We provide a simulator for a range of bivariate stochastic processes of various application in the physics of stochastic fibrous networks. We illustrate the effects of local correlation on the statistics of voids in the bulk and the surface of fibre mats in general and paper in particular. The reference case of random isotropy has an inherent ‘ground-state’ correlation of adjacent free-fibre-lengths; this explains the classical observation of Corte that pores seem mainly ‘roundish’ in real paper samples. In the isotropic case, the mean pore radius can be reduced from that in a random network by 20% through structural changes associated with increased flocculation. The mean eccentricity of pores seems to give a measure of the variability in free-fibre-length distributions that is not due to local correlation. We find a uniform effect of local correlation on mean pore eccentricity over a range of stochastic network structures; at a given correlation, increased flocculation increases mean eccentricity slightly.