over time, while the zigzag provides a model for price pattern.

Fractal geometry and market behavior
Figure 3 is a weekly chart of the Standard & Poor’s 500 as of January 2012, with different generators overlaid over several time periods.

Mandelbrot used a frond of a fern as an example in defining a fractal by showing how each fern frond is itself a fractal and made up of still-smaller leaf clusters — smaller fractals. As the plant grows, it generates more fronds, which grow into shoots, which grow into mature branches of the plant — larger fractals.

While his use of the fern to help us grasp the definition of a fractal was both helpful and insightful and his generator a great model for identifying and measuring price action, he did not, in my view, make the next step clear enough and show how both markets and plants exhibit similar growth curves.

…Continued in the November issue of Technical Analysis ofStocks & Commodities