We report the results of a computer simulation of the evolution of structure in a two component fluid consisting of a liquid phase and a dispersed colloidal phase subjected to a biaxial field. A biaxial field, such as a rotating field, can induce the organization of polarizable particles into two-dimensional sheets, in contrast with the essentially one-dimensional columns formed in a uniaxial field. Our primary objective is to explore the kinetics of coarsening, the emergence of structure, and the anisotropy in materials properties. Using an efficient, linear-N simulation method we report studies of systems of N=10 000 particles over the concentration range of phi = 10-50 vol %. We present a variety of methods of characterizing the structures that emerge, including the two dimensional pair correlation, velocity correlations, microcrystallinity, optical attenuation, dipolar interaction energy, conductivity, and permittivity. The anisotropies that we compute are generally inverted relative to those found in materials structured by a uniaxial field.