Modeling 3-D anisotropic fractal media

Modeling 3-D random media

I show three different realizations of an anisotropic model with different aspect ratios along the three coordinate axes. The model is a 64 points cube with characteristic scales $a_x=15$, $a_y=25$, and $a_z=35$. The media are characterized by Gaussian, exponential, and van karman autocorrelation functions, respectively. We notice the increase in model roughness as we move from the Gaussian medium to the exponential field (i.e, $\nu=.5$) and then to the von Karman field with $\nu=.2$.

In the physical world, these fields may represent media at different scales varying from the microscopic to the megascopic.