Natural Fractal Financial Patterns
Jan 31, 2008 in Grow Financially
It appears that there are many natural systems which occur as fractal combinations of smaller natural designs. The components of a typical architectural drawing are squares and triangles, etc, the patterns that are easily communicated to each other. But the components of a dynamic system can be a combination of truly naturally occurring patterns, which are usually not easily communicated. Commodity and currency dynamics are certainly likely to be best communicated with naturally occurring patterns rather than what we typically use when drawing on ticker symbol charts (lines, triangles, and rectangles).
Here is a clip from a description of a natural dynamic system, the electromagnetic fields around a coil and their measurement. However, I’ve clipped it here for his simply elegant description of a fractal behavior.
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That is, “…take a nonlinear process and feed back some form of its output to its input”, is exactly what we would like to do when studying financial histories. We would like to use some of the output (history, or patterns preceding the present point) and use it as input to the future pattern of the chart.
Also noted in his description on the same page, he discusses “infinite information” in white noise, as opposed to “lack of information”, to describe the lack of disorder in chaos. Quoting again:
And the fractal road of bifurcations is a map (perhaps one of many) of the territory. It is the virtue of the fractal approach to ungainly systems that high orders of complexity can often be collapsed to a very simple model which mimics the overall characteristics, not in the sense of a linearized approximation, but in the manner in which noise and order (or information) are transmitted by the system.
Beautifully applicable statement!! This, too, is quite applicable to financial histories. We would like to use the outputs (history patterns) from not only the immediate past, but the preceding immediate past, and the histories preceding those, in a lessening degree. The older the pattern, we tend to think it will have less influence (input) to the current pattern forming. But we definitely should not disregard the “Daily chart” or “Weekly chart” while predicting the trend over the next hour. These “older histories” have a blurring effect on the present, and can be represented with dampening equations or infinite series expansions. Yet, we also toss around quips and quotes that “the history has no bearing on the present”, and still make statistical predictions in direct violation of this principle.
Quoting again from the same reference:
“This seed is then used as the basis in what is called a fractal transformation. If the 384 numbers are considered as elements of a discreet function v(n), then the function f(n) is the fractal transform given by:f(n) = sum( v(n*(a**i)) / a**i ) for i = -infinity to + infinity
This function is constructed of an infinite number of versions of the original function which are stretched or compressed, and added together. In practice the number of additions need only go as far as required for numeric accuracy.”
In conclusion, what I am suggesting is that financial patterns could be modeled using natural shapes, which are stretched or compressed, added together, dampening their influence over time. Let me hope to be the first to say that the naturally occurring patterns fractally-combined in financial charts are “capacitor charge/discharge” and “spring dampening”.
