  We examine the geometry of the spaces between particles in diffusion-limited
cluster aggregation, a numerical model of aggregating suspensions. Computing
the distribution of distances from each point to the nearest particle, we show
that it has a scaled form independent of the concentration phi, for both two-
(2D) and three-dimensional (3D) model gels at low phi. The mean remoteness is
proportional to the density-density correlation length of the gel, xi, allowing
a more precise measurement of xi than by other methods. A simple analytical
form for the scaled remoteness distribution is developed, highlighting the
geometrical information content of the data. We show that the second moment of
the distribution gives a useful estimate of the permeability of porous media.
