What is chaos theory? What is a fractal?
Fractals As Entry and Add-On Points
Fractals Entries Minimize Risk
This involves less risk because if the reversal of direction fails at these points, it is immediately evident and a trader can exit quickly with only a small loss. One prominent trading book suggests adding only at the point where the previous high was surpassed (the red-arrow fractals in this chart), but I don't agree. By taking a new trade only as the most recent high is surpassed, a trader must accept that the trade very likely will go negative for at least a short time in the future. If, on the other hand, a trader buys at the green arrows just as prices confirm above the Exponential Moving Average, most likely the trade will be in the profit within a minute or two (and usually less), and will never go negative at any point. To me, this minimizes risk and maximizes profits.
Fractals and Phantom's Rules
This concept of using fractals at these inflection points is also harmonious with Phantom's Rules because it disciplines a trader to react quickly to remove or reduce a position unless it proves correct almost immediately under Rule #1. Fractals also provide a very clear point to add onto an existing position under Phantom's Rule #2, providing that all conditions are met for the add-on.
Definitions of "Fractal"
fractal (frac tl)
n. A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Fractals are used especially in computer modeling of irregular patterns and structures in nature.
n. Mathematics, Physics. a geometrical or physical structure having an irregular or fragmented shape at all scales of measurement between a greatest and smallest scale such that certain mathematical or physical properties of the structure, as the perimeter of a curve or the flow rate in a porous medium, behave as if the dimensions of the structure (fractal dimensions) are greater than the spatial dimensions.
Chaos Theory Explained
(Mathematics ) A dynamical system that has a sensitive dependence on its initial conditions.
(Physics) a dynamical system that is extremely sensitive to its initial conditions.
(definitions from Dictionary.com)
Stochastic behavior is probabilistic behavior. (Stewart, Does God Play Dice?)
By placing both stochastic and deterministic in the same definition, the mathematicians have formed a bridge between the two sciences - two sciences that were regarded as mutually exclusive until then. Chaos is the study of deterministic systems that are so sensitive to measurement that their output appears random.
(excerpts from Introduction to Chaos Theory, by Mike Andrews)
Chaos Theory can be generally defined as the study of forever-changing complex systems. Discovered by a meteorologist in 1960, chaos theory contends that complex and unpredictable results will occur in systems that are sensitive to small changes in their initial conditions...
Although chaotic systems appear to be random, they are not. Beneath the random behavior patterns emerge, suggesting, if not always revealing, order. Recognizing that the stock market is a non-linear, dynamic, chaotic system /one stock market mathematician/ applies the principles of Chaos Theory in order to determine the pattern behind apparent random nature of market prices.
(from a website called, "Pi, The Movie")
Following are some images of fractal patterns as they occur in nature. They are often beautiful to behold. Fractals are the beauty and order of nature's chaos!
Fern fractals
Leaf fractals
Fractals in the meanderings of a river
Fractals in brassicas
Other
