An exact spatio-temporal simulation of a pulse incident on a collection of random dielectric ellipsoids. The simulation is undertaken by evolving a field distribution in accordance with the Maxwell's equations. One obtains both the near-field features and the far field effects in this simulation. In contrast to the traditional simulations based on Monte-Carlo technique, our simulations contain all coherent effects arising out of the interplay of phases of the field. The different colors depict various field strengths, the wavelength of the field is chosen to be 3 units, with Gaussian profiles of width 3.0 in the transverse direction and 8.0 in the longitudinal direction. The refractive indices of the ellipsoids vary randomly from 1.1 to 1.6, the radii along the axis of each ellipsoid varies from 0.5 to 1.0. The above simulation is for the TE mode. Absorbing boundary conditions are applied at the edges of the spatial integration domain.