Power Trader©
An introduction to Chaos Theory and Fractals
In mathematics, chaos theory describes the behavior of certain dynamical systems that is, systems whose states evolve with time that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, which manifests itself as an exponential growth of perturbations in the initial conditions, the behavior of chaotic systems appears to be random. This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions, with no random elements involved, this behavior is known as deterministic chaos, or simply chaos.
Chaotic behavior is also observed in natural systems, such as the weather. This may be explained by a chaos-theoretical analysis of a mathematical model of such a system, embodying the laws of physics that are relevant for the natural system.
A fractal is an irregular pattern that is not easily defined by classical geometry, which is based on the study of smooth, continuous curves and shapes. Fractals are irregular and complex, and are much more representative of the way the world actually is, rather than the idealized world of classical Euclidean geometry.
Although it's easy to identify when something is a fractal, it's almost impossible to come up with an easy definition of this concept. Indeed, the father of fractals, Benoit Mandelbrot, defined them in this way: "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension."
Luckily you don't have to understand such definitions to apply fractal analysis into financial markets!
Fractals are all around us in nature, in mountains, trees, snowflakes, rivers, clouds, and turbulence. There are even fractals in our bodies, in the system of blood vessels.
But the most important and fascinating fractals in nature occur in financial markets.
Fractal market analysis is a pioneering approach to the study of financial markets, using chaos and quantum theories to study and characterize the inherent predictability of financial markets.Over the last 40 years, a language has sprung up to address what is happening in seemingly random natural systems -- such as the weather, and financial markets -- in order to study what may be predictable in such systems. This is chaos theory, which is trying to understand the order hidden within seemingly random chaos.
Fractal market analysis discovers and characterizes the order hidden within seemingly random financial markets, and determines the probability of future events.
A fractal pattern is a recurring pattern in a chaotic environment. A defining characteristic of a fractal pattern is that it is self-similar in all time-frames; that is, the smaller components have the same basic shape and pattern as the larger components. Financial markets are fractal in this way, as it is impossible to look at an unlabeled price chart and determine whether it is an hourly, monthly, or even a 5 minute chart of the trading action. They all look the same. Markets are fractal.
We've spent many years studying and researching the way that financial markets actually behave, using chaos theory and empirical observation in real-time of unfolding fractal patterns to characterize the way they move. Power Trader is a fractal projection method which tells us in surprising detail how a market fractal pattern is going to develop.
The main advantage of knowing these fractal patterns and projections is they identify specific critical balance points where the potential energy may resolve in one direction or another. With Power Trader you can identify ahead of time where these points are, so you can know as early as possible where a market is going to go.
Interestingly, there is not much published in the field of fractal market analysis -- at least nothing of any real value. There are dispersed groups of people working on these ideas, but few publish their work, primarily because of the significant edge it is providing in financial markets.
We continue to be surprised about how there is still such a wide-open frontier in market analysis, in spite of the trillions of dollars, and the best and brightest minds round the globe devoted to the markets. It's our belief that 99.999% of all market participants are approaching the markets the wrong way and are not using the right set of analytical tools.
There is no direct relationship between the inputs into a market -- such as earnings, economic reports, liquidity, etc. -- and the output, which is the price. There is no proportional relationship. The markets have to be studied as chaotic, non-linear systems, yet almost nobody studies them in this way.
But over the years this will certainly change. Fractal analysis is pushing into the still-unexplored frontier of market thought, but in a few years just about every market follower will be well-versed in many of these ideas.
