Fractal dimension estimation of fractional Brownian motion

Fractal dimension provides an objective means for quantifying the fractal property of an object and comparing objects observed in the natural world. One of the most useful mathematical models for the random fractals found in nature has been fractional Brownian motion. Two algorithms are used to simulate fractional Brownian motion. An important characteristic of fractals useful for their description and classification is their fractal dimension. Several methods are developed to estimate fractal dimension: the variance method, the spectral method, and the morphological method. These methods are used for simulated samples of fractional Brownian motion, and their performances are compared. It is found that the performance of these fractal dimension estimation methods is usually related to what kind of fractals are to be estimated and the range in which the fractal dimension falls.<>