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A two-dimensional homogeneous and isotropic random field is described which is generated by a polygonal partition process on the plane. In particular, the plane is divided into elementary disjoint polygonal regions by a Poisson line process. Gray levels within these elementary polygonal regions are assigned to have specified correlation wilh gray levels in contiguous regions. Explicit evaluation of the resulting autocorrelation function and power spectral density is provided. Several applications are described.