# The Strange Attractor

The phenomenon in which one regular cycle locks into another is called entrainment, or mode locking. Entrainment explains why stock market components are like flocking birds and herd behavior of land animals

The 3Ms were wondering why miracles exist and then they realized, miracles were more frequent than random. It was like life on earth. It seemed like a freak accident, but there were more life systems in the universe. Nature forms many such miraculous patterns.

James Gleick’s award-winning Chaos details the phenomena. Christian Huygens, the Dutch physicist behind the pendulum clock and the classical science of dynamics, stumbled upon an observation. One day, a set of pendulum clocks placed against a wall happened to be swinging in a perfect synchronized chorus. Nothing in the mathematical description could explain this propagation of order from one pendulum to other; clocks could not be that accurate. Huygens surmised the clocks were coordinated by vibrations transmitted through the wood. This phenomenon in which one regular cycle locks into another is now called entrainment, or mode locking. Entrainment also explains why stock market components are like flocking birds, the shoaling behavior of fish, the swarming behavior of insects and herd behavior of land animals. Entrainment is also the scientific explanation for inter-market analysis, why the Dow 30 performance is connected to Sensex 30, gold is connected to the dollar and a host of other flocking performances in the capital market.

Though there is a pattern in the flocking of birds in the sky, the form is not always predictable. But there is a difference between random and unpredictable. The weather is unpredictable but not random. Unpredictable events or systems can be described as those we are unable to forecast or only able to partially forecast, due to a lack of information. Random systems are systems in which no deterministic relationship exists. Stock markets are non-random dynamical systems; you can partially understand and forecast these.

Looking at stock markets as dynamic chaotic systems can change our approach to investment. One, we accept noise as a part of the unpredictability. Second, we accept that the idea of average is redundant. If weather over the long term does not have an average, the idea of an average return for the stock market is redundant. This means it’s the group (the flock of birds) that is more important than the index itself, which can sleep or be driven by the group.

Third, entrainment suggests that ‘in sync’ and ‘out of sync’ performances can happen between asset classes, correlations can get positive and negative, conventional relationships can work or fail, and cause and effect can be humbled. Hence, working on extrapolations or simple trends can increase risk rather than decrease it. Fourth, data mining, pattern identification and looking for universality becomes a mother lode not just for science but for stock markets, too. Fifth, the very fact that chaos is mathematical allows us to model stock markets.

Is the universality we see in nature also be seen in stock markets? Yes. Lorenz’s sensitive dependence, Feigenbaum bifurcation constants, and Mandelbrot fractals are a part of chaotic systems. Stock markets are sensitive and clearly, depict the butterfly effects. The very fact that equities around the world crash together exhibits sensitive dependence.

Technicians swear by proportion. And, the fact that market data are replete with statistical fits and Fibonacci proportions suggests overlap with Cantorian Feigenbaum constants. Finally, we know of the famous debate Mandelbrot avoided regarding Elliott’s work. The master technician talked about fractals 30 years before Mandelbrot.

Another universality seen across data assets is the extreme(s) reversion. Whenever the bird separates from the flock, it is strangely attracted back into the fold. The outliers don’t remain outliers; the attractor keeps them together. Call it a miracle but the worst outliers invariably deliver.