The response of polycrystals to deterministic and random deformations is investigated with respect to the evolution of the crystallographic
orientation and its probability density function, the ODF. The crystals analyzed are highly simplified, being two-dimensional and with only
two active slip systems. A differential equation is derived which governs the evolution of the orientation under arbitrary applied inelastic
deformation. Evolution of the ODF is analyzed by either solution of a Fokker-Planck equation or Monte Carlo simulation. Two main results
are presented. Applied deformation tends to reduce heterogeneity of polycrystals with an initially uniform ODF. The presence of randomness
in the applied deformation leads the ODF to evolve to forms which are not obtained under any form of deterministic deformation.