# Fractal Dimension

A measure of the complexity of data. What is particularly interesting for precious metals investors, a fractal dimension can measure the complexity of price paths (or charts of prices) of metals. The higher the fractal dimension is the more complicated the price paths (charts) are. Fractal dimension is one of the things that Fractalyzer's fractal index is based on.

The guys are in a car on their way to the football game. John is driving while Eric and Jill are having an animated chat.

#### Eric, the Beginner

Jill, you told me about fractals on the gold market. Remember?

I surely do.

#### Eric, the Beginner

So my question is: what is the fractal dimension?

If one remembers that near tops or bottoms the charts of gold tend to become jagged and the price movements more rapid in both sides, then one might imply that these charts are more complicated near bottoms or tops (or during sideway trends). This suggests that a high value of the fractal dimension might indicate a top or a bottom (or a sideway trend).

On the other hand, during rallies or slumps the prices tend to follow a rather simple pattern – they follow a trend line. This, in turn, suggests that low values of the fractal dimension might indicate that one is a witness of an ongoing rally or decline.

If one analyzes the price trend together with the fractal dimension, they might be able to properly identify future turning points in the price paths of metals (the prices have fallen recently, but now the chart seems to become more and more jagged… wait a moment, the fractal dimension is quite high… is a top likely to occur?...). This is extremely important as it might enable you to close your positions before the anticipated decline or to open new positions right after the bottom.

## A little bit more about the fractal dimension

Now that we know how the fractal dimension might be of help to you let us concentrate on the concept itself. As we have written before, a fractal dimension is a measure of the complexity of data. It can be used as a measure of the complexity of prices of metals and therefore might be used as an indicator of tops and bottoms.

However, there is no widespread agreement as to how the fractal dimension should be calculated. Hitherto, various measures have been proposed as estimates of the fractal dimension and various ways of calculating these measures have been presented. This lack of uniformity makes it relatively difficult for precious metals investors to use fractals to analyze the market.

On the other hand the most popular measures that are used to calculate the fractal dimension have some common features. Because of that the fractal dimension usually ranges from 0 to 2, where values close 0 indicate a structure that is relatively simple (e.g. a trend line) and values in the proximity of 2 indicate a structure that is extremely complicated. To show that, we will resort to an example.

The chart above presents prices of gold between November 18th and November 25th, 2010. It is clear that the price path in this time span is not particularly complicated. What is more, one might say that the price of gold followed a trend line during that period. Because of that, one would expect the fractal dimension to be relatively low for that time span. As a matter of fact, the fractal dimension proves to be approximately 0.12 (which is relatively close to 0).

To see how the price paths look like when the fractal dimension is close to 2, please examine the chart below, which represents the price of gold between October 29th and December 9th, 2010.

As one might notice, the prices of gold do not follow any clear trend line. What is more the chart is jagged and we might point to several short-term tops and bottoms. This would be consistent with a relatively high value of the fractal dimension. As luck would have it, the fractal dimension turns out to be approximately 1.95 (relatively close to 2).

These examples show that the use of the fractal analysis might be helpful in anticipating possible tops and bottoms. This use is particularly interesting for precious metals investors as it might support your decision whether a top or bottom is in and this might be the advantage that will allow you to improve your risk-reward ratio.

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