  A variety of intriguing polarization patterns are created when polarization
observations of the single pulses from radio pulsars are displayed in a
two-dimensional projection of the Poincare sphere. In many pulsars, the
projections produce two clusters of data points that reside at antipodal points
on the sphere. The clusters are formed by fluctuations in polarization
amplitude that are parallel to the unit vectors representing the polarization
states of the wave propagation modes in the pulsar magnetosphere. In other
pulsars, however, the patterns are more complex, resembling annuli and bow ties
or bars. The formation of these complex patterns is not understood and largely
unexplored. An empirical model of pulsar polarization is used to show that
these patterns arise from polarization fluctuations that are perpendicular to
the mode vectors. The model also shows that the modulation index of the
polarization amplitude is an indicator of polarization pattern complexity. A
stochastic version of generalized Faraday rotation can cause the orientation of
the polarization vectors to fluctuate and is a possible candidate for the
perpendicular fluctuations incorporated in the model. Alternative models
indicate that one mode experiences perpendicular fluctuations and the other
does not, suggesting that the fluctuations could also be due to a
mode-selective random process, such as scattering in the magnetosphere. A
polarization stability analysis of the patterns implies that processes
intrinsic to the emission are more effective in depolarizing the emission than
fluctuations in the orientation of its polarization vector.
