The spatial distribution of root length density (RLD) is important because it affects water and nutrient uptake. It is difficult to obtain reliable estimates of RLD because root systems are very variable and heterogeneous. We identified systematic trends, clustering, and anisotropy as geometrical properties of root systems, and studied their consequences for the sampling and observation of roots. We determined the degree of clustering by comparing the coefficient of variation of a simulated root system with that of a Boolean model. We also present an alternative theoretical derivation of the relation between RLD and root intersection density (RID) based on the theory of random processes of fibres. We show how systematic trends, clustering and anisotropy affect the theoretical relation between RLD and RID, and the consequences this has for measurement of RID in the field. We simulated the root systems of one hundred maize crops grown for a thermal time of 600 K d, and analysed the distribution of RLD and root intersection density RID on regular grids of locations throughout the simulated root systems. Systematic trends were most important in the surface layers, decreasing with depth. Clustering and anisotropy both increased with depth. Roots at depth had a bimodal distribution of root orientation, causing changes in the ratio of RLD/RID. The close proximity of the emerging lateral roots and the parent axis caused clustering which increased the coefficient of variation.