A Gaussian random walk has a fractal dimension of exactly 1.5

; But how has this been calculated?

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.

And what does the fractal dimension in the stock market mean?

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