In this study, it was investigated the interface patterns of two immiscible, viscous fluids into the geometry of a horizontal Hele-Shaw cell, considering that one of the fluids is an aqueous magnetic fluid. In general, the total energy of a magnetic fluid system consists of three components: gravitational, surface, and magnetic. For a magnetic fluid into a horizontal Hele-Shaw cell, the gravitational energy is constant and can be inessential, thus leaving only the surface and magnetic energies. The interface between two immiscible fluids, one of them with a low viscosity and another with a higher viscosity, becomes unstable and starts to deform. Dynamic competition in such confined geometry leads finally to the formation of fingering patterns of a magnetic fluid in a Hele-Shaw cell. The computational study upon the interface instabilities patterns in aqueous magnetic fluids was accomplished evaluating fractal dimension in finger-type instabilities. Between the fractal dimension and experimental instability generation time a correlation was established.