Many types of retinal neurone are arranged in a spatially regular manner so that the visual scene is uniformly sampled. Several mechanisms are thought to be involved in the development of regular cellular positioning. One early-acting mechanism is the lateral inhibition of neighbouring cells from acquiring the same fate, mediated by Delta-Notch signalling. We have used computer modelling to test whether lateral inhibition might transform an initial population of undifferentiated cells into more regular populations of two types of differentiated cells. Initial undifferentiated cells were positioned randomly, subject only to a minimal distance constraint. Each undifferentiated cell then acquired either primary or secondary fate using one of several lateral inhibition mechanisms. Mosaic regularity was assessed using the regularity index and the packing factor. We found that for irregular undifferentiated mosaics, the arrangement of resulting primary (but not secondary) fate cells was more regular than in the initial undifferentiated population. However, for regular undifferentiated mosaics, no further increases in the regularity of the primary fate mosaics were observed. We have used this model to test the specific hypothesis that on- and off-centre retinal ganglion cells emerge from an initial, irregular undifferentiated population of ganglion cells. Lateral inhibition can subdivide an initially irregular population into two types of cell that are mildly regular. However, lateral inhibition alone is insufficient to produce mosaics of the same regularity as observed experimentally. Likewise, and in contrast to earlier reports, cell death alone is insufficient to match the regularity of experimental mosaics. We conclude that lateral inhibition can transform irregular distributions into regular mosaics, upon which subsequent processes (such as lateral cell movement or cell death) can further refine mosaic regularity.