What is a Mandelbrot Set?

The diagram to the left of this text is a “Mandelbrot Set” named after mathematician Benoit Mandelbrot.  This mathematical feedback loop illustrates the “profound connections between fractal geometry and chaos theory,” according to Mandelbrot.  As one of Mandelbrot’s most famous illustrations, the Mandelbrot set is created from fractal geometry, or the study of roughness and self-similarity.

Mandelbrot cites many applications for fractal geometry including data compression techniques, brain wave analysis, design of radio attennae, fiber optics, anatomy and yes—global finance as well.

Upon reviewing the Gaussian models which underpin modern financial theory, Mandelbrot proposed that markets and pricing do not follow smooth bell curve distributions. Instead, Mandelbrot proposed a better model to describe mathematical laws of chance—fractals. This theory—still hotly contested even after the recent financial meltdown in 2008—holds that markets and prices are not independent, prices leap (are not continuous), and investors are not rational.  Instead, Mandelbrot says we need to, “assume the market is not efficient, instead a wild and complex shape.”

What does any of this have to do with marketing?

Marketers who seek to understand customer behavior by using current and historical data and statistical analysis would be wise to remember the following takeaways from Mandelbrot’s research:

  1. Correlation does not equate to causation (a major mistake made by marketing and finance executives alike)
  2. A mathematical forecast can never be fully accurate and precise as there are too many (actually infinite) variables to consider that affect the forecast
  3. Relying solely on a mathematical forecast or model for decisioning leads to certain death (just ask LTCM, Magnetar Capital,  Bear Stearns, AIG et al)
  4. Markets and customers are extremely complicated (good luck figuring them out!)
  5. Acts of one person, team, company do not exist in a vacuum and can have large repercussions on the whole
  6. Customers are not “coin flips” meaning that their actions are not independent of each other and indeed customers have long memories
  7. Complexity is often birthed from simplicity (simple rules build complex structures)
  8. Power laws exist and are prevalent in markets. This means that marketing executives should always be thinking about the next Black Swan on the horizon. We may not be able to predict exactly what it is or when it happens, but we can do our best to prepare.
  9. Over reliance on statistical techniques (such as root mean square) for forecasting is dangerous. My favorite Mandelbrot quote; “Almost all of our statistical tools are obsolete—least squares, spectral analysis, all our established theory, closed distributions.”
  10. There is no such thing as normal

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