A random walk is generally the set of points created by starting at some initial point and then randomly "walking" or displacing the point each iteration.  The distribution of the random displacements determines the fractal dimension of the walk.


In financial (and other) analyses, one generally creates a time-series representation of the underlying phenomenon (like the price of a given stock over time) and determines the fractal dimension of that dataset.  A larger dimension implies more volatility in the stock (or turbulence, if the data represent have some fluid mechanical representation); a smaller dimension implies a smoother path.

Kerry

I'm about to do some work trying to predict the stock market!     I fear this is a well trodden path.

I wonder what use Fractals could be.. 

Of course!

My task is to try and find correlations between two datasets - both prices of different stocks over time.  If I can find that two datasets are correlated over a specific time window, then the subsequent time window may be used to predict how the stock will move next.  I was going to brute-force scanning through various time windows and ranges of both datasets, and see how each is correlated (I am looking at the Excel function CORREL at the moment), but this looks like a massive task.

There may be some mileage in using fractal dimension of a subrange of a dataset in order to reduce the sheer number of comparisons as it may be fruitless to compare subranges with wildly disparate fractal dimensions.  I say 'may be', this is something I'll have to look into.

see also http://en.wikipedia.org/wiki/Fractomancy