# Why is there periodicity in the output of Richard Voss' fractional Brownian motion?

I am trying to figure out why the output of fractional Brownian motion (fBm) as described by Richard Voss (Random fractal forgeries. In: Fundamental Algorithms for Computer Graphics, R. A. Earnshaw (eds.). Springer-Verlag, Berlin. 805-835. ISBN-13: 978-3-540-54397-8) is characterized by periodicity.

In particular, the images produced according to its Fractal Forgeries paradigm seem to come with an x=y axis of symmetry.

What is the mathematical or numerical reason for that?

Is it something inherent to the fractal model itself, or is it due to the fact that inverse FFT is applied in order to reconstruct the function, and thus the fractal surface? Thanks.