This thread is a continuation of an earlier thread (, in which I asked for some math help for the Fractal Dimension Index. While FatTails & I explored the subject (thanks again FatTails!), it became apparent that the subject of Fractal Dimensions deserve a thread of their own.
What are "fractal dimensions"?
According to Erik Long (here ():
So, not only do Fractal Dimensions help us in uncovering the underlying movement in a seemingly random process, it also is based on other mathematical principles than regular technical analysis, thus giving us another view of the market.
Though the math may seem challenging, the simplified principle behind fractal dimension is straightforward: if we assume that the prices move in a random walk (meaning no trend or order), the amount that the movement of the price deviates from this random walk is the amount of trend that occurs.
For example, the 6E one period log price changes look visually quite random:
However, if we compare the returns over a longer time period, the randomness decreases and we visually can a trend in the log price changes:
In this image we can see there's more of a trend in 6E. By comparing the price changes to random, sideways movements, (which we often do visually) we can see that there is more of a trend in the second image compared with the first.
Indicators that use Fractal Dimensions should help us better differentiate between trending and range bound market, which could be the most important filter there is, since if we know the trend, we "only" have to trade in the direction of the trend.