The Weibel instability is investigated with PIC simulations of an initially unmagnetized and spatially uniform electron plasma. This instability, which is driven by the thermally anisotropic electron distribution, generates electromagnetic waves with wave vectors perpendicular to the direction of the higher temperature. Two simulations are performed: a 2D simulation, with a simulation plane that includes the direction of higher temperature, demonstrates that the wave spectrum is initially confined to one dimension. The electric field components in the simulation plane generated by the instability equalize at the end of the simulation through a secondary instability. A 1D PIC simulation with a high resolution, where the simulation box is aligned with the wave vectors of the growing waves, reveals details of the electron phase space distribution and permits a comparison of the magnetic and electric fields when the instability saturates. It is shown that the electrostatic field is driven by the magnetic pressure gradient and that it and the magnetic field redistribute the electrons in space.