Pyramidal neurons in the mammalian cerebral cortex can be described by a fractal dimension (Mandelbrot, 1982), which is an objective, quantitative measure of the complexity of their soma/dendritic borders. In the cat, the fractal dimensions of lamina V cells, which include pyramidal tract neurons (PTN), indicate that these cells are more complex than other pyramidal neurons (PN) in the same region of motor cortex. The lamina V cells of the cat are also more complex than those in motor cortex of the monkey. Moreover, lamina III neurons in the monkey are more complex than monkey lamina V neurons. The fractal dimension of the intracortical axon collateral arborizations of the same pyramidal neurons indicated, in all cases, that the branching of these terminals is less complex than the branching of the dendrites of the same cells. In line with the observation that the fractal dimensions of some homologous cellular populations are different in different species, it is suggested that the fractal dimension and the degree of morphological complexity may relate to the requirement for the number of separable functions to be accommodated within one neuron. For example, as the size of the cortex and the number of neurons in a region increase, the opportunity exists within a given cortical zone, for individual functions to be segregated and for functional specialization to be accommodated with less morphological complexity of the individual neurons performing each of these functions.