Synthesis of two-dimensional fractional brownian motion via circulant embedding

Fractional Brownian motion (fBm) is a useful model to represent various natural phenomena and its synthesis has been a topic of interest in literature. This paper presents an algorithm to generate two-dimensional fBm based on circulant embedding method. Although this method has been proven in simulating one-dimensional fBm, its extension into two-dimensional is not straightforward. To solve the problem, we use circulant embedding as an exact method to synthesize the second-order increments of fBm, and recover the desired fBm via integration in frequency domain. The advantage of using second-order increments is its direct extensibility to any dimension. Experimental results show that the proposed method works efficiently fast and offers acceptable results when compared to the theoretical statistics of fBm.