The connectivity within the dendritic array of Purkinje cells in the cerebellum and pyramidal cells of the neocortex of the rat, stained by the Golgi-Cox method, has been quantified by the method of network analysis. Connectivity was characterized either by applying the system of Strahler ordering, which assigns a relative order of magnitude to each branch of the arborescence or by the identification of unique topological branching patterns within the tree. The former method has been used to define the entire dendritic array of the Purkinje cell and the apical system of neocortical pyramids. It has been shown that the relation between the numbers of branches of successive Strahler order in Purkinje cells form an inverse geometric series in which the highest order is unity and the ratio between successive orders approximates to 3. On the other hand, the apical dendrites of neocortical pyramids exhibit two bifurcation ratios, i.e. a ratio of 3 between low orders and a ratio of 4 between higher orders. A computer simulation technique was used to generate networks of a size comparable with the Purkinje cell networks and grown according to two hypotheses namely, a 'terminal growth model' in which additional segments were added randomly to the terminal branches only and a 'segmental growth model' in which additional segments were added randomly to any branch within the array including terminal branches. Subsequent ordering of the simulated trees revealed that the relation between the numbers of successive orders for networks generated according to the 'segmental model' tended towards an inverse geometric series with a ratio of 4 and that generated according to the 'terminal model' tended towards a ratio of 3. This result showed that the dendritic tree of Purkinje cells grow in a manner indistinguishable from a system adding branches to random terminal segments and that neocortical apical dendrites add their collateral branches to random segments of the apical shaft but that the collateral branches themselves grow by random terminal branching. The possibility that such conclusions may be influenced by loss of branches incurred by either a failure of impregnation, by sectioning, or by environmental influences was investigated by means of a computer technique...