In the June 2010 issue of TASC, John Ehlers and Rick Ways introduced a groundbreaking concept in their article titled "Fractal Dimension As A Market Mode Sensor." Let's dive into what this means for us traders.
What is Fractal Dimension?
The concept of fractal dimension is pretty fascinating. Market prices are inherently fractal in nature. If you take a look at price charts across different time frames—be it five minutes, daily, or weekly—they often resemble one another. Strip away the labels, and you might find it hard to tell them apart!
Fractal shapes maintain a level of self-similarity, displaying the same roughness and sparseness no matter the time interval. This self-similarity can be quantified by the fractal dimension, which describes how sparse the data is at various magnification levels.
How Do We Calculate Fractal Dimension?
To figure out the fractal dimension of a generalized pattern, we cover it with a number N of small objects of different sizes S. The relationship between the number of objects in two sets of sizes can be illustrated as follows:
Interpreting the Fractal Dimension Index
It’s important to note that the fractal dimension index (FDI) is not directional. Instead, it helps us determine whether there is a trend in the market. If the FDI value is below a certain threshold, it indicates that the market is ranging (no trend). Conversely, if the FDI exceeds that threshold, we can conclude that the market is trending.
Understanding the fractal dimension can give you an edge in your trading strategy. By keeping an eye on the FDI, you can better navigate the ups and downs of the market!
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