The extracellular space of the glomerular capillary wall is occupied by a complex meshwork of fibrous molecules. Little is understood about how the size, shape, and charge recognition properties of glomerular ultrafiltration arise from this space-filling fiber matrix. We studied the problem of size recognition by visualizing the void volume accessible to hard spheres in computer-generated three-dimensional homogeneous random fiber matrices. The spatial organization of the void volume followed a complex "blob-and-throat" pattern in which circumscribed cavities of free space within the matrix ("blobs") were joined to adjacent cavities by narrower throats of void space. For sufficiently small solutes, chains of blobs and throats traversed the matrix, providing pathways for trans-matrix permeation. The matrices showed threshold or gating properties with respect to permeation: solutes whose radius exceeded a critical value, at which a throat on the last connected trans-matrix pathway pinched off, could not cross, whereas smaller solutes had nonzero permeability. The thresholds may give the glomerular fiber matrix porelike response properties and explain why pore models have been such a useful means of treating permselectivity.